Tracking multiple conformations occurring on angstrom-and-millisecond scales in single amino-acid-transporter molecules

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Version of Record updated: February 23, 2023 (This version)
Version of Record published: February 17, 2023 (Go to version)
Accepted: January 15, 2023
Preprint posted: July 31, 2022 (Go to version)
Received: July 25, 2022

1. Of interest
Schema-based predictive eye movements support sequential memory encoding

Jiawen Huang, Isabel Velarde ... Christopher Baldassano

Research Article Mar 27, 2023
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Abstract

Most membrane protein molecules undergo conformational changes as they transition from one functional state to another one. An understanding of the mechanism underlying these changes requires the ability to resolve individual conformational states, whose changes often occur on millisecond and angstrom scales. Tracking such changes and acquiring a sufficiently large amount of data remain challenging. Here, we use the amino-acid transporter AdiC as an example to demonstrate the application of a high-resolution fluorescence-polarization-microscopy method in tracking multistate conformational changes of a membrane protein. We have successfully resolved four conformations of AdiC by monitoring the emission-polarization changes of a fluorophore label and quantified their probabilities in the presence of a series of concentrations of its substrate arginine. The acquired data are sufficient for determining all equilibrium constants that fully establish the energetic relations among the four states. The K_D values determined for arginine in four individual conformations are statistically comparable to the previously reported overall K_D determined using isothermal titration calorimetry. This demonstrated strong resolving power of the present polarization-microscopy method will enable an acquisition of the quantitative information required for understanding the expected complex conformational mechanism underlying the transporter’s function, as well as those of other membrane proteins.

Editor's evaluation

This study uses a single-molecule polarization microscopy approach to identify the different conformation states that the arginine/agmatine antiporter AdiC transitions through during transport. Four states are identified and proposed to correspond to the key steps in the transport cycle, including inward-open, inward occluded, outward occluded and outward open, setting the stage for measurements of equilibrium constants and kinetics associated with transport. This is a cutting-edge and challenging approach that offers the potential for obtaining direct information of protein conformational equilibria that will be of interest to anyone studying membrane transport mechanisms.

https://doi.org/10.7554/eLife.82175.sa0

Introduction

Biological membranes enclose individual cells and thereby separate them from their environments. Proteins embedded in the membrane play important roles such as the receptor-mediated signal transduction, and the ion-channel- or transporter-mediated movement of inorganic ions or organic molecules across the membrane. To accomplish these tasks, the protein molecules undergo many necessary conformational changes. An understanding of the mechanism underlying these changes requires the ability to resolve individual conformational states. However, three-dimensional (3D) protein-conformational changes are not only rapid but also occur usually on an angstrom scale. For these reasons, at the single-molecule level, the tasks to reliably resolve the multistate conformational changes of typical proteins, which occur in four dimensions (4D) on angstrom-and-millisecond scales, remain extremely challenging, not to mention the need for acquiring a sufficiently large amount of data for examining complex conformational mechanisms. For example, protein conformational changes have been probed using a fluorescence resonance energy transfer (FRET)-based method, which allows the deduction of distance between a fluorescence donor and an acceptor, generally on a nanometer scale (Stryer, 1978). This deduction requires knowing the actual fluorescence transfer efficiency, which is often difficult to assess because it depends on the local environment and, in most cases, on the relative orientation of the fluorophore pair. When a protein exists in multiple states, resolution and unambiguous identification of conformational states are even more challenging.

Importantly, while a protein molecule undergoes conformational changes, some secondary structures, e.g., α-helices, which are spatially constrained by other secondary structures, inevitably adopt unique spatial orientations in each conformational state. Thus, this feature offers the opportunity to track these conformational states, without the need of determining their detailed 3D features, by monitoring such an α-helix’s spatial orientation defined in terms of the inclination and rotation angles (θ and φ; Figure 1A) with a method of adequate resolution.

Figure 1 with 1 supplement see all

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Illustration of the attachment of fluorophore to the AdiC protein and the protein to a glass surface.

(**A, B**) The orientation of the fluorophore dipole, defined in in terms of θ and φ, can be directly related to that of the alpha helix (A), to which bifunctional rhodamine is attached via two mutant cysteine residues (B) where both orientations of the fluorophore dipole and the helix are indicated by the respective arrows. (C) Cartoon illustrating the attachment of an AdiC molecule to a streptavidin-coated coverslip glass via a biotin moiety covalently linked to the N-terminus and two streptavidin-binding tags fused to the N- and C-termini in each of its two subunits, totaling six available sites for binding to streptavidin molecules. (D) Structure of AdiC shown as a dimer (PDB: 7O82). (E) Spatially aligned structures of E_O and E_X states of AdiC shown with a single subunit (PDB: 3OB6, 3L1L). Helix 6, chosen as a labeling site, is indicated in either structure. The substrate Arg⁺ (orange) and a Trp residue external to it in the two states (blue and purple) are represented using space-filling models.

One effective way to track the orientation change of a protein is to monitor the emission polarization change of a bifunctional rhodamine attached to an α-helix (Figure 1B) using a polarization microscope (Sase et al., 1997; Warshaw et al., 1998; Ha et al., 1998; Adachi et al., 2000; Sosa et al., 2001; Forkey et al., 2003; Beausang et al., 2008; Rosenberg et al., 2005; Forkey et al., 2005; Fourkas, 2001; Ohmachi et al., 2012; Lippert et al., 2017; Lewis and Lu, 2019c). The polarization of individual emitted photons, unlike their travel direction, is not meaningfully affected by the diffraction caused by a so-called polarization-preserving objective. The documented resolutions of such polarization-based detection of rotation motion within a protein had been ≥25°, estimated on the basis of 2.5 times of the standard deviation (σ) of angle measurements (Rosenberg et al., 2005; Forkey et al., 2005; Ohmachi et al., 2012; Lippert et al., 2017). Thus, this technique has been limited to the investigation of proteins that undergo large-angle changes, e.g., the lever-arm of a myosin that rotates as much as 80°. Recently, our group assembled a polarization microscope with four polarized-emission-recording channels and tracked the orientation change of an isolated, soluble domain of the MthK K⁺ channel via a bifunctional fluorophore label attached to an α-helix within the protein (Lewis and Lu, 2019c; Lewis and Lu, 2019a; Lewis and Lu, 2019b). By finding optimal hardware, devising necessary numerical corrections for certain system parameters, and developing essential analyses, we have achieved an effective σ as low as 2°, translating to 5° resolution for detecting changes in both θ and φ. For reference, the estimated median radius of proteins is ~20 Å (Brocchieri and Karlin, 2005; Erickson, 2009), and a rotation of 5° or 10° of a site 20 Å away from the origin would lead to an 1.7 or 3.5 Å change in the chord distance. Thus, the capability to resolve this small angle change allows one to track protein-conformational changes that occur on an angstrom scale in proteins of typical sizes.

While we have succeeded in tracking the conformational changes in the artificially excised, soluble gating-domain protein of MthK, our main goal here is to further develop this method for tracking the conformational changes in a membrane protein. In principle, we can use a protein artificially engineered for this purpose, or a biological protein minimally or heavily modified to enable the required measurements. Simply put, what is required here is merely a membrane protein that adopts multiple conformational states, which can be reported by a fluorophore label, so that we can determine whether our method can (i) resolve its conformational changes by tracking orientation of the dipole of an attached fluorophore at the expected resolution set by the signal-to-noise ratio (SNR), (ii) collect a required large amount of data, (iii) analyze the data acquired from individual protein molecules that are attached to the support glass with some flexibility, and (iv) demonstrate how to extract all the equilibrium constants that fully determine the energetic relations among the resolved states, relations that constrain an equilibrium model.

We chose the bacterial transporter AdiC protein for its expected adaptation of multiple states that we can use as a convenient preparation to test the resolving capability of our method in a membrane protein (Gong et al., 2003; Iyer et al., 2003). An understanding of the detailed biological mechanism of AdiC is not the primary goal here.

For a general context, AdiC, a member of the amino-acid and polyamine organocation (APC) transporter superfamily (Jack et al., 2000; Casagrande et al., 2008; Bosshart and Fotiadis, 2019), is a critical component of a proton-extruding system in pathogenic enterobacteria, e.g., Escherichia, Salmonella, and Shigella, which helps the bacteria to survive the insult inflicted by a host’s highly acidic gastric defense barrier with a pH value of as low as 2 (Gong et al., 2003; Foster, 2004; Fang et al., 2007; Iyer et al., 2003; Krammer and Prévost, 2019). AdiC facilitates the movement of arginine (Arg⁺) into and agmatine (Agm²⁺) out of bacteria, along their gradients. Inside bacteria, Arg⁺ is rapidly decarboxylated to Agm²⁺ by the enzyme AdiA, consuming a proton (Gong et al., 2003; Foster, 2004; Fang et al., 2007; Iyer et al., 2003; Tsai and Miller, 2013). An exchange between extracellular Arg⁺ of a single positive charge and intracellular Agm²⁺ of two charges effectively extrudes H⁺. The direction of the net exchange of the two substrates is dictated by their natural energy gradient. However, as an intrinsic property, AdiC can facilitate the movement of a given substrate in either direction, where the transport of one type of substrate does not markedly depend on which type of substrate is on the opposite side.

Results

Sample preparations

To monitor the conformational changes of AdiC, we chose to attach a fluorophore label to the surface-exposing helix 6a in one of its two subunits (Figure 1; Gao et al., 2009; Fang et al., 2009; Gao et al., 2010; Kowalczyk et al., 2011; Ilgü et al., 2016, Ilgü et al., 2021). Hereafter, unless specified otherwise, AdiC simply refers to one of its two functionally independent subunits (Figure 1D and E). Helix 6A is spatially constrained by other secondary structures, and moves along with them, adopting differing spatial orientations between two different known structural states of AdiC (Figure 1E). A bifunctional rhodamine molecule was attached via two mutant cysteine residues, spaced seven residues apart, to helix 6a in the region extracellular to the substrate-binding site to avoid affecting the binding affinity (see ‘Discussion’). Such an attachment aligned the fluorophore dipole along the axis of the helix (Corrie et al., 1998; Figure 1B). Under the same labeling condition, there was little detectable fluorescent labeling in the absence of the mutant cysteine residues (Figure 1—figure supplement 1A and B). To minimize the background labeling, we removed two native cysteine residues. Removal of native cysteine residues in AdiC has been shown to have very limited impacts on its function (Tsai et al., 2012).

For microscopic examination, individual AdiC protein molecules were inserted into nanodiscs (Ritchie et al., 2009; Denisov et al., 2019). For attaching the protein molecules to streptavidin adhered to the polylysine-coated surface of a piece of coverslip glass, the protein was made to contain a biotin-moiety covalently linked to the N-terminus and the streptavidin-binding tags linked to the N- and C-termini in each of its two functionally independent and structurally symmetric subunits, totaling six sites available for the binding of streptavidin molecules (Figure 1C and Figure 1—figure supplement 1C; ‘Materials and methods’). Assessed with isothermal titration calorimetry (ITC), the protein resulting from the cDNA construct genetically engineered for the present purpose exhibited a K_D of 104 μM for Arg⁺ (Figure 1—figure supplement 1D), which is within the previously reported range of 32–204 μM for AdiC (Fang et al., 2007; Casagrande et al., 2008; Gao et al., 2010; Tsai et al., 2012; Wang et al., 2014). To minimize the potential constraint of the tag-mediated attachment on the conformational movement of the protein, we included multiple flexible spacer sequences between (i) the Avi and Strep II tags, (ii) these tags and the N-terminus of AdiC, (iii) the thrombin cleavage and Strep II sequences, and (iv) these two sequences and the C-terminus (Figure 1—figure supplement 1C). Consequently, the inclination angle θ varied considerably among molecules. Thus, we needed to develop the analytical method discussed below to spatially align individual molecules.

The density of protein molecules on a cover slip was sufficiently low such that individual fluorescent particles could be readily resolved spatially on microscopic images. The probability of individual AdiC molecules being attached with a single fluorophore was optimized with an empirical protein-to-fluorophore ratio during the labeling procedure, and such molecules were identified during the offline analysis on the basis of a single-step bleaching of fluorescence.

Reconstitution of the protein into lipid-containing nanodiscs, tags, attachment, mutations, and the fluorophore label are all necessary components of the present method, potentially contributing to system errors. Currently, there are no other techniques that can be used to assess, under the same conditions, the ultimate impact of these factors on AdiC, which highlights the need to develop the present method. In terms of energetic impact, a practically relevant question would be whether the $K_{D}$ values estimated using the present method with all those potentially impactful factors are comparable to those values estimated for the wild-type protein by means of an already established method, such as ITC (see ‘Discussion’). As such, we would only know in the end whether the estimates by our method were valid, underscoring the importance of a judicious deliberation in designing the preparation and experiments on the basis of available information, which will help to maximize the chance to obtain a successful outcome.

Fluorescence intensity recordings

The fluorophores attached to individual AdiC protein molecules were excited by an evenescent field generated by a circularly polarized laser beam under a total internal reflection (TIR) condition. The light emitted from individual attached fluorophores was captured via the objective of a TIR fluorescence (TIRF) microscope. To assess the polarization of the captured fluorescence light, we first split it into two equal portions and then further split one portion into 0° and 90° polarized components ( $I_{0}$ and $I_{90}$ ) and the other portion into 45° and 135° components ( $I_{45}$ and $I_{135}$ ) (Figures 2 and 3; Lewis and Lu, 2019c). These polarized components of fluorescence were recorded with an electron-multiplying charge-coupled device (EMCCD) camera. Effectively, the intensity counts recorded in the four polarization channels encode the full 3D information regarding the orientation of the fluorophore dipole.

Figure 2

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Schematic for four polarized emission intensities collected via a microscope and imaged on an EMCCD camera.

Photons, emitted from a fluorophore excited by a circularly polarized laser beam, are collected by an objective and directed to a non-polarizing beam splitter (NPBS) that splits it evenly to two beams. Beam 1 is further split into 0 and 90° polarized components (I₀ and I₉₀) with a glass (N–SF1) polarizing beam splitter (PBS-1), and beam 2 into 45 and 135° components (I₄₅ and I₁₃₅) using a wire grid polarizing beam splitter (PBS-2). These four beams are aligned along one path using pick-off mirrors and directed onto separate sections of an EMCCD camera.

Figure 3 with 2 supplements see all

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Polarized intensity components of single fluorescent particles and θ and φ angles calculated from the components.

(A) Consecutive frames of four intensity components (I₀, I₄₅, I₉₀ and I₁₃₅) of a bifunctional-rhodamine-labeled apo AdiC molecule captured over a 300 ms interval in a 7.2 s recording (Figure 3—video 1). (**B, C**) The time courses of integrated intensities color-coded for I₀, I₄₅, I₉₀ and I₁₃₅ of two bifunctional-rhodamine-labeled AdiC molecules in the absence (B) or presence (C) of 0.75 mM Arg⁺, from which I_tot is calculated. Each vertical line in the black traces, superimposed on the colored traces, indicates the time point at which a change in the fluorophore’s orientation is identified, whereas the horizontal lines represent the mean intensity between two identified consecutive time points. (**D–G**) The traces θ_L and φ_L (**D, E**) in the laboratory frame of reference calculated from black intensity traces, which were rotated into the local frame of reference (**F, G**). (**H, I**) Values of Ω calculated according to Equation 33 from the changes in either θ_L and φ_L or θ and φ.

Figure 3—source data 1 Intensity and angle data for [Arg]=0 mM condition.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig3-data1-v2.xlsx
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Figure 3—source data 2 Intensity and angle data for [Arg]=0.75 mM condition.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig3-data2-v2.xlsx
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We integrated the individual intensity images (Figure 3A) and plotted the resulting values against time. As an example, a set of intensity traces for a molecule, each examined in the absence or the presence of 0.75 mM Arg⁺, is shown in Figure 3B and C. From these traces, we calculated the trace of total emitted intensity (I_tot) using Equation 12 (equations with a number greater than 6 are given in ‘Materials and methods’; the bleaching step is shown in Figure 3—figure supplement 1).

From Equations 1 and 2 derived for ideal conditions, one can see that the orientation of the tracked fluorophore would be specifically reflected by the relative intensities, or underlying photon counts, of its four polarized components (Lewis and Lu, 2019c; for the solution of three channels, see Fourkas, 2001).

φ = \frac{1}{2} \tan^{-1} \frac{I_{45} - I_{135}}{I_{0} - I_{90}}

θ = \sin^{-1} [2 \sqrt{\frac{\sqrt{{(I_{0} - I_{90})}^{2} + {(I_{45} - I_{135})}^{2}}}{(I_{0} + I_{90} + I_{45} + I_{135})}}]

Given that either angle would be a function of an intensity ratio, its resolution should be primarily limited by the SNR of intensities. Thus, one can visually notice intramolecular motions that occur on the angstrom scale from the relative variations in the four intensities (Figure 3A, Figure 3—video 1).

Detection of intensity changes

As a protein molecule transitions from one conformation to another conformation, the orientation of the attached fluorophore changes with respect to the fixed polarization angles of the two polarized beam splitters. Consequently, the intensities of the four polarized fluorescence components undergo characteristic changes. For example, when the fluorophore’s mean dipole vector moved such that its φ angle increased from 0 to 90°, the intensity recorded in the 0° channel would decrease, whereas that in 90° would increase accordingly; the intensities of 45° and 135° channels would also characteristically change in directions opposite to each other. Compared to many other types of fluorescence-based methods, such as FRET, the expected concurrent, characteristic changes in all four channels here, which serve as a critical constraint in analysis, markedly increase the confidence of the detection of transitions, given that such types of changes are not expected for statistically random changes, namely, the so-called noise.

By examining the characteristic changes in the four fluorescence components with a so-called changepoint algorithm (Chen and Gupta, 2001), we detected the time point where a change in the fluorophore’s orientation occurred, which was brought about by the underlying protein conformational change. To do so, we assessed the change in the number of recorded photons ( $N$ ) per unit time with 95% confidence by evaluating the likelihood of two alternative possibilities that a change did or did not occur within a given time interval. This assessment was based on concurrent changes in the recorded $N$ among all four polarized components, redundancy that markedly increased the confidence that identified transitions were genuine.

During individual consecutive 10 ms recording intervals, the mean $N$ for all four polarization components together was 92 (‘Materials and methods’), with an effective SNR of 7. As shown in Figure 3B and C, individual detected transitions are demarcated by the vertical lines in the black traces superimposed on the data traces. From the polarization properties of 92 photons on average, we could reliably detect the individual transitions in the fluorophore orientation among different conformational states at the intended time resolution. Thus, this method offers an exquisitely sensitive detection of changes in the fluorophore orientation.

Angle calculation and state identification

Resolution of individual conformational states in terms of θ and φ angles requires a higher SNR and thus a much greater number of photons than what is required for detecting the fluorophore’s orientation changes. One way to solve this problem would be to increase the number of emitted photons by raising the intensity of the excitation laser, but a strong excitation intensity would undesirably shorten the lifetime of the fluorophore. An alternative way to increase SNR is to use the total number of photons recorded from each of the four channels within the duration of an event when an examined protein molecule adopts a specific conformation, dubbed dwell time. Practically, given that angles were calculated from ratios of intensities, a calculation using the total or the average number of photons recorded during an event would yield the same result.

Our ability to identify individual state-transition points was a prerequisite for us to perform such a summation, or averaging, of the number of recorded photons for a given event because individual dwell times were demarcated by these points. As shown in Figure 3B and C, while the vertical lines in the black traces, superimposed on the observed intensities traces, indicate the individual orientation-transition points, the average intensities over individual dwell times are shown as the horizontal lines in the black traces.

From these black traces of $I_{0}$ , $I_{90}$ , $I_{45}$ , and $I_{135}$ , we calculated θ_L and φ_L traces that are color coded (Figure 3D and E); these two angles are defined in the standard laboratory (L) frame of reference for microscopy studies where the z-axis is defined as being parallel to the optical axis of the objective and the x-y plane parallel to the sample coverslip. All angle calculations were done using expanded versions of Equations 1 and 2 (Equations 11 and 13), which contain four necessary, predetermined system parameters. These previously established parameters numerically correct for incomplete photon collection (α) (Axelrod, 1979), depolarization caused by imperfect extinction ratios of the polarizers (f) (Lewis and Lu, 2019c) and by fast wobble motion of the fluorophore dipole (δ) (Forkey et al., 2005), and slightly different intensity-recording efficiency of the four polarization channels (g). In the angle calculation, we used the information from all photons (1740 photons on average) recorded from all four polarization channels during individual dwell times to determine the corresponding (mean) angles over these individual durations with adequately low σ. The relations between σ for the two angles and SNR among individual analyzed particles are shown in Figure 4, in which the highest value of <4° is translated to a resolution of better than 10°.

Figure 4

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Experimental resolution of conformational states.

(**A, B**) The σ values of the θ (A) and φ (B) populations, built with data acquired from individual single AdiC molecules labeled with bifunctional rhodamine, are plotted against SNR.

Figure 4—source data 1 Data for the relation between SNR and σ of φ and θ.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig4-data1-v2.xlsx
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Subsequently, conformational state populations could be identified from both angles together to increase resolvability and confidence, without any preconceived kinetic model. For the ease in technique development, in a previous study of the isolated gating ring of the MthK channel, the orientation of individual protein molecules was strictly constrained such that their central axis was well aligned with the optical axis. Under such a stringent condition and for that specific protein, its conformations could be resolved from the differences in the θ angle alone. As such, the conformational states could be directly sorted in terms of θ and φ, which is mathematically a 2D operation. Because one angle was adequate there, the sorting effectively became a 1D operation. Here, we need to rely on the combined differences on a 3D sphere. The asymmetric characteristics of θ and φ, illustrated below, would introduce some biases in state identification if these two angles were used in a 2D sorting operation. The angles θ and φ are related to x,y,z coordinates in the corresponding Cartesian system as

θ = a r c s i n \sqrt{\frac{x^{2} + y^{2}}{x^{2} + y^{2} + z^{2}}}

and

φ = a r c t a n \frac{y}{x}

where $θ$ contains the information of all x, y, and z, whereas $φ$ contains that of only x and y. Furthermore, the two angles are related to x and y differently. To ensure equal weighting of the contributions from all three dimensions in the sorting operation, we mapped the information of the two angles on a unit sphere defined in a Cartesian coordinate system and performed the sorting in terms of x, y, and z coordinates on the basis of the shortest distance principle.

This 3D-sorting task would be extremely challenging for us to do manually on subjective visual guidance, if possible. Thus, to effectively sort individual events into distinct populations, we developed a k-means-clustering algorithm to achieve the solution for the shortest-distance case, which was optimized with two coupled algorithms (simulated annealing plus Nelder–Mead downhill simplex) (Press et al., 2007). The program examined from the case of a one-state distribution to the case of k-state distributions, one at a time in a series of separate operations. When two consecutive events were determined to belong to the same state distribution, the transition between them identified by the changepoint algorithm would most likely be part of the expected false-positive outcomes. These events would then be merged to form a single event for the state distribution. This operation reduces the false-positive identification of transition points.

For each successful operation with a specifically set number of states, the resolution criterion was ensured, that is, peaks of all populations were separated by at least 2.5σ. By this common criterion, the highest number of resolvable states was 4 over the examined Arg⁺ concentration range (Figures 5 and 6); in these two figures, θ and φ are the angle coordinates of a local framework transformed from θ_L and φ_L of the standard laboratory framework, as described below. The conformational states are numerated according to the sequence in the solution to achieve the shortest pathway among the four states, denoted as C₁, C₂, C_3, and C₄ (‘Materials and methods’). To illustrate the sorting result, x, y, and z coordinates of individual events in the Cartesian system or their angle coordinates in a spherical system are presented in Figure 7, in which they are color-coded according to states. Thus, the minimal model must have four states for either the apo or the substrate-bound forms, totaling eight states.

Figure 5

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Ensemble 3D probability density distributions of θ and φ.

The θ and φ distributions of four individual states in the absence or presence of the indicated concentrations of Arg⁺, in which the value of φ is plotted along the x-axis, the value of θ along the y-axis, and the value of probability density along the z-axis. Distributions were built with the data analyzed from 91 or 75 number of particles with a total 3048 or 1494 number of events. Data columns for the conformational state C₁ are colored yellow, C₂ colored blue, C₃ colored orange, and C₄ color cyan.

Figure 5—source data 1 φ angles for probability density distributions, organized by state and [Arg⁺].: https://cdn.elifesciences.org/articles/82175/elife-82175-fig5-data1-v2.xlsx
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Figure 5—source data 2 θ angles for probability density distributions, organized by state and [Arg⁺].: https://cdn.elifesciences.org/articles/82175/elife-82175-fig5-data2-v2.xlsx
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Figure 5—source data 3 φ and θ sample histogram data for [Arg⁺] = 0 mM.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig5-data3-v2.xlsx
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Figure 5—source data 4 φ and θ sample histogram data for [Arg⁺] = 0.75 mM.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig5-data4-v2.xlsx
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Figure 6

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Angle values of individual conformational states.

The values of θ and φ (mean ± sem) for each of the four conformations are plotted against the concentration of Arg⁺. The number of events is 691–3084. The symbols for the conformational state C₁ is colored yellow, C₂ colored blue, C₃ colored orange, and C₄ color cyan. Note that θ for both C₁ (yellow) and C₄ (cyan) are set to 90° as described in the text and are thus overlapped.

Figure 6—source data 1 Table of mean values for θ and φ organized by state and [Arg⁺].: https://cdn.elifesciences.org/articles/82175/elife-82175-fig6-data1-v2.xlsx
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Figure 7 with 1 supplement see all

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The orientations of the dipole vector of the fluorescence probe in different conformational states.

(**A–D**) The positions of the arrowheads of individual dipole vectors are mapped onto a unit sphere, on the basis of being in a Cartesian coordinate system defined according to the usual laboratory framework (**A, B**) or a local one (**C, D**), described in the text. The X_L, Y_L, and Z_L positions calculated from θ_L and φ_L, determined in Figure 3, and a radius of a unit length. (**E–H**) The inclination and rotation angle values are plotted against each other in the laboratory (**E, F**) or the local (**G, H**) frame of reference. The data points for conformational state C₁ are colored yellow, C₂ colored blue, C₃ colored orange, and C₄ color cyan.

Figure 7—source data 1 Orientation information of the fluorophore for [Arg] = 0 mM.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig7-data1-v2.xlsx
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Figure 7—source data 2 Orientation information of the fluorophore for [Arg] = 0.75 mM.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig7-data2-v2.xlsx
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Spatial alignment of individual molecules

For greater likelihood to accurately estimate angle values, we need to determine their mean values from individual events of numerous molecules that had already been analyzed individually for necessary precision of angle measurements and thus spatial resolution. This operation requires all molecules be aligned in the same orientation. Unfortunately, individual molecules on the coverslip, and consequently the tracked helix, were randomly oriented in the x-y plane relative to the x-axis, that is, their φ_L varying randomly among different molecules. This problem previously prevented us from building the distribution of φ_L for a given state among individual molecules (Lewis and Lu, 2019c). Furthermore, each dimer molecule of AdiC is anchored to the cover slip coated with streptavidin through two available biotin moieties and four streptavidin-binding tags, each of which was covalently linked to an N- or C-terminus of the polypeptides of two subunits. As mentioned above, these terminal binding regions were of some flexibility. Consequently, the twofold symmetry axis of the individual dimer molecules was not aligned with the optical (z) axis of the microscope framework. As such, the orientation of one molecule varied considerably from that of another (e.g., Figure 7A versus Figure 7B or Figure 7E versus Figure 7F). Resolving this issue would also pave the way for studying individual randomly oriented molecules in the future.

To align all the molecules during analysis, we mathematically rotate them from the laboratory frame of reference into a local coordinate system defined on the basis of the spatial features of the tracked helix in the protein (Figure 7—figure supplement 1A). This system is defined such that the tracked helix in C₁ is always aligned with the local x-axis, that is, mean φ₁=0°, and the helix in the plane defined by C₁ and C₄ is always in the local x-y plane, that is, mean θ₁ or θ₄=90°. These two features fully define the x,y,z-axes, and thus θ and φ in the local framework of AdiC. Evaluated in this local framework (Figures 3F, G, 7C, D, G and H), individual events of the same state observed with all molecules under a given condition could be used to build a single distribution (Figure 5). From the distribution for each state, we determined the mean θ_i and φ_i. To specify the six mean direct-angle Ω_i,j values among the tracked dipole orientations in the four states, which were calculated using Equation 33, we used four unit-vectors to specify the orientations in the local framework (Figure 8A). The mean θ_i, φ_i, and Ω_i,j values are all summarized in Figure 8B and C.

Figure 8

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Comparison of the orientations of helix 6A in the corresponding states determined from the crystal structures and in the polarization study.

(A) Depiction of the six Ω angles among the four orientations of the helix in the four states, represented by four arrows color-coded for states. (**B, C**) The θ and φ angles (B) of the helix for corresponding states determined from the crystal structures and in the polarization study, as well as the Ω angles (C), are compared in the local frame of reference. All angle values for the conformational states determined by polarization are presented as mean ± standard deviation (σ). In the structural analysis, the AdiC structures in the states E_O (blue) (PDB: 7O82) and E_X (yellow) (PDB: 3L1L), and the BasC and ApcT structures in the states I_O (orange) (PDB: 6F2G) and I_X (cyan)(PDB: 3GIA) were used.

Figure 8—source data 1 θ and φ values of the four conformational states.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig8-data1-v2.xlsx
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Figure 8—source data 2 Ω values of the four conformational states.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig8-data2-v2.xlsx
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Following the rotation operation, we could also build a distribution of mean angle values of individual molecules to illustrate the molecule-to-molecule variation in θ_i and φ_i (Figure 9). If the contribution of each molecule were weighted by the length of the trace, the mean value of each distribution in Figure 9 should statistically be the same as the corresponding one in Figure 5, built with the values of individual events from all molecules. Although the ensemble mean angle values should be more accurate statistically, the apparent angle resolution would be poorer. Indeed, compared with σ for individual particles (Figure 4), the ensemble angle distributions built with data determined from molecule-by-molecule analyses have much larger σ (8–11°, Figures 5 and 8B), except for those of φ₁ and θ₁ or θ₄ which are normalized such that their mean values equal 0° and 90°. Thus, the initial molecule-by-molecule data analysis, as shown in Figure 3, was essential for resolving individual conformational states in terms of θ and φ.

Figure 9

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3D probability density distributions of mean θ and φ determined from individual molecules.

The value of φ is plotted along the x-axis, the value of θ along the y-axis, and the value of probability density along the z-axis, obtained in the absence (top) and presence (bottom) of a saturating concentration of Arg⁺. Distributions were built with the data analyzed from 34 or 91 number of particles with a total 691 or 3048 number of events. Data column for the conformational state C₁ is colored yellow, C₂ colored blue, C₃ colored orange, and C₄ color cyan.

Figure 9—source data 1 φ data for mean angle distributions.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig9-data1-v2.xlsx
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Figure 9—source data 2 θ data for mean angle distributions.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig9-data2-v2.xlsx
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Determination of equilibrium constants among the Apo and Arg⁺-bound conformational states

As an essential evaluation of the basic energetic properties of the protein’s individual states, we examined individual AdiC molecules in the presence of a large series of Arg⁺ concentrations. Both sides of an AdiC molecule facing the same solution allowed us to determine the probabilities of individual conformational states under conditions where the system as a whole was in equilibrium, through which we could straightforwardly obtain equilibrium constants (K_i,j) among the states, including dissociation constants (K_D_i) to be compared in ‘Discussion’ with previously reported K_D values.

Shown in Figure 5 are plots of the probability density distributions of θ_i and φ_i of each of the four states in a series of Arg⁺ concentrations, built with the data from numerous individually analyzed particles. These angle distributions contain the information regarding the probabilities of occupying each of the four states in the presence of the corresponding Arg⁺ concentrations (Figure 10A). All four states appeared in the absence and the presence of Arg⁺. With increasing concentration, the probability of C₃ increased whereas that of C₂ decreased. In contrast, the probability of C₁ or C₄ exhibited relatively small changes. Nonetheless, these observations indicate that all states bind Arg⁺ because any state that could not bind Arg⁺ would practically vanish in a saturating concentration of Arg⁺. The observation of all four conformations in the absence or the presence of Arg⁺ is consistent with the Monod–Wyman–Changeux model for ligand-dependent conformational mechanism of allosteric proteins in that all conformations of a protein occur in the absence of ligand, and the binding of a ligand does not create a new conformation but merely energetically stabilizes a spontaneous conformation that is ready to capture the ligand (Monod et al., 1965).

Figure 10

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Ligand dependence of the probabilities of conformational states and the diagram of a conformational state model of AdiC.

(A) The probabilities of individual states (mean ± sem, number of events is 691–3084) are plotted against the Arg⁺ concentration on a logarithm scale. The four curves superimposed on the data correspond to a global fit of a model in which the interaction between the subunit of AdiC and Arg⁺ has an one-to-one stoichiometry. The fitted values of all parameters are summarized in Table 1. (B) An eight-state model that accounts for the observed conformational behaviors of AdiC: four apo states and four ligand-bound states.

Figure 10—source data 1 State probabilities and associated errors organized according to [Arg⁺].: https://cdn.elifesciences.org/articles/82175/elife-82175-fig10-data1-v2.xlsx
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Here, a model with a minimum number of eight states is required to account for the observed conformational behavior of AdiC: a set of four without ligand bound (C₁, C₂, C_3, and C₄) and another set of four with the Arg⁺ ligand (L) bound (C₁.L, C₂.L, C₃.L, and C₄.L) (Figure 10B). The probability p_i of occupying state i is expressed as

p_{i}^{} = \frac{K_{i,1} +^{L} K_{i, 1}^{} \frac{[L]}{K_{D 1}}}{\sum_{i = 1}^{4} K_{i,1} + \sum_{i = 1}^{4}^{L} K_{i, 1}^{} \frac{[L]}{K_{D 1}}}

where C₁ is used as a reference for the other states (C_i) to define equilibrium constants:

K_{i, 1} = \frac{[C_{i}]}{[C_{1}]};^{L} K_{i, 1} = \frac{[C_{i} . L]}{[C_{1} . L]}; K_{D i} = \frac{[C_{i}] [L]}{[C_{i} . L]}; i = 1, 2, 3, 4

where K_1,1 is defined to equal one. Each equilibrium constant reflects the free energy difference between a pair of states that may or may not be connected kinetically. In principle, the equilibrium constants for the apo or Arg⁺-bound states are constrained by the state probabilities under the condition of zero or saturating Arg⁺, and $K_{D i}$ by the so-called midpoint positions of the curves (Figure 10A). In practice, we determined these parameters by fitting Equation 5 to the four plots in Figure 10A simultaneously as a global fit, all summarized in Table 1. Together, these constants would fully define the energetic relations among the eight states. If needed, the remaining six equilibrium constants ( $K_{3, 2}$ , $K_{4,2}$ , $K_{4, 3}$ , $^{L} K_{3, 2}$ , $^{L} K_{4, 2}$ , and $^{L} K_{4, 3}$ ) could be calculated from the ones given in Table 1. Note that even though the concentration-dependent plot of the probability of C₁ or C₄ is relatively flat, their $K_{D}$ values are determinable. This is because the model can be fully specified by a certain combination of merely seven equilibrium constants, e.g., three of the six $K_{i,1}$ values, three of the six $^{L} K_{i, 1}$ values, and only one of the four $K_{D}$ values. As such, in the present so-called overdetermined case, the $K_{D}$ values of the relatively flat traces are fully constrained by those more curved traces in a global fit to all four plots simultaneously.

Table 1

Probabilities and equilibrium constants for apo and Arg⁺ bound states.

Apo state
		P₁	0.192 + 0.015/–0.024
K_2,1	2.566 + 0.589/–0.244	P₂	0.492 + 0.040/–0.014
K_3,1	0.923 + 0.061/–0.149	P₃	0.177 + 0.011/–0.037
K_4,1	0.729 + 0.225/–0.103	P₄	0.140 + 0.026/–0.014
Arg⁺ bound state				K_D (µM)
		^argP₁	0.172 + 0.020/–0.020	^argK_D1	49 + 46/–25
^argK_2,1	1.795 + 0.298/–0.319	^argP₂	0.308 + 0.013/–0.025	^argK_D2	69 + 67/–33
^argK_3,1	1.782 + 0.272/–0.193	^argP₃	0.306 + 0.019/–0.018	^argK_D3	25 + 20/–14
^argK_4,1	1.250 + 0.228/–0.188	^argP₄	0.214 + 0.018/–0.015	^argK_D4	28 + 31/–14

Parameters from fit of Equation 5 to the plots of AdiC conformational state probabilities versus [Arg⁺] (Figure 10A). 95% confidence intervals were calculated from the maximum likelihood optimization of 1000 sets of simulated data obtained from bootstrapping.

Discussion

In this study, on the basis of θ or φ alone, the smallest angle changes resolved, namely, those between C₂ and C₃, are ≥10° (Figure 8B), which requires a σ ≤ 4°. Thus, it is justified to use ultimately the intensity data with SNR of ≥ 5, which corresponds to σ for the θ and φ distributions of < 4°, translated to a minimum resolution of better than 10° (Figure 4). Note that our actual use of the combined information of θ and φ should lead to higher effective resolution.

The present examination of the properties of conformational changes was performed under equilibrium conditions, which allowed us to determine straightforwardly the K_D values of four conformations from the dependence of their probabilities on the ligand concentration. The resulting values of K_D1 through K_D4 ranges from 25 to 69 μM (Table 1), statistically comparable with the previously reported overall K_D determined by ITC: a relatively narrow range of 32–93 μM for one lab without lab-to-lab variations (Fang et al., 2007; Tsai et al., 2012), or a wider range of 32–204 μM when data from other labs are included (Casagrande et al., 2008; Gao et al., 2010; Wang et al., 2014). Thus, the K_D values estimated by the present method are valid. Maneuvers such as introducing cysteine mutations and attaching the fluorophore to the AdiC molecule, which are part of what contributes to system errors of the present method, have no markedly consequential energetic impacts on its affinity for Arg⁺. Such a finding is not particularly surprising because the chosen labeling part is on the surface of the protein such that it is not at, but external to, the ligand-binding site. Thus, as an advantage of the present method, one can and should choose to attach the label to the surface of a moving part of the protein, a part that is not of functional activity.

Generally, a transporter is expected to adopt four main types of structure-function states in terms of the accessibility of its external and internal sides to substrates, dubbed the externally open (E_o), externally occluded (E_x), internally open (I_o), and internally occluded (I_x) states (Post et al., 1972; Gao et al., 2010; Krammer and Prévost, 2019). By this definition, when a transport molecule adopts the E_o and I_o states, it is accessible only to extracellular and intracellular ligands, respectively. The molecule in the E_x or I_x state is inaccessible to ligands from either side. Thus far, the crystal structures of AdiC in the E_o and E_x state have been solved (Gao et al., 2009; Fang et al., 2009; Gao et al., 2010; Kowalczyk et al., 2011; Ilgü et al., 2016, Ilgü et al., 2021). Additionally, the structures of BasC and ApcT (Shaffer et al., 2009; Errasti-Murugarren et al., 2019), which share the same fold with AdiC, were solved in I_o and I_x states, respectively.

Intriguingly, as shown in the results, the present study of fluorescence polarization resolved four macroscopic conformational-state populations, which was performed without any preconceived number of states. The probabilities of C₂ and C₃ clearly vary with the concentration of Arg⁺, and these two states should thus be open states (Figure 10A). In contrast, the probabilities of C₁ and C₄ vary little, and thus are not open states directly accessible to ligands, which are consistent with occluded states in adopting the prevailing nomenclature. Under the present conditions, the comparable probabilities of C₂ and C₃ in a practically saturating concentration of Arg⁺ are consistent with the following experimental findings obtained from previous flux assays: both sides of AdiC have comparable K_m, and the apparent maximal net flux rates of radioactive Arg⁺, which were separately measured for the two opposite directions, are also comparable (Tsai et al., 2012; confer Krammer et al., 2016).

In the previous study of the isolated gating ring of the MthK channel, we could easily relate the states identified in the polarization study to the structural states on the basis of the matching relations of θ angles alone, which is effectively an 1D operation. For ease of communication, the former types of state will be referred to as the conformational states. However, to relate two sets of structural and conformational states in a 3D operation would require a quantitative approach. Thus, as an additional exercise, we illustrate below such an approach that we have developed.

Thus far, only the structures of the E_o and E_x states of AdiC have been solved, so for this exercise we used the structures of the transporters BasC and ApcT in the I_o and I_x states as proxies for those of AdiC because they all have the same structural fold (Shaffer et al., 2009; Gao et al., 2010; Errasti-Murugarren et al., 2019; Ilgü et al., 2021). This exercise can be readily repeated when the I_o and I_x structures of AdiC become available. The helix 6 in the two AdiC structures and that of its counterparts in BasC and ApcT adopts different orientations. To illustrate these differences, the four structures are aligned spatially, and their relevant portions are shown in Figure 11A and B. The orientation of the helix 6 or its counterpart is represented by a vector that is color-coded for a specific structural state (open arrow heads, Figure 11C). There are 24 possible ways of relating the four structural states to the four conformational states. To determine the best matching relation, we fit the unit-vectors (open heads, Figure 11C) and consequently their θ and φ (open circles, Figure 11D), which specify the helix’s orientations in the four structural states, to those of the conformational states in the local framework (closed heads or circles), while the internal spatial relations among four states in either set of compared data were fixed. To our surprise, in the statistically best matching case (Figure 11C), the four mean orientations of the fluorophore attached to the helix 6 apparently well match the orientations of this helix in the structures of AdiC, BasC, and ApcT captured in four different states (Figure 8B and C).

Figure 11

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Relations between the structural and conformational states determined respectively from the crystal structures and in the polarization study.

(**A, B**) Alignments of AdiC’s helix 6A in the structural states E_O (blue) (PDB: 7O82) and E_X (yellow) (PDB: 3L1L) with the corresponding helices of BasC and ApcT in the states I_O (orange) (PDB: 6F2G) and I_X (cyan) (PDB: 3GIA), with (A) or without (B) the rest of the protein represented by a mesh contour. (C) The four mean orientations of the helix in the four conformational states are represented by a set of four unit-vectors (closed heads) in the local framework of coordinates whereas those for the four structural states by another set of unit vectors (open heads). The vectors for the conformational states are drawn according to mean θ and φ values obtained from their respective distributions and color-coded for the corresponding states. The two sets of vectors are overlaid as described in the text. (D) Scatter plots of mean θ versus φ values (closed circles) for four conformational states, which are compared with those for the four structural states (open circles); all are color coded for states. (E) The inverse values of combined least-distance-squares between the locations of the arrow heads of the two compared groups (open versus closed) in (C) for all 24 possible combinations among them.

Figure 11—source data 1 Tables comparing mean angles calculated from polarization measurements and those from structure. Table listing the inverse values of combined least-distance-squares of the different state combinations.: https://cdn.elifesciences.org/articles/82175/elife-82175-fig11-data1-v2.xlsx
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For further illustration, we calculated the combined least-square ( ${L S}_{c}$ ) values between the two sets of open and closed arrowheads in Figure 11C for all 24 combinations, and plotted the $\frac{1}{{L S}_{c}}$ values in Figure 11E. In the statistically best matching case based on the largest $\frac{1}{{L S}_{c}}$ , C₁ would correspond to E_x, C₂ to E_o, C₃ to I_o, and C₄ to I_x, in which the values θ_i and φ_i and Ω are comparable between the corresponding conformational and structural states (Figure 8B and C). In terms of open versus occluded states, the assignments of C₂ and C₃ as open states, and C₁ and C₄ as occluded states are consistent with those based on the Arg⁺ concentration dependence, discussed above. In terms of sidedness, judging from the structures of AdiC, that is, E_o and E_x, the spatial orientations of helix 6A in them (θ and φ) are compatible with those of C₂ and C₁.

In summary, using a state-of-the-art fluorescence polarization microscopy system assembled in house, we have, for the first time, successfully tracked conformational changes in a single integral membrane protein molecule among four states that occur on angstrom and millisecond scales. The resolving power of this technique allowed us to experimentally establish a fully determined quantitative model of eight states required to account for the energetics of the observed conformational changes of an AdiC transport molecule with or without a ligand bound. This capability of resolving and tracking the conformational states of individual molecules forms the foundation for performing the kinetic study to acquire the necessary dynamic information for understanding the transporting mechanism, and for creating an experiment-based 4D model to quantitatively account for the complex spatiotemporal behaviors of a transporter molecule, which can be applied to the investigation of other membrane proteins.

Materials and methods

Materials

Detergent n-dodecyl-β-D-maltopyranoside (DDM) was purchased from Anatrace, 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) from Avanti Polar Lipid Inc, bifunctional rhodamine bis-((N-iodoacetyl)-piperazinyl)-sulfonerhodamine from Invitrogen (B10621), strep-tactin resin from IBA, and cover slip (#1.5) and microscope slide glass from Fisher Scientific or VWR. Unless specified otherwise, all other reagents were purchased from Sigma, Thermo Fisher Scientific, or EMD Millipore.

Cloning, protein expression, and purification

A double-stranded DNA fragment, synthesized by Integrated DNA Technologies (IDT), contains, from the N-terminus to the C-terminus, Avi tag for recognition by biotin ligase, a Strep II tag, a linker (GGGSGGGS), the gene of AdiC of Escherichia coli, a linker (GGGS), a thrombin protease recognition site, a C-termini Strep II tag, and a stop codon, which was cloned into the pET28b vector. The removal of two native cysteines (C238A and C281A) and introduction of the double G188C and S195C cysteine mutations in helix 6a for attaching bifunctional rhodamine were carried out using the QuickChange technique and verified by DNA sequencing.

The AdiC protein was expressed in E. coli BL21(DE3) cells transformed with AdiC-gene-containing plasmids. The transformed cells were grown in Luria Broth at 37°C to an A₆₀₀ of ~1.0. Protein expression was induced with 0.5 mM iso-propyl β-D-thiogalactopyranoside (IPTG) at 22°C overnight. The cells were harvested and resuspended in a solution containing 100 mM NaCl, 50 mM tris-(hydroxymethyl)-aminomethane (Tris) titrated to pH 8.0, 1 mM phenylmethylsulfonyl fluoride (PMSF), 4 mM tris-(2-carboxyethyl)-phosphine (TCEP), 1 µg/ml leupeptin, and 1 µg/ml pepstatin A. To extract membrane proteins, 40 mM DDM was added to the cell suspension; the conical tube containing this suspension was placed on a rotating device in a 4°C cold room for 2–3 hr. The cell suspension was then sonicated, the cell lysate was centrifuged at 12,000 × g for 20 min, and the resulting supernatant was loaded onto a gravity flow column packed with strep-tactin super-flow resin (IBA). The column was washed with a wash buffer (WB) containing 100 mM NaCl, 50 mM Tris titrated to pH 8.0, 2 mM TCEP, and 2 mM DDM. AdiC protein was eluted from the column using WB added with 10 mM desthiobiotin. The AdiC-containing fractions were pooled and then concentrated with an Amicon Ultra concentrator (50K MWCO) before a further purification with a size-exclusion FPLC column (superdex 200 10/30, GE) equilibrated in WB.

Labeling and reconstitution of AdiC into nanodiscs

Purified AdiC was mixed with POPC and the MSP2N2 membrane scaffold protein purified as described (Ritchie et al., 2009; Denisov et al., 2019) in an 1:1500:10 molar ratio of the AdiC dimer:POPC:MSP2N2. The mixture was incubated at 4°C for at least 2 hr. Nanodiscs were assembled during a dialysis of the mixture against a buffer containing 100 mM NaCl, 20 mM Tris titrated to pH 8.0, and 0.5 mM TCEP at 4°C overnight. After the dialysis, the nanodiscs were labeled with biotin using the BirA Enzyme (Avidity) following the protocol provided by the manufacturer, and then mixed with bifunctional rhodamine in a 2:1 molar ratio of the AdiC dimer:bifunctional rhodamine, a ratio to maximize the chance of only one AdiC monomer in each dimer to be labeled; this mixture was incubated at room temperature for more than 4 hr. The remaining free dye was removed first with Biobeads (SM-2, Bio-Rad) and then by size-exclusion chromatography (Superose 6 10/30 or Superderx 200 10/300, GE) equilibrated with a solution containing 100 mM NaCl and 50 mM Tris titrated to pH 8.0. As expected, the peak of the protein containing the two mutant cysteine residues, detected at 280 nm, co-migrated with that of the fluorophore dye detected at 550 nm. In contrast, no notable absorbance peak at 550 nm co-migrated with the peak of the protein without these mutant cysteine residues. Thus, there was no detectable background labeling (Figure 1—figure supplement 1A and B). The final product of nanodiscs harboring labeled AdiC was aliquoted, flash frozen in liquid nitrogen, and stored in a –80°C freezer.

Sample preparation for data collection with polarization TIRF microscope

For adhesion of streptavidin, one side of a cover slip is exposed to 0.01% poly-L-lysine solution for 1 hr, before being rinsed with distilled water and air dried. Prior to an experiment, a cover slip was attached, via thin transparent Scotch adhesive tapes placed on its left and right edges, to a microscopy slide, with the poly-L-lysine-coated side of the cover slip facing the bottom side of the slide. Solutions were to be placed in the space between the two pieces of glass created by the adhesive tapes that acted as a spacer. The poly-L-lysine-coated side of the cover slip was exposed to 5 mg/ml streptavidin (Promega) in this space for 15 min, and the remaining free streptavidin was washed away with a solution containing 50 mM HEPES titrated to pH 7.5 and 100 mM NaCl.

An AdiC-containing nanodisc sample was diluted to 30–100 pM, estimated from an evaluation of the absorbance of the sample at 550 nm wavelength against the extinction coefficient of bifunctional rhodamine. The diluted sample was flowed into the space between the assembled cover slip and slide. After allowing a biotin-moiety covalently linked to the N-terminus and the streptavidin-binding tags linked to the N- and C-termini in each of AdiC subunit (i.e., totaling six available attachment points per AdiC dimer) to bind to streptavidin on the cover slip, the space was thoroughly washed to remove unattached AdiC with a solution (pH 5) containing 100 mM NaCl, 100 mM dithiothreitol (DTT, Fisher, BP172), and 50 mM acetic acid titrated to pH 5, without or with arginine at a specific concentration. DDT was used to scavenge oxygen to minimize its adverse impact on the fluorophore’s emitting intensity and lifetime.

Fluorescence polarization microscope and intensity recording

As previously described, the fluorescence polarization microscope was built from a Nikon TIRF microscope (model Ti-E) (Lewis and Lu, 2019c). To produce an evanescent field at the surface of the sample coverslip, a 140 mW linearly polarized laser beam (532 nm) generated from a 500 mW laser (Crystalaser CL532-500-S) was directed to pass through a ¼ λ-plate, which transformed the linear polarization to circular polarization. After passing through a polarization-preserving, high numerical aperture 100× objective (Nikon Achromatic, NA = 1.49), the beam approached the coverslip with an incident angle of 68°, the so-called critical angle that leads to TIR required for the formation of an evanescent field (Axelrod et al., 1984). The emission of polarized fluorescent light from individual fluorophores excited by the evanescent field was directed to a 50:50 non-polarizing beam splitter (Thorlabs CM1-BS013) after passing through the objective (Figure 2), and then to a 540/593 nm bandpass filter (Semrock FF01-593/40-25) that prevents the propagation of excitation light. One resulting beam was further split by a glass (N-SF1) polarizing beam splitter (Thorlabs CM1 PBS251) along 0° and 90° and the other by a wire-grid polarizing beam splitter (Thorlabs WP25M-Vis) along 45° and 135°. These four emission intensity components, labeled as $I_{0}$ , $I_{45}$ , $I_{90}$ , and $I_{135}$ , were individually directed onto four designated sectors in the CCD grid of an EMCCD camera (Andor iXon Ultra 897), where the four intensities from a given fluorophore appeared in the corresponding positions of the four sections.

Here, fluorescence intensities from individual bifunctional rhodamine molecules, each attached to helix 6A in AdiC, were collected with the microscope and captured every 10 ms with an EMCCD camera at the room temperature 22°C. Following extraction of temporal information from the intensities with the changepoint analysis described below, we applied a Gaussian filter (with a corner frequency of 7.5 Hz) to all four intensity traces to reduce high-frequency noise, where the rise time was 22 ms. From these filtered intensities, we calculated angles as described below.

The experiments were performed on five separate occasions. Data collected among these separate collections are statistically comparable and were pooled together, resulting in sufficiently narrow distributions as illustrated in Figure 5. The width of the distributions reflects both technical and biological variations. Outlier data were excluded on the following basis. First, while fluorescence intensity is expected to vary among different polarization directions, the total intensity should not exhibit large variations unrelated to protein-conformational changes, such as more than one step bleaching of fluorescence. Second, for a given recording, at least 15 events are required to obtain a 95% confidence level for state identification, so any short traces with less than 15 events were excluded on the assumption that the short and long traces belong to the same distribution. All traces used contain four states and have an average length of ~4 s. There were no traces with an expected resolvable SNR that did not exhibit transitioning events. Third, for event detection and state identification, an SNR greater than 5 is necessary for the required minimum angle resolution. Thus, any set of intensity traces with this ratio less than 5 were excluded. The sample sizes were estimated on the basis of previous studies (Lewis and Lu, 2019c; Lewis and Lu, 2019a; Lewis and Lu, 2019b) to yield sufficiently small standard errors of mean to obtain accurate estimate of the mean. Practically, the error bars are comparable to the sizes of the symbols of data as illustrated in Figures 6 and 10A. The 95% confidence intervals are provided for all determined equilibrium constants in Table 1.

System parameters

Theoretical aspects of the three-channel polarized emission system have been previously described (Fourkas, 2001), and extended to and practically implemented with four channels (Ohmachi et al., 2012; Lippert et al., 2017; Lewis and Lu, 2019c). Briefly, the intensity of a given polarized component with angle ψ, I_ψ, collected by the microscope’s objective from the emission of a fluorophore, which is excited by an evenescent field generated by a circularly polarized laser beam under a TIR condition, is dependent on the fluorophore’s orientation. As such, I_ψ is defined by the spherical coordinates θ and φ in a manner that

I_{ψ} = \frac{1}{4} g_{ψ} I_{tot} (X_{4} (δ) (\sin^{2} θ (f_{ψ} X_{1} (α) \cos (2 (φ - ψ)) + X_{2} (α)) - \frac{2}{3} X_{2} (α)) + X_{3} (α))

where the polarization angle ψ = 0°, 45°, 90°, or 135°. The factor f_ψ corrects for systematic reduction in the maximal achievable anisotropy of the light per channel ψ. The coefficients X₁, X_2, and X₃ correct for the incomplete collection of photons by a microscope objective with collection half-angle α:

\begin{matrix} X_{1} (α) = \frac{π}{12} (7 - 3 \cos α - 3 \cos^{2} α - \cos^{3} α) \\ X_{2} (α) = \frac{π}{2} (\cos α - \cos^{3} α) \\ X_{3} (α) = \frac{2 π}{3} (1 - \cos α) \end{matrix}

Ideally, when presented with a beam of non-polarized light, the system splits that beam into four of equal intensity. Small deviations from this theoretical equality are corrected by normalizing each intensity of a given channel (ψ°) to that of the 90° channel chosen as the reference here:

g_{ψ} = \frac{I_{t o t, 90}}{I_{t o t, ψ}}

Besides those three types of system parameters, the coefficient X₄ corrects for the fast diffusive motion (‘wobble’) of the probe relative to the attached protein, which is measured in terms of the half-angle δ of the wobble cone:

X_{4} (δ) = \frac{1}{2} \cos δ (1 + \cos δ)

The parameter δ was experimentally estimated to be 22.5° in a separated macroscopic anisotropy study of the proteins as previously described (Lewis and Lu, 2019c).

Analytic solutions have been found for θ, φ and I_tot from Equation 7 (Lewis and Lu, 2019c):

φ = \frac{1}{2} \tan^{-1} (\frac{(I_{45} - I_{135}) (f_{0} \cos 2 ψ_{0} - f_{90} \cos 2 ψ_{90}) - (I_{0} - I_{90}) (f_{45} \cos 2 ψ_{45} - f_{135} \cos 2 ψ_{135})}{(I_{0} - I_{90}) (f_{45} \sin 2 ψ_{45} - f_{135} \sin 2 ψ_{135}) - (I_{45} - I_{135}) (f_{0} \sin 2 ψ_{0} - f_{90} \sin 2 ψ_{90})})

I_{tot} = \frac{1}{2} (\frac{[X_{2} + X_{1} f_{0} \cos 2 (φ - ψ_{0})] I_{90} - [X_{2} + X_{1} f_{90} \cos 2 (φ - ψ_{90})] I_{0}}{X_{1} (X_{3} - \frac{2}{3} X_{2} X_{4}) (f_{0} \cos 2 (φ - ψ_{0}) - f_{90} \cos 2 (φ - ψ_{90}))} + \frac{[X_{2} + X_{1} f_{45} \cos 2 (φ - ψ_{45})] I_{135} - [X_{2} + X_{1} f_{135} \cos 2 (φ - ψ_{135})] I_{45}}{X_{1} (X_{3} - \frac{2}{3} X_{2} X_{4}) (f_{45} \cos 2 (φ - ψ_{45}) - f_{135} \cos 2 (φ - ψ_{135}))})

θ = \sin^{-1} (\sqrt{\frac{1}{2 X_{1} X_{4} I_{tot}} (\frac{I_{0} - I_{90}}{f_{0} \cos 2 (φ - ψ_{0}) - f_{90} \cos 2 (φ - ψ_{90})} + \frac{I_{45} - I_{135}}{f_{45} \cos 2 (φ - ψ_{45}) - f_{135} \cos 2 (φ - ψ_{135})})})

The angle θ was defined from 0° to 90° and φ from 0° to 180° (originally calculated as –90° to 90°) with degenerate solutions of θ or 180°- θ and φ or 180° + φ. The solutions for individual events of a given molecule, which were expected to be limited within an appropriately defined quarter sphere because of the expected small angle changes of about 10°–40°, were chosen on the basis of minimizing the variance of the distribution of the resulting angles for the events. When θ is near 90°, the noise of intensities might prevent a solution of θ, in which case we simply set the θ values to 90°. We only analyzed data from the particles with no more than a few percent of such data points.

Calibrations of the camera

Photons hitting the CCD chip of an EMCCD camera result in the release of individual electrons in accordance with the photoelectric effect. These electrons pass through multiple layers, at each of which they have a probability to cause the release of additional electrons, effectively amplifying the original signal with a gain (G) (Lidke et al., 2005; Heintzmann, 2016). The relationship of the N photons released over a given time interval Δt and the recorded intensity I is expressed as

I \cdot Δ t = G \cdot N + o f f s e t

As an inherent feature of EMCCD cameras, the offset is the intensity recorded by the camera when the shutter is fully closed. These parameters are estimated by analyzing the relationship between photon intensities recorded at multiple laser intensities versus the corresponding SNR. For photon count N, the standard deviation σ due to shot noise is given by the square root of N. In addition, EMCCD cameras add an additional multiplicative noise that effectively scales the σ due to shot noise by a factor of √2 that relates the SNR to N via the expression

S N R = \frac{I}{\sqrt{2} σ} = \sqrt{\frac{N}{2}}

Substituting Equation 15 into Equation 14 yields

I \cdot Δ t = 2 G \cdot S N R^{2} + o f f s e t

On a plot of I·Δt versus SNR², the slope is twice the gain, whereas the y-intercept is the offset. For our system, the value of the gain was found to be 146 and that of the offset was 220.

Furthermore, when the signal from an interested fluorophore is split from the background signal, the combined intensity signal recorded is related to N by the following relation

S i g n a l = G \cdot N + G \cdot N_{b a k} + o f f s e t

rearranged to

N = \frac{S i g n a l - o f f s e t}{G} - N_{b a k}

where $N_{b a k}$ is the number of photons underlying the background signal, which needs to be subtracted. The quantum efficiency (QE) of the Andor Ixon EMCCD camera is estimated as ~0.95 in the visible light range, meaning that 95% of photons contacting the CCD chip are detected. Therefore, the actual photon count is calculated as N_det = N / QE, and the effective SNR is also scaled accordingly.

Detection of event transitions

The photon flux intensity recorded in a given channel changes when the orientation of the fluorophore is changed. To detect these transitions within the measured polarized intensities, we adopted a version of the changepoint algorithm (Chen and Gupta, 2001; Beausang et al., 2008). Such a process was based on calculating a log likelihood ratio over a period of time to determine the maximal ratio that identified the point where the perceived change of photon-release rate occurred, that is, the time at which the fluorophore transitions from one orientation to another. This method has previously been applied to analyzing the photon-arrival time captured on a continuous basis with photon-multiplier-based multi-channel recordings (Beausang et al., 2008), which was adapted for analyzing photons collected over a fixed time interval with an EMCCD camera (Lewis and Lu, 2019c).

When a camera is used as a detector, photons emerging from each channel are effectively binned over each frame. A series of consecutive k frames with a constant exposure time (Δt) is expressed as

t_{0}, t_{1}, \dots, t_{i}, t_{i+1}, \dots, t_{m-1}, t_{m} = 0, Δ t, \dots, i Δ t, (i + 1) Δ t, \dots, (k - 1) Δ t, k Δ t

For a given frame i, the intensity $I_{i}$ is defined by the rate of photon release:

I_{i} = \frac{n_{i}}{Δ t}

where n_i is the number of photons release within frame i. The cumulative distribution, m_j, is built by adding the number of photons for the successive time frames:

m_{j} = \sum_{i=0}^{j} n_{i}

If during an interval T the rate changes from I₁ to I₂ at the time point τ = iΔt, and the number of emitted photons prior to this change is m (Equation 21) and N – m after the change, then the likelihood ratio of a transition occurring at frame i in the log form is described by

L L_{R} = \sum_{r=1}^{h} (m_{r} l n (\frac{m_{r}}{τ}) + (N_{r} - m_{r}) l n (\frac{N_{r} - m_{r}}{T - τ}) - N_{r} \ln (\frac{N_{r}}{T}))

where h equals 4, the number of emission channels in the system. We set the threshold of significance for LL_R at the level that limits the false-positive events to 5% on the basis of simulation studies for the corresponding levels of SNR, and the resulting false-negative events were about 1%.

The program was started by identifying one transition over the entire trace. If a change-point X was identified, it would then search for additional transitions between the start of the trace and point X and between X and the end. This iterative search with successively shortened stretches continued until no more transitions were identified.

State identification

Following the detection of intensity transition time points using the changepoint method and subsequent calculation of angles, the states of individual events, each demarcated by two consecutive transition timepoints, were identified on the basis of x,y,z values, calculated from the corresponding θ and φ values, along with $r$ of a unity value, in accordance with the transformation relations between the Cartesian and spherical coordinate systems:

\begin{matrix} \begin{matrix} x = r \sin θ \cos φ \\ y = r \sin θ \sin φ \end{matrix} \\ z = r \cos θ \end{matrix}

Given the $r$ of a unity value, which carries no information regarding spatial orientation, for all cases, x,y,z in all cases would always be on a unit sphere and fully encode the orientation information specified by θ and φ.

The identification of the states is done by using a ‘nearest-neighbor’ method in a Cartesian coordinate system, where a given event was assigned to the closest state distribution. Closeness was determined by the minimum distance d_i,k between the x,y,z coordinates of the ith event and the distribution means $〈x_{k}〉$ , $〈y_{k}〉$ and $〈z_{k}〉$ , where k is the number of potential states, calculated as:

d_{i,k} = \sqrt{{(⟨ x_{k} ⟩ - x_{i})}^{2} + {(⟨ y_{k} ⟩ - y_{i})}^{2} + {(⟨ z_{k} ⟩ - z_{i})}^{2}}

Minimization was performed by using a k-means clustering algorithm optimized with two coupled algorithms (simulated annealing plus Nelder–Mead downhill simplex)(Press et al., 2007), as we described previously in more detail (Lewis and Lu, 2019c). The resulting four conformational state distributions are denoted as C₁ – C₄.

States must be indexed so that they are always numerated in the same sequential order among individual molecules, a prerequisite for correctly relating the states identified here to those identified crystallographically. This indexing is based on the shortest, if not straightest, path distance between the first and last states, C₁ and C_M (where M = 4 in our case) as they detour through the remaining states (Figure 7—figure supplement 1B). This path length is calculated as the sum of the cumulative distances between two adjacent states, denoted as d_tot:

d_{t o t} = \sum_{i = 1}^{M - 1} d_{i, i + 1}

where the number 1 indicates a chosen starting state and the distance d_i,j between states indicated by positions i and j in a Cartesian coordinate system is defined as:

d_{i, j} = \sqrt{{(x_{i} - x_{j})}^{2} + {(y_{i} - y_{j})}^{2} + {(z_{i} - z_{j})}^{2}}

If the states were located along a perfect line, the total path distance would equal the distance between states 1 and M, that is, d_1,M, where d_1,M = d_tot. However, if they were not on a line, d_tot would be greater than d_1,M by Δd such that

(\sum_{i = 1}^{M} d_{i, i + 1}) - d_{1, M} = Δ d

Upon calculating $Δ d$ for each of the 24 possible sequences relating the four states, the shortest path can be found on the basis of the smallest value of $Δ d$ , which has two solutions with equal path length, that is, 1-2-3-4 versus 4-3-2-1 (Figure 7—figure supplement 1C vs. Figure 7—figure supplement 1D). The sequence of C₁-C₂-C₃-C₄ shown in Figure 7—figure supplement 1C was consistently chosen.

Transformation of the laboratory framework to a local framework

As explained in the text, individual molecules did not have the same orientation. Thus, a direct comparison among them requires all molecules be rotated from the laboratory frame of reference into a common local frame of reference (Figure 7—figure supplement 1A). In the local frame, the x,y-plane is defined by the vectors representing C₁ (V₁) and C₄ (V₄) and the x-axis is defined by V₁. The z-axis is perpendicular to the x,y-plane. The x, y, and z-axes, represented by unit vectors, are defined by:

X = \frac{V_{1}}{| V_{1} |}; Y = \frac{X \times V_{N_{s t a t e s}} \times X}{| X \times V_{N_{s t a t e s}} \times X |}; Z = \frac{X \times Y}{| X \times Y |}

where

V_{i} = (\begin{matrix} x_{i} \\ y_{i} \\ z_{i} \end{matrix})

θ and φ in the local frame of reference are then calculated as:

θ_{i}^{} = \cos^{- 1} (\frac{Z}{| Z |} \cdot \frac{V_{i}}{| V_{i} |})

φ_{i}^{} = \sin^{- 1} (\frac{Y}{| Y |} \cdot \frac{V_{i}^{p r o j}}{| V_{i}^{p r o j} |})

where

V_{i}^{p r o j} = \frac{Z \times V_{i} \times Z}{| Z \times V_{i} \times Z |}

Calculation of the direct angle change Ω between two states

The direct angle change Ω_i,j between two states i and j, as represented by the vectors V_i and V_j defined above, can be calculated from the relation:

Ω_{i,j} = \cos^{- 1} (\frac{V_{i} \cdot V_{j}}{| V_{i} | \cdot | V_{j} |})

Data availability

Source-data files for all relevant figures are provided.

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Decision letter

Kenton J Swartz

Senior and Reviewing Editor; National Institute of Neurological Disorders and Stroke, National Institutes of Health, United States
Janice L Robertson

Reviewer; Washington University in St. Louis, United States

Our editorial process produces two outputs: (i) public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]

Thank you for submitting the paper "Tracking multiple conformations occurring on Å-and-millisecond scales in single amino-acid-transporter molecules" for consideration by eLife. Your article has been reviewed by 4 peer reviewers, including Janice L Robertson as Reviewing Editor and Reviewer #1, and the evaluation has been overseen by a Senior Editor.

Comments to the Authors:

We are sorry to say that, after consultation with the reviewers, we have decided that this work will not be considered further for publication by eLife.

The reviewers agreed that your study presents a cutting-edge approach that offers the potential for monitoring conformational equilibria of proteins, such as membrane transporters. In particular, the observation of arginine linked changes in the polarization distributions of AdiC is promising. However, major questions were raised during the review that indicate additional investigation is necessary to test whether the single-molecule data, and post-processing, leads to a robust determination of conformational states that pertain to transport. All of the points are listed in the comprehensive reviews below, but the major concerns are summarized here:

1. In both studies, it is reported that Ex-Ix, i.e. external-occluded to internal-occluded or C1-C4, transitions occur in the apo condition. The analysis also shows that equilibrium between these states (K4,1) is comparable to that in substrate saturating conditions. Therefore, this presents a model for AdiC that is an uncoupled uniporter. This means that if arginine is present on one side of the membrane, without any substrate on the other side, then AdiC would be expected to dissipate the arginine gradient because it could return back to the substrate-loaded side via the apo transition. However, Fang et al., JBC, 2007, carried out these experiments and showed that AdiC does not transport unless there is substrate on both sides of the membrane. Therefore, AdiC is a coupled antiporter that does not transition between the Ex-Ix states without substrate. Since the current study reports the observation of apo occluded state transitions, it raises a major concern that the states that have been identified do not represent the states in the full transport cycle. Further investigation is needed to consolidate the proposed model with the strictly coupled mechanism that has already been demonstrated for AdiC.

2. The conversion of the single-molecule trajectories to state transitions requires substantial post-processing, including averaging, step detection and clustering. Numerous reviewers raised the question of whether the four-state model that is being proposed is objectively determined from the traces or is imposed by restraining the k-means clustering analysis. Along these lines, testing alternate state models and comparing other clustering algorithms that do not require a pre-classification of states is necessary here in order to know if the 4-state model is robust, or equally likely compared to other multi-state models.

3. Following this, the study would be greatly strengthened if additional validation was carried out to test the identification of states, and perturb AdiC transport in a known way. Can a certain state be cross-linked to see whether the single-molecule trajectories report on the isolation of a single state? For perturbing transport, there are examples of mutations or conditions (i.e. high pH, different substrates) that are known to slow transport. Is the data capable of reporting on these changes, and do they agree with the expected shift in transport behavior? These validation studies are important to test the robustness of the single-molecule data and the state models to inform on the overall transport cycle.

4. Finally, macroscopic transport assays of AdiC would be extremely informative alongside the single-molecule studies. This would allow for important controls that will test transport activity of the actual construct being studied here, as well as help to consolidate any discrepancies in the protein behavior that was raised above.

Reviewer #1 (Recommendations for the authors):

1. Confirmation of function after labeling. The version of AdiC that is being studied here is labelled by a bis-maleimide-TMR, solubilized in POPC nanodiscs, removed 2 native cysteines, N-terminal Avi-tag and Strep-tag, and C-terminal Strep-tag. However, I do not see that a validation has been carried out to test if this construct/conditions independently yield the same KD for arginine or agmatine binding, or similar transport properties. Experiments of binding (e.g. by ITC) and transport (e.g. by radioactive uptake assays in proteoliposomes) of the labelled construct that is currently being studied are important controls to validate whether the single-molecule polarization data can be compared to wild-type data published previously.

2. The effect of anchoring AdiC on the slide. The strategy for conjugating the sample to the slide is via Strepavidin binding to the protein termini directly. The need for anchoring the protein to slide in order to observe polarization changes is understood. However, it also raises questions whether this anchoring may bias the observation of conformational equilibria. Since there is a small linker at both N- and C-termini, some benchmarking studies would be appropriate to test whether the linker length impacts the equilibria. Shortening the linkers may shift the balance to stabilize certain states, and lengthening (to a limit, within the range where polarization changes can still be observed) would demonstrate if more states become observable and the number of states becomes invariant with linker length.

3. Background labeling? Considering the labeling conditions of pH 8.0 and 4 hours, there is a possibility of background labeling of the maleimides with primary amines. Was the background labeling measured, for instance with constructs that do not contain the reactive cysteines? Also, it was mentioned that bleaching steps were used to assess labeling, but this was not shown so it is unclear what information was being obtained from these analyses. Both of these points should be addressed to give confidence that the label is attaching in the mode described and that there are no other possibilities of non-specific labeling.

4. Robustness of the clustering results. The clustering, as indicated in Figure 5, is not evident by eye and appears more as a continuum of conformations. It also reasons that the clustering results are dependent on the averaging, changepoint detection and k-means clustering parameters. Thus, the robustness of the identification of states should be shown across a range of parameters for each analysis step. In addition, testing different state models (e.g. 2-8 states) would be important to understand if the 4-state clustering is robustly determined or other state models also suitably fit the data.

5. Validation of the model with mutations that are known to shift the equilibrium between states. While the results showing the linkage of the states to arginine binding corresponding to the macroscopic measurements of AdiC KD provides some supportive evidence, additional investigation that tests the different states would strengthen the proposed model. For example, can a mutation be engineered, or reagent applied that stabilizes the inward-open or outward-open state, to see that conferred in the single-molecule polarization traces?

6. A cartoon of the full gene sequence and schematic of the AdiC construct that is being used here would be useful as supplementary information, in order to understand the sizes of tags and linkers applied to the protein.

7. In Figure 9, the colors in the plot do not appear to match the legend (different shades of blue).

8. Since the data is analyzed over single trajectories, how long are these traces typically? How long do the traces have to be in order to observe enough transitions between states?

9. The fitting of the KDs for states C1 and C4 are not justified as there does not appear to be a significant change in the probabilities over the arginine titration. Therefore, they should not be reported with confidence. Along these lines, are the errors that are being reported in Table 1 on the best-fits or are they over different samples?

Reviewer #2 (Recommendations for the authors):

Moreover, the identified 4 states and their substrate affinities reported in this manuscript do not significantly advance our understanding of Adic and the APC superfamily. Therefore, I would suggest combining this and the companion manuscript into a single paper. In addition, some more specific questions and suggestions are:

1) The key difference of the data processing described in this manuscript compared to the earlier published work is the introduction of the normalization step. Due to the random X-Y orientation of the transporter proteins on the surface, each protein molecule needs to be analyzed individually to get its own theta and phi angles in the laboratory frame (Cartesian coordinate). Normalization of the angles based on one of the identified states allows to directly compare the results for different particles directly. This is an interesting improvement, so the authors may need to mention this in the abstract.

2) In principle, the normalization may improve the accuracy of the mean angle values even as the deviations might increase. It would be helpful if the authors compared the ensemble-averaged mean values and the single-trace mean values.

3) From my understanding, to better differentiate the states, traces visiting all 4 states should be analyzed. When the authors select the traces with at least 12 transition events, do the events include transitions between all four states? The authors might want to clarify.

4) It is unclear how the authors establish the number of distinct states to be considered in the system. Is the number of states based on the expected structurally resolved 4 states or obtained from the analysis of the traces themselves? There is a proposed so-called full occluded state. Could/should this state be included in the data analysis?

5) The fluorophore is attached via two cysteines. Therefore, in the same conformation, the fluorophore has two orientations related by 180-degree rotation. Will this affect the detected signal? If not, then would a protein conformational change, which makes the fluorophore rotate by 180 degrees, be detected?

6) The protein is modified by a bi-functional fluorophore and surface-immobilized with multiple binding tags. How do you evaluate whether these manipulations affect the state populations and transport activity? The structures of Adic were all solved in the outward-facing states. Simulation (PLoS ONE 11(8): e0160219) also indicated that the inward-facing states, especially the inward-open state, are relatively unstable, suggesting that the population of the inward-facing states should be low. However, in Figure 7B, the inward-open state is highly populated, which seems inconsistent with the expectations. It seems that some additional experiments and or more extensive discussion are needed to support the authors' estimates of the state populations.

7) The state assignments are based on the similarity of the theta and phi angles to those calculated from the four crystal structures. To me, this does not seem entirely convincing, especially regarding the inward-facing states, expected to be lowly populated. The authors might need to use mutants or ligands to stabilize the inward-facing states to verify the assignment.

8) The authors need to describe how they estimate the errors in Table 1.

Reviewer #3 (Recommendations for the authors):

1. This work monitors only a single transmembrane helix (helix 6a) in AdiC. This was presented as an advantage, but in reality it also creates strong limitations for data interpretation. By comparing the orientations of helix 6a in PM-identified states (C1-C4) and in structural states, C1-C4 were dubbed externally open (Eo), externally occluded (Ex), internally open (Io), and internally occluded (Ix) states. Such assignment comes with high uncertainty even in optimal conditions. For example, without "seeing" the rest of the protein, how do the authors know that a particular PM state is not an intermediate state not observed in structural studies? Such a concern arises in part because of the assignment of C1 as Ex and C4 as Ix, with a state possibility of 0.19 and 0.14, respectively. Why would an antiporter sample occluded states so often without ligands? Is it possible that C1/C2 are both externally open (with some differences in helix 6a orientations) and C3/C4 both internally open and the occluded states are too rare to be observed when there is no ligand?

2. The assignment of PM states was actually done under not-so-optimal conditions. AdiC structures were only determined in ligand-free Eo and ligand-bound Ex states, so the authors used BasC and ApcT structures to represent the Io and Ic states of AdiC. Multiple questions about data treatments follow naturally. What's the justification to compare ligand-free PM states with ligand-bound structural states (Figure 6)? Although BasC (complexed with a nanobody) and ApcT have similar LeuT fold like AdiC, their sequences are not particularly similar and it's conceivable that AdiC's helix 6a might have significantly different orientations in Io and Ic states than the helix 6a in BasC and ApcT. How would such a possibility affect the assignment of the PM states?

3. Another main issue is about the relation of ligand-free and ligand-bound PM states. There are four ligand-bound PM states, labeled as C1L, C2L, C3L, and C4L to indicate that they correspond to the ligand-free C1, C2, C3, C4 states. However, the ligand-free and ligan-bound PM states appear to have quite different θ/ψ profiles (Figure 5), and the latter were not compared to the structures. How did the authors link ligand-bound PM states to the structural states? How to know for sure that C1 is related to C1L, C2 to C2L, etc? Moreover, it could be misleading to distinguish the corresponding ligand-bound and -free states just by an "L" as if their only difference is the ligand – the technique here provides no such resolution.

4. The authors might want to consider utilizing additional strategies to verify their state assignments. One possibility is to use structures as guidance to lock AdiC in a particular state via Lysine crosslinking and see how such maneuver affects PM results. The determined KD reflects how ligands drive the protein from ligand-free to ligand-bound conformational equilibria without providing much insight into the conformational details in each set of equilibrium.

Reviewer #4 (Recommendations for the authors):

In this paper, Zhou et al. propose a polarization microscope for measuring the emission polarization of bifunctional rhodamine molecules attached to AdiC transporters. The polarization is used to resolve the orientation of the fluorophores, which allows the authors to successfully resolve the four conformations of AdiC at a temporal resolution of tens of milliseconds. The measured orientation for each conformation is validated with the results using crystallography.

Overall, I believe the paper is well written and demonstrates a great application for orientation imaging using polarized microscopes. Detailed experimental procedures, calibrations, and mathematical frameworks are included. I have the following recommendations to improve the manuscript.

1) On page 20, the authors note that they set a threshold to filter out molecules whose total intensity varies during the measurements. The statement that "while fluorescence intensity is expected to vary among different polarization directions, the total intensity should be essentially invariant" is not true. Since the authors use TIRF illumination to excite the molecules, the excitation polarization component along the tilting direction (e.g., along the y-axis) of the excitation is 0, i.e., molecules oriented along that direction (e.g., y-oriented) will be excited less effectively compared to other orientations.

2) Could the authors provide more details regarding how the clusters are ranked? The authors note that C1-C4 are "ranked according to the values of both angles". It is not clear to me how this is done. Also, what is the range of the measured theta_L and phi_L? And how is the warping of the spherical coordinates handled in the ranking process, e.g., a change from 350 deg to 10 deg is +20 deg or -340 deg.

3) Is the k-means clustering also based on the distance in the Cartesian space, similar to the state identification?

Following comment (1) from above, could the authors comment on the possibility of further improving the measurement precision and accuracy using the excitation-dependent total intensity? Since the authors report a wobble angle of 22.5 degrees, the excitation dipole moments should be mostly aligned with the emission dipole moments.

https://doi.org/10.7554/eLife.82175.sa1

Author response

[Editors’ note: The authors appealed the original decision. What follows is the authors’ response to the first round of review.]

1. In both studies, it is reported that Ex-Ix, i.e. external-occluded to internal-occluded or C1-C4, transitions occur in the apo condition. The analysis also shows that equilibrium between these states is comparable to that in substrate saturating conditions. Therefore, this presents a model for AdiC that is an uncoupled uniporter. This means that if arginine is present on one side of the membrane, without any substrate on the other side, then AdiC would be expected to dissipate the arginine gradient because it could return back to the substrate-loaded side via the apo transition. However, Fang et al., JBC, 2007, carried out these experiments and showed that AdiC does not transport unless there is substrate on both sides of the membrane. Therefore, AdiC is a coupled antiporter that does not transition between the Ex-Ix states without substrate. Since the current study reports the observation of apo occluded state transitions, it raises a major concern that the states that have been identified do not represent the states in the full transport cycle. Further investigation is needed to consolidate the proposed model with the strictly coupled mechanism that has already been demonstrated for AdiC.

In this manuscript, as outlined above, we mainly demonstrate the application of the method in a membrane protein. Additionally, we evaluated the energetic differences among the resolved states in the form of equilibrium constants calculated from state probabilities. This operation does not require the kinetic information regarding state connectivity. As such, we now place a dash line (without any arrow) between a given pair of states to solely indicate an equilibrium constant for a pair of neighboring states (Figure. 10B). The connectivity was quantitatively dealt with in the original companion paper. Given that we limited the scope here, this comment would no longer be directly applicable here but is applicable to the kinetic study that we will revise for a later, separate publication.

Regarding the hypothesis that AdiC is an obligatory exchanger, we will discuss, in a transparent and analytic manner, the experimental evidence that disapproves this hypothesis when we address, in the future, the kinetic mechanism underlying AdiC’s conformational changes and its transport of substrate in the revised version of the original companion manuscript.

2. The conversion of the single-molecule trajectories to state transitions requires substantial post-processing, including averaging, step detection and clustering. Numerous reviewers raised the question of whether the four-state model that is being proposed is objectively determined from the traces or is imposed by restraining the k-means clustering analysis. Along these lines, testing alternate state models and comparing other clustering algorithms that do not require a pre-classification of states is necessary here in order to know if the 4-state model is robust, or equally likely compared to other multi-state models.

Our inadequate presentation apparently made the reviewers think that we might have only evaluated the conformation model with four (macroscopic) states. In fact, as described previously in the cited paper (Lewis and Lu, 2019c, NSMB), we evaluated all possible numbers of state that can be resolved with the common microscopy resolution criterion defined as a separation of 2.5σ (standard deviation) between the peaks of two state populations (‘Resutls’), here in terms of spatial orientation (θ and ϕ ). The analysis is done without any preconceived kinetic models (now stated in ‘Results’), including the common four-state transport model.

As stated in ‘Results’, we first detected the fluorophore orientation change with respect to two stationary polarizers from the relative changes in photon counts that occur simultaneously in all four different, resulting polarization components using the changepoint algorithm. Unlike other types of fluorescence-based method, such as FRET, the requirement of concurrent changes in all four channels, here, markedly increases the confidence of the detection of transitions. Two consecutive transition points demarcate an event during which the protein molecule adopts a specific conformation. We then calculated the mean θ and ϕ angles of a given event from all four intensities. This calculation is done with ratios of intensities, so the same result is achieved whether we use the total number or the average number of photons recorded from each channel during that event (‘Results’). It is noteworthy that unlike random noise, the directions of intensity changes between a pair of intensity channels should be related in a specific way, which is another advantageous feature, compared to other types of fluorescence-based method. For example, when the fluorophore’s mean electrical-field vector moved such that its ϕ angle increased in the direction of 0 to 90°, the intensity recorded in the 0° channel would decrease whereas that in 90° should increase accordingly; the intensities of 45° and 135° channels would also characteristically move in opposing directions (‘Results’).

After the angles of individual events were calculated, we separated them into different populations on the basis of the information of θ and ϕ angles together in a three-dimensional operation, as mentioned above and detailed in ‘Materials and methods’; we now explain the essence of the three-dimensional sorting in ’Results’ as well. It is practically impossible to identify the state from either a θ trace or a ϕ trace alone. Thus, we used the k-means clustering (i.e., shortest distance) algorithm to assist us to perform this 3D-sorting task in a Cartesian coordinate system, which would be extremely challenging for us to do manually on subjective visual guidance, if possible. Our program examined the case of one-state distribution to the case of k-state distributions, one at a time in a series of separate operations. These operations were done on the basis of the information of both θ and ϕ together so as to reach the maximal resolvability for the present study and high confidence. For each successful operation, the resolution criterion was ensured, i.e., peaks of all populations were separated by at least 2.5σ. By this common criterion, the highest number of resolvable states was four at each examined substrate concentration, so the minimal conformation model here must have four states for either apo or substrate-bound forms (shown now in Figures 5 and 6), totaling eight states. Again, we did not pick four states because of the knowledge that a typical transporter is expected to have four types of conformation.

Given that we tracked all four states, we could determine their probabilities in all examined concentrations of Arg⁺. From these probabilities, we can in turn determine all the equilibrium constants that quantitatively and fully defines the four-state energetic model of conformational changes. Furthermore, the probabilities of conformations C₂ and C₃ clearly varied with the Arg concentration whereas the other two states varied little, C₂ and C₃ should be two open states that could directly interact with substrates, and the remaining two should be the occluded states (in adopting the conventional name)(‘Discussion’), four of which are arranged in a symmetric manner. We do not need any other information to reach this point. Note that the relative invariability of the probability of C₁ or C₄ with the substrate concentration does not mean these two states do not bind substrates. In the present case of multistates, this invariability actually indicates that they do bind substrates because if C₁ or C₄ did not bind Arg⁺ with any meaningful affinity while other states do, C₁ or C₄ would practically vanish in a saturating concentration of Arg⁺.

Regarding the sidedness of the model (‘Discussion’), the relation between the orientations determined from polarization measurements and those from the structures of known states helps distinguish between the so-called internal and external conformations. The external open and external occluded structures of AdiC are available. Fortunately, for these two states, the two methods yield consistent orientations. Furthermore, we also used the internal open and internal occluded structures of two related transporter as proxies, or space holders, for the corresponding states of AdiC in the exercises to illustrate how to perform multistate spatial alignment.

3. Following this, the study would be greatly strengthened if additional validation was carried out to test the identification of states, and perturb AdiC transport in a known way. Can a certain state be cross-linked to see whether the single-molecule trajectories report on the isolation of a single state? For perturbing transport, there are examples of mutations or conditions (i.e. high pH, different substrates) that are known to slow transport. Is the data capable of reporting on these changes, and do they agree with the expected shift in transport behavior? These validation studies are important to test the robustness of the single-molecule data and the state models to inform on the overall transport cycle.

In our first study of AdiC, we chose to perturb the system in the arguably most naturally consequential way, i.e., by examining AdiC in various concentrations of its natural substrate Arg⁺, totaling 13 concentrations (Figure 10A). From the concentration dependence, we determined the conformations that substrates could directly access versus those that they could not directly access, and their energetic characteristics. The examination of the impact of pH and mutations on AdiC’s properties is the natural progression of the present study, and will undoubtedly be informative. Each type of this examination is a major undertaking. As such, we plan to perform these secondary studies in a manageable manner.

If the molecules were “frozen” in one conformation, we could no longer align individual molecules in the absence of other conformations as references. At a minimum, individual molecules and thus the attached probes are expected to be randomly orientated on the sample-supporting glass in term of the rotation angle ϕ around the z-axis, even without considering the variation in the inclination angle θ yet. We thus would not be able to obtain a mean spatial orientation among all particles for comparison with the expected orientation for the conformation. Furthermore, each of the four channels would have a statistically constant intensity. Then, we would not be able to tell whether a protein molecule were in a frozen state versus in a defunct state caused by the chemical reaction. As outlined above, we do not need to freeze the molecule in a state to identify the types of tracked conformational states, which can be tested in future.

The outcomes of our study are comparable to published estimates of K_d (in this manuscript) K_m and “k_cat” (in the original companion manuscript) in that: our estimates are within the range of K_d measured with ITC (‘Discussion’), which is a factor of 3 for the Miller lab alone; our estimated K_m value on average is 2.38 fold smaller than the average of functional estimates; our estimated “k_cat” on average is 1.25 fold less than the average of functional estimates. These ratios would correspond to 0.87 kT and 0.22 kT if they were evaluated as errors between the two approaches, in terms of the underlying substrate binding energy and the activation energy, respectively. For reference, according to the equipartition theorem, the average energy of individual atoms in a monoatomic ideal gas in thermal equilibrium is ~1.5 kT. Arguably, the system and statistical errors of their flux assay in terms of K_m should not be less than the observed error range of ITC that is a factor of 3 for the Miller lab. The upper limit of this range of K_d differs from that of another lab by a factor of >2. If so, the differences between our estimates and the function-and-biochemical estimates of the Miller lab are within the system and statistical errors of their approaches. As such, our approach has independently led to comparable estimates, and our estimates are thus valid.

4. Finally, macroscopic transport assays of AdiC would be extremely informative alongside the single-molecule studies. This would allow for important controls that will test transport activity of the actual construct being studied here, as well as help to consolidate any discrepancies in the protein behavior that was raised above.

As described below, our method can independently and straightforward estimate the K_d K_m and “k_cat”, and as described above, our estimates are comparable to existing estimates. We do not know any discrepancies between our estimates and existing estimates to the levels that concern us. We mutated two native cysteine residues because removing all native cysteine residues have no major impact on the functional properties (Tsai et al., Biochemistry 2012). A bi-functional rhodamine molecule was attached via two mutant cysteine residues to helix 6a in the region extracellular to the substrate-binding site to avoid affecting the binding affinity. Furthermore, as we explained in ‘Results’, spacer sequences were put between tags and between a tag and the AdiC sequence to introduce flexibility to the extent that the inclination angle varied considerably among molecules. Now stated in ‘Results’, as assessed with ITC, the protein resulting from the cDNA construct genetically engineered for the present purpose exhibited a K_D of 104 μM for Arg⁺ (Figure 1—figure supplement 1D), which is within the previously reported range of 32 to 204 μM for AdiC.

With more than a decade of effort, we developed the present high-resolution fluorescence-polarization method to track the conformational dynamics of a protein. Structural conformations of a protein are the physical basis of its functional properties. If so, accurate conformational information of a protein acquired with adequate spatial and temporal resolutions is expected to report the corresponding functional behaviors. This expectation should be fulfillable without the guidance of any concurrent assays of functional properties at any steps, before the final outcomes are yielded for comparison with independently acquired functional data. Upon the completion of development of our method, we test if we could fulfill this expectation for a successfully developed method, within the expected errors of the data independently obtained by others with reference methods. Also, such a test would be a typical validation approach in physics, i.e., carrying out the entire process completely independent of the reference method.

As a first test, we chose to examine the isolated gating ring of the Ca²⁺-dependent MthK channel (Lewis and Lu, 2019A-C, NSMB), because the electrophysiological approach tends to yield more accurate measurements than many other types of functional measurements, such as flux assays. Based on polarization measures, without any concurrent examination of functional properties of the channel, i.e., ionic current, during data collection and deduction, we have successfully established an analytic model that quantitatively predicts the P_o-[Ca²⁺], k_on-[Ca²⁺], and k_off-[Ca²⁺] of relations of the whole channel, within the standard errors of individual data points previously published by others. In a mean-to-mean comparison, the biggest discrepancy in terms of free-energy difference is only about ¼ kT, which occurred at an electrophyisiological data point measured under a condition that is expected to yield less accurate data. This comparison shows a high degree of accuracy of our method in terms of determining state probabilities, lifetimes, and connectivity, from which equilibrium constants and rate constants are calculated.

Here, as a second test, we try to test our method on a membrane protein using the AdiC transporter. The method again allows very accurate determination of, e.g., state probabilities (with standard errors being about or less than the size of the data symbols; Figure. 10A), and thus that of the equilibrium constants (K) for individual states. For reference, the error range of ΔG, estimated from $k T l n \frac{K + σ}{K - σ}$ or $kTln \frac{K + 2 σ}{K - 2 σ}$ , is 0.16 or 0.32 kT. Furthermore, in the original companion manuscript, we determined the rate-limiting first-order transition. From the difference between the forward and backward rates of this transition alone, we can calculate the maximum net flux rate of a given substrate species (“k_cat”). These two forward and backward rates are solely determined by the two underlying rate constants and probabilities of the two connected states, which we have determined accurately, judging from standard errors. From the substrate-concentration dependence of the net flux rate, we can estimate K_m. Thus, our method enables us to independently estimate K_d, K_m and k_cat values in a straightforward manner, and to compare the final outcomes with those previously determined by the Miller lab using ITC and flux assays. The system and statistical errors of flux assay are generally large, much greater than those of electrophysiological recordings. Nonetheless, we are pleased to learn that the differences between our estimates and those estimated using ITC and the flux assay by the Miller lab are within the expected error range of their assays, as mentioned above. Thus, all of the technical maneuvers, which we made, had apparently limited impacts on the protein conformation-energetic and -kinetic properties, maneuvers including mutations and the attachment of protein molecules to a glass surface via tags, which are part of what may contribute to the system errors of our approach. Again, if the mutations or tags had huge impacts on the conformational energetic and kinetics, we would see much greater differences in the comparison of our estimates with their estimates. The fact that our model is solely reached from and fully constrained by polarization measurements alone gives us, and hopefully others as well, the confidence that the resulting relation between our estimates by the polarization method and those of the Miller lab by a functional method objectively reflects the total system-and-statistical errors of the two compared approaches, which are within the expected error range of their approach alone.

Reviewer #1 (Recommendations for the authors):

1. Confirmation of function after labeling. The version of AdiC that is being studied here is labelled by a bis-maleimide-TMR, solubilized in POPC nanodiscs, removed 2 native cysteines, N-terminal Avi-tag and Strep-tag, and C-terminal Strep-tag. However, I do not see that a validation has been carried out to test if this construct/conditions independently yield the same KD for arginine or agmatine binding, or similar transport properties. Experiments of binding (e.g. by ITC) and transport (e.g. by radioactive uptake assays in proteoliposomes) of the labelled construct that is currently being studied are important controls to validate whether the single-molecule polarization data can be compared to wild-type data published previously.

These comments have been addressed above under the responses to summative comment #4.

As stated at the beginning of our responses and now more clearly in ‘Results’ of the manuscript, we deliberately introduced flexible spaces such that the molecules are not strained and adopted differing orientations. The attachments did not appear to be markedly impactful because our estimated K_d values by ITC or by the polarization method are comparable to preciously reported ITC values. (Furthermore, the kinetic parameters yielded from the simulated fluxes using the rate constants and probabilities are within the expected error range, as reported in the original companion manuscript. These simulations were done under the conditions that the concentrations on both sides of the membrane were recalculated for each time point, i.e., they were not fixed.)

We now state in ‘ Results’, under the same labeling condition, there was little detectable fluorescent labeling in the absence of the mutant cysteine residues (Figure 1—figure supplement 1A,B). To minimize the background labelling, we removed two native cysteine residues. Removal of native cysteine residues in AdiC has been shown to have very limited impacts on its function. Furthermore, in ‘Results’ and ‘Materials and methods’, we state that the peak of the protein containing the two mutant cysteine residues, detected at 280 nm, co-migrated with that of the fluorophore dye detected at 550 nm. In contrast, no notable absorbance peak at 550 nm co-migrated with the peak of the protein without these mutant cysteine residues. Thus, there was little detectable background labeling (Figure 1-figure supplement 1A,B).

The total intensity traces, each with a bleaching step, are now shown in Figire 3—figure supplement 1 (Results).

We now state in the Results that the program examined the case of one-state distribution to the case of k-state distributions, one at a time in a series of separate operations. For each successful operation, the resolution criterion was ensured, i.e., peaks of all populations were separated by at least 2.5σ (‘Results’).

See responses to summative comment #3.

It is now provided in Figure 1—figure supplement 1C.

7. In Figure 9, the colors in the plot do not appear to match the legend (different shades of blue).

The correct color has now been used.

8. Since the data is analyzed over single trajectories, how long are these traces typically? How long do the traces have to be in order to observe enough transitions between states?

The average length of the trace is ~4 s (‘Materials and methods’), which is, on an empirical basis, adequate in terms of containing all 4 states and >15 events.

We now explain this issue in ‘Results’: even though the concentration dependence plot of the probability of C₁ or C₄ are relatively flat, their $K_{D}$ values are determinable. This is because the model can be fully specified by a certain combination of only even equilibrium constants, e.g., three of the six $K_{i,j}$ values, three of the six $_{}^{L} K_{i,j}$ values, and merely one of the four $K_{D}$ values. As such, in the present so-called over-determined case, the $K_{D}$ values of the relatively flat traces are fully constrained by those more curved traces in a global fit of Eq. 5 to all four plots simultaneously. The errors are confidence intervals obtained by a boot-strapping method, which is now stated in the foot note of the table.

Reviewer #2 (Recommendations for the authors):

1. The key difference of the data processing described in this manuscript compared to the earlier published work is the introduction of the normalization step. Due to the random X-Y orientation of the transporter proteins on the surface, each protein molecule needs to be analyzed individually to get its own theta and phi angles in the laboratory frame (Cartesian coordinate). Normalization of the angles based on one of the identified states allows to directly compare the results for different particles directly. This is an interesting improvement, so the authors may need to mention this in the abstract.

The reported study represents the first time that a high-resolution polarization microscopy has been applied to the investigation of a membrane protein. During the struggle in the past 7 years to make this happen, we have developed methods to prepare the samples, and made a number of improvements. Three analytic advances are highlighted in the manuscript including “normalization of the angles”. Indeed, observing four states is not a mechanistic advance. However, the ability to detect them together in a membrane protein, analyze the data, and extract energetic and kinetic information about them are significant advances.

2. In principle, the normalization may improve the accuracy of the mean angle values even as the deviations might increase. It would be helpful if the authors compared the ensemble-averaged mean values and the single-trace mean values.

We now add current Figure. 9 to show the distribution of the mean angle values of individual particles.

3. From my understanding, to better differentiate the states, traces visiting all 4 states should be analyzed. When the authors select the traces with at least 12 transition events, do the events include transitions between all four states? The authors might want to clarify.

All analyzed traces are long enough and contain all four states, which is now stated in ‘Materials and methods’. The transitions among all four are observed as described in the original companion manuscript which address the kinetic aspects of the observed conformational changes. Given the present manuscript concerns primarily resolution of individual conformations and the free energy difference among them but not their kinetics, the connectivity information is not directly relevant here. We intend to share this information in a revised version of that manuscript for future publication, in which we will discuss the experimental evidence that disproves the hypothesis that AdiC is an obligatory exchanger.

4. It is unclear how the authors establish the number of distinct states to be considered in the system. Is the number of states based on the expected structurally resolved 4 states or obtained from the analysis of the traces themselves? There is a proposed so-called full occluded state. Could/should this state be included in the data analysis?

The determination of the number of states is not influenced by any preconceived model. As stated above under summative comment#2 and now in ‘Results’, four states are the highest number that we can detect while satisfying the common resolution definition for microscopy, without any preconceived kinetic model. (The "cul-de-sac” state that connect to each of the two “occluded” state in the 24-state kinetic model presented in the original companion manuscript might be interpreted as fully occluded state, which could in principle be connected by transition in a rapid equilibrium.)

5. The fluorophore is attached via two cysteines. Therefore, in the same conformation, the fluorophore has two orientations related by 180-degree rotation. Will this affect the detected signal? If not, then would a protein conformational change, which makes the fluorophore rotate by 180 degrees, be detected?

Given the dipole of the fluorophore has an inherent two-fold symmetry, it has the same spatial relation to the two cysteines. Thus, this attachment does not affect the signal. By definition, an “exact” 180-degree rotation motion around the symmetry center of the fluorophore is undetectable in any dipole-polarization-based analysis. In this rare case, a different technique is certainly needed. The present method is developed to detect small movement by resolving small angle changes. There are many techniques that can be used to detect large movement.

6. The protein is modified by a bi-functional fluorophore and surface-immobilized with multiple binding tags. How do you evaluate whether these manipulations affect the state populations and transport activity? The structures of Adic were all solved in the outward-facing states. Simulation (PLoS ONE 11(8): e0160219) also indicated that the inward-facing states, especially the inward-open state, are relatively unstable, suggesting that the population of the inward-facing states should be low. However, in Figure 7B, the inward-open state is highly populated, which seems inconsistent with the expectations. It seems that some additional experiments and or more extensive discussion are needed to support the authors' estimates of the state populations.

The first part has been responded under summative comment #3.

As now stated in ‘Results’, reconstitution of protein into lipid-containing nanodiscs, tags, attachment, mutations, and fluorophore labels are all necessary components of the present system, contributing to system errors. Currently, there are no other techniques that can assess, under the same conditions, the ultimate impact of these factors on the properties, which highlights the need to develop the present method. In terms of energetic impact, a practically relevant question would be whether the $K_{D}$ values estimated using the present method with all of those potentially impactful factors are comparable to those values estimated for the wild-type protein by means of an already established method, such as ITC, and the probabilities and rate constants that we estimated can predict kinetic parameters. As we outlined above, and in ‘Discission’, the Kd values that we estimated are compatible with previously reported ITC values, and in the original companion manuscript, kinetic parameters are within the expected error range of the previously reported values.

Regarding the sidedness, in the quoted study, the MD simulation of outward-facing states were based on partial AdiC structures whereas inward-facing states was based on a different transporter (GadC). The results of simulating the inward-facing with GadC appear to heavily depend on the residues introduced. In any case, Tsai et al. (Biochemistry 2012) have shown that AdiC is relatively symmetric in term of flux kinetics: comparable Km values for both sides and comparable maximal flux rates in either direction (‘Discussion’). Our model is consistent with their measurements. This point has now been discussed. We emphasize that the observed symmetric property may not occur under different experimental conditions, such as a different pH.

7. The state assignments are based on the similarity of the theta and phi angles to those calculated from the four crystal structures. To me, this does not seem entirely convincing, especially regarding the inward-facing states, expected to be lowly populated. The authors might need to use mutants or ligands to stabilize the inward-facing states to verify the assignment.

As mentioned above under summative comment #2, the open versus “occluded” states were determined on the basis of substrate dependence (‘Discussion’). Regarding the sidedness (‘Materials and methods’), the relation between the orientations determined from polarization measurements and those from the structures of known states helps distinguish between the so-called internal and external conformations. The external open and external occluded structures of AdiC are available. Fortunately, for these two states, the two methods yield consistent orientations. Furthermore, we also used the internal open and internal occluded structures of two related transporter as proxies, or space holders, for the corresponding states of AdiC in the exercises to illustrate how to perform multistate spatial alignment.

8) The authors need to describe how they estimate the errors in Table 1.

The confidence intervals were obtained by a boot-strapping method, which is now stated in the footnote of the table.

Reviewer #3 (Recommendations for the authors):

1. This work monitors only a single transmembrane helix (helix 6a) in AdiC. This was presented as an advantage, but in reality it also creates strong limitations for data interpretation. By comparing the orientations of helix 6a in PM-identified states (C1-C4) and in structural states, C1-C4 were dubbed externally open (Eo), externally occluded (Ex), internally open (Io), and internally occluded (Ix) states. Such assignment comes with high uncertainty even in optimal conditions. For example, without "seeing" the rest of the protein, how do the authors know that a particular PM state is not an intermediate state not observed in structural studies? Such a concern arises in part because of the assignment of C1 as Ex and C4 as Ix, with a state possibility of 0.19 and 0.14, respectively. Why would an antiporter sample occluded states so often without ligands? Is it possible that C1/C2 are both externally open (with some differences in helix 6a orientations) and C3/C4 both internally open and the occluded states are too rare to be observed when there is no ligand?

2. The assignment of PM states was actually done under not-so-optimal conditions. AdiC structures were only determined in ligand-free Eo and ligand-bound Ex states, so the authors used BasC and ApcT structures to represent the Io and Ic states of AdiC. Multiple questions about data treatments follow naturally. What's the justification to compare ligand-free PM states with ligand-bound structural states (Figure 6)? Although BasC (complexed with a nanobody) and ApcT have similar LeuT fold like AdiC, their sequences are not particularly similar and it's conceivable that AdiC's helix 6a might have significantly different orientations in Io and Ic states than the helix 6a in BasC and ApcT. How would such a possibility affect the assignment of the PM states?

The above two related comments are addressed together below.

We now discuss in the manuscript explicitly: The conformational states resolved in the present study are defined by the orientation of the dipole of a fluorophore attached to an α-helix that interacts with and is thus spatially constrained by other surrounding secondary structures (‘Results’). On the basis of structures in different states, the orientation changes of the dipole are thus expected to reflect the rotation motion of the protein.

For reference, in FRET, each of a pair of fluorophore labels is attached to a residue in a secondary structure within a domain. The transfer efficiency is being used to report the relative movement between the two domain or two proteins. Strictly speaking, each label would not directly report the behavior of the rest of the protein either. As such, one fundamental difference between FRET and PM is that FRET requires two fluorophores, and PM requires only one.

As already mentioned under summative comment#2, given that the probabilities of conformations C₂ and C₃ clearly varied with the Arg⁺ concentration whereas the other two states varied little, C₂ and C₃ should be two open states that could directly interact with substrates, and the remaining two would then likely be the occluded states (in adopting the conventional name). Regarding the sidedness of the model, the relation between the orientations determined from polarization measurements and those from the structures of known states helps distinguish between the so-called internal and external conformations. The external open and external occluded structures of AdiC are available. Fortunately, for these two states, the two methods yield consistent orientations. Thus, our data are consistent with the relation of C1 as Ex and C2 as Eo, and by symmetry, C3 as Io and C4 as Ix, which are consistent with spatial relations observed in the Io and Ix states of two transporters containing the same structural fold. If anything, we put forward a model or hypothesis for future testing, on the basis of a set of consistent relations.

To be sure, the above exercise of spatial alignment, in which internal open and internal occluded structures of two related transporter are used as proxies, or space holders, for the corresponding states of AdiC, is primarily to illustrate an algorithm for performing multi-state spatial alignment.

In the revised version of the original companion manuscript for future publication, we will discuss the experimental evidence that disproves the hypothesis that AdiC is an inherently obligatory substrate-exchanger in a transparent, analytic manner.

3. Another main issue is about the relation of ligand-free and ligand-bound PM states. There are four ligand-bound PM states, labeled as C1L, C2L, C3L, and C4L to indicate that they correspond to the ligand-free C1, C2, C3, C4 states. However, the ligand-free and ligan-bound PM states appear to have quite different θ/ψ profiles (Figure 5), and the latter were not compared to the structures. How did the authors link ligand-bound PM states to the structural states? How to know for sure that C1 is related to C1L, C2 to C2L, etc? Moreover, it could be misleading to distinguish the corresponding ligand-bound and -free states just by an "L" as if their only difference is the ligand – the technique here provides no such resolution.

We now show in Figure. 5 the probability density of each state plotted against θ and φ, and in Figure. 6 in the mean angle values, for many Arg⁺ concentrations in the tested range. The probability densities change but the angle values do not exhibit systematic variations across the concentration range. In a model based on the PM data, the states are then denoted as C_i and C_iL as traditionally done. This type of elementary notations in an energetic model is consistent with the Monod-Wyman-Changeux model (J. Mol. Biol., 1965) for ligand-dependent conformational mechanism of allosteric proteins in that all conformations of a protein occur in the absence of ligand, and the binding of a ligand does not create a new conformation but merely energetically stabilizes a spontaneous conformation that is ready to capture the ligand (‘Results’).

4. The authors might want to consider utilizing additional strategies to verify their state assignments. One possibility is to use structures as guidance to lock AdiC in a particular state via Lysine crosslinking and see how such maneuver affects PM results. The determined K_D reflects how ligands drive the protein from ligand-free to ligand-bound conformational equilibria without providing much insight into the conformational details in each set of equilibrium

See responses to summative commnet#3.

Reviewer #4 (Recommendations for the authors):

1) On page 20, the authors note that they set a threshold to filter out molecules whose total intensity varies during the measurements. The statement that "while fluorescence intensity is expected to vary among different polarization directions, the total intensity should be essentially invariant" is not true. Since the authors use TIRF illumination to excite the molecules, the excitation polarization component along the tilting direction (e.g., along the y-axis) of the excitation is 0, i.e., molecules oriented along that direction (e.g., y-oriented) will be excited less effectively compared to other orientations.

We originally intended to mean implicitly a particle with large total intensity changes due to such a factor as fluorescence bleaching in more than one step would be excluded, because this phenomenon would most probably reflect the attachment of more than one fluorophore to a single protein molecule. We have now stated this point clearly.

2) Could the authors provide more details regarding how the clusters are ranked? The authors note that C1-C4 are "ranked according to the values of both angles". It is not clear to me how this is done. Also, what is the range of the measured theta_L and phi_L? And how is the warping of the spherical coordinates handled in the ranking process, e.g., a change from 350 deg to 10 deg is +20 deg or -340 deg.

If stated literally, the conformational states are numerated according to the sequence in the solution to achieve the shortest pathway among the four states evaluated in a Cartesian system, denoted as C₁, C₂, C₃ and C₄. This operation was done after assigning the angle values. We now make this clear in ‘Results’, and remove the use of angles as proxies.

θ is defined from 0° to 90° and φ from 0° to 180° with degenerate solutions of θ, 180° – θ and φ, 180° + φ, which was given in a previous paper, and is now included in ‘Materials and methods’. Because the angle changes predicted from the structures are small, about 10 – 40°, a change of +20º change instead of -340º would be chosen.

3) Is the k-means clustering also based on the distance in the Cartesian space, similar to the state identification?

Yes. We now explicitly explained this in ‘Results’ and in ‘Material and methods’.

Following comment (1) from above, could the authors comment on the possibility of further improving the measurement precision and accuracy using the excitation-dependent total intensity? Since the authors report a wobble angle of 22.5 degrees, the excitation dipole moments should be mostly aligned with the emission dipole moments.

As the reviewer implied, we could use multiple linear excitations of different polarizations in a multiplexing operation, with 8 to 16 channels. Analyzing the intensity changes caused by different excitations at different emission channels could in principle improve somewhat the precision and accuracy of θ determination near 0º and 90º. We chose to use a circularly polarized laser because it is technically much easier to implement, and has thus far been adequate for our purposes. Importantly, a simpler system will also be easier for other labs that are interested in this technique to adopt. Note that the use of circular polarization eliminates the confounding slow wobble of the fluorophore that leads to a difference in the average orientations of the excitation and emission dipoles during individual sampling periods.

https://doi.org/10.7554/eLife.82175.sa2

Article and author information

Author details

Yufeng Zhou

Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, United States

Contribution
Data curation, Formal analysis, Validation, Investigation, Methodology, Writing – review and editing

Competing interests
No competing interests declared
John H Lewis

Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, United States

Contribution
Data curation, Software, Formal analysis, Validation, Investigation, Methodology, Writing – review and editing

Competing interests
No competing interests declared
Zhe Lu

Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, United States

Contribution
Conceptualization, Supervision, Funding acquisition, Investigation, Writing - original draft, Project administration, Writing – review and editing

For correspondence
zhelu@pennmedicine.upenn.edu

Competing interests
No competing interests declared

"This ORCID iD identifies the author of this article:" 0000-0001-7108-9303

Funding

National Institute of Diabetes and Digestive and Kidney Diseases (DK125521)

Zhe Lu

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This study was supported by the grant DK125521 from the National Institute of Diabetes and Digestive and Kidney Diseases.

Senior and Reviewing Editor

Kenton J Swartz, National Institute of Neurological Disorders and Stroke, National Institutes of Health, United States

Reviewer

Janice L Robertson, Washington University in St. Louis, United States

Publication history

Received: July 25, 2022
Preprint posted: July 31, 2022 (view preprint)
Accepted: January 15, 2023
Version of Record published: February 17, 2023 (version 1)
Version of Record updated: February 23, 2023 (version 2)

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This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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Yufeng Zhou
John H Lewis
Zhe Lu

(2023)

Tracking multiple conformations occurring on angstrom-and-millisecond scales in single amino-acid-transporter molecules

eLife 12:e82175.

https://doi.org/10.7554/eLife.82175

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Illustration of the attachment of fluorophore to the AdiC protein and the protein to a glass surface.

Schematic for four polarized emission intensities collected via a microscope and imaged on an EMCCD camera.

Polarized intensity components of single fluorescent particles and θ and φ angles calculated from the components.

Figure 3—source data 1

Figure 3—source data 2

Experimental resolution of conformational states.

Figure 4—source data 1

Ensemble 3D probability density distributions of θ and φ.

Figure 5—source data 1

Figure 5—source data 2

Figure 5—source data 3

Figure 5—source data 4

Angle values of individual conformational states.

Figure 6—source data 1

The orientations of the dipole vector of the fluorescence probe in different conformational states.

Figure 7—source data 1

Figure 7—source data 2

Comparison of the orientations of helix 6A in the corresponding states determined from the crystal structures and in the polarization study.

Figure 8—source data 1

Figure 8—source data 2

3D probability density distributions of mean θ and φ determined from individual molecules.

Figure 9—source data 1

Figure 9—source data 2

Ligand dependence of the probabilities of conformational states and the diagram of a conformational state model of AdiC.

Figure 10—source data 1

Probabilities and equilibrium constants for apo and Arg+ bound states.

Relations between the structural and conformational states determined respectively from the crystal structures and in the polarization study.

Figure 11—source data 1

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Yufeng Zhou

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John H Lewis

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Competing interests

Zhe Lu

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For correspondence

Competing interests

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Probabilities and equilibrium constants for apo and Arg⁺ bound states.