1. Neuroscience
Download icon

When complex neuronal structures may not matter

  1. Adriane G Otopalik Is a corresponding author
  2. Alexander C Sutton
  3. Matthew Banghart
  4. Eve Marder Is a corresponding author
  1. Brandeis University, United States
  2. Harvard Medical School, United States
Research Article
Cited
2
Views
1,728
Comments
0
Cite as: eLife 2017;6:e23508 doi: 10.7554/eLife.23508

Abstract

Much work has explored animal-to-animal variability and compensation in ion channel expression. Yet, little is known regarding the physiological consequences of morphological variability. We quantify animal-to-animal variability in cable lengths (CV = 0.4) and branching patterns in the Gastric Mill (GM) neuron, an identified neuron type with highly-conserved physiological properties in the crustacean stomatogastric ganglion (STG) of Cancer borealis. We examined passive GM electrotonic structure by measuring the amplitudes and apparent reversal potentials (Erevs) of inhibitory responses evoked with focal glutamate photo-uncaging in the presence of TTX. Apparent Erevs were relatively invariant across sites (mean CV ± SD = 0.04 ± 0.01; 7–20 sites in each of 10 neurons), which ranged between 100–800 µm from the somatic recording site. Thus, GM neurons are remarkably electrotonically compact (estimated λ > 1.5 mm). Electrotonically compact structures, in consort with graded transmission, provide an elegant solution to observed morphological variability in the STG.

https://doi.org/10.7554/eLife.23508.001

Introduction

Neuronal circuits can generate stable output despite variable underlying parameters across animals (Marder and Goaillard, 2006; Marder, 2011). Work in invertebrate central pattern-generating circuits shows that circuit function can be maintained across animals despite variable synaptic, intrinsic, and modulator-induced currents in identified constituent neurons (Prinz et al., 2004; Schulz et al., 2006; Marder and Goaillard, 2006; Goaillard et al., 2009; Norris et al., 2011; Marder, 2011; Roffman et al., 2012; Williams et al., 2013; Gutierrez et al., 2013; Rodriguez et al., 2013). This previous work has revealed the principle that neurons compensate for variable ionic conductances at the circuit (Grashow et al., 2010) and single-neuron levels (Tobin et al., 2009; Ball et al., 2010; O'Leary et al., 2013, 2014).

The unique physiology of any given neuron is a consequence of its palette of ionic conductances, and its morphology (Mainen and Sejnowski, 1996; Vetter et al., 2001). A neuron’s distributed, geometric cable properties: the length, diameter, taper, and branching of its neurites, shape passive current flow and voltage propagation (Rall, 1959, 1977; Goldstein and Rall, 1974). This resulting electrotonic structure plays a central role in determining whether voltage signals arising at disparate sites across the dendritic tree are integrated or segregated (Rall, 1959, 1967, 1969a, 1969b; Rall and Rinzel, 1973, 1974; Goldstein and Rall, 1974; Agmon-Snir and Segev, 1993; Vetter et al., 2001). In this way, ion channel expression, when superimposed on morphology, gives rise to neuronal physiology, input-output computations, and circuit-level function (for reviews, see Koch and Segev, 2000; London and Häusser, 2005).

In the present study, we investigated the physiological consequences of animal-to-animal variability in neuronal morphology in the crab stomatogastric ganglion (STG), a central pattern-generating circuit composed of 26–27 neurons. The identified neuron types of the STG exhibit highly conserved physiological waveforms and circuit-level functions (Harris-Warrick et al., 1992), despite their complex and variable morphologies across animals (Wilensky et al., 2003; Baldwin and Graubard, 1995; Bucher et al., 2007; Goeritz et al., 2013; Otopalik et al., 2017). STG neurons display large somata (50–100 µm in diameter) and primary neurites that ramify throughout the STG neuropil (Selverston et al., 1976King, 1976a, 1976b; Baldwin and Graubard, 1995; Kilman and Marder, 1996).

Synaptic transmission between neurons is predominantly graded, inhibitory cholinergic and glutamatergic transmission (Eisen and Marder, 1982; Marder and Eisen, 1984; Maynard and Walton, 1975; Graubard et al., 1980; Manor et al., 1997, 1999). Synaptic sites are sparsely distributed throughout finer processes in the neuropil region (King, 1976a, 1976b). There are no synapses on somata in these neurons (King, 1976a, 1976b) and spike initiation zones are located in the periphery where axons exit the ganglion (Raper, 1979; Miller, 1980). Thus, synaptic integration and release occurs predominantly in the neuropil. In individual STG neurons, pre- and post-synaptic sites are often tightly apposed on the same neurites (King, 1976a, 1976b). This juxtaposition of synaptic input and output suggests that current will flow in all directions across the neurite tree, centripetally and centrifugally, in the intact circuit, and allow for integration of voltage signals arising from disparate loci on the neurite tree, should the neuron be sufficiently electrotonically compact.

Previous investigation of electrotonic structure in STG neurons employed simultaneous electrophysiological recordings at the soma and primary neurite, wherein electrodes were separated by several hundred microns (Miller, 1980; Golowasch and Marder, 1992). These recordings showed low-pass filtering of high-frequency voltage events across the primary neurite, as is typically imposed by the membrane capacitance (Rall, 1977). In contrast, slow voltage oscillations were subject to less electrotonic decrement. This frequency-dependent decay of electrical signals was consistent with the findings of contemporary theoretical and experimental works (Rall, 1977; Johnston and Brown, 1983; Spruston et al., 1993, 1994; Jaffe and Carnevale, 1999). This early characterization of electrotonic structure in the STG may have been a satisfactory description at the time, given that STG circuit function is mediated predominantly by graded transmission (Eisen and Marder, 1982; Marder and Eisen, 1984; Maynard and Walton, 1975; Graubard et al., 1980; Manor et al., 1997, 1999) and slow oscillations (Graubard and Ross, 1985; Ross and Graubard, 1989), and continues to oscillate in the absence of spikes (Graubard, 1978; Raper, 1979; Graubard et al., 1983;Anderson and Barker, 1981). However, these early experiments left the electrotonic properties of more distal sites and higher-order branches to the imagination.

Relevant voltage events must arise at more distal, finer processes, where pre- and post-synaptic connections are located (King, 1976a, 1976b; Kilman and Marder, 1996). Thus, a full experimental characterization of the electrotonic structure of STG neurons requires electrophysiologically sampling numerous sites across the dendritic tree. Of course, recording at many sites, let alone on the tiniest of neurite processes, presents technical challenges that few have overcome in situ. In one STG neuron type, the gastric mill (GM) neuron, we have utilized focal photo-uncaging techniques in tandem with electrophysiology to examine propagation of voltage events evoked at processes that vary in size and distance from the somatic recording site. We present a surprising case wherein geometrical complexity and variability appear not to constrain passive physiology.

Results

The stomatogastric ganglion (STG) of the crab Cancer borealis is composed of 26–27 neurons situated around a dense neuropil region, wherein each of the neurons branches extensively. This central-pattern-generating circuit mediates the coordinated rhythmic contractions of the animal’s foregut. The gastric mill (GM) neuron is one of fourteen identified neuron types in the STG. There are typically four GM neurons in each animal. Figure 1A shows a schematic of one GM neuron and its axonal projections in the intact stomatogastric nervous system, as dissected for in vitro experiments. Filling the neuron with fluorescent dye reveals the complex morphology of the GM neuron in situ (Figure 1B). The GM neuron ramifies throughout the neuropil region and can be distinguished by multiple axons, projecting to and innervating extrinsic gastric muscles 1a, 1b, 2, 3a, and 3b via the anterior lateral (aln) and dorsal ventral (dvn) nerves (Maynard and Dando, 1974; Selverston and Mulloney, 1974; Weimann et al., 1991). GM neurons participate in the episodic gastric mill rhythm (Hartline and Maynard, 1975). When bursting (Figure 1C), GM activity evokes rhythmic contractions of its target muscles, resulting in grinding movements of the gastric mill ossicles and attached teeth for internal chewing of food (Russell, 1985; Heinzel, 1988). GM neurons are unambiguously identified by matching their spiking activity with spiking units on extracellular nerves known to contain GM axonal projections (Figure 1D; Maynard and Dando, 1974).

The stomatogastric nervous system (STNS) and identification of gastric mill (GM) neurons.

(A) Schematic of an in vitro, isolated STNS with descending inputs intact (from bilateral commissural ganglia (CoGs) and esophogeal ganglion (OG)). The stomatogastric ganglion (STG; green box) contains identifiable motor neurons that project their axons onto specific muscle groups via the medial ventral nerve (mvn), anterior lateral nerves (aln), dorsal ventricular nerve (dvn) and lateral ventricular nerve (lvn), and dorsal gastric nerve (dgn). An example of the axonal projection path of a GM neuron is shown in green. Extracellular nerve recordings (locations indicated with gray circles) are utilized for physiological identification of GM neurons (as in D). (B) Example of an alexa488 dye-fill (green) of a GM neuron, with the STG, nerve projections, and other neurons outlined in white. (C) The GM neuron participates in a slow, episodic gastric mill rhythm that is highly conserved across animals. Top: an intracellular recording of GM with simultaneous extracellular nerve recordings of the dgn and lvn show concurrent, single-neuron and circuit-level activities. (D) GM neurons are identified physiologically by matching intracellular spike activity with extracellular nerve spike units in the dgn, which contains GM axonal projections (shown in green on dgn). Hyperpolarizing and depolarizing current pulses (Iinj) make this identification unambiguous. These identifications are verified with microscopy and identification of axons projecting bilaterally into the alns, as in B. In C and D, horizontal bars indicate an intracellular voltage of −50 mV.

https://doi.org/10.7554/eLife.23508.002

Variability in GM neuron morphology

We generated three-dimensional confocal stacks of Lucifer Yellow dye-fills of 14 GM neurons situated in the STGs of 14 different animals. Figure 2A shows six examples of maximum z-projection images generated from GM neuronal dye-fills. GM neurons exhibit large somata (with a mean diameter ± SD of 74 ± 13 µm) and expansive neurite branches that span the neuropil region. Non-axonal neurite branches spanned an average ellipsoid volume of 4.98 ± 1.43 × 106 µm3 (mean ± SD).

GM neurons exhibit expansive and complex morphologies.

(A) Maximum z-projections of 3-dimensional confocal image stacks capturing Lucifer yellow dye-fills of six GM neurons (taken at 20x magnification). (B) Skeletal reconstructions of the six neurons shown in A, generated by manual tracing in KNOSSOS software and used for quantitative morphological analyses shown in C-–F. All scale bars in A and B are 150 µm. (C) Boxplot of total cable lengths (excluding axonal projections; Mean + SD = 8112.6 + 2453.6 µm). (D) Boxplot of the total number of branch points (excluding axonal branch points; mean + sd = 148 + 63 branch points). For C and D, red line indicates the median, the blue box spans the 25th and 75th percentiles, and the whiskers span the range of data points not considered to be outliers. (E) Histograms show the distributions of paths from soma to terminating neurite for individual GM neurons (from top to bottom). (F) Histograms showing the tortuosities for soma-to-tip paths for individual GM neurons (from top to bottom). Tortuosity was calculated as the ratio of measured soma-to-tip path length (as in E) over the Euclidean distance from soma to tip. On right, diagram indicates the interpretation of tortuosity for a given path (blue) relative to the Euclidean distance (black). For E and F, the darker shaded region spans the 25th and 75th percentiles, solid lines indicate the mean, and dashed lines indicate the median. The y-axes are scaled to the maximum number of paths among bins within each neuron. Note the leftward bias in the tortuosity distributions (F). For CF, metrics were calculated for N = 14 GM neurons in 14 different animals.

https://doi.org/10.7554/eLife.23508.003

Using KNOSSOs software (freely available online at knossostool.org, see Materials and methods), we manually traced and generated 3-dimensional skeletal reconstructions of these neuronal dye-fills (skeletal reconstructions of the six neuronal dye-fills in Figure 2A are shown in Figure 2B; Supplementary file 1-Neuronal Structures Hoc files). From these skeletal reconstructions, we were able to measure total cable lengths, number of branch points, and soma-to-tip path lengths and tortuosities (excluding axons) using a suite of custom morphology analytical tools (see Materials and methods). These neurons present expansive structures, with a mean total cable length of 8840 ± 3678 µm (Figure 2C) and numerous branch points (mean number of branch points ± SD was 155 ± 126; Figure 2D). Notably, across animals, total cable lengths and branch point numbers varied by 40% of the mean (CV = 0.4 for both metrics). Note that these numbers are underestimates and smaller than reported in Otopalik et al. (2017). This is due to the lower resolution used for reconstruction of this large set of neurons, resulting in loss of some of the smallest profiles. Otopalik et al. (2017), reported similar animal-to-animal variability in these metrics across a smaller sample size.

We also measured all soma-to-tip paths within each neuron (Figure 2E). These path length distributions varied within and across neurons, with distances ranging between 200–1000 µm and a mean coefficient of variation of 0.81. The mean soma-to-tip path length was 450 ± 80 µm. Thus, if synaptic voltage events arising at the neurite tip are measured electrophysiologically at the soma, such signals would travel this distance, on average.

In Figure 2A and B, it is visually evident that GM neurons display tortuous three-dimensional structures. This is quantified in Figure 2F, which shows the tortuosities of soma-to-tip paths (path length/Euclidean distance from soma to tip location). For a given soma-to-tip path, a tortuosity of one suggests a minimal, Euclidean path from soma to tip, whereas tortuosities greater than one suggest winding paths that deviate from the minimal Euclidian distance (Figure 2F, right). Across GM neurons, tortuosity distributions vary. But, each neuron presents a broad tortuosity distribution and has a mean tortuosity that is modestly greater than one (Figure 2E; the mean across all neurons is 2.1 ± 0.5). Taken together, these data suggest that GM neurons are tortuous and expansive, and somewhat variable in their macroscopic morphology.

The functional consequences of morphological complexity and variability are best considered in light of how voltage signals arising from presynaptic inputs are integrated and transformed into spike patterns. Previous work suggests that pre- and post-synaptic connections are distributed throughout the finer process within the STG neuropil (King, 1976b; Kilman and Marder, 1996) and that spike initiation zones are located in the periphery, where the axons exit the neuropil (Raper, 1979; Miller, 1980). Thus, axon number, location, and branching patterns relative to each neuron’s neurite tree may speak to how voltage signals arising from presynaptic inputs are integrated. GM neurons typically have between 3–5 axons (Figure 3A), with at least one projection to the aln and one projection to the dvn (this is consistent with previous findings; Maynard and Dando, 1974). In 2/14 neurons, only two axons were identified. This is likely due to an incomplete dye-fill or atypical branching of axonal projections beyond the microscope’s field of view. Branch order distributions varied across neurons, as did axonal branch point orders (Figure 3B). As is illustrated in Figure 3C–G, in some GM neurons all axons projected from the same branch point (as in Figure 3D), whereas in other GM neurons each axon projected from a distinct subtree (as in Figure 3G). Taken together, variable axon numbers, locations, and branching patterns suggest that each GM neuron differentially integrates voltage signals arising from varying proportions of lower and higher branch orders.

Variable axon location and branching patterns in GM neurons.

(A) Histogram shows the number of distinguishable axonal projections for 14 GM neurons. (B) Histograms show the distribution of branch orders across 14 GM neurons. Axonal branch point orders are indicated with green lines. Dark purple shading indicates the range between the 25th and 75th percentiles. For easy comparison across neurons, histograms were plotted with 100 bins and y axes were normalized to the maximum number of branch points given the 100 bins. (C) Pie chart summarizes axonal branching patterns across 14 GM neurons. (DG) Examples of the different axonal branching pattern possibilities in C are illustrated with dendrograms of four GM neurons from the tested population. Axonal branch points are indicated with colored circles indicating the number of axons projected from that branch point: orange = 4 axons, blue = 2 axons, red = 1 axon.

https://doi.org/10.7554/eLife.23508.004

Variable glutamate responses across the neuronal structure

One might expect that complex and variable neuronal morphologies would yield complex and variable electrotonic structures. To probe the distributed cable properties of GM neurons, we employed a custom-built microscope to focally photo-uncage MNI-glutamate (Tocris) with ultraviolet light at many sites across the GM neuronal structure (in TTX to attenuate spiking activity and overall circuit activity). In each GM neuron (N = 10), we used two-electrode current clamp at the soma to measure voltage responses arising from glutamate receptor activation at the soma, primary neurite, and more distal sites (Figure 4; 7–20 photo-uncaging sites per neuron with 1 ms, 30 mW UV pulses and a bath concentration of 250 µM MNI-glutamate). Experiments probing the spatial resolution of our photo-uncaging system demonstrated that the effective photo-uncaging radius was approximately 15 µm, a resolution high enough to target individual neurites (Figure 4—figure supplement 1A–D).

Figure 4 with 1 supplement see all
Focal glutamate responses across GM neuronal structures.

(AC) show maximum z-projections of confocal stacks of neuronal dye-fills with photo-uncaging sites indicated with colored circles. In each case, raw traces are shown on the right for maximal inhibitory glutamate responses evoked with 1 ms pulses at 30 mW UV laser intensity while. holding the membrane potential at −40 mV using two-electrode current clamp at the somatic recording site. Note the variability in response amplitude across different photo-uncaging sites within each neuron. Image scale bars are 150 µm.

https://doi.org/10.7554/eLife.23508.005

Focal glutamate photo-uncaging evoked hyperpolarizing voltage deflections across the neuronal structure (Figure 4). These inhibitory potentials are consistent with ionotropic glutamate-gated inhibitory currents described in previous work (Marder and Paupardin-Tritsch, 1978; Eisen and Marder, 1982; Marder and Eisen, 1984; Cleland and Selverston, 1995). Although voltage responses were uniformly inhibitory across the neuronal structure, their amplitudes varied (Figure 4A–C). Figure 4A–C show dye-fills of three individual GM neurons with photo-uncaging sites indicated with colored circles (left) and maximal responses to focal glutamate photo-uncaging that vary in amplitude across these sites (right). These focal glutamate responses were relatively stable, desensitizing only when the inter-pulse period (IPPs) was less than 10 s (Figure 4—figure supplement 1E–G).

Across GM neurons (N = 10), a non-zero response (measured at the soma) to glutamate applied to the soma was observed in only one GM neuron. Response amplitudes varied across positions with a mean maximum amplitude of 2.15 ± 1 mV. The mean coefficient of variation of non-zero responses, across preparations, was 0.4 ± 0.1 (N = 10), suggesting that, on average, non-zero responses varied by approximately 40% of the mean response amplitude within each neuron.

The electrotonic decrement of a voltage signal, from photo-stimulation site to recording site, is dependent on a number of factors: the diameter of the neurite through which it propagates (which influences the axial resistance to current flow), the membrane resistance, the extent of branching and associated loss of conductance at branch points, and the absolute distance the signal travels (Rall, 1959; Goldstein and Rall, 1974). To quantify the dependence of response amplitude on each neuron’s cable properties, we generated ‘lolliplots’ of response amplitude, measured at the soma, to each photo-stimulated site, as a function of their distance from the somatic recording site, branch order, and neurite size (measured in terms of neurite diameter in the x-y plane; Figure 5). The lolliplots show that the greatest response amplitudes can occur from photo-stimulation at sites with any distance from the soma, of any branch order, and of any size. Linear regression analyses of response amplitudes as a function of each of these geometric parameters showed no significant linear relationships, with insignificant p-values>0.1 (Figure 5—figure supplement 1, Table 1). Taken together, these data suggest that there is no apparent dependence of somatic response amplitude on where the responses were evoked.

Figure 5 with 1 supplement see all
Response amplitudes as a function of various cable properties.

Each lolliplot shows the normalized maximal response amplitudes for photo-uncaging sites that vary in distance from the soma, branch order, and neurite diameter. Each color is indicative of focal responses from a single neuron (N = 10). Focal glutamate responses were evoked at a depolarized membrane potential (−40 or −50, constant within each neuron), in two-electrode current clamp at the soma. Scatter plots at the bottom show these same data from all 10 neurons on the same axes. To allow comparison across neurons, voltage responses. were normalized to the maximum voltage response within each preparation. Distance and branch order measurements were generated from skeletal reconstructions. Diameter measurements were measured manually from neuronal dye-fill confocal stacks. Results from linear regression analyses of the above data are shown in the Figure 5—figure supplement 1 and in Table 1.

https://doi.org/10.7554/eLife.23508.007
Table 1

Linear regression analysis for response amplitudes as a function of distance, branch order, and neurite diameter. Each row corresponds to a different GM neuron, with same color scheme, as shown in Figure 5 and Figure 5—figure supplement 1. Note insignificant p values suggesting no dependence of the response amplitude on these cable properties. n corresponds to the number of photo-uncaging sites in each GM neuron.

https://doi.org/10.7554/eLife.23508.009

Distance

Branch order

Diameter

Neuron

MSE

R

p

slope (mV/um)

MSE

R

p

slope (mV/order)

MSE

R

p

slope (mV/um)

n

0.11

−0.27

0.418

−0.0009

0.12

−0.20

0.55

−0.0104

0.10

0.39

0.24

0.1028

11

0.02

0.28

0.592

0.0003

0.02

0.26

0.62

0.0052

0.03

0.01

0.99

0.0007

7

0.03

−0.19

0.656

−0.0003

0.03

−0.21

0.62

−0.0057

0.02

−0.44

0.28

−0.0331

9

0.59

0.42

0.229

0.0026

0.51

0.54

0.11

0.0472

0.57

−0.45

0.19

−0.1713

11

0.14

0.22

0.679

0.0005

0.14

0.23

0.66

0.0100

0.12

−0.48

0.33

−0.0680

7

0.01

0.90

0.002

0.0013

0.02

0.68

0.07

0.0232

0.01

−0.75

0.03

−0.0728

9

0.02

-−0.49

0.269

−0.0005

0.03

−0.44

0.33

−0.0073

0.03

0.32

0.48

0.0338

8

0.11

0.20

0.443

0.0008

0.11

0.24

0.35

0.0142

0.10

−0.37

0.14

−0.0682

18

0.02

0.26

0.579

0.0004

0.02

0.32

0.49

0.0060

0.01

−0.60

0.16

−0.0244

8

0.32

−0.27

0.477

−0.0021

0.25

−0.53

0.15

−0.0455

0.25

0.51

0.16

0.3891

11

Mean

0.14

0.11

0.434

0.0002

0.12

0.09

0.39

0.0037

0.12

−0.19

0.30

0.0089


SD

0.18

0.41

0.214

0.0013

0.15

0.41

0.23

0.0242

0.17

0.45

0.27

0.1520


In each neuron, heterogeneous response amplitudes are likely a consequence of variable receptor densities and cable properties. Thus, simply measuring the maximal response amplitudes arising from photo-stimulation at each of these sites and regressing them against their varying cable properties does not negate the possibility that the measured amplitudes are a consequence of both of these factors.

Probing electrotonic structure with reversal potential measurements

A neuron’s distributed cable properties, or electrotonic structure, can be quantitatively assessed by measuring the reversal potentials (more specifically, the apparent Erevs measured at the soma) of local glutamate responses evoked at sites varying in distance from the somatic recording site (Calvin, 1969; Carnevale and Johnston, 1982). This approach distinguishes the degree to which the passive cable properties cause electrotonic decrement of voltage signals in their path of propagation to the somatic recording site, independent of the maximal conductance or receptor density at the photo-stimulation site. To demonstrate this logic, we built a library of passive cable models in the NEURON simulation platform (Hines and Carnevale, 1997; see Materials and methods) and simulated activation of local inhibitory chloride currents (actual Erev = −70 mV) at varying distances from the recording site. Apparent Erevs were measured by manipulating the membrane potential (Vm) with current injections between −8 and +2 nA at the recording site. First, we demonstrate that the apparent Erev of an inhibitory event evoked 200 µm away from the recording site (as shown in Figure 6A) is independent of its maximal conductance (or receptor density; Figure 6B–C). The apparent Erevs were measured with four maximal conductance (gmax) values: 1, 5, 10, and 50 nS. Although the response amplitudes measured at the recording site vary with gmax, all voltage responses flip their sign at −77 mV (Figure 6B). This is shown graphically in Figure 6Ci, where response amplitude (deltaV) is plotted as a function of Vm (as measured at the recording site at 0 µm). For each gmax value, the apparent Erev was calculated as the x-intercept of the linear regression of the deltaV versus Vm curve (R > 0.9 and p<0.01 in each case). The inset in Figure 6Ci and Figure 6Cii clearly show that the x-intercepts are the same for all four gmax values. The apparent Erev is independent of gmax magnitude, regardless of the activation site’s distance from the recording site (Figure 6—figure supplement 1).

Figure 6 with 1 supplement see all
Passive cable simulations show that apparent Erev measurements are independent of maximal conductance (gmax) and dependent on the distance between activation and recording sites.

(A) An inhibitory current (actual Erev = −70 mV, τ = 3 ms) was activated 200 µm from the recording site (at 0 µm). (B) Voltage events as measured at 0 µm. The membrane potential at the recording site was manipulated with current injections between −8 and + 2 nA. Colors correspond to responses evoked at 200 µm with different gmax values (as indicated). (C) (i) Response amplitude (deltaV) plotted as a function of membrane potential (Vm) as measured at 0 µm. Apparent Erevs were identified for each gmax by calculating the x- intercept of linear fits to these curves (R > 0.9 and p<0.01 in all cases). The inset shows a magnification along the x-axis and illustrates that all curves share the same x-intercept, regardless of. gmax value. (ii) Apparent Erev plotted as a function of gmax values. (D) To determine the dependence of apparent Erev as a function of activation site distance from recording site, inhibitory currents (Erev = −70 mV, τ = 3 ms, gmax = 5 nS) were evoked at 0, 200, 400, 600, 800,. and 1000 µm from the recording site. (E) Voltage events as measured at 0 µm. The membrane. potential at the recording site was manipulated with current injections between −8 and + 2 nA. Colors correspond to responses evoked at different activation sites (as indicated in D). (F) (i) Response amplitude (deltaV) plotted as a function of membrane potential (Vm) as measured at 0 µm. Apparent Erevs were identified for each activation site distance by calculating the x-intercept of linear fits to these curves (R > 0.9 and p<0.01 in all cases). The inset shows a magnification along the x-axis and illustrates the hyperpolarizing shift in apparent Erev as activation site distance increases. This is explicitly plotted in (ii). The cable model used to generate all of these data had a passive conductance of 20 nS·cm−2 and axial resistance of 30 Ω·cm (see Materials and methods).

https://doi.org/10.7554/eLife.23508.010

Second, we show that the apparent Erev for a locally activated inhibitory current changes as a function of distance from the recording site (Figure 6D–F). The apparent Erevs were measured for inhibitory currents of the same gmax (5 nS) but with increasing distance from the recording site: 0 to 1000 µm, at increments of 200 µm (Figure 6D). It is evident from the traces in Figure 6E that the apparent Erev, or membrane potential at which the responses change sign, occurs at increasingly hyperpolarized membrane potentials as a function of increasing distance from the recording site. This hyperpolarizing shift in apparent Erev is illustrated in Figure 6Fi, where the x-intercepts for the deltaV versus membrane potential curves (as measured at the recording site at 0 µm) shift leftward with increasing activation site distance (shown clearly in the inset, a magnification of the x-intercepts). The apparent Erev shifts from an accurate measure of the actual Erev of −70 mV when activated at the recording site (0 µm) to −110 mV when activated 1000 µm away (Figure 6Fii). Thus, from considering one cable model with one set of passive properties, we can deduce that the apparent Erev of a locally-activated inhibitory current is independent of its maximal conductance (or receptor density) and is dependent on the site’s distance from the recording site.

Figure 7 demonstrates that the dependence of the apparent Erev on distance is contingent upon the effective electrotonic structure of the voltage signal’s path of propagation, from activation site to recording site. With a similar set-up to the simulation shown in Figure 6C–F, apparent Erevs were measured for responses arising from activation of the inhibitory current at sites with increasing distance from the recording site (Figure 7A). We conducted this simulation in a library of cable models with uniform diameters (5 µm) and lengths (1000 µm), but varying passive properties. Specifically, this set of 20 cable models varied in their combinations of passive leak conductances (gpas): 5, 10, 20, or 50 nS/cm2 and axial resistances (Ra): 1, 5, 10, 30, or 50 (Ω·cm). Thus, each cable model is distinguished by its electrotonic length constant (λ), determined by the expression: λ=rRm2Ra where Rm=1gpas. λ, in µm or mm, is equivalent to the distance at which a propagating voltage signal decrements to 37% of the maximal voltage signal (as would be measured at the site of activation). Figure 7B shows inhibitory voltage events evoked at increasing distances from the recording site (at 0 µm) in three cable models with different λ values (200, 460, and 800 µm). With distance, the apparent Erev undergoes a hyperpolarizing shift (as was the case Figure 6E). However, the rate at which this apparent Erev hyperpolarizes, as a function of distance, is dependent on the electrotonic length constant of the cable (Figure 7C). When λ = 800 µm, all apparent Erevs are −70 mV, regardless of activation site distance. When λ = 460 µm, apparent Erevs shift from −70 mV at the recording site (0 µm) to −88 mV at 1000 µm. When λ = 200 µm, the apparent Erev shifts from −70 mV at 0 µm to well below −100 mV when the activation site is 1000 µm away. It is evident that the apparent Erev undergoes a greater hyperpolarizing shift with distance with decreasing λ values. Figure 7D shows the dependence of apparent Erev as a function of activation site location for all 20 cable models with λ values ranging between 200–5000 µm. Considering a subset of these cable models, with λ values between 300–1700 µm, the apparent Erevs measured at different activation site distances diverge as λ decreases to 300 µm and converge as λ increases beyond 1000 µm (Figure 7E).

The shift in apparent Erev with activation site distance is contingent upon the electrotonic length constant, λ.

(A) For each of the 20 cable models, with varying passive properties and, consequently, λ values (see Materials and methods), an inhibitory current (actual Erev = −70 mV) was evoked at varying distances from the recording site 0 µm. (B) Voltage events as measured at 0 µm for cables with λ = 200, 460, and 800 µm. The membrane potential at the recording site (Vm) was manipulated with current injections between −8 and + 2 nA. Colors correspond to responses evoked at different activation sites (as indicated in A and Figure 6D). With increasing activation site distance, the voltage deflections flip sign at increasingly hyperpolarized Vms at the recording site. This hyperpolarizing shift is more drastic in the cable with the lowest λ. (C) Plot of the apparent Erev (measured at 0 µm) as a function of activation site distance, in the three cables shown in B. The colors are indicative of the activation site distance, as in the traces in B. (D) Plot of apparent Erev (measured at 0 µm) as a function of activation site distance for all 20 cable models. The blue colorbar indicates relative λ values, ranging between 200 µm and 5 mm. (E) Plot of apparent Erev (measured at 0 µm) as a function of λ, as measured in cables with λs between 300 and 1600 µm. As λ increases, apparent Erevs of responses evoked at different activation site distances converge toward the actual Erev.

https://doi.org/10.7554/eLife.23508.012

Taken together, these proof-of-principle simulations show the unmistakable relationship between electrotonic structure and apparent Erevs measured for activation sites varying in their distance from the recording site. Invariant apparent Erevs suggest a relatively high electrotonic length constant, whereas heterogeneous Erevs suggest a lower electrotonic length constant. As is shown in Figure 6, this approach to characterizing the electrotonic structure, or passive cable properties, of a neuron is independent of differential gmax values, or receptor densities, across the neuronal structure.

In this simulation paradigm, current was injected at the recording site and flowed from the recording site to the stimulation site, changing the membrane potential at the distal site. The difference between the apparent Erev and the actual Erev is indicative of the ease of current flow in this direction and ability to manipulate the membrane potential at this distal site. Thus, there will always be a discrepancy between the voltage at the soma and the voltage at the photo-uncaging site and this discrepancy will depend on the effective electrotonic length constant of the neurite path. Therefore, this assay tests the passive cable properties of the path of propagation as is most relevant to current flow from recording site to stimulation site. Even so, the observations of sizeable voltage events at the recording site and reasonable reversal potentials are suggestive of a level of electrotonic compactness that is relevant to voltage signal propagation in either direction.

Distributed reversal potentials in GM neurons are nearly invariant

Using two-electrode current clamp at the soma, we measured apparent Erevs of local inhibitory responses evoked by focal photo-uncaging of glutamate at positions varying in distance from the somatic recording site. In these experiments, current was injected at the somatic recording site and flowed centrifugally from the recording site to the photo-uncaging site, changing the membrane potential at this distal site. Figure 8 illustrates the apparent Erevs of local inhibitory responses evoked at 7–15 sites, varying in their cable properties, across the same GM neuronal structure described in Figure 4C (a second example is shown in the Figure 8—figure supplement 1). For each photo-uncaging site, response amplitudes measured at the soma were plotted as a function of somatic membrane potential (Figure 8B,C; Figure 8—figure supplement 1B and C). These data were fit with linear regression analyses (R > 0.9 in all cases) and the reversal potentials were determined by calculating the x-intercepts of the linear fits. The linear fits for each position show little variation in the reversal potential across all positions within each preparation, with a within-neuron coefficient of variation of 0.04 ± 0.01 (mean ± SD; Figure 8D; Figure 8—figure supplement 1D). Although apparent Erevs were nearly invariant within each neuron, mean reversal potentials across neurons did vary, with a pooled mean of –78.6 ± 7 mV (Table 2). This could be attributed to real differences in the ionic current, which could be carried by potassium, chloride, or a combination of the two ions (Marder and Paupardin-Tritsch, 1978; Eisen and Marder, 1982). A consequence of variable response amplitudes across positions yielded variable linear fit slopes within neurons (as shown in Figure 8D and Figure 8—figure supplement 1D). This is likely a reflection of variable receptor densities or maximal conductances at the different photo-uncaging sites (consistent with the simulations shown in Figure 6A–C). There was no significant linear relationship between input resistances measured at the soma (Table 2) and the mean within-neuron reversal potentials (p=0.2; data not shown graphically, but available in Table 2).

Figure 8 with 1 supplement see all
Reversal potentials are nearly invariant across individual neuronal structure.

(A) Photo-uncaging sites are indicated as unique colors on the skeletal reconstruction of one GM neuron. (B) Raw voltage traces show focal glutamate responses as measured at the soma in two-electrode current clamp when evoked at positions indicated in A. (C) Plots of response peak amplitude (deltaV) as a function of membrane potential at soma (Vm) for each photo-uncaging site. (D) Linear functions for each position generated by linear regression analyses of data shown in C. Note that the x-intercepts (apparent Erevs) are highly invariant across photo-uncaging sites. The mean apparent Erev + SD = −84.6 + 4.3 mV and coefficient of variation (CV) is 0.05 in this neuron.

https://doi.org/10.7554/eLife.23508.013
Table 2

Linear regression analysis for reversal potentials as a function of distance, branch order, and neurite diameter. Each row corresponds to a different GM neuron, with same color scheme, as shown in Figure 8 and Figure 8—figure supplement 1. Note slopes of nearly zero across all 10 neurons, suggesting invariant reversal potentials across the neuronal structure. n corresponds to the number of photo-uncaging sites in each GM neuron.

https://doi.org/10.7554/eLife.23508.015

Reversal potentials

Distance

Branch order

Diameter

Neuron

Mean (mV)

SD

CV

MSE

R

p

slope (mV/um)

MSE

R

p

slope (mV/order)

MSE

R

p

slope (mV/um)

n

Rinput (MΩ)

−73.8

2.9

−0.04

5.99

0.44

0.18

0.012

6.52

0.35

0.30

0.139

6.52

0.34

0.30

0.712

11

10

−79.2

1.2

−0.02

1.21

0.00

0.99

0.000

1.16

−0.21

0.68

−0.029

0.54

−0.75

0.09

−0.513

6

15

−81.9

3.2

−0.04

8.80

0.14

0.76

0.006

8.86

0.12

0.80

0.071

5.86

−0.59

0.16

−1.123

7

12

−83.6

4.3

−0.05

13.13

0.45

0.23

0.013

13.35

0.43

0.24

0.175

14.39

−0.35

0.35

−0.613

9

12

−75.6

3.8

−0.05

9.42

0.15

0.90

0.0010

9.61

-0.05

0.97

−0.058

0.34

−0.98

0.12

−10.756

3

11

−87.7

2.7

−0.03

5.18

0.34

0.51

0.009

5.27

0.32

0.54

0.142

5.20

0.34

0.51

0.478

6

7

−64.8

3.6

−0.06

8.59

−0.50

0.26

−0.011

7.53

−0.58

0.17

−0.185

11.38

−0.04

0.93

−0.084

7

5

−69.9

3.3

−0.05

9.37

−0.22

0.46

−0.008

9.01

−0.29

0.33

−0.146

9.84

0.05

0.87

0.015

11

7

−84.6

3.0

−0.04

7.88

-−0.02

0.97

−0.001

7.80

0.10

00.83

0.039

7.88

−0.0

0.96

−0.020

7

10

−85.0

2.2

−0.03

3.02

−0.53

0.28

−0.042

4.11

0.13

0.80

0.144

2.84

0.57

0.24

1.805

6

10

Pooled Mean

−78.6

−0.04

7.26

0.03

0.55

−0.001

7.32

0.03

0.57

0.029

6.48

−0.14

0.45

−1.010


9.9

Pooled SD

7.4



3.47

0.35

0.32

0.016

3.34

0.32

0.29

0.128

4.57

0.51

0.34

3.518


2.9

Lolliplots for each preparation, showing apparent Erevs for each photo-uncaging site as a function of their distance from the somatic recording site, diameter, and branch order (Figure 9), confirm no dependence of the apparent Erev on these cable properties. Linear regression analyses revealed near-zero slopes for all 10 neurons (Figure 9—figure supplement 1; Table 2). This suggests that, even though these sites vary in their absolute distance, diameter, and branch order, they do not vary substantially in their electrotonic distance from the somatic recording site. The minimal hyperpolarizing shift for apparent Erevs measured for activation sites between 100 and 800 µm from the recording site is consistent with a λ > 1.5 mm (referencing Figure 7D and E). Taken together, these results demonstrate that GM neurons are surprisingly electrotonically compact, despite their expansive structures and morphological complexity.

Figure 9 with 1 supplement see all
Reversal potentials as a function of various cable properties.

Each lolliplot shows the glutamate response apparent reversal potentials (Erevs) for photo-uncaging sites as function of their distance from the soma, branch order, and neurite diameter. Each color and lolliplot is indicative of the set of reversal potentials across sites within a single neuron (N = 10). Focal glutamate responses were evoked at varying membrane potentials (between −120 and −40 mV) with two-electrode current clamp at the soma. Apparent Erevs for each photo-uncaging site were determined as in Figure 6. Distance and branch order measurements were generated from skeletal reconstructions. Diameter measurements were generated by manual measurement of neuronal dye-fill confocal stacks.

https://doi.org/10.7554/eLife.23508.016

Discussion

Neuronal circuits function reliably despite remarkable animal-to-animal variability in the synaptic and intrinsic conductances of their constituent neurons (Goaillard et al., 2009; Norris et al., 2011; Roffman et al., 2012 ; Sakurai et al., 2014); see Calabrese et al. (2011) and Marder et al. (2015) for reviews). Given that neuronal physiology also depends on the passive cable properties arising from geometry, we examined the physiological consequences of animal-to-animal variability in neuronal morphology. Despite their expansive and complex morphologies, GM neurons have electrotonically compact structures. This effectively compensates for morphological variability and contributes to consistent neuronal and circuit-level function across animals.

Complex yet compact

Here, we present the ostensible conundrum wherein an identifiable neuron type, despite its complex, highly-branched, neurite tree, is surprisingly electrotonically compact. This result differs from studies in a variety of neuron types that attribute specific physiological computations and plasticity rules to compartmentalized electrotonic structures. Early work in insect identified neurons with stereotyped dendritic branching patterns showed that electrotonically distinct dendritic subtrees result in the weighted integration of sensory inputs (Murphey et al., 1984; Bacon and Murphey, 1984; Miller and Jacobs, 1984; Jacobs and Miller, 1985). Studies in hippocampal pyramidal neurons (Spruston and Johnston, 1992; Carnevale et al., 1997; Mainen and Sejnowski, 1996; Jaffe and Carnevale, 1999), have attributed Hebbian plasticity in part to the passive normalization of postsynaptic potentials arising from the electrotonically distant apical and basal dendritic tufts. Work in medium spiny neurons (MacAskill et al., 2012) and thalamocortical neurons (Connelly et al., 2016) have demonstrated that the activation pattern of spatially-distributed, electrotonically distant, synaptic inputs produces different neuronal and circuit-level computations. The present work differs from these other studies of neuronal electrotonus and enriches our framework for understanding how morphology maps (or does not map) to physiological function. Otherwise stated: structural complexity does not necessarily yield compartmentalized computations.

Physiological implications

In GM neurons, synaptic voltage events may propagate tortuous neurite paths that extend beyond half a millimeter in length (Figure 2). Yet, current can be injected at the somatic recording site and effectively alter the membrane potential at such distal and distant sites allowing for reasonable apparent Erevs (approximately −80 mV). Likewise, the amplitude of the voltage response at the photo-uncaging site must be larger than what we observe at the soma. Because distally evoked events, initiated as far as 1 mm away, can be observed at the somatic recording site, the electrotonic decrement of these distal events must be small enough so that apparent reversal potentials can be recorded. Lastly, the invariance in apparent Erevs across sites (a measure independent of receptor density) suggests relatively little variance in the electrotonic decrement of signals coming from disparate sites across the neurite tree. In this sense, these neurons function almost like a single compartment, despite their complex structures.

The geometric and/or passive cable properties provide the most plausible explanation for this electrotonically compact structure. Recent work has quantified the fine anatomical properties of GM neurons and other STG neuron types, showing that the primary neurite can be as large as 15–20 µm in diameter and that the most distal neurite branches may taper to diameters between <1 and 10 µm (Otopalik et al., 2017). GM neurites may have relatively low axial resistances as a consequence of large neurite diameters. It is possible that voltage signal decrement may also be minimized by high membrane resistances across neurite branches. Given that these neurons are electrotonically compact, the input resistance as measured at the soma is likely a reflection of the resistance of the membrane surface area of much of the entire neuron. Thus, it is not surprising that input resistances measured at the soma are relatively low (mean of approximately 10 MΩ (Table 2), consistent with many years of recordings from STG neurons). If the neuron were less electrotonically compact, the input resistance measured at the soma would be higher, as the measurement would be restricted to the surface area of the local, somatic membrane.

Other neuron types compensate for passive attenuation of voltage responses with distance-dependent scaling of synaptic receptor density (Andrasfalvy and Magee, 2001; Magee and Cook, 2000; Smith et al., 2003). Our experiments showed heterogeneous maximal response amplitudes across the neuronal structure. Due to the uniformity of their apparent Erevs, it is likely that these variable response amplitudes arise from local variations in receptor densities. Because the response amplitudes across sites vary in a manner that is independent of distance from the recording site (Figure 5; Figure 5—figure supplement 1; Table 1), it is unlikely that receptor densities are scaling with distance in a systematic way.

These experiments provide an ‘upper bound’ on the effective electrotonic length constant and, therefore, the compactness of GM neurons. These experiments were done in TTX, wherein TTX-sensitive, voltage-gated sodium channels are blocked and circuit activity is silenced. While the overall membrane conductance may be higher in the absence of TTX (although, no change in input resistance as measured at the soma was detected before and after TTX addition), we would not expect these TTX-sensitive currents to substantially alter inhibitory voltage signal propagation at the range of membrane potentials probed here (−120 to −40 mV). Furthermore, spike initiation zones, where TTX-sensitive channels are most likely to reside, are located in the periphery, where the axons exit the neuropil (Raper, 1979; Miller, 1980). Thus, it is unlikely that TTX-sensitive voltage-gated channels would shunt the current arising from these evoked events in the same way as has been seen in other systems (Laurent, 1990). In STG neurons, it is an intriguing possibility that separation of synaptic integration and slow waves from spike initiation zones may be a morphological strategy established to avoid shunting of synaptic currents. Future experiments in varying pharmacological and modulatory conditions could shed light on how different voltage-gated currents, modulatory currents, and ongoing synaptic input during rhythmic activity, may effectively compartmentalize these otherwise compact passive neuronal structures.

Electrotonic structure in circuit context

GM electrotonic structure is best understood in light of STG circuit architecture. The identified neurons of the STG exhibit complex morphologies (Wilensky et al., 2003; Baldwin and Graubard, 1995; Bucher et al., 2007; Goeritz et al., 2013; Otopalik et al., 2017). Like the GM neuron, all STG neurons display large somata (50–150 µm in diameter) and primary neurites that ramify throughout the STG neuropil, wherein synaptic partners form numerous, sparse synapses (King, 1976a, 1976b; Baldwin and Graubard, 1995). If each neuron type were highly electrotonically compartmentalized, yet variable across animals, wiring this circuit would be a puzzling developmental task. The fact that these neurons present electrotonically compact structures simplifies our understanding of the developmental wiring rules that may be required and how such a circuit can be relatively immune to structural differences.

The neurons of the STG rely on graded transmission and slow oscillations, rather than fast spikes, to maintain phase relationships at the circuit level (Graubard, 1978; Raper, 1979; Graubard et al., 1980, 1983; Anderson and Barker, 1981; Manor et al., 1997, 1999; Bose et al., 2014). Given the relatively slow temporal precision of this circuit, an electrotonically compact structure is sufficient for integrating activity of many, yet sparsely distributed, synaptic inputs from each presynaptic neuron (King, 1976a, 1976b), independent of synaptic site locations. In this way, electrotonic compactness both masks the observed heterogeneity in glutamate sensitivity across the neuronal structure (Figures 4 and 5) and diminishes the consequences of presumed variability in synaptic site location arising from observed animal-to-animal variability in GM morphology (also see Otopalik et al., 2017).

In this scenario, presynaptic inputs may influence GM neuron activity with equivalent efficacy regardless of synaptic site location. This synaptic democracy (Häusser, 2001) is achieved by combining an electrotonically compact structure with graded transmission resilient to electrotonic decrement across sparsely distributed, synchronous presynaptic sites. This strategy is in stark contrast to the tight tuning of receptor or ion channel distributions employed by some neuron types. For example, CA1 pyramidal neurons compensate for passive attenuation of voltage responses with distance-dependent scaling of synaptic receptor density (Andrasfalvy and Magee, 2001; Magee and Cook, 2000; Smith et al., 2003). It is feasible that strategies for achieving synaptic democracy vary across circuit contexts. The input-output computations of pyramidal neurons are typically dependent on spikes and fast voltage transients, whereas the neurons of the stomatogastric ganglion rely more heavily on graded transmission and slow oscillations to serve their circuit-level function (Graubard, 1978; Raper, 1979; Graubard et al., 1980, 1983; Anderson and Barker, 1981; Manor et al., 1997, 1999; Bose et al., 2014). Electrotonic structure may reflect the temporal precision of the neuronal and circuit-level computations performed.

Morphologies that are ‘good enough’ rather than optimal

Numerous works have argued that specific neuronal geometries are optimal for precise neuronal computations (Mainen and Sejnowski, 1996; Stiefel and Sejnowski, 2007; Cuntz et al., 2010). Experimentalists and theorists alike have suggested that neurons employ developmental growth rules that fine-tune neuronal geometry for optimal current transfer and wiring costs (Chklovskii, 2000, 2004; Chen et al., 2006; Wen and Chklovskii, 2008; Cuntz et al., 2007, 2010; Kim et al., 2012). Many of these works rely on studies in neuron types with both recognizable morphologies and known computations and/or plasticity rules. In this way, such rules hinge on a somewhat circular premise that specific neuronal functions arise from specialized geometries. As is evident in the present work, not all neuron types exhibit conserved morphologies across animals, yet show stereotyped physiological properties and circuit-level functions. We present a case in which the solution to the morphology-to-physiology transform is many-to-one.

Meaning in morphology

Neuron types can have characteristic, recognizable morphologies. Many studies have explored stereotypy in macroscopic dendritic and axonal arborization patterns in a variety of systems, including cricket (Miller and Jacobs, 1984) and grasshopper (Goodman, 1976, 1978) sensory interneurons, the insect (Cuntz et al., 2008) and mammalian (Bloomfield and Miller, 1986; Hong et al., 2011) retina, and somatosensory (Wang et al., 2002), motor (Ghosh and Porter, 1988), and visual (Martin et al., 1983; Martin and Whitteridge, 1984a, 1984b) cortices. That said, there are remarkably few instances (Cuntz et al., 2008; Wang et al., 2002) in which multiple examples of relatively complete reconstructions have been published in enough detail to judge whether the ranges of neuronal morphological features shown here, pertinent to a neuron’s cable properties, are typical or more pronounced than in other systems.

Here, we argue that the fine structural details of complex morphology may not matter for the neuronal and circuit-level function of an identified neuron type. In the STG, neurons rely predominantly on slow oscillations for circuit function, and electrotonically compact structures elegantly compensate for a high degree of animal-to-animal variability in morphology. The degree of animal-to-animal variability in neuronal morphology, and whether it is compensated for, may depend on the system and the precision of the neuronal and circuit-level computation(s) to be performed.

Materials and methods

Animals and dissections

Adult male Jonah Crabs (Cancer borealis) were purchased from Commercial Lobster (Boston, MA) and maintained in artificial seawater at 10–13°C on a 12 hr light/12 hr dark cycle without food. On average, animals were acclimated at this temperature for one week before use. Prior to dissection, animals were anesthetized for 30 min on ice. Dissections were performed as previously described (Gutierrez and Grashow, 2009) in saline solution (440 mM NaCl, 11 mM KCl, 26 mM MgCl2, 13 mM CaCl2, 11 mM Trizma base, 5 mM maleic acid, pH 7.45). In brief, the stomach was dissected from the animal. The intact stomatogastric nervous system (STNS) was isolated from the stomach, including: the two bilateral commissural ganglia, esophageal ganglion, and stomatogastric ganglion (STG), as well as the lvn, mvn, dgn. The STNS was pinned down in a Sylgard-coated petri dish (10 mL) and continuously superfused with chilled saline.

Electrophysiology and dye-fills

The STG was desheathed and intracellular recordings from somata were performed with 20–30 MΩ glass microelectrodes filled with internal solution (10 mM MgCl2, 400 mM potassium gluconate, 10 mM HEPES buffer, 15 mM NaSO4, 20 mM NaCl as in Hooper et al., 2015). Intracellular signals were amplified with an Axoclamp 900A amplifier (Molecular Devices). For extracellular nerve recordings, Vaseline wells were built around the lvn, mvn, and dgn and stainless steel pin electrodes were used to monitor extracellular nerve activity (Figure 1A). Extracellular nerve recordings were amplified using model 3500 extracellular amplifiers (A-M Systems). Data were acquired using a Digidata 1440 digitizer (Axon Instruments) and pClamp data acquisition software (Axon Instruments, version 10.5). For GM identification, one of two electrodes was impaled into the soma and spiking activity was matched with GM spike units on the dgn. GM identity was verified with positive and negative current injections (Figure 1D). Following unambiguous identification, the GM soma was impaled with a second electrode containing dilute alexa488 dye (2 mM Alexa Fluor 488-hyrazide sodium salt (ThermoFisher Scientific, catalog no. A-10436, dissolved in internal solution)). The GM neuron was iontophoretically dye-filled with negative current pulses (−4 nA, 500 ms at 0.5 Hz) for 15–25 min. For two-electrode current clamp, the electrode containing alexa488 was typically used for recording and amplified with a 0.1xHS headstage. The electrode used for cell identification was used for current injection and amplified with a 1xHS headstage. Resting membrane potential and input resistance were monitored throughout the experiment to ensure the integrity of the preparation (neurons with input resistances <5 MΩ were discarded). In TTX, the mean input resistance, as measured at the somata and in the linear range of the current-voltage curve, was 9.9 ± 2.9 MΩ across preparations (Table 2). Input resistances did not change significantly before and after addition of TTX to the bath (data not shown). Reversal potentials for the glutamate response were determined by evoking at least three responses at >6 membrane potentials spanning −110 mV to −40 mV. In three preparations, an offset in the membrane voltage recording occurred during the dye-fill. This offset remained unchanged for the remainder of the experiment. This offset was corrected post-hoc during analysis of the recordings.

Focal glutamate uncaging

For photo-uncaging experiments, preparations were superfused with a multi-channel Ecoline re-circulating pump (Ismatec/Harvard Apparatus, catalog no. PY2 72–6432) to maintain a stable bath volume and superfusion rate. 250 µM MNI-caged-L-glutamate (dissolved in saline; Tocris Bioscience, catalog no. 1490) was bath applied. 10−7 M teterodotoxin (TTX) was also superfused to minimize spike-driven synaptic activity. Alexa488-filled GM neurons were visualized with a custom-built epifluorescence microscope (Figure 10) equipped with a 40x water-immersion UV fluorescence objective (Olympus, LUMPLFLN 40XW) and a 470 nm LED (Thor Labs, M470L2). The emitted fluorescence was imaged with a monochrome CCD camera (Scientifica, SciCam). Focal photo-activation of MNI-glutamate was achieved with a small ultraviolet (UV) spot (~10 µm in diameter; Figure 4—figure supplement 1) projected through this same 40x objective lens. By situating the custom microscope on a micromanipulator (Sutter MPC-200), this UV spot could be lased at different positions on the GM neuronal structure. Three-dimensional coordinates for each photo-uncaging site were tabulated during the experiment. Glutamate responses were evoked with 30 mW (as measured at the back aperture of the objective), 1 ms UV pulses with inter-pulse periods no less than 30 s to minimize photo-damage and desensitization (Figure 4—figure supplement 1). To achieve this small UV spot, the UV laser beam (DPSS Lasers, model no. 35-07–100, 0.96 W, 100 kHz repetition rate) was coupled to a 50 µm diameter fiber optic cable (Thor Labs, M50L02S-A) with a UV lens (Thor Labs) and collimated with a 50 mm focal length plano-convex lens (Thor Labs, LA4148-UV). This collimated UV beam was delivered into the 40x objective lens to produce a focused spot of UV light on the preparation. A neutral density filter wheel was situated in the beam path for manipulation of the beam intensity (Thor Labs, NDM2). To ensure consistent beam intensities across experiments, the intensity was monitored in real-time using a photodiode (Thor Labs, PDA25K) previously calibrated with a power meter (Thor Labs, S302C). For precise temporal control of UV stimuli, a shutter (Thor Labs, SH1) was situated in the beam path. Both the laser Q-Switch and shutter were triggered by a set of coupled model 2100 isolated pulse stimulators (A-M Systems). The effective photo-uncaging radius in the x-y plane (15 µm) was determined by photo-uncaging at peripheral, distal neurites and moving away at 5 µm increments in the x-y plane (Figure 4—figure supplement 1) in a number of neuron types: pyloric dilater (PD), lateral pyloric (LP), and GM neurons.

Microscope schematic showing laser (purple), fluorescence excitation (blue), and fluorescence emission (green) paths.

A 1 Watt 355 nm laser (1) is focused by a plano-convex lens (2) and coupled to a 50-micron fiber optic cable (3) situated on an x-y translating fiber adaptor (4). The UV beam is collimated with a plano-convex lens situated in a z-translator (5). The beam intensity can be manually adjusted with a neutral density filter wheel (6) and passes through a 40x UV water immersion objective (7) onto the STNS preparation (8). The UV beam intensity is measured in real-time with a calibrated photo-diode (9) measuring a signal proportional to the power administered to the preparation. A 470 nm blue LED (10) is collimated by a plano-convex lens (11) and passes through a 466/40 nm band-pass filter (12) and field diaphragm (13). This light is re-directed by a 495 nm dichroic beamsplitter (14) and passes through a tube lens (15) and 405 nm low-pass dichroic beamsplitter (16). This is directed through the same 40x objective (7) and excites the alexa488 dye-filled preparation. This fluorescence passes through the 405 nm low-pass dichroic beamsplitter (16), tube lens (15), and 495 nm dichroic beamsplitter (14) and is subsequently captured by the CCD array of a firewire monochrome camera (Scientifica).

https://doi.org/10.7554/eLife.23508.018

Dye-fill amplification and immunohistochemistry

Following photo-uncaging experiments, GM neurons were secondarily dye-filled with 2% Lucifer Yellow CH dipotassium salt (LY; Sigma, catalog no. L0144) in filtered water using a low-resistance electrode (10–15 MΩ). LY was injected for 20–50 min with negative current pulses (−6 to −8 nA, 500 ms at 0.5 Hz). Once fine neurites of the cell could be visualized with a fluorescent stereomicroscope (Leica MF165 F), a preliminary image was acquired at 11.5x magnification with an attached monochrome digital camera (Leica DFC365 FC). LY-filled preparations were fixed for 40 min at 21°C or overnight at 4°C in 2% paraformaldehyde in phosphate-buffered saline (PBS; 440 mM NaCl, 11 mM KCl, 10 mM Na2HPO4, 2 mM KH2PO4, pH 7.4). Preparations were washed with 0.1 M PBS-T ((0.1–0.3%% Triton X-100 in PBS) and stored in PBS for 0–3 days prior to immunohistochemistry. The LY signal was amplified by 16 hr incubation with a polyclonal rabbit anti-LY antibody (1:500; Molecular Probes). After washing 5 × 15 min in PBS-T at room temperature, preparations were incubated in a secondary Alexa Fluor-488-conjugated goat-anti-rabbit antibody (1:500; Molecular Probes) for 1.5 hr at room temperature. Preparations were washed 5 × 15 min in PBS at room temperature before mounting on pre-cleaned slides (25 × 75 × 1 mm, superfrost, VWR) in Vectashield (Vector Laboratories, Burlingame, CA), with 9 mm diameter, 0.12 mm depth silicone seal spacers (Electron Microscopy Sciences, Hatfield, PA) under #1.5 coverslips (Fisher Scientific). Mounting in Vectashield with a spacer was sufficient to maintain the 3-dimensional structure of the neuron and ganglion (as in Goeritz et al., 2013).

Confocal imaging and 3D reconstructions

Confocal stacks of the LY-filled neurons were acquired with a SP2 Leica Microscope and Leica Application Suite Advanced Fluorescence (LAS AF) software. Image stacks were acquired with a 20x dry objective (Leica HC PL APO CS 20x) at 1024 × 1024 resolution in 0.5 µm steps. Image stacks were visualized in both FIJI (ImageJ) software and KNOSSOS 3D image visualization and annotation software (developed by teams at the Heidelberg University and Karlsruhe Institute of Technology, employed by the Max Planck Institute for Medical Research, and freely distributed at: http://www.knossostool.org/). KNOSSOS software was used to manually trace and generate skeletons of the GM neuronal structures in three dimensions (Supplementary file 1-Neuronal Structures Hoc files; as in Otopalik et al., 2017). It is important to note that the resolution used here allowed us to reconstruct many neurons, but resulted in smaller total cable lengths and branch point numbers than reported in Otopalik et al. (2017), where neuronal dye-fills were imaged at 60x magnification. This higher magnification would have precluded completion of the reconstructions and photo-uncaging experiments reported here.

Morphological analysis

Following 3D skeleton generation, morphological analyses were completed across all GM neurons (n = 14), using a suite of custom analysis scripts written in Python using the iPython command line (freely available at: https://python.org and https://ipython.org, respectively) by AS. For each skeleton, branch points, lengths, and orders were measured in reference to the soma and used to generate dendrogram representations with normalized path lengths. Branch, or path, lengths were measured as the most direct neurite path from the soma to each branch tip. Tortuosities were calculated for each path length, as the ratio of the path length over the Euclidean distance from soma to branch tip. Axon locations were identified as the last branch points without terminating branch tips. Photo-uncaging positions were re-located on preliminary fluorescence images of the Lucifer yellow dye-fill (as situated during experiment, at 11.5x magnification) using a custom alignment script written in MATLAB (Mathworks, version 2015b) by AO, and then manually re-located in the 3D skeleton using KNOSSOS (Supplementary file 2-Uncaging Coordinates Hoc files). The branch order, path length, and diameter were determined for each photo-uncaging site, based on the confocal image stack. All quantitative morphology analysis scripts are freely available at the Marder Lab GitHub website (https://github.com/marderlab/Quantifying_Morphology).

Electrophysiology analysis

Recordings acquired using Clampex software (pClamp Suite by Molecular Devices, version 10.5) and were visualized offline using a MATLAB waveform analysis toolbox written by Ted Brookings and analyzed with custom MATLAB scripts written by AO. Briefly, this pipeline of analysis scripts was used to detect and browse evoked glutamate responses, measure voltage response amplitudes and membrane potentials, plot raw recordings and processed data, and perform some statistical analyses. To determine reversal potentials at a given photo-uncaging position, raw response amplitudes were plotted as a function of membrane potential. These data were fit with a linear function (with an R value > 0.9 in all cases). In some cases, response amplitudes saturated and the linear regression analyses were performed only in the linear range of these data. The x-intercept of the resulting linear function indicated the reversal potential at that position. All electrophysiology analysis scripts are available at the Marder lab GitHub (https://github.com/marderlab).

Passive cable models

A library of equivalent cylinder models was constructed in NEURON (freely available at: https://www.neuron.yale.edu/neuron), to simulate apparent reversal potential (Erev) measurements of inhibitory responses generated at positions varying in distance from the recording site. The cables were uniform in their geometric properties: 1000 µm in length and 5 µm in diameter. All cables had a membrane capacitance of 1 µF·cm−2. However, their passive properties were varied combinatorically with four passive conductance (gpas) values (5, 10, 20, and 50 nS/cm2) and five axial resistance (Ra) values (1, 5, 10, 30, 50 Ω·cm). Consequently, each cable can be distinguished by its electrotonic length constant (λ in µm) such that, λ=rRm2Ra where Rm=1gpas. λ values ranged between 200 µm and 5 mm (Figure 11). To measure the apparent Erevs at the 0 µm end of the cable, the membrane potential was manipulated at the recording site with current injections between −8 and +2 nA. An inhibitory current (actual Erev = −70 mV, 𝜏 = 3 ms, gmax = 1, 5, 10, or 50 nS) was activated at sites varying in distance from the recording site (at 0 µm). For a given cable and activation site, the apparent Erev was calculated by plotting the response amplitude (deltaV) as a function of membrane potential at the recording site. For each curve, linear regression analysis was completed (R > 0.9 and p<0.01 in all cases). The apparent Erevs were identified as the x-intercept of the linear fit.

Passive parameters used for cable model library.

All pairwise combinations. of passive conductance (gpas; 5, 10, 20, 50 nS/cm2) and axial resistance (Ra; 1, 5, 10,. 30, 50 Ω•cm) values were used to generate a library of 20 cable models with varying. electrotonic length constants (λ; shown numerically and in gray scale, in microns, as grid. elements below) between 220 µm and 5 mm.

https://doi.org/10.7554/eLife.23508.019

References

  1. 1
    Signal delay and input synchronization in passive dendritic structures
    1. H Agmon-Snir
    2. I Segev
    (1993)
    Journal of Neurophysiology 70:2066–2151.
  2. 2
  3. 3
    Distance-dependent increase in AMPA receptor number in the dendrites of adult hippocampal CA1 pyramidal neurons
    1. BK Andrasfalvy
    2. JC Magee
    (2001)
    The Journal of Neuroscience 21:9151–9160.
  4. 4
  5. 5
  6. 6
  7. 7
    A functional organization of ON and OFF pathways in the rabbit retina
    1. SA Bloomfield
    2. RF Miller
    (1986)
    The Journal of Neuroscience 6:1–13.
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
    Electrophysiological characterization of remote chemical synapses
    1. NT Carnevale
    2. D Johnston
    (1982)
    Journal of Neurophysiology 47:606–621.
  13. 13
    Comparative electrotonic analysis of three classes of rat hippocampal neurons
    1. NT Carnevale
    2. KY Tsai
    3. BJ Claiborne
    4. TH Brown
    (1997)
    Journal of Neurophysiology 78:703–723.
  14. 14
  15. 15
    Optimal sizes of dendritic and axonal arbors in a topographic projection
    1. DB Chklovskii
    (2000)
    Journal of Neurophysiology 83:2113–2119.
  16. 16
  17. 17
    Glutamate-gated inhibitory currents of central pattern generator neurons in the lobster stomatogastric ganglion
    1. TA Cleland
    2. AI Selverston
    (1995)
    The Journal of Neuroscience 15:6631–6639.
  18. 18
  19. 19
  20. 20
  21. 21
  22. 22
    Mechanisms underlying pattern generation in lobster stomatogastric ganglion as determined by selective inactivation of identified neurons. III. synaptic connections of electrically coupled pyloric neurons
    1. JS Eisen
    2. E Marder
    (1982)
    Journal of Neurophysiology 48:1392–1415.
  23. 23
  24. 24
  25. 25
  26. 26
  27. 27
    Ionic currents of the lateral pyloric neuron of the stomatogastric ganglion of the crab
    1. J Golowasch
    2. E Marder
    (1992)
    Journal of Neurophysiology 67:318–331.
  28. 28
  29. 29
  30. 30
  31. 31
  32. 32
    Graded synaptic transmission between identified spiking neurons
    1. K Graubard
    2. JA Raper
    3. DK Hartline
    (1983)
    Journal of Neurophysiology 50:508–529.
  33. 33
  34. 34
    Synaptic transmission without action potentials: input-output properties of a nonspiking presynaptic neuron
    1. K Graubard
    (1978)
    Journal of Neurophysiology 41:1014–1025.
  35. 35
  36. 36
  37. 37
    Dynamical Biological Networks: The Stomatogastric Nervous System 
    1. RM Harris-Warrick
    2. E Marder
    3. AI Selverston
    (1992)
    Cambridge, MA: MIT Press.
  38. 38
    Motor patterns in the stomatogastric ganglion of the lobster panulirus argus
    1. DK Hartline
    2. DM Maynard
    (1975)
    The Journal of Experimental Biology 62:405–420.
  39. 39
  40. 40
    Gastric mill activity in the lobster. I. spontaneous modes of chewing
    1. HG Heinzel
    (1988)
    Journal of Neurophysiology 59:528–550.
  41. 41
  42. 42
  43. 43
  44. 44
  45. 45
    Passive normalization of synaptic integration influenced by dendritic architecture
    1. DB Jaffe
    2. NT Carnevale
    (1999)
    Journal of Neurophysiology 82:3268–3285.
  46. 46
    Interpretation of voltage-clamp measurements in hippocampal neurons
    1. D Johnston
    2. TH Brown
    (1983)
    Journal of Neurophysiology 50:464–486.
  47. 47
  48. 48
  49. 49
  50. 50
  51. 51
  52. 52
    Voltage-dependent nonlinearities in the membrane of locust nonspiking local interneurons, and their significance for synaptic integration
    1. G Laurent
    (1990)
    The Journal of Neuroscience 10:2268–2280.
  53. 53
  54. 54
  55. 55
  56. 56
  57. 57
    Temporal dynamics of graded synaptic transmission in the lobster stomatogastric ganglion
    1. Y Manor
    2. F Nadim
    3. LF Abbott
    4. E Marder
    (1997)
    The Journal of Neuroscience 17:5610–5621.
  58. 58
    Network oscillations generated by balancing graded asymmetric reciprocal inhibition in passive neurons
    1. Y Manor
    2. F Nadim
    3. S Epstein
    4. J Ritt
    5. E Marder
    6. N Kopell
    (1999)
    The Journal of Neuroscience 19:2765–2779.
  59. 59
    Transmitter identification of pyloric neurons: electrically coupled neurons use different transmitters
    1. E Marder
    2. JS Eisen
    (1984)
    Journal of Neurophysiology 51:1345–1361.
  60. 60
  61. 61
  62. 62
  63. 63
  64. 64
  65. 65
  66. 66
  67. 67
  68. 68
  69. 69
    Relationships between neuronal structure and function
    1. JP Miller
    2. GA Jacobs
    (1984)
    The Journal of Experimental Biology 112:129–145.
  70. 70
    Mechanisms Underlying Pattern Generation in the Lobster Stomatogastric Ganglion
    1. JP Miller
    (1980)
    San Diego: University of California.
  71. 71
    Neurospecificity in the cricket cercal system
    1. RK Murphey
    2. WW Walthall
    3. GA Jacobs
    (1984)
    The Journal of Experimental Biology 112:7–25.
  72. 72
  73. 73
  74. 74
  75. 75
  76. 76
  77. 77
  78. 78
  79. 79
    Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input
    1. W Rall
    (1967)
    Journal of Neurophysiology 30:1138–1168.
  80. 80
  81. 81
  82. 82
    Handbook of Physiology: The Nervous System. Cellular Biology of Neurons
    1. W Rall
    (1977)
    39–97, Core conductor theory and cable properties of neurons, Handbook of Physiology: The Nervous System. Cellular Biology of Neurons, Bethesda, MA, American Physiological Society.
  83. 83
  84. 84
  85. 85
  86. 86
  87. 87
  88. 88
    Neural basis of teeth coordination during gastric mill rhythms in spiny lobsters, panulirus interruptus
    1. DF Russell
    (1985)
    The Journal of Experimental Biology 114:99–119.
  89. 89
  90. 90
  91. 91
  92. 92
  93. 93
  94. 94
  95. 95
    Voltage- and space-clamp errors associated with the measurement of Electrotonically remote synaptic events
    1. N Spruston
    2. DB Jaffe
    3. SH Williams
    4. D Johnston
    (1993)
    Journal of Neurophysiology 70:781–802.
  96. 96
    Perforated patch-clamp analysis of the passive membrane properties of three classes of hippocampal neurons
    1. N Spruston
    2. D Johnston
    (1992)
    Journal of Neurophysiology 67:508–537.
  97. 97
  98. 98
  99. 99
    Propagation of action potentials in dendrites depends on dendritic morphology
    1. P Vetter
    2. A Roth
    3. M Häusser
    (2001)
    Journal of Neurophysiology 85:926–937.
  100. 100
  101. 101
    Neurons that form multiple pattern generators: identification and multiple activity patterns of gastric/pyloric neurons in the crab stomatogastric system
    1. JM Weimann
    2. P Meyrand
    3. E Marder
    (1991)
    Journal of Neurophysiology 65:111–122.
  102. 102
  103. 103
  104. 104

Decision letter

  1. Indira M Raman
    Reviewing Editor; Northwestern University, United States

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

[Editors’ note: a previous version of this study was rejected after peer review, but the authors submitted for reconsideration. The first decision letter after peer review is shown below.]

Thank you for submitting your work entitled "When complex neuronal structures may not matter" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Gilles Laurent (Reviewer #3). Our decision has been reached after extensive consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered for publication in eLife because we think addressing the issues will take longer than the allotted two months for revision. However, if you wish to undertake an extensive revision, we would be glad to reconsider the manuscript.

Summary:

The reviewers all found the topic interesting and commented on the quality of the experiments and the intriguing nature of the result. Nevertheless, they were mixed in their assessment of the manuscript. The strongest concerns were, specifically, that in the absence of a more detailed investigation of cable properties, the reported electrical compactness is not well or easily reconciled with the low input resistances, and generally, that some of the approaches might not be ideal (somatic recordings to infer dendritic properties, effects of glutamate uncaging with possibly non-uniform receptor density, synaptic reversal potentials to test compartmentalization, simplified model to explore dendritic complexity) and some key parameters might be inadequately constrained (electrical attributes of the dendrites, and effect of TTX on the measurements). The reviewers also expressed concern that without a resolution of the apparent conflict between the compactness and low input resistance, it is not be possible to judge whether or under what conditions the observations might apply to any other kinds of neurons. Addressing these concerns would involve (1) validating and/or justifying the uncaging approach, (2) providing information about passive cable properties, (3) reconsidering and/or discussing limits on synaptic reversal potentials, (4) extending modeling, e.g., to test whether passive cable properties might normalize PSP amplitude with distance; to more fully consider dendritic complexity; to explore the phenomenon with numerical simulation experiments that add plausibility arguments to the results. These points are explained in more detail in the reviewers' comments, which are included in full below.

Reviewer #1:

This study examines how variation in dendritic morphology influences synaptic integration in Gastric Mill (GM) neurons of the crab stomatogastric ganglion (STG). The authors combine somatic 2-electrode voltage-clamp recordings with focal glutamate uncaging experiments to show that the amplitudes of glutamate responses appear not to depend strongly on distance or variations in local dendritic geometry. These are interesting, experiments, and the questions addressed are of broad general interest. However, the paper suffers from the fact that the authors are constrained to infer dendritic properties from somatic recordings without any direct measurements, and there are assumptions about the nature of the glutamate uncaging that are not adequately justified. Also, the computer models do not explore the very dendritic complexity that the study purports to address. In the end, I don't think readers will be convinced that the current data set provides sufficient mechanistic insight into the nature of dendritic integration in GM neurons. My major comments are detailed below.

1) The premise of this study rests on the use of uncaged glutamate responses as a means to elicit uniform currents at many spatial locations in the dendrites. However, for this approach to be valid, the density of (presumably mostly extra-synaptic) glutamate receptors must be uniform across the dendritic arbor. While the uncaged responses appear quite reliable in Figure 4 at a given location, responses at adjacent locations in Figure 5 are highly variable, possibly reflecting variations in receptor density along the dendrites. There seems to be no systematic changes in response amplitude with local dendrite diameter or branch order, but it is not known what the amplitude of the responses are at the site of uncaging. With so many unknown free parameters (receptor density, surface area, local input resistance) it is not clear how these data can be interpreted cleanly. It is also not clear how these responses relate to the function of actual synapses, which according to the authors are located on the finer distal branches.

2) Considering how important passive cable properties are to the interpretation of the data, it is perhaps surprising how little information is provided about the actual passive electrical properties of GM cells. The only hint at these properties is the statement in the Methods that recorded GM cells had input resistances greater than 5 MΩ. This rather low value for input resistance (though perhaps not for invertebrate neurons) seems at odds with the authors' conclusion that GM neurons are electrically tight. There are modeling parameters reported in Table 2, but it is not clear whether these values are based on real measurements or just reasonable guesses. Some more detailed information about GM cell electrical properties would be helpful and important.

3) In general, synaptic reversal potentials are not sensitive predictors of the extent of dendritic compartmentalization. The manner in which reversal potentials are measured produces conditions that reduce the influence of dendritic filtering (since voltages during long command stimuli have reached a steady state). Also, voltages show less attenuation in the centrifugal vs. centripetal direction due to decreasing diameter and surface area of more distal dendritic branches. Williams and Mitchell (2008) elegantly explored these and other issues of dendritic filtering in neocortical pyramidal neurons…and yet these neurons show compartmentalized responses and significant attenuation of synaptic events propagating from the dendrites to the soma. The ability of a voltage clamp circuit to measure reversal potentials of distal synapses with reasonable accuracy does not necessarily mean that local and propagated synaptic responses do not depend on dendritic morphology.

4) The discussion in the last paragraph of the subsection “Electrotonic Structure in Circuit Context" contrasts the authors' present results and interpretations with results from hippocampal CA1 pyramidal neurons, where distance dependent attenuation of synaptic potentials is compensated via an increase in postsynaptic AMPA receptors (not voltage-gated conductances, as stated in the manuscript). In neocortical pyramidal neurons, though, distance dependent compensation for much of the dendritic voltage attenuation of synaptic events arises from the passive electrotonic structure of the dendritic arbor (e.g. Williams and Stuart 2002). It seems to me that either or both of these mechanisms could potentially explain the current findings. Given that neither of these mechanisms is explored directly in the current study, I don't know that the authors are in a strong position to argue that GM neurons operate differently.

Reviewer #2:

This manuscript reports an unusual electrotonic compactness in one neuron type in the crustacean stomatogastric ganglion. The GM neurons have varied morphology and dendritic branching patterns, yet all respond similarly during the motor pattern they participate in. The authors argue that this is because the neurons are very electrotonically compact, and current loss from distal dendrites is small. The experiments to show this are well done and convincing, including an interesting failure to detect a distance dependence of the apparent reversal potential of the synaptic responses. They do no experiments to determine how this compactness occurs, nor do they provide any explanation for this result. This discussion is important because to a naive reader the results appear to contradict simple cable property measures of current flow in branched processes. If such explanation (preferably with experimental verification) were provided, this would be a much stronger manuscript.

Reviewer #3:

This very nice paper explores the morphological and electrical geometry of an identified neuron (GM) in the crustacean STG. The authors find that the morphological features of this neuron are variable across animals, but that the responses, as measured from the soma, of the same neurons to uncaged Glu at various locations on its neuritic tree, vary little (across sites for a given neuron). Because most synaptic interactions are slow, and in a mostly passive regime, this leads to the conclusion that the electronic structure of GM is compact and its morphological architecture not relevant for integration/computation.

The paper is beautifully written, the figures limpid, the work quite extensive, the literature well researched and integrated. The main important result is that dendritic geometry may matter little when signals are slow and electrotonic structure compact.

[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]

Thank you for submitting your article "When complex neuronal structures may not matter" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Gary Westbrook as the Senior Editor. The following individual involved in review of your submission has agreed to reveal his identity: Gilles Laurent (Reviewer #1).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

This work demonstrates that variation in morphology of the Gastric Mill (GM) neuron of the crab stomatogastric ganglion (STG) has relatively little influence on synaptic integration and the resultant voltage responses, owing to electrical compactness of the neurons.

Essential revisions:

The reviewers agreed that the appealed and revised version of the manuscript was improved, with many clarifications of the points that were initially raised. Two essential points remain:

1) The first, extensively discussed by the reviewers, has to do with whether the conclusion that morphology has relatively little effect on voltage responses is adequately supported by the modeling, given that the specific parameters of neurite morphology were not considered. Reviewers recognized that the main point may not be to rule out the idea that any dendritic computations took place, but rather that the slow graded signals characteristic of these cells are not greatly affected by morphology; nevertheless, it was acknowledged that this distinction could be emphasized further. As stated in the consultation, "The main thesis of the paper is that a long length constant of the neurite allows voltages from anywhere in the dendritic tree to propagate throughout the cell with minimal voltage attenuation, so the passive properties of their specific cell morphology is a central concern." One way to address this point, would be to import a real GM cell morphology into NEURON and express their passive properties uniformly in all compartments to test (a) whether the voltage attenuation or amplitude at the soma similar for long currents injected in distal neurites and (b) whether the length constant depends significantly on direction of propagation. The outcomes could serve either to support the results or place appropriate constraints on the conclusions. However, the reviewers agreed to leave the specific way of allaying these concerns to you, i.e., such a model is not required if you find alternative ways to clarify and/or limit the conclusions. The original "major comments" on this matter are included below for your reference, to guide and inform your revision.

2) The second point has to do with the placing constraints on the basis for electrotonic compactness. The Discussion mentions two possible explanations for how neurons with very low input resistance can be so electrotonically compact: very low internal resistance due to large diameter of initial processes (though this would not apply to the fine processes where the input-output synapses are located) and possibly high membrane resistance at branch points (though this would not block the passive spread of current along the internal resistance of the branches). The reviewers pointed out that it would be informative for the estimates of the length constant (1.5 mm) to be integrated with measurements of the input resistance (~ 10 MΩ) to come up with boundaries of Ri and Rm (given that Rin = (2/π)(RmRi)1/2(d)3/2 for a semi-infinite cylinder, and λ= ((RmRi)(d/4))1/2 (from Rall, 1977).

Comments related to Essential revision 1:

1) My main concern, before and now, has to do with whether the authors have truly shown that dendritic morphology plays little role in shaping voltage responses. The authors' argument is that the dendrites and soma are nearly equipotential, and that as a result inputs on any part of the structure have similar voltage contributions throughout the arbor. I don't see that this hypothesis has been adequately supported because the modeling does not take into account the actual neurite morphology the authors have quantified. The simulations in Figure 7 show that under conditions favorable for voltage propagation (a moderately large, constant diameter neurite exhibiting a long 800 µm length constant), there is still >50% attenuation of PSPs along its length despite the fact that the Erev can be accurately measured at these same distances. But the authors show in several figures (e.g. Figure 5) that there are striking reductions in diameter in the more distal regions, which will impart a directional asymmetry in the efficacy of voltage propagation. In a passive neuron, centrifugal propagation will be more effective in a tapering structure such as the one exhibited by GM neurons, which help explain why Erev can be measured so effectively even at distal uncaging sites in experiments. However, propagation toward the larger diameter neurites and soma will be comparatively unfavorable. The simulations in Figure 7 may thus underestimate the attenuation of voltages during propagation toward larger neurites.

I think the authors need to examine voltage propagation in a realistic morphological structure. If a conductance is introduced in neurites of differing orders, diameters and distances from the soma in a model neuron with realistic morphology, would these events yield comparable voltages at the soma? I do not expect that the authors must necessarily provide a full mechanistic explanation for their results, but I think such an examination would provide a better understanding of how spatially compact GM neurons are under more realistic conditions, and whether passive properties are sufficient to explain their uncaging results.

[In the words of another reviewer:] The other issue to discuss (also from Rall) is the large difference in voltage attenuation depending on the direction of the current flow (from a single dendritic point to the soma vs. from the soma to the dendrites). Your measurements of ipsp amplitude after stimulation at a single point are examples of the first, while your measurements of the Vrev from the soma are examples of the second. I think this will not be a problem for your analysis, but it should be explicitly discussed in the Discussion. The integration of spatially distributed synaptic inputs by the neuron would be an example of current flow from the periphery to the center, and from basic principles might show more attenuation.

2) There were some misunderstandings concerning my previous comments regarding the diversity of responses at adjacent locations and the lack of diversity of responses from neurites of different diameters. Put a different way, if a similar response is obtained from uncaging a 10 µm spot over a 1 vs. 10 µm diameter neurite (for example), does this not imply that there must be some other mechanism(s) in place to boost the amplitudes despite the 10-fold reduction in surface area and receptor density? A higher local input resistance might raise the local PSP amplitude, but such a mechanism might be limited due to the proximity of the reversal potential to rest. The authors have stated in their rebuttal that their concern is with voltage propagation and not local integration, but it seems to me that both issues are interrelated and central to understanding the results of their uncaging experiments.

3) In their rebuttal, the authors state that it is unlikely that receptor densities change along the dendrites because the "response amplitudes across sites within each neuron show no quantitative dependence on distance from the recording site." This assumes there is no significant centripetal attenuation of voltage, but as detailed earlier, there is some uncertainty in this premise. If there is even moderate voltage attenuation between the small diameter, distal neurites and the soma, would not another mechanism be needed to restore the amplitude of the response?

https://doi.org/10.7554/eLife.23508.022

Author response

[Editors’ note: the author responses to the first round of peer review follow.]

Summary:

The reviewers all found the topic interesting and commented on the quality of the experiments and the intriguing nature of the result. Nevertheless, they were mixed in their assessment of the manuscript. The strongest concerns were, specifically, that in the absence of a more detailed investigation of cable properties, the reported electrical compactness is not well or easily reconciled with the low input resistances, and generally, that some of the approaches might not be ideal (somatic recordings to infer dendritic properties, effects of glutamate uncaging with possibly non-uniform receptor density, synaptic reversal potentials to test compartmentalization, simplified model to explore dendritic complexity) and some key parameters might be inadequately constrained (electrical attributes of the dendrites, and effect of TTX on the measurements). The reviewers also expressed concern that without a resolution of the apparent conflict between the compactness and low input resistance, it is not be possible to judge whether or under what conditions the observations might apply to any other kinds of neurons. Addressing these concerns would involve (1) validating and/or justifying the uncaging approach, (2) providing information about passive cable properties, (3) reconsidering and/or discussing limits on synaptic reversal potentials, (4) extending modeling, e.g., to test whether passive cable properties might normalize PSP amplitude with distance; to more fully consider dendritic complexity; to explore the phenomenon with numerical simulation experiments that add plausibility arguments to the results. These points are explained in more detail in the reviewers' comments, which are included in full below.

The low input resistances measured in these neurons was cause for concern by reviewers 1 and 2. We address this issue in the revised manuscript in several locations. We have listed the input resistances measured at the soma in TTX in Table 2; these measurements are described in the Methods subsection “Electrophysiology and Dye-Fills”, presented in the Results subsection “Distributed reversal potentials in GM neurons are nearly invariant”, and interpreted in the Discussion subsection “Physiological Implications”. Reconciling the low input resistances (as measured at the soma) with the electrotonic compactness of these structures may not be intuitive. In the Discussion, we write: “Given that these neurons are electrotonically compact, the input resistance as measured at the soma is likely a reflection of the resistance across the membrane surface area of much of the entire neuron. Thus, it is not surprising that input resistances measured at the soma are relatively low (mean of approximately 10 MΩ (Table 2), consistent with many years of recordings from STG neurons). If the neuron were more electrotonically compact, the input resistance measured at the soma would be higher, as the measurement would be restricted to the surface area of the local, somatic membrane.”

In the revised manuscript, we sought to clarify that the goal of this work is to assess how the passive cable properties of these neurons may influence voltage signal propagation. Thus, the term “compartmentalization,” is used very carefully and in reference to that which may be imposed by the passive cable properties of these neurons. It is true that there are different mechanisms (synaptic inputs, voltage-gated ion channels, modulatory receptors) that may superimpose on the passive cable structures and effectively compartmentalize these neurons in the intact circuit. But, probing these other mechanisms is not the objective of this work, but an intriguing phenomenon to address in future work. In the Discussion, we write: “These experiments were done in TTX, wherein TTX-sensitive, voltage-gated sodium channels are blocked and circuit activity is silenced. […] Future experiments in varying pharmacological and modulatory conditions could shed let on how different voltage- gated currents, modulatory currents, and ongoing synaptic input during rhythmic activity, may effectively compartmentalize these otherwise compact passive neuronal structures.”

In the new manuscript, we present an expanded passive cable model simulation (subsection “Probing electrotonic structure with reversal potential measurements”) that clearly shows:

i) the independence of apparent reversal potential measurements on receptor density (or maximal conductance).

ii) the dependence of apparent reversal potential measurements on activation site distance from the recording site

the contingency of this distance-dependency on the electrotonic length constant (λ) This simulation utilizes a library of cable models with varying membrane and axial resistances and electrotonic length constants varying between 200 µm and 5 mm. By expanding the parameter and stimulus spaces of the simulation, we believe we have shown these three above results and resolved much of the confusion expressed by reviewers 1 and 2.

Courses of Action

In the general summary, we were asked to address these issues by taking the following courses of action:

Validating and/or justifying the uncaging approach. In the Introduction, we write that previous work had used dual recordings in the soma and primary neurite to probe passive filtering of high and low frequency voltage signals. However, “relevant voltage events must arise at more distal, finer processes, where pre- and post-synaptic connections are located (King 1976a, b; Kilman and Marder, 1996). […] We present a surprising case wherein geometrical complexity and variability appear not to constrain passive physiology”. We feel that this is justification for use of this methodology, which provides a means of activating voltage events at sites varying in distance from the recording site. Given the unmistakable relationship between the apparent reversal potentials for responses evoked across the neuronal structure and the electrotonic length constant (as described in subsection “Probing electrotonic structure with reversal potential measurements”), this methodology is an adequate approach to address our scientific objective.

Providing information about passive cable properties. As described above, the input resistance measurements are now listed in Table 2, described in the Methods and Results, and interpreted in the Discussion. The geometrical properties are also described: neurite lengths are shown in Figure 2, diameters are presented in Figures 5 and 8, and neurite taper in diameter is discussed in the subsection “Physiological Implications”.

Reconsidering and/or discussing limits on synaptic reversal potentials and extending modeling. Both of these points are addressed with the expanded passive cable simulations and are sufficient for addressing the clarified objective of this study.

Reviewer #1:

This study examines how variation in dendritic morphology influences synaptic integration in Gastric Mill (GM) neurons of the crab stomatogastric ganglion (STG). The authors combine somatic 2-electrode voltage-clamp recordings with focal glutamate uncaging experiments to show that the amplitudes of glutamate responses appear not to depend strongly on distance or variations in local dendritic geometry. These are interesting, experiments, and the questions addressed are of broad general interest. However, the paper suffers from the fact that the authors are constrained to infer dendritic properties from somatic recordings without any direct measurements, and there are assumptions about the nature of the glutamate uncaging that are not adequately justified. Also, the computer models do not explore the very dendritic complexity that the study purports to address. In the end, I don't think readers will be convinced that the current data set provides sufficient mechanistic insight into the nature of dendritic integration in GM neurons. My major comments are detailed below.

These experiments utilized two-electrode current clamp, not voltage clamp, at the soma to measure voltage responses evoked at varying distances from the somatic recording site. The objective of this work was not to address local dendritic integration; in the revised manuscript, we sought to clarify that the goal of this work is to assess how the passive cable properties of these neurons may influence voltage signal propagation. This concern has been addressed in response to the Summary above.

1) The premise of this study rests on the use of uncaged glutamate responses as a means to elicit uniform currents at many spatial locations in the dendrites. However, for this approach to be valid, the density of (presumably mostly extra-synaptic) glutamate receptors must be uniform across the dendritic arbor. While the uncaged responses appear quite reliable in Figure 4 at a given location, responses at adjacent locations in Figure 5 are highly variable, possibly reflecting variations in receptor density along the dendrites. There seems to be no systematic changes in response amplitude with local dendrite diameter or branch order, but it is not known what the amplitude of the responses are at the site of uncaging. With so many unknown free parameters (receptor density, surface area, local input resistance) it is not clear how these data can be interpreted cleanly. It is also not clear how these responses relate to the function of actual synapses, which according to the authors are located on the finer distal branches.

There were no efforts made to uniformly activate currents. The laser power, pulse duration, and glutamate concentrations were kept constant throughout the duration of the experiment (as described in the Results (subsection “Variable Glutamate Responses Across the Neuronal Structure”) and Methods (subsection “Focal Glutamate Uncaging”). This approach allowed us to measure the endogenous and heterogeneous glutamate sensitivities across different sites on a single neuron. The possibility of heterogeneous glutamate receptor densities as an explanation for the variable response amplitudes was discussed in the subsection “Variable Glutamate Responses Across the Neuronal Structure”, last paragraph, subsection “Distributed reversal potentials in GM neurons are nearly invariant”, first paragraph and subsection “Physiological Implications”, second paragraph. In the Discussion, we write: “Other neuron types compensate for passive attenuation of voltage responses with distance- dependent scaling of synaptic receptor density (Andrásfalvy and Magee, 2001; Magee and Cook, 2001; Smith et al., 1990). […] Because the response amplitudes across sites within each neuron show no quantitative dependence on distance from the recording site (Figure 5; Supplement to Figure 5; Table 1), it is unlikely that receptor densities are scaling with distance in a systematic way.” It is true that we cannot be certain of receptor densities without measuring responses at the photo-uncaging sites. Here, we wished to express that receptor densities appear not to scale so as to result in similar amplitudes after passive propagation to the somatic recording site (as has been shown in these other cited cases).

2) Considering how important passive cable properties are to the interpretation of the data, it is perhaps surprising how little information is provided about the actual passive electrical properties of GM cells. The only hint at these properties is the statement in the Methods that recorded GM cells had input resistances greater than 5 MΩ. This rather low value for input resistance (though perhaps not for invertebrate neurons) seems at odds with the authors' conclusion that GM neurons are electrically tight. There are modeling parameters reported in Table 2, but it is not clear whether these values are based on real measurements or just reasonable guesses. Some more detailed information about GM cell electrical properties would be helpful and important.

We have addressed this concern in response to the Summary above.

3) In general, synaptic reversal potentials are not sensitive predictors of the extent of dendritic compartmentalization. The manner in which reversal potentials are measured produces conditions that reduce the influence of dendritic filtering (since voltages during long command stimuli have reached a steady state). Also, voltages show less attenuation in the centrifugal vs. centripetal direction due to decreasing diameter and surface area of more distal dendritic branches. Williams and Mitchell (2008) elegantly explored these and other issues of dendritic filtering in neocortical pyramidal neurons…and yet these neurons show compartmentalized responses and significant attenuation of synaptic events propagating from the dendrites to the soma. The ability of a voltage clamp circuit to measure reversal potentials of distal synapses with reasonable accuracy does not necessarily mean that local and propagated synaptic responses do not depend on dendritic morphology.

Much of these concerns are addressed in response to the Summary above. It is true that voltage propagation may face different degrees of electrotonic decrement, depending on propagation direction. This question was not addressed in this work. Here, we measured voltage propagation in what might be considered the “centripetal” direction, although it is important to note that these neurons are not bipolar in structure, and that neurites serve as sites of both input and output (King 1976a, b). Our investigation of voltage propagation from neurite sites to the soma is relevant to the function of these neurons, given that synaptic events arise at secondary and higher-order neurites and must eventually propagate ‘centripetally’ toward the primary neurite and out to axonal projections to evoke spikes. As reviewer #1 stated, substantial decrement of voltage signals is seen in the centripetal direction in hippocampal neurons (Williams & Stuart, 2008). Our results are, indeed, a counter-example to what is seen in pyramidal neurons. We hope that readers will appreciate this result as a demonstration that not all neurons utilize the same strategies to produce reliable physiology, and that pyramidal neurons present one case in neuronal physiology, not the rule.

4) The discussion in the last paragraph of the subsection “Electrotonic Structure in Circuit Context" contrasts the authors' present results and interpretations with results from hippocampal CA1 pyramidal neurons, where distance dependent attenuation of synaptic potentials is compensated via an increase in postsynaptic AMPA receptors (not voltage-gated conductances, as stated in the manuscript). In neocortical pyramidal neurons, though, distance dependent compensation for much of the dendritic voltage attenuation of synaptic events arises from the passive electrotonic structure of the dendritic arbor (e.g. Williams and Stuart 2002). It seems to me that either or both of these mechanisms could potentially explain the current findings. Given that neither of these mechanisms is explored directly in the current study, I don't know that the authors are in a strong position to argue that GM neurons operate differently.

Our reference to distance-dependence scaling of AMPARs has been corrected for this error. We’ve addressed the remaining concerns in this comment in response to reviewer #1, point #1.

Reviewer #2:

This manuscript reports an unusual electrotonic compactness in one neuron type in the crustacean stomatogastric ganglion. The GM neurons have varied morphology and dendritic branching patterns, yet all respond similarly during the motor pattern they participate in. The authors argue that this is because the neurons are very electrotonically compact, and current loss from distal dendrites is small. The experiments to show this are well done and convincing, including an interesting failure to detect a distance dependence of the apparent reversal potential of the synaptic responses. They do no experiments to determine how this compactness occurs, nor do they provide any explanation for this result. This discussion is important because to a naive reader the results appear to contradict simple cable property measures of current flow in branched processes. If such explanation (preferably with experimental verification) were provided, this would be a much stronger manuscript.

We hope that we have adequately addressed the general concerns of reviewer 2 by: 1) adding a section to the Discussion titled “Physiological Implications,” which discusses possible mechanisms for electrotonic compactness and 2) expanding our cable model simulation to more clearly demonstrate the direct relationship between apparent reversal potential invariance, across activation sites varying in distance from the recording site, and electrotonic structure.

This more comprehensive simulation also serves as justification for our experimental approach.

[Editors' note: the author responses to the re-review follow.]

Essential revisions:

The reviewers agreed that the appealed and revised version of the manuscript was improved, with many clarifications of the points that were initially raised. Two essential points remain:

1) The first, extensively discussed by the reviewers, has to do with whether the conclusion that morphology has relatively little effect on voltage responses is adequately supported by the modeling, given that the specific parameters of neurite morphology were not considered. Reviewers recognized that the main point may not be to rule out the idea that any dendritic computations took place, but rather that the slow graded signals characteristic of these cells are not greatly affected by morphology; nevertheless, it was acknowledged that this distinction could be emphasized further. As stated in the consultation, "The main thesis of the paper is that a long length constant of the neurite allows voltages from anywhere in the dendritic tree to propagate throughout the cell with minimal voltage attenuation, so the passive properties of their specific cell morphology is a central concern." One way to address this point, would be to import a real GM cell morphology into NEURON and express their passive properties uniformly in all compartments to test (a) whether the voltage attenuation or amplitude at the soma similar for long currents injected in distal neurites and (b) whether the length constant depends significantly on direction of propagation. The outcomes could serve either to support the results or place appropriate constraints on the conclusions. However, the reviewers agreed to leave the specific way of allaying these concerns to you, i.e., such a model is not required if you find alternative ways to clarify and/or limit the conclusions. The original "major comments" on this matter are included below for your reference, to guide and inform your revision.

We have chosen not to pursue additional modeling of a realistic GM morphology in NEURON for three predominant reasons:

i) The first reason is scientific. One take-home message of this work is that similar physiology can arise from variable morphologies. Thus, it is not scientifically sound to upload one GM neuronal structure into NEURON as a means of elucidating ubiquitous biophysical mechanisms underlying their compact electrotonic structures, when it is evident that there are many solutions.

The purpose of the reduced cable model in this manuscript (as in the present and original submissions) is to provide a theoretical but intuitive explanation for the experimental approach. On the other hand, a model of a fully reconstructed neuron would strive to provide a mechanistic explanation of the result. Due the issue of multiple solutions, a model of one fully reconstructed neuron would not yield more insight than that of the discussion regarding biophysical mechanisms provided in the Discussion of the manuscript.

ii) The second reason is practical. We are not equipped to accurately model the full neuronal structure in NEURON due to three issues pertaining to the cross- sectional areas of STG neurites being ovular, rather than circular. (1) We do not have the data for the cross-sectional areas of all the neurites composing any one neuronal structure. This is partially because no reconstruction software, to our knowledge, allows manual tracers to assign non-circular cross-sections. And, the collection of these data, even if possible, would take months. To date, this is why we have chosen skeletal reconstructions for interrogation of STG neuronal morphology. (3) NEURON assumes circular cross-sections, making it impossible to accurately model these neurons. (3) We would have to “make up” data about the ion channel distributions over the extended cable.

iii) The final reason is of a philosophical nature. In the present study, the data provide an interesting story in their own right: GM morphology is complex and variable; this variability may be masked by compact electrotonic structures. The data stand on their own.

However, we have addressed the reviewers’ concerns by clarifying the text of the manuscript with the following:

i) In the Introduction we emphasize the arrangement of pre- and postsynaptic sites and spike initiation zones on the neurite tree and explain the physiological relevance of current flow direction in these neurons. This is important because it provides a rationale for our assay of electrotonic structure. We write:

“Synaptic transmission between neurons is predominantly graded, inhibitory cholinergic and glutamatergic transmission (Eisen and Marder, 1982; Marder and Eisen, 1984; Maynard and Walton, 1975; Graubard, et al., 1980; Manor et al., 1997, 1999). […] This juxtaposition of synaptic input and output suggests that current will flow in all directions across the neurite tree, centripetally and centrifugally, in the intact circuit, and allow for integration of voltage signals arising from disparate loci on the neurite tree, should the neuron be sufficiently electrotonically compact.”

ii) In the Results section, we specify the direction of current flow in both the cable model simulations and the physiological experiments. We write:

“In this simulation paradigm, current was injected at the recording site and flowed from the recording site to the stimulation site, changing the membrane potential at the distal site. […] Even so, the observations of sizeable voltage events at the recording site and reasonable reversal potentials are suggestive of a level of electrotonic compactness that is relevant to voltage signal propagation in either direction”

“Using two-electrode current clamp at the soma, we measured apparent Erevs of local inhibitory responses evoked by focal photo-uncaging of glutamate at positions varying in distance from the somatic recording site. In these experiments, current was injected at the somatic recording site and flowed centrifugally from the recording site to the photo- uncaging site, changing the membrane potential at this distal site.”

iii) In the Discussion, we revised our interpretation of the data and discuss how the result relates to the direction of the current injection and direction of initiated voltage signal propagation. We write:

“In GM neurons, synaptic voltage events may propagate tortuous neurite paths that extend beyond half a millimeter in length (Figure 2). […] In this sense, these neurons function almost like a single compartment, despite their complex structures.”

2) The second point has to do with the placing constraints on the basis for electrotonic compactness. The Discussion mentions two possible explanations for how neurons with very low input resistance can be so electrotonically compact: very low internal resistance due to large diameter of initial processes (though this would not apply to the fine processes where the input-output synapses are located) and possibly high membrane resistance at branch points (though this would not block the passive spread of current along the internal resistance of the branches). The reviewers pointed out that it would be informative for the estimates of the length constant (1.5 mm) to be integrated with measurements of the input resistance (~ 10 MΩ) to come up with boundaries of Ri and Rm (given that Rin = (2/π)(RmRi)1/2(d)3/2 for a semi-infinite cylinder, and λ= ((RmRi)(d/4))1/2 (from Rall, 1977).

As suggested, we did a series of calculations yielding values of Ri (Ω · cm) and Rm (Ω · cm2) for specified diameters (d), the observed average Rinput (10 MΩ), and predicted upper bound for λ (1.5 mm). For example, if d = 0.5 µm, Ri = 30 µΩ · cm and Rm = 550 µΩ · cm2. If d = 20 µm, Ri = 1.97 Ω · cm and Rm= 0.88 Ω · cm2. We have chosen not to include these calculations because exact values for Rmor Riwould not do justice to the complex and variable structures observed across animals.

As a conceptual point, we estimated an effective λ (which is an upper bound) for the entirety of the neuronal structure. Presumably, the λ of specific segments of neurite may vary, depending on their biophysical and geometrical properties. As shown in Figure 6, neurite diameters (at the photo-uncaging sites) can range between 0.5 µm < d < 20 µm. In another anatomical study (Otopalik, et al., in review), we find that diameters of primary, secondary, tertiary, and terminating neurites can vary widely. While there is a trend of decreasing diameter from primary neurite to tip, a given neurite path does not necessarily taper linearly or exponentially with distance. In fact, diameters can increase and decrease non-systematically with distance (this can be observed visually in the confocal micrographs).

Given the wide range of diameters and λ values expected to arise across these neurite trees, one is left with an infinite matrix of possible combinations of resistivities and diameters that would yield the range of λ values sufficient for producing the compact neuronal physiology demonstrated in these experiments.

Comments related to Essential revision 1:

1) My main concern, before and now, has to do with whether the authors have truly shown that dendritic morphology plays little role in shaping voltage responses. The authors' argument is that the dendrites and soma are nearly equipotential, and that as a result inputs on any part of the structure have similar voltage contributions throughout the arbor. I don't see that this hypothesis has been adequately supported because the modeling does not take into account the actual neurite morphology the authors have quantified. The simulations in Figure 7 show that under conditions favorable for voltage propagation (a moderately large, constant diameter neurite exhibiting a long 800 µm length constant), there is still >50% attenuation of PSPs along its length despite the fact that the Erev can be accurately measured at these same distances. But the authors show in several figures (e.g. Figure 5) that there are striking reductions in diameter in the more distal regions, which will impart a directional asymmetry in the efficacy of voltage propagation. In a passive neuron, centrifugal propagation will be more effective in a tapering structure such as the one exhibited by GM neurons, which help explain why Erev can be measured so effectively even at distal uncaging sites in experiments. However, propagation toward the larger diameter neurites and soma will be comparatively unfavorable. The simulations in Figure 7 may thus underestimate the attenuation of voltages during propagation toward larger neurites.

I think the authors need to examine voltage propagation in a realistic morphological structure. If a conductance is introduced in neurites of differing orders, diameters and distances from the soma in a model neuron with realistic morphology, would these events yield comparable voltages at the soma? I do not expect that the authors must necessarily provide a full mechanistic explanation for their results, but I think such an examination would provide a better understanding of how spatially compact GM neurons are under more realistic conditions, and whether passive properties are sufficient to explain their uncaging results.

[In the words of another reviewer:] The other issue to discuss (also from Rall) is the large difference in voltage attenuation depending on the direction of the current flow (from a single dendritic point to the soma vs. from the soma to the dendrites). Your measurements of ipsp amplitude after stimulation at a single point are examples of the first, while your measurements of the Vrev from the soma are examples of the second. I think this will not be a problem for your analysis, but it should be explicitly discussed in the Discussion. The integration of spatially distributed synaptic inputs by the neuron would be an example of current flow from the periphery to the center, and from basic principles might show more attenuation.

2) There were some misunderstandings concerning my previous comments regarding the diversity of responses at adjacent locations and the lack of diversity of responses from neurites of different diameters. Put a different way, if a similar response is obtained from uncaging a 10 µm spot over a 1 vs. 10 µm diameter neurite (for example), does this not imply that there must be some other mechanism(s) in place to boost the amplitudes despite the 10-fold reduction in surface area and receptor density? A higher local input resistance might raise the local PSP amplitude, but such a mechanism might be limited due to the proximity of the reversal potential to rest. The authors have stated in their rebuttal that their concern is with voltage propagation and not local integration, but it seems to me that both issues are interrelated and central to understanding the results of their uncaging experiments.

These above concerns are addressed above in response to Essential revisions 1 and 2.

3) In their rebuttal, the authors state that it is unlikely that receptor densities change along the dendrites because the "response amplitudes across sites within each neuron show no quantitative dependence on distance from the recording site." This assumes there is no significant centripetal attenuation of voltage, but as detailed earlier, there is some uncertainty in this premise. If there is even moderate voltage attenuation between the small diameter, distal neurites and the soma, would not another mechanism be needed to restore the amplitude of the response?

In fact, we state that receptor densities across neurite sites likely do vary. But, our data suggests that they do not vary in a manner that is distance- or diameter-dependent. Because the reversal potentials are relatively constant across sites, we can rule out that the cable properties give rise to these variable response amplitudes. Thus, we are left with receptor density as the main determinant in voltage response amplitude heterogeneity. If receptor density scaled with distance or diameter (in such a way that compensated for these geometric properties) we might see a zero-slope in the linear fits, suggesting that voltage signal decrement is normalized by increasing receptor densities; or perhaps we would see increasing amplitude with distance, which might suggest over-compensation of receptor density; regardless, we would see some quantitative trend. To clarify our interpretation, we have re-written a section to read:

“Because the response amplitudes across sites vary in a manner that is independent of distance from the recording site (Figure 5; Figure 5—figure supplement 1; Table 1), it is unlikely that receptor densities are scaling with distance in a systematic way.”

https://doi.org/10.7554/eLife.23508.023

Article and author information

Author details

  1. Adriane G Otopalik

    Volen Center, Biology Department, Brandeis University, Waltham, United States
    Contribution
    AGO, Conceptualization, Data curation, Software, Formal analysis, Funding acquisition, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing
    For correspondence
    aotopali@brandeis.edu
    Competing interests
    No competing interests declared.
    ORCID icon 0000-0002-3224-6502
  2. Alexander C Sutton

    Volen Center, Biology Department, Brandeis University, Waltham, United States
    Present address
    Boston Consulting Group, Boston, Massachusetts, United States
    Contribution
    ACS, Software, Writing—review and editing
    Competing interests
    No competing interests declared.
  3. Matthew Banghart

    Department of Neurobiology, Harvard Medical School, Boston, United States
    Present address
    Neurobiology Section, Division of Biological Sciences, University of California San Diego, San Diego, United States
    Contribution
    MB, Resources, Supervision, Methodology
    Competing interests
    No competing interests declared.
  4. Eve Marder

    Volen Center, Biology Department, Brandeis University, Waltham, United States
    Contribution
    EM, Conceptualization, Resources, Supervision, Funding acquisition, Writing—original draft, Writing—review and editing
    For correspondence
    marder@brandeis.edu
    Competing interests
    EM: Deputy editor eLife
    ORCID icon 0000-0001-9632-5448

Funding

National Institute of Neurological Disorders and Stroke (F31NS092126)

  • Adriane G Otopalik

National Institute of Neurological Disorders and Stroke (R37NS017813)

  • Eve Marder

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

Acknowledgements

We thank: Frank Mello for assistance in constructing mechanical components of rig; Bernardo Sabatini for optics expertise while constructing the custom microscope; Matthew Stenerson and Richard Ho for manual tracing of neuronal dye-fills; Philipp Rosenbaum for completion of several technical experiments; Cosmo Guerini for generating additional analytical tools in Python; Edward Dougherty and the Confocal Imaging Lab at Brandeis University.

Reviewing Editor

  1. Indira M Raman, Reviewing Editor, Northwestern University, United States

Publication history

  1. Received: November 21, 2016
  2. Accepted: February 6, 2017
  3. Accepted Manuscript published: February 6, 2017 (version 1)
  4. Version of Record published: February 23, 2017 (version 2)

Copyright

© 2017, Otopalik et al.

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.

Metrics

  • 1,728
    Page views
  • 376
    Downloads
  • 2
    Citations

Article citation count generated by polling the highest count across the following sources: PubMed Central, Crossref, Scopus.

Comments

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)

Further reading

    1. Neuroscience
    Simon Nimpf et al.
    Research Article Updated
    1. Cell Biology
    2. Genes and Chromosomes
    Wei Zhang et al.
    Research Article Updated