Figures and data
LUNA-based platform for CSR single-cell imaging and illustration of optical principle.
a, Schematic of hypothesized single-cell bacterial CSR inferred from population-level OD analysis. The red dashed line indicates the time of cold shock (CS) application. After CS, OD ceases to increase, entering an acclimation phase, after which it resumes increase. At the single-cell level, possible cellular size changes following CS include decrease, stasis, or continued increase. b, Schematic of our bespoke LUNA-based platform. Diagram includes the phase-contrast imaging unit, microfluidic-compatible temperature control device and LUNA optical path. Circulating water is indicated by the color cyan. In LUNA, laser beam is reflected into the main optical train by a dichroic mirror. Red dashed line: reflected light. FC, fiber collimator; CL, cylindrical lens; DL, detector lens; FLE, focal length extender. The implementation of LUNA follows this design. c, Computed intensity distribution in the dimensionless space under 100× objective. Computations were performed using the optical model: An off-axis Gaussian beam propagates through an objective lens of radius a and focal length f. Coordinates (x’, y’, z’) equals (kβx, kβy, kβ2z), where k is wavenumber, β = a / f. Images at each axial position were individually normalized. Triangle markers indicate the crescent spots. d, Computed intensity distribution in x-z space. The dashed line indicates the centroid locations of the brightest crescent spots along the z-axis. Image contrast was adjusted for better exhibition (Gamma = 0.5). e, Magnified defocus distance on the detection plane in the ray tracing simulation. Linear regression with slope (95% confidence intervals) and fit goodness is shown. Scale bar, 60 µm. f, Working principle of LUNA. Set Plane1 (Plane2) as the interested focal plane by specifying the centroid location of the line spot on the detector as the origin. The defocus distance Δz between the target and defocused Plane2 (Plane1) is inferred by the displacement Δd. Autofocusing is then achieved by repositioning the spot to the origin. RI, reflection interface; Obj., objective.
Comprehensive performance metrics of LUNA.
a, Focus drift monitoring at 1 Hz in the laboratory environment. Right histogram shows the focal plane positions after each autofocusing procedure. b, Focusing accuracy and precision assessment. Dots and error bars represent the mean and s.d. values of the focus errors. Color palette in b, c, different set thresholds. c, Focusing time measurement for autofocusing procedures at different intervals. Lines those marked with dots emphasize the representative constraints. d, System states over time when imaging bacteria. CS occurs at t = 0. T, temperature of cell environment; RD, relative drift of sample stage before autofocusing; FT, corresponding focusing time. Data in scatter form represent the average of all imaged sites (n = 45). Shaded region indicates the rapid temperature drop period. Error bands in c, d, s.e.m. e, Representative images and onset of autofocusing procedure. Scale bar, 4 µm. Intervals between consecutive procedures indicate the time consumption of phase-contrast imaging and stage motion.
Investigation of single-cell dynamics in CSR using LUNA.
a, Temporal montage of a single microchannel in the microfluidic chip. CS occurs at t = 0. Image was superimposed by cell contours with identified colors according to their generation marks. Timeline unit, hour. Intervals in the left and right panels are 6 and 10 mins, respectively. Scale bar, 4 µm. b, Average growth dynamics of cells. Arrhenius range of growth is shaded in inset. c, Growth deceleration as function of time. The time window of the three Phases is 0-3 min, 3-10 min and 10-120 min, respectively. Error bands in b, c, s.e.m. d, Temperature dependence of growth rate during the dynamic cooling process. Linear fitting to the reciprocal temperature and logarithm of λ is shown as line. Dot lines indicate the 95% prediction bounds. Arrhenius range of growth is shaded. e, An illustration of the allocation of different proteins synthesis at different stage during CSR. Percentage data were retrieved from reference5. f, Average elongation rate across generations as function of normalized interdivision time. g, Average growth rate across generations as function of normalized interdivision time. Error bands in f, g, s.e.m. The color code in f and g marks the same generation as in a.
Cell size regulation and growth synchronism under CS.
a, Notations in cell cycle. ξ, relative CS onset time since cell birth; τd, interdivision time. Dashed cells, expected exponential growth in the steady-state. b, Percentage change of division length of each generation after CS compares to GN. Data are presented as box plots with the edges at the 0.25 and 0.75 quantiles, the central line at the median, and the whiskers at the minima and maxima within 1.5× interquartile range from the box. Circles, outliers outside the whiskers. Each box is located at the average division time of that generation. c, Percentage change of division length of each group between G0 and their corresponding predecessors. Data are presented as box plots as in b. d, Relationship between length extension and birth length across generations (rescaled by the expectation of Lb). Gradient colors indicate data density of each generation. Linear regressions of all the measured cycles and Kendall’s τ are shown. n represents cycle number. e, Lag matrix for distinct groups of ξ. Values were computed by locating the cross-correlation maximum. f, Representative lineages with synchronized elapsed cycles (ξ is 0.10 and 0.90, respectively). e.c., elapsed cycles. g, Elapsed cycle numbers of all the grouped lineages as functions of time. Errors shown in Figure S14b.
Analysis of CS experiments of batch culture.
a, Measurements with temperature dropped to 14 ℃. Measured and computed OD600 values (top). Computed data was scaled at t0. Bottom: cell concentrations and average volumes extracted from the flow cytometer, normalized to t0 and average value before CS, respectively. Relative cell density ρdry was computed and scaled for present. Shaded region indicates the acclimation. b, Theoretical σ across a range of equivalent cell volumes of simulated cells. Power exponent was determined by linear regression on the logarithmically transformed data (R2 = 0.996, confidence interval is ±0.01). c, Computed σ from experimental data as function of relative volume. Power exponent was obtained as same process in b (R2 = 0.971, confidence interval is ±0.12). Dashed lines indicate the 95% prediction bounds. a.u., arbitrary units. d, Computed total dry mass plotted as a function of OD. The solid line represents a linear fit forced through the origin, based on the physical constraint that mass must be zero at zero OD. Fitting for the acclimation has a R2 of -0.263 (Pearson correlation coefficient -0.00). Mass increment during the acclimation is indicated as the height of the shaded area and marked in the inset. Error bars in a, c, d, s.d. e, Total protein measurement of MG1655 strain. Temperature drops to 12 ℃ were performed.
Incident beam at the pupil plane.
The radius of the objective pupil is a. The dashed circle indicates the incident beam. The origin of polar coordinates (ρ, θ) is the pupil center. The origin of polar coordinates (r, φ) is the incident beam center (ρ0, θ0).
Convergence of intensity calculation with increasing series terms.
Relative differences (%) compared to direct calculation of the double integral is shown. Five locations (u) on the optical axis were chosen.
Computation time comparison between direct and simplified methods for varying pixel size.
Lines, average time cost; error bars, standard deviation.
Computed intensity distributions corresponding to different AC values.
Image contrast was adjusted for better exhibition (Gamma = 0.5). k is wavenumber, β = a / f.
Calculated values of scaling ratio in the simulation.
Color bar represents scaling ratio S / V0.66 for each cell. White contour lines indicate the elevation.
Gating strategy for isolating target cell population.
Enclosed areas with colored lines: selected particle subpopulations, marked with data percentage.
Time-lapse experiment with induced temperature downshift using commercial microscope.
Time-lapse phase-contrast imaging of E. coli cells in a microfluidic chip (1 min interval, 20 position of views) was performed using a commercial microscope (Nikon Instruments, Ti2 with autofocusing unit PFS). The microscope stage and objective (100×, with lens heater) were enclosed in an incubator-style chamber with an external air-heating unit. Temperature was maintained at 37 ℃ until the start of cooling (t = 0), when the heating unit (and the lens heater) was turned off. The flow medium for cells was replaced with 10 ℃ medium, and the chamber cooled passively to room temperature (temperature stabilized at 25 ℃ after ∼60 min). The commercial autofocusing unit remain active throughout the experiment. Representative images from selected time point are shown.
Optical model schematic and computed contrast comparison.
a, Schematic diagram of the optical model. An off-axis Gaussian beam (red lines) propagates through an objective lens of radius a and focal length f. Q, point in which a light ray in the image space intersects the reference sphere that approximately fills the objective pupil; P, arbitrary point near focus. b, Comparison of spot contrast with and without coma aberration. The contrast-to-noise ratio metric, which influences the detection accuracy of the focus state, was introduced to evaluate the spot quality. Metric values were calculated from the computed intensity distribution images at different axial position. Coordinate z’ = kβ2z, where k is wavenumber, β = a / f. Inset image: Airy pattern at -90 axial position in the dimensionless space in an aberration-free system.
Ray tracing simulation of LUNA’s optics design.
a, Comparison of numerical simulation and implementation. Left panel: Retrieved images from the detection planes in the simulation and LUNA implementation, respectively. Right panel: intensity profiles along the lines in both images. px, pixel. b, Intensity on the entrance pupil plane in the simulation. Polar coordinates were normalized by the aperture of the objective (100×). Colored lines indicate isophotes. Beam center distance is approximately ρ0 = 0.15. c, Intensities on the reflection planes in the simulation. Images at each axial position were individually normalized. Triangle markers indicate the outermost crescent spots. d, Magnified defocus distance on the reflection plane. Linear regression with slope (95% confidence intervals) and fit goodness is shown.
Flowchart of LUNA.
FP, focal plane; AM, effective magnification from axial position to centroid location; XF, focal plane location; Δz, detected drift; TD, set threshold; PI, proportional-integral controller. Morphological process costs ∼2 ms for a single captured image from LUNA’s detector on the control computer with 3.60 GHz CPU.
Supplemental performance metrics of LUNA.
a, Calibration curve (left) and measurement error distribution (right) for representative objectives. Shaded regions in the left panels indicate the linear range of the corresponding objective. Linear regressions with slope (95% confidence intervals) and fit goodness are shown. b, Focusing accuracy and precision assessment. Dots and error bars represent the mean and s.d. values of the focus errors.
Evaluation metrics of linear regressions under different range.
The regression range was symmetrically selected with the zero point as the center and multiples of the corresponding DOF. Critical N multiples of DOF was determined by restricting the fitting root mean squared error (RMSE) less than 1. Numbers in the subscripts indicates the objective magnification.
Impacts of intensity fluctuations on focusing accuracy.
All data for the 10 set thresholds are presented as box plot with the edges at the 0.25 and 0.75 quantiles, the central line at the median, the width at the standard deviation, and the whiskers at the minima and maxima within 1.5× interquartile range from the box. Colored dots indicate average power stability of the 10 thresholds (right legend). Colored line, probability distribution.
Ridgeline plot of relative drift after the previous autofocusing procedure.
Drift distributions under different set thresholds at 1 Hz measurement. Colors indicate different set thresholds, unit in nm.
Cumulative distribution function of focusing time at 1 Hz measurement.
CDF, Cumulative distribution function. Colored lines indicate different set thresholds, unit in nm.
Stage drift over time.
Data in scatter form represent the average of all imaged sites (n = 45). Shaded region indicates the rapid temperature drop period. Error bands, s.e.m.
Quantitative image analysis and drift calibration.
a, Microfluidic Architecture based Resilient Contour Expansion Analysis (MARCEA) pipeline. ROI, region of interest. b, Lateral drift of imaging sites over time. Data in scatter form represent the average of all imaged sites (n = 45). Shaded region indicates the rapid temperature drop period. Error bands, s.e.m.
Dynamic details of grouped lineages.
a, Elongation rate details of distinct ξ across generations. b, Growth rate details of distinct ξ across generations. In a, b, only 5 of 9 groups are shown; Error bands, s.e.m.
Growth dynamics of different group of cells.
Average curve indicates the value of all cells. Arrhenius range of growth is shaded in inset. Error bands, s.e.m.
Synchronization in elapsed cycle number.
a, Elapsed cycle numbers that centered by the average of all lineages as functions of time. b, Errors (s.e.m.) of elapsed cycle numbers as functions of time. Each group is centered by the average.
Numerical simulations based on scattering theory.
a, Illustration of light scattering by a cell in the suspending medium. A small portion of scattered light is collected by the detector. b, Relative angular scattering intensity of single bacteria computed through the numerical simulation. V, equivalent volume in µm3. c, Simulation of cells with varying parameters. Color bar represents computed total cross section σ for each cell. White contour lines indicate the elevation of σ.
Supplemental results of batch culture.
a, Measurements with temperature dropped to 12 ℃. Measured and computed OD600 values (top). Computed data was scaled at t0. Bottom: cell concentrations and average volumes extracted from the flow cytometer, normalized to t0 and average value before CS, respectively. Relative cell density was computed and scaled for comparison. Shaded region indicates the acclimation. b, Computed σ from experimental data as function of relative volume. Power exponent was determined by linear regression on the logarithmically transformed data (R2 = 0.913, confidence interval is ±0.17). Dashed lines indicate the 95% prediction bounds. a.u., arbitrary units. c, Computed total dry mass plotted as a function of OD, together with linear fittings. Fitting for the acclimation has a R2 of -0.741 (Pearson correlation coefficient -0.59). Mass increment during the acclimation is indicated as the height of the shaded area and marked in the inset. Error bars in a-c, s.d.
Supplemental results of batch culture without temperature downshift.
a, Measured and computed OD600 in the batch culture without changing temperature. b, Correlation of measured OD600 in a with cell concentration and computed dry mass. Linear fittings were performed by data points within shaded area of which OD < 0.5. R2 of the fitting is shown. Error bars in a, b, s.d.
Percentage change of dry mass and OD600 during the acclimation.
Temperature drops to 12 ℃ and 14 ℃ were performed separately for both strains: MC, MC4100 strain; MG, MG1655 strain. TP, total protein of MG1655 strain.
LUNA performance results with different objective lenses from Nikon.
