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The authors have declared that no competing interests exist.

Conceived and designed the experiments: TU RMWC SW DB KCH. Performed the experiments: TU RMWC SW. Analyzed the data: TU RMWC DB KCH. Contributed reagents/materials/analysis tools: TU RMWC SW. Wrote the paper: TU RMWC DB KCH.

The emergent behaviors of communities of genotypically identical cells cannot be easily predicted from the behaviors of individual cells. In many cases, it is thought that direct cell-cell communication plays a critical role in the transition from individual to community behaviors. In the unicellular photosynthetic cyanobacterium

Communities of bacterial cells exhibit social behaviors that single cells cannot engage in alone. These behaviors are often a product of direct interactions that allow cells to communicate with each other. In the unicellular photosynthetic cyanobacterium

The collective migration and spatial organization of cellular communities are often the result of integration of chemical signals

One such example of community behavior is the directed surface-dependent motility of cyanobacteria either toward or away from a light source

To dissect this community behavior, we developed a minimal biophysical reaction-diffusion model based on our experimental observations in which cells undergo a light-biased random walk with motility dictated by the local concentration of a cell-secreted substance. Simulations based on this model recapitulate the wide range of observed motility patterns. Furthermore, exploration of the phase space of this model showed that varying the cell density, light bias, and persistence of the cell-dependent surface modification could tune the shape, dynamics, and steady-state speed of the community, consistent with experimental observations. Based on physical arguments and our computational modeling, we present heuristics for the scaling of these features that could apply to a broad class of motile, structured communities. We were also able to confirm key qualitative predictions of our model by performing experiments in which we systematically varied the initial cellular concentration of the community. Thus, the computational models developed in this study predict that the physical properties of cellular microenvironments play a critical role in regulating single-cell behavior and that these behaviors are transduced into community organization.

We used a well-established phototaxis assay in which a small volume of exponentially growing

A) Time-lapse imaging of a

The spatially separated, finger-like projections were surrounded by an optical halo distinguished by a different index of refraction from the surface (

A) Typical fingering of a

When the cells in one finger encountered the trail left by cells in a neighboring finger, we observed two changes that indicated that the trail affected motility. First, cells in the merging finger sped up upon encountering the trail left by a neighboring finger: both the mean and width of the velocity distribution increased approximately three-fold, indicating a faster and less coordinated group of cells (

Our finger merging experiments indicated that the motility and coherence of cellular groups at the tips of

A) As shown schematically, each cyanobacterium (green) is assumed to undergo a biased random walk toward the light source (LED). Each cell secretes EPS (blue), whose local concentration increases the cell's mobility

We assume that cells produce EPS at a constant rate _{s}_{0} is the maximum mobility in the presence of saturating EPS.

In the absence of a directed light source, we assume based on the observed, approximately random walk behavior that the cellular concentration spreads diffusively over time

For simplicity, we ignore reproduction in all of the following simulations in order to define the phase space of community patterns in terms of a fixed total cellular mass _{s}_{0},

In order to determine the conditions under which our model predicts phototactic fingering to occur and the types of spatiotemporal dynamics that are accessible, we explored the phase space of emergent behaviors by solving our reaction-diffusion model (

In these simulations, the direction of light bias (white arrows) is rotated 90 degrees between frames 1 and 2. The cells (green) leave an EPS trail (red), and when a finger intersects the EPS trail left by a neighboring finger, the group of cells speeds up and spreads out (blue arrows, frame 3). We observed the same qualitative changes in finger merging experiments (

These simulations of cellular and EPS concentrations exhibited morphological and dynamic properties that were amenable to quantification (

Using computational image processing at each time point, we quantified the number of fingers and their ramp time, size, and speed. The inset shows the cells (orange), cell front morphologies at evenly-spaced time points (blue contours), the group center positions over time (green lines), and the EPS field at the final time point (grayscale). These data provide a set of quantitative metrics for mapping model parameters to community behaviors.

To quantify the extent of the region of parameter space for which our model produces morphologies relevant to the biological system, we used simulations to comprehensively map the space of possible community behaviors by varying the dimensionless total cellular biomass and the dimensionless light bias strength (

A) Simulations grouped into classes as a function of dimensionless bias force and mean cellular concentration, resulting in the phase diagram shown on logarithmic axes. Colored circles represent parameters with a sufficient degree of directed movement and cell front instability to result in simulations with finger-like morphologies. Different shades correspond to the values of the bias force. In the simulations represented by the grey circles, cells move in a directed fashion toward the light source but do not spontaneously gather into groups due to high cell density, and thus high local EPS production. For the simulations represented by the black circles, little to no cellular movement resulted due to insufficient EPS production and/or bias force. Numbers correspond to the frames in (B). B) Representative morphologies at the end of simulations with parameters from different regions of the phase diagram. In numbered frames, cells are shown in green, EPS is shown in red, and orange indicates co-localization of cells and EPS. The simulations in frames 1–4 have finger-like morphologies with varying group sizes and spacing. The simulation depicted in frame 5 has a moving but uniform cell front (i.e., no distinct groups), while frame 6 reflects a simulation of essentially non-motile cells.

Given the complex range of behaviors represented in our simulations, we wrote custom software to quantify the community morphologies at every simulation time point (

For the subset of parameters that exhibited finger-like projections, we quantified motile group size, speed, and ramp time as a function of mean cellular concentration (_{0} and _{s}_{0} and _{s}

A) The number of cells in each motile group as a function of initial cellular concentration follows an approximately linear relationship independent of bias force (gray dashed line). B) The mean speed of cellular groups approximately follows a 1/3-power law. C) The ramp time associated with the formation of finger-like morphologies follows an approximately inverse square-root power law. D) The number of cells in each finger and the speed toward the light source are positively correlated for all bias forces. In all panels, colors refer to the bias force legend and correspond to dots in the phase diagram of

In our simulations, each finger reaches a steady-state velocity that approximately scales as the mean cellular concentration to the 1/3 power (

For the initial, transient phase of our simulations, when cells begin to aggregate into distinct fingers, the ramp time is the time scale over which the fingers reach a terminal velocity. In this phase, the bias force leads small collections of cells to move forward with an approximately constant velocity as they travel over the EPS left by cells in front of them. The cells eventually collect at the leading edge of the initial cellular deposition, a behavior that mimics the crescent morphology observed experimentally in

These physical arguments indicate that the rate of finger development, number of cells in a finger, and finger speed are all positively related to mean cell concentration and to each other, at all relevant bias forces (

Phototaxis time-lapse of _{730} (from left to right) of 0.6, 0.8, 1.0, 1.2, and 1.4. Time-lapse images were taken at 0, 11, 24, 36, and 49 hr. The images show a negative correlation between initial cell density and time to finger formation, and a positive correlation between initial cell density and number of cells in each finger, both of which are trends predicted by our biophysical model. Scale bar is 1 mm.

While all experiments performed with sufficient initial cell number and in the presence of a directed light source showed the formation of distinct fingers at the front edge of the spot of cells, some experiments also displayed fingers forming within the deposition area (

A) Experimental example of cells splitting into multiple fronts that head toward the light source. B) Phase diagram of the EPS decay model at a constant bias force. In the red region, cells form discrete, motile groups that head toward the light source in one or more cellular fronts. In the gray region, cells move toward the light source but do not form discrete groups. In the black region, cells are essentially non-motile due to insufficient EPS production and/or rapid decay of EPS. C) Late time-point snapshots of simulations from regions of the phase diagram in (B), with a light source at the top (green, cells; red, EPS; orange, colocalization of cells and EPS). Frames 1–4 depict results from simulations in the red region in (B), in which multiple fronts with finger-like morphologies can form similar to (A) with varying group sizes and numbers of distinct cell fronts. Groups of cells behind the primary front often catch up by following EPS trails left by forward groups (inset of frame 2). Frame 5 is from a simulation in the gray region of (B), in which cells move toward the light but do not form discrete groups. Frame 6 depicts the result from a simulation in the black region of (B); the cells are essentially non-motile. Scale bars are 1 mm.

For a given cellular concentration, the EPS concentration plateaus at a steady-state value

We performed simulations using our reaction-diffusion model with

Interestingly, in simulations that resulted in multiple fronts, motile groups that formed later and hence lagged behind the most forward groups often advanced by following the transient EPS trails of earlier fingers. Upon catching up, the two groups coalesced to form a larger, faster moving group that even more easily followed other transient EPS trails (

We have developed a minimal biophysical model of the phototactic motility of

Our model predicts the formation of distinct groups of cells (fingers) under a variety of light intensities (bias) and cell densities (

Secreted EPS provides information about the concentration of cells that have recently resided at a particular location on the surface, a situation similar to chemical quorum sensing in which autoinducer molecules indicate the cell density of the population

Our goal is to connect the microscopic cellular properties incorporated into our model with the macroscopic, observable behavior of cellular communities. Whereas previous models explicitly assumed that neighboring cells experience local interactions or that cells switch between discrete states associated with different behaviors

Our use of a mean-field reaction-diffusion model assumes that the stochasticity of single-cell movement can be averaged over the population of cells; similar models have been applied to intracellular protein networks

The role of the local microenvironment in regulating both motility and the structure of the community can have a strong impact on a wide range of biological systems, including the migration of germ layer progenitor cells in the developing zebrafish embryo

_{730} = 0.6–1.3 (25,000–55,000 cells/µL; measured with an Ultrospec 3100 pro spectrophotometer, Amersham Biosciences, Sweden).

Motility assays were carried out on 0.4% (w/v) agarose in BG-11 in 50-mm plastic petri dishes (BD Falcon, New Jersey, USA) at 30°C. One microliter of cells (OD_{730} = 0.8, or ∼40,000 cells) was placed in the center of a plate, and then inverted to minimize evaporation of the agarose. In ^{2}s, as measured with an LI-189 light meter (LI-COR Biosciences, NE, USA).

Entire drops (

Cell tracking was performed using custom MATLAB (The Mathworks, Natick, MA, USA) software to quantify the positions and velocities of individual cells over time. In each frame, individual cells were segmented using thresh-holding and a watershed transform, and the locations of their centers of mass were recorded. The track of each cell was found using probabilistic nearest-neighbor connected-component analysis across frames. The average speeds of single cells were calculated from the total path length traveled over the preceding 50 seconds.

Simulations were performed with custom code written in MATLAB. Simulations were carried out on a rectangular grid 2×4 mm in physical size, corresponding to 360×720 simulated grid elements with a grid spacing of 0.25 natural length scale units. In all instances, the simulation area was subject to zero flux boundary conditions and the EPS concentration was initially set to zero everywhere. The initial cellular mass was spread in a uniform random distribution over a region covering the bottom 20% of the simulation area. The cellular and EPS concentrations were calculated using a forward Euler method with a spatial and temporal resolution high enough for numerical stability. The time step (

The EPS production rate _{s}_{0} set the fundamental length and time scales of the biophysical model. Both of these parameters were estimated from time-lapse imaging data. We assume that the optical halo around groups of cells is formed by the liquid (EPS)/air interface under which the cells reside. For regions where the width of the halo was small compared with the size of the EPS covered region, we assumed that the movement of this interface resulted from production of new EPS, and thus used this edge to approximate the area covered by EPS. We estimated the EPS production rate at

Custom MATLAB software was written to quantify the morphological features of the simulations. Simulations in which less than 50% of the cell mass had moved into fresh territory by the end of the simulation were considered non-motile (black dots in phase diagrams). For the majority subset that was motile, we used an adaptive threshold to determine the position of the moving cellular front as a function of time. We calculated the standard deviation of the points forming the cell front normalized by the mean distance that the cell front had moved, yielding a dimensionless metric of the growth rate of the morphological instability; a perfectly flat cell front would have a value of zero, and a highly unstable front with finger-like projections would have a value close to 1. Simulations that showed an instability growth rate below 0.01 were considered to have a stable front without distinct groups (gray dots in phase diagrams). Simulations with front instability >0.01 exhibited distinct cellular groups that moved toward the simulated light source. In