The authors have declared that no competing interests exist.
Conceived and designed the experiments: CWH IA MA. Performed the experiments: CWH IA. Analyzed the data: CWH HD ZX DK IA MA. Contributed reagents/materials/analysis tools: CWH HD ZX DK IA MA. Wrote the paper: CWH HD ZX DK IA MA. Designed computational models: CWH HD ZX DK IA MA Ran simulations: CWH HD ZX Compared simulation results with experiments: CWH HD ZX DK IA MA.
The formation of spore-filled fruiting bodies by myxobacteria is a fascinating case of multicellular self-organization by bacteria. The organization of
Understanding bacteria self-organization is an active area of research with broad implications in both microbiology and developmental biology.
The organization of
Although the nascent fruiting body contains on the order of
We present, in this paper, an integrative approach that combines a new experimental technique using infra-red optical coherence tomography (OCT) with computational models to study the patterns of spores as they form within a fruiting body. Viewing fruiting bodies by this tomography method revealed that regions of high spore concentrations in the fruiting body were surrounded by less dense regions. Based upon the experimental findings, we developed a hypothesis based on the the underlying biology of
To test if the hypothesis is plausible, we developed two separate models that use different degrees of biological detail. In the two models that we present, we focus on the later stage of the fruiting body process when cells have already aggregated in some domain and the sporulation is beginning. The general modeling approach studies how the coordinated self-propelled cell movement and C-signaling can give rise to the spatial patterns of spore clusters observed in experiments.
We begin with a one dimensional (1D) model that tests how jamming and C-signaling generate clustering on a circular track. The second two dimensional (2D) model implements cell shape and movement and utilizes C-signaling that requires end-to-end cell alignment. The simplicity of the 1D model allows us to study a very wide range of parameter values in order to gain insight into the relative importance of two specific aspects of cell clustering — jamming by cells encountering spores and impact of C-signaling. The 2D model is more computationally demanding and cannot explore the same range of parameter values, but instead focuses on adding more biological details such as connecting cell shape and movement with C-signaling that requires alignment. Model simulation results were compared with the experimentally observed clustering of spores. The hypothesized mechanism based on cells aligning and signaling by contact to coordinate sporulation was able to recover the structure of the fruiting body observed in the experiments. In addition to gaining new insight into bacterial fruiting body formation, better understanding of cell self-organization based on cell-cell signaling and interaction is of real importance for developmental biology.
In order to carry out these studies, we developed an apparatus that integrated the motorized stage of a microscope with a stand alone Optical Coherence Tomography (OCT) device and ran fully computerized scans using LabView to control timing of scans and probe position. Then, we developed preprocessing routines in ImageJ to extract planar cross-sections of data that could then be analyzed by additional programs written in Matlab. The analysis programs extracted statistical properties from the three-dimensional (3D) intensity data and also rendered 3D images of the mound.
We used CTT agar plates for both normal and starved growing conditions of
In order to examine 3D bacterial density distribution, we employed non-invasive high-resolution infrared optical coherence tomography (OCT)
Scanning electron microscopy (SEM) is a technique that has been used previously to show that spores within a mound are tightly packed
Other researchers concerned with these limitations used laser scanning confocal microscopy (LSCM) with fluorescently labeled bacteria to probe the internal structure of mounds
GFP fluorescence uses 480 nm excitation light and emits at a wavelength of 510 nm
In addition to the scattering,
Microscopy was performed on an inverted Olympus microscope and images were taken with a Spot Boost EMCCD 2100 (Diagnostic Instruments Inc.) high sensitivity camera. The camera was still sensitive to the IR probe from the OCT device which appeared as a small white dot in the field of view. This is what enabled the accurate positioning of the probe over specific mounds.
In order to obtain 3D OCT scans of fruiting bodies, we search for a desired region using bright field microscopy at low magnification. Then, using a three-axis micrometer driven translational stage, we position the probe head over the site. The inverted microscope allows for accurately positioning the probe because the mounds can still be seen while the probe head is in the optical path of the microscope (see
The two boxes highlight same field for the two images. A) 2× magnification of swarm plate without probe. Fruiting bodies appear as dark black circles and ovals with bright perimeters. B) White arrow points to probe head positioned over mounds.
In order to analyze the 3D OCT intensity scan, the 2D slices are loaded into Matlab as a 3D matrix. The raw data is a Red-Green-Blue (RGB)-value image that is converted to an 8-bit grayscale image with an intensity range between 0 and 255. For the OCT scans, the largest intensity values observed were between 180 and 190. Towards the perimeter of each cross section, the values drop to below 10 corresponding to the surface of the mound. There are interior regions where the intensity values reach as low as 80. In-plane cross-sections were extracted from the 3D data by fixing the z-value to obtain a 2D image in the xy-plane parallel to the agar surface. For each in-plane cross section, the image moments
The 3D renderings of the mound are made using the isosurface function in Matlab. The outer shell is an isosurface using an isovalue of 10 and given a large transparency. For the multi-layer isovolume rendering, the highest isovalues which are largely in the interior were rendered with higher opacity. Subsequent lower isovalues were drawn with decreasing opacity so that the internal structure could be visualized.
To study how the motion of cells and cell-contact signaling within a developing fruiting body could give rise to the patterns characterized by dense pockets showing up as a kind of bumpiness in the OCT, we use computational models that captures the movement of cells in a fruiting body environment. Previously, a 3D Lattice Gas Cellular Automata model was used to study cell aggregation and fruiting body formation as well as spore transport and spatial organization
In both models, we begin simulations with cells in an aggregate and accumulating C-signal. While the vast majority of cells die during the fruiting body process, as evidenced by the fact that 1.0% or less become spores
Drawing from the expectation that the trajectories of individual cells are confined to the hemisphere of the fruiting body, we developed a zeroth order approximation by modeling cells moving along a 1D circular track. This simplifed model can be used to study the effects of jamming and signaling when cells travel along the same path.
In this 1D track model, cells are initialized randomly throughout the discretized track and move with a constant rate around the track. As cells move along the circular track, they can eventually come to a region that is occupied by spores. This can lead to traffic jams where cells and spores accumulate. In each simulation step, every cell tries to move to the next position in the track. Even though the track is 1D, we do not restrict a position in the track to a single cell. If multiple cells occupy the same position in the track, we say that the cells are side by side in space. This added degree of freedom makes this model a pseudo 2D model. We ignore directional reversals and assume all cells move in same direction. When a cell tries to move into a position that contains spores, a passing probability (
In this model, motile cells become non-motile spores when they accumulate enough C-signal. To our knowledge, the amount of C-signal required for cells to become spores is unknown. However, in
Each cell is also initialized with some amount of C-signal concentration between 0 and 0.5. We assume that C-signal concentration increases by 0.005 each simulation step. Signaling between cells is modeled by a transfer rate (
Simulations are run until all cells become spores and then analyzed to study the distribution of spores along the track.
In addition to the simplified track model, we extended a 2D stochastic model that was previously developed for the study of myxo swarming in
The features of this model include movement algorithms for
Stochasticity is introduced by adding random contribution to the direction of a cell. The position of each cell is updated by first moving the head node with a constant velocity in a direction determined by the contributing factors — A-motility, S-motility, and slime tracks. A weighted sum of these factors is obtained and normalized to obtain the unit vector pointing in the direction of movement. The weights for each factor is included in
The relative strength of the factors determining direction, the reversal frequency, as well as the bending and stretching coefficient are important parameters in the model. The values for these parameters which reliably capture the collective movement of
Unlike the 1D model where cell-spore interaction is described by a probability, in the 2D model, the cell-spore interaction is determined by the collision process. When a cell tries to move into a position that results in the body of the cell overlaping with the body of another cell, the moving cell attempts to bend and resolve the collision with the other cell. This bending process during cell collisions uses the elastic energy Hamiltonian (H) and metropolis criteria to accept the bent configuration of nodes making up the cell. If a cell's bending is rejected by the metropolis step, then the cell stalls until the next time step. Such stalling is resolved by either a change in positions of the other cells surrounding the stalled cell or by the stalled cell reversing. Similarly, when a cell collides with a spore, it must do this bending procedure in order to get around the spore. Since spores are round instead of rod-shape, the spatial effect of cell-spore collisions is different from the cell-cell collisions. Because the movement of cells determines the cell-spore interaction, there is no need to include a parameter that defines a passing probability like that used in the simplified 1D model.
Because the model was already validated for cell movement, the extensions we made focused on C-signaling and sporulation. In order to extend this model for testing our hypothesis of the mound structure formation, we added components describing the C-signaling and sporulation. This was done by assigning each cell a counter for the C-signal and introducing two cell states: 1) motile cell and 2) non-motile spore. Motile cells accumulate C-signal by contact with other motile cells. Signal transfer between cells requires cells to be aligned and touching end to end. From each cell, we define the orientation as the vector pointing from head to tail and consider cells aligned if the angle between two cells orientation is less than 30 degrees. The polarity of cells does not matter (i.e. contact between two heads, two tails, or a head and a tail all cause signal exchange). As with the track model, side-by-side cells did not exchange signal. At every simulation step, we test to see if two cells match the requirement for signaling and, if so, the two cells exchanged signal. Each signal exchange between two cells causes the C-signal counter of the cells to increment by 1. When a cell reaches a signal threshold of 500, the state of a cell is changed from motile to non-motile and the rod-shape body is replaced by a round circular spore.
Since the amount of C-signal increase is set to one unit per signaling event, the threshold determines the rate of C-signal accumulation. By setting the threshold lower, each C-signal event accounts for a larger increment relative to the threshold. In contrast, setting the threshold higher causes each C-signal event to be a smaller increment. In a simulation where the threshold was set twice as high as the default value of 500, we did not see a significant difference in the spatial patterning despite the additional time needed by cells to become spores.
In order to simulate the aggregation of a fruiting body, we set up a 500×500 micron area with a periodic boundary containing 4 discs with a radius of 50 microns. Initially,
All cells are position randomly throughout domain, but cells that fall within the region of the discs have the orientation set tangent to the radius of the disc. Orientation of cells outside disc is random.
The use of the OCT method to scan fruiting bodies was expected to accurately reveal the internal structure due to the improved scanning depth of IR light (technical details for this reasoning are made in the
The two different modes are shown using two different focal planes. A) and C) are focused near the top of the mound, while B) and D) are focused closer to the surface. The large scale irregularities seen in the OCT scans can be optical observed in C) and D). No internal structure is seen in visual light, panels A) and B).
Individual slices made by the OCT can be seen in
The dark region is the space above the surface of the agar plate. The red area is the agar. The yellow area is the mound as well as the bacteria on the surface. A) Dry Scan. B) Oil Immersion Scan of mound in (A). C) Dry Scan. D) Glycerol Immersed Scan of mound in (C). Brighter regions below mounds in (A) and (C) demonstrate lensing effects for dry scans.
To improve the quality of image, we place a drop of microscopy oil on the surface of the agar plate and submerged the probe head into the oil.
The detailed analysis of an OCT scan of a fruiting body mound was carried out to study its internal structure. The image analysis (described in
Scans show no indications of a shell and core structure that was suggested by the LSCM study
The top image is a sample mound illustrating a 3D rendering of OCT scan of a mound. The colorbar indicates the intensity value. Higher intensity values corresponds to more back scattered signal which is indicative of regions with higher optical density. In the bottom row, 3D renderings of isovolumes for different intensity values. The intensity value for each isovolume is marked on colorbar. (Lighting and rendering effects causes the color to appear slightly different than the corresponding color in the colorbar).
Left Column Panel: A 2D rendered cross section from sequence of OCT slices. A) Raw data cross section. B) Gray-Scale image used for image analysis. The elliptical domains for radial density are overlayed on the image. C) Zoomed in region of (B). D) Analysis shows the average intensity (black line) and intensity distribution for cross-sectional discs as a function of height from the base of the mound. The x-axis is the height of each disc in the mound where zero is the base. Data is from mound shown in
The upper row of images shows 3D renderings of three different mounds. For each mound, the lower row of the figure plots semi-major and semi-minor axis for cross sections as a function of the height from the base of the mound. The orientation as a function of height is shown in same plot. The axis plots are in microns while the orientation is in degrees.
In addition to the radial distribution, we performed measurements of the angular distribution of intensity. This was done by dividing the domain into sectors (i.e. pie slices) and averaging the intensity within each sector. The results for one cross-section are shown in
A) Image of cross section. The white line shows where the reduced intensity occurs around 90 degrees. B) Intensity distribution as a 2D plot. C) Distribution shown as polar plot.
The more striking features that are revealed by the 3D OCT scan are the large interconnected structure of caverns with in the mound.
The findings from the experiments were used to contemplate the bigger picture of fruiting body formation, which is presented here. In the fruiting body process, a mound of constantly moving cells gives rise, after several days, to a mature, spore-filled fruiting body
Departing from the traveling waves, the surviving cells are seen to migrate to the outer edge of each wave crest where they become one of the small motile aggregates
Based on the foregoing description of slime trails in a dynamic motile aggregate, it follows that cells would be clustered and aligned on the many trails that would branch from each other. Since individual cells are eating each other as they move, they are also racing to be one of the predators that survive rather than one of the prey that expire. In such a race, long chains of rod-shaped cells, moving on the same trail, would break into shorter segments of fewer and fewer cells until only 1% — to take some definite number since the number depends on residual nutrient — of starting cells remain on the trails and able to transmit C-signal. When two counter-migrating cells on the same trail collide end-to-end, they exchange C-signal with each other. C-signal transmission continuously raises the signal level in each cells outer membrane through positive feedback and the Act system
To test the hypothesis described in the previous section, we ran simulations with the two models we developed.
One advantage of the 1D model is the ability to explore a large parameter space due to the low computational demand. To study the impact of the passing probability and rates of signal transfer, simulations were run for a range of passing probability from 0.05 to 1.0 and a range of
A) Plot shows the effect of decreasing the passing probability from 1.0 to 0.1 by looking at the fraction of empty positions in the track. The different curves correspond to different rates of C-signal transfer between neighbors. Results are shown for 20 different values of passing probability and five different transfer rates. Averages were taken from 100 simulations for each set of parameters. B) Spore distribution along circular track for three simulation results. The radial distance corresponds to the number of spores while the angular position denotes the position in the circular track (The outer circle is for a spore count of 10 while the middle circle corresponds to five spores). The passing probability P varies for the three simulations from 1.0 to 0.05. Figure demonstrates how spores clustering is increased as passing probability decreases.
It should be pointed out that the passing probability parameter in the 1D model is a simplification of the cell-spore interaction and does not attempt to define the nature of the cell-spore interaction. The impedance of a spore to a passing cell could be adhesive, spatial, or some combination of both. The parameter only defines how much impedance a spore presents to a moving cell. However, in the 2D model, we specify the cell-spore interaction as collisions with no adhesive interaction (see section “2d Stochastic Model”).
An example of how spores are distributed along the circular track at the end of several simulations is given in
For this range of passing probabilities and
We have the following explanation for the fact that high jamming (i.e. low passing probabilities) and larger signal transfer rates lead to less clustering (i.e. smaller void fractions). By increasing the C-signal transfer rate in the model, cells will reach the threshold for sporulation more quickly. Because C-signal molecules need to bind to a receptor on another cell, an increase in the C-signal transfer rate is analogous to the binding between C-signal molecules and receptors occurring more easily. The faster cells become spores, the less likely it is for them to move to a point on the track containing a cluster of spores. In contrast, smaller transfer rates allows a cell to reach a cluster on the track, become stuck, and then change into a spore. In the range of higher passing probabilities (
It is interesting to note that jamming in the absence of signaling (i.e.
The aggregation sites of spores are the discrete positions on the track where clusters of 5 – 10 cells can accumulate as seen in
While some general observations on the level of clustering can be drawn from the 1D track model, simulations using the 2D stochastic model provide insight into how the coordinated movement of cells and alignment-dependent signaling lead to the patterns of spore clusters. During the simulation, the movement of cells inside the disc is rotational due to the cells aligning with their local neighbors and the slime trails that are set up by other cells in the disc. In
A–C) Snapshots from simulation over time. Frame (A) shows the initial locations of the first few spores within the mound. Blue arrows in (B) point to regions where groups of two and three spores form together. (C) Later stage of simulation shows the distribution of spores filling in around the disc. D) Spore positions in disc at end of simulation. Radius of disc is 50 microns. E) Local density field for simulation results in (D). Circles show several radii values for radial local density. F) Radial local density distribution for (E).
In order to compare with experimental data, we determined the local density of spores inside a disc from our simulations. A square region of 400×400 pixels containing a disc was divided into a 100×100 rectangular grid. The number of spores contained within each grid point inside the disc was used to determine the concentration field. A local density field was created by convolving the concentration field with a gaussian filter. By using the gaussian filter at each grid point of the concentration field, we calculated a weighted average of spore concentration for each grid point. This averaging is similar to the measurements made by the OCT device due to the finite diameter of the scanning beam.
To compare with the experimental angular distribution, we performed an analogous measurement on the simulation data. From the concentration map, an angular distribution of spores is obtained by summing up the number of spores in grid points that fall within the same three degree sector of the disc (i.e. a pie slice). Results for this measurement are shown in
A) Local density map for 2D simulation. The dashed white line shows where the reduced spore concentration occurs next to high concentration pocket around 150 degrees. B) Concentration of spores in sector of disc as a 2D plot. C) Concentration shown as polar plot.
A novel imaging technique – infrared optical coherence tomography – revealed that hundreds of thousands of spores in a mature fruiting body of
First, our 1D track model provided two possible explanations for the formation of the cavernous structures of the fruiting bodies. One explanation was that early sites of spore formation act as focal regions for spore clusters due to jamming of the motile rod-shaped cells that continued to move around the track. This explanation suggested that high levels of clustering could result from spores strongly inhibiting the motility of cells. The highest level of clustering was observed when cells had the smallest passing probability and no C-signal transfer. However, in simulations with higher passing probabilities, (i.e. motile cells were not strongly inhibited by spores), more clustering was seen when C-signal exchange by local cells was present than when only jamming was considered. Experimental movies from our previous study on cell-cell collisions
The 1D model simulations initially confirmed that contact-based C-signaling would generate spore clusters when the cell-spore interaction was not characterized by strong spatial jamming. These findings were the motivation for focusing on the movement and alignment of cells in a more detailed model. Thus, the 2D model was used which could account for the biological details such as cell-shape, movement, and alignment-dependent C-signaling. The 2D model simulations have shown how the patterns of spore clusters could be produced by cells moving, aligning and C-signaling to coordinate differentiation. In the simulations, spores begin to form within a disc as small clumps (see
To summarize, we first formulated a hypothesis based upon the experimental observation of spore patterns in fruiting bodies. We hypothesized that pockets of dense regions of spores form because cell movement, alignment and signaling result in coordination of the cell differentiation. The 1D simulations demonstrated that cell-signaling was capable of regulating the level of clustering inside a fruiting body. The 2D model simulations determined what patterns of spore clustering would emerge from cells aligned movement along slime trails and C-signaling by the end-to-end contact. In addition, the movement and interaction of cells in the 2D model included cell-cell and cell-spore collisions as well as cell reversals that reinforced alignment within the aggregate. We found that the coordinated movement of cells — by way of self-propelled motion, slime trail following, cell-cell and cell-spore collisions, and cell reversals — can facilitate the contact-dependent signal accumulation that drives cell differentiation into spores.
The integration of novel experimental observations with computational simulations provided new insight into the mechanisms that could give rise to the structure with a pattern of dense spore pockets seen during fruiting body formation. This can be improved upon through use of newer OCT devices with better resolution and even applied to other biological systems of cell aggregation such as that seen in dictyostelids, social amoeba known to form multicellular aggregates observed as slugs under starvation conditions.
Understanding how cells can undergo differentiation under specific spatial patterning is important to biology in general. It is known that chemical signals and reaction-diffusion processes can lead to coordination of cell patterning and differentiation. In the fruiting body process, we have shown how this patterning and differentiation could arise in the absence of a diffusive signal.
(AVI)
(EPS)
We thank Dr. Felix Feldchtein for the help with OCT.