Mechanically-driven phase separation in a growing bacterial colony

Abstract

Secretion of extracellular polymeric substances (EPSs) by growing bacteria is an integral part of forming biofilm-like structures. In such dense systems, mechanical interactions among the structural components can be expected to significantly contribute to morphological properties. Here, we use a particle-based modeling approach to study the self-organization of nonmotile rod-shaped bacterial cells growing on a solid substrate in the presence of self-produced EPSs. In our simulation, all of the components interact mechanically via repulsive forces, occurring as the bacterial cells grow and divide (via consuming diffusing nutrient) and produce EPSs. Based on our simulation, we show that mechanical interactions control the collective behavior of the system. In particular, we find that the presence of nonadsorbing EPSs can lead to spontaneous aggregation of bacterial cells by a depletion attraction and thereby generates phase separated patterns in the nonequilibrium growing colony. Both repulsive interactions between cell and EPSs and the overall concentration of EPSs are important factors in the self-organization in a nonequilibrium growing colony. Furthermore, we investigate the interplay of mechanics with the nutrient diffusion and consumption by bacterial cells and observe that suppression of branch formation occurs due to EPSs compared with the case where no EPS is produced.

Keywords: biofilms; depletion interaction; extracellular polymeric substance; mechanical interaction; phase separation.

Fig. 1.

Representation of (A) bacterial cell as spherocylinder, (B) coiled polymers (EPSs) are assumed as spheres (red), (C) repulsive interaction between two cells, and (D) repulsive interaction of a cell and an EPS particle.

Fig. 2.

Schematic representation of how depletion attraction operates in a colony of bacteria producing exopolysaccharide. Bacterial cells are large spherocylinders (magenta) and coiled polymers (EPSs) are assumed as small spheres (yellow). The dashed lines around each bacteria are zones of excluded volume as shown in A and B, which is not accessible to the center of mass of a given EPS after it has been secreted into the medium. In A, as bacterial cells are separated from each other, the area of excluded volume is large, an area that could be partially accessible for the EPS particles if the cells come closer and form aggregates, as is shown in B.

Fig. 3.

Snapshot of growing bacterial colony in presence of EPS particles. Bacterial cells are represented by spherocylinders (color: magenta) and EPS particles as spheres (color: yellow). Snapshot of cell-eps assembly after time t = 190: (A) in the presence of low repulsive interaction among the components of biofilm: $E_{cell-cell}=E_{cell-eps}=E_{eps-eps}=2\times {10}^5$; (B) in the presence of moderate repulsive interaction: $E_{cell-cell}=E_{cell-eps}=E_{eps-eps}=4\times {10}^5$; and (C) in the presence of high cell-EPS repulsive interaction: $E_{cell-cell}=E_{eps-eps}=4\times {10}^5,E_{cell-eps}=6\times {10}^5$. (D) Enlarged view of a small rectangular segment taken from the center of A. (E) Enlarged view of a small rectangular segment taken from the center of B. (F) Enlarged view of a small rectangular segment taken from the center of C. The rest of the parameters of the simulations are given in Table 1.

Fig. 4.

Comparison of 2D distribution of angles of orientation between two cells and corresponding intercell distance in presence of (A) low and (B) high depletion effect provided by varying repulsive force constants. The parameters are kept same as in Fig. 3 A and C.

Fig. 5.

Comparison of local orientational order parameter q6 in presence of low and high depletion effect. The parameters are kept the same as used in Fig. 3 A and C. The probability distribution is normalized such that ${\displaystyle {\int }_0^{\infty }\left[P\left(q_6\right)\right]d{q}_6}=1$.

Fig. 6.

Comparison of radial distribution function [g(r)] for different components of the colony: (A) cell, (B) EPS, and (C) entire biofilm in the presence of low (cyan) and high (red) depletion effect obtained from varying the repulsive force constant of the components of biofilm. Parameters are same as used in simulations of Fig. 3 A and C.

Fig. 7.

Comparison of static structure factor [S(q)] for different components of the colony: (A) cell, (B) EPS, and (C) entire biofilm in the presence of low (cyan) and high (red) depletion effect. x and y axes are in logarithmic scale. Parameters are same as used in simulations of Fig. 3 A and C.

Fig. 8.

Effect of high production rate of EPSs. (A) Modified with permission of the Royal Society, where white cylindrical objects are S. meliloti bacteria and the gray region is the extracellular medium. Note that this picture is not produced by a growth experiment and hence cannot be directly compared with our simulations. (B) Snapshot of growing bacterial colony with small cellular aggregates. (C) Enlarged view of a cluster and surrounding EPS particles indicated by the blue-colored rectangular segment of the colony shown on the left. All other parameters are the same as Fig. 3C except $k_{eps}=10$.

Fig. 9.

Snapshot of cell–EPS assembly in the absence of a nutrient effect assuming the constant growth of cells in presence of depletion effect varying repulsive elastic force constants. (A) $E_{cell-cell}=E_{cell-eps}=E_{eps-eps}=2\times {10}^5$, $k_{eps}=0.35$. (B) $E_{cell-cell}=E_{eps-eps}=4\times {10}^5,E_{cell-eps}=6\times {10}^5,k_{eps}=0.35$. (C) $E_{cell-cell}=E_{eps-eps}=4\times {10}^5,E_{cell-eps}=6\times {10}^5$, $k_{eps}=1.0$. Other parameters are kept the same as given in Table 1, except that the effect of nutrient is absent.

Fig. 10.

Suppression of the branching effect in the presence of EPS. Simulating bacterial colonies for the same amount of time $t=400$ (A) if there is no production of EPS; production of EPS along with growth of bacterial colony in the presence of (B) low depletion effect and (C) high depletion effect, for a high value of consumption rate $k=20$. Other parameters are similar as in Fig. 3 A and C.