Cutting through the complexity of cell collectives

Abstract

Via strength in numbers, groups of cells can influence their environments in ways that individual cells cannot. Large-scale structural patterns and collective functions underpinning virulence, tumour growth and bacterial biofilm formation are emergent properties of coupled physical and biological processes within cell groups. Owing to the abundance of factors influencing cell group behaviour, deriving general principles about them is a daunting challenge. We argue that combining mechanistic theory with theoretical ecology and evolution provides a key strategy for clarifying how cell groups form, how they change in composition over time, and how they interact with their environments. Here, we review concepts that are critical for dissecting the complexity of cell collectives, including dimensionless parameter groups, individual-based modelling and evolutionary theory. We then use this hybrid modelling approach to provide an example analysis of the evolution of cooperative enzyme secretion in bacterial biofilms.

Figure 1.

A three-dimensional rendering of a biofilm (128 μm length × 128 μm width × 20 μm height) of the pathogen Vibrio cholerae, grown in a microfluidic chamber and imaged by confocal scanning laser microscopy. The three strains are identical except for their constitutive expression of teal, yellow or red fluorescent protein; each colour patch descends from a single ancestral cell, resulting in spatial separation of different genetic lineages.

Figure 2.

Still frames of individual-based biofilm simulations, adapted with permission from [42]. (a) Black cells no longer have access to sufficient nutrient concentrations for growth, while green cells are growing and compose the cell group's active layer. The active layer depth is related to a dimensionless number, δ, which compares the relative rates of nutrient diffusion into the biofilm and nutrient consumption within the biofilm (see main text). (b–d) Three separate individual-based simulations of growing biofilms initiated with a 1 : 1 mixture of two strains that are identical except for a neutral colour tag. Biofilm surface roughness and lineage segregation increase as the active layer becomes thinner (decreasing δ).

Figure 3.

Time-series of one-dimensional spatial simulations of competition among asexually reproducing individuals (different mutants denoted by different colours), adapted with permission from [55]. Stars denote the birth of a novel beneficial mutant. (a) Periodic selection occurs when the fixation time for beneficial mutations (t_fix) is less than the wait time for the occurrence of a new beneficial mutation (t_mut). (b) Clonal interference occurs when t_mut≪t_fix leading to competition among two or more beneficial mutations and slowing the rate at which different beneficial mutations reach fixation. When populations are constrained in space, t_fix increases, making clonal interference more likely to occur than in well-mixed populations of comparable size.

Figure 4.

Competition between cells producing a growth-enhancing enzyme (blue) and non-producing cells (red) in a biofilm. The agent-based simulations were carried out for a range of B_L values, and B_L was varied by independently changing its composite parameters b, k_E, D_E and r_cell. Each simulation was replicated eight times (symbols) and fitted to a logistic curve (lines). The competition outcome, determined by the ratio of producer to cheater fitness (w_P/w_C), depends on the value of B_L but is independent of the specific values of b, k_E, D_E and r_cell. Insets show frames from biofilm simulations.

Figure 5.

Competition between cells producing a growth-enhancing enzyme (blue) and non-producing cells (red) in a biofilm. The analysis from figure 4 was extended by examining the length scale of extracellular enzyme production, B_L (as in figure 4), together with the effects of growth limitation by a different nutrient diffusing towards the biofilm from a bulk fluid layer. Nutrient penetration into biofilms decreases as the dimensionless group δ decreases (see main text). (a) A heat map illustrating the outcomes of competition for a range of δ and B_L values, which shows that nutrient limitation restricts the range of conditions favourable for producers (b). However, when B_L is high enough to favour producers, the increased genetic segregation that results from nutrient limitation under low δ conditions increases the strength of selection for enzyme production (c).