PubMed · 508485
The source did not provide an abstract. Follow the original record for more information.
Explore connections, maps & timelines
1979. Symbols for compartmental models.. https://doi.org/10.1093/bja%2F51.9.815
Cite the original work for its findings. Save a collection to share your selection of sources.
KEEP EXPLORING
The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.
Microbial colony growth is shaped by the physics of biomass propagation and nutrient diffusion and by the metabolic reactions that organisms activate as a function of the surrounding environment. While microbial colonies have been explored using minimal models of growth and motility, full integration of biomass propagation and metabolism is still lacking. Here, building upon our framework for computation of microbial ecosystems in time and space (COMETS), we combine dynamic flux balance modeling of metabolism with collective biomass propagation and demographic fluctuations to provide nuanced simulations of E. coli colonies. Simulations produced realistic colony morphology, consistent with our experiments. They characterize the transition between smooth and furcated colonies and the decay of genetic diversity. Furthermore, we demonstrate that under certain conditions, biomass can accumulate along "metabolic rings" that are reminiscent of coffee-stain rings but have a completely different origin. Our approach is a key step toward predictive microbial ecosystems modeling. A record of this paper's transparent peer review process is included in the supplemental information.
How do growing bacterial colonies get their shapes? While colony morphogenesis is well studied in two dimensions, many bacteria grow as large colonies in three-dimensional (3D) environments, such as gels and tissues in the body or subsurface soils and sediments. Here, we describe the morphodynamics of large colonies of bacteria growing in three dimensions. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria generically become morphologically unstable and roughen as they consume nutrients and grow beyond a critical size-eventually adopting a characteristic branched, broccoli-like morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between two-dimensional (2D) and 3D colonies; while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient limited in its interior, driving a transition to unstable growth at its surface. We elucidate the onset of the instability using linear stability analysis and numerical simulations of a continuum model that treats the colony as an "active fluid" whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies-as well as other forms of growing active matter, such as tumors and engineered living materials-in 3D environments.