181 research outputs found
Evolutionary and Population Dynamics: A Coupled Approach
We study the interplay of population growth and evolutionary dynamics using a
stochastic model based on birth and death events. In contrast to the common
assumption of an independent population size, evolution can be strongly
affected by population dynamics in general. Especially for fast reproducing
microbes which are subject to selection, both types of dynamics are often
closely intertwined. We illustrate this by considering different growth
scenarios. Depending on whether microbes die or stop to reproduce (dormancy),
qualitatively different behaviors emerge. For cooperating bacteria, a permanent
increase of costly cooperation can occur. Even if not permanent, cooperation
can still increase transiently due to demographic fluctuations. We validate our
analysis via stochastic simulations and analytic calculations. In particular,
we derive a condition for an increase in the level of cooperation.Comment: 12 pages, 5 figure
Mobility, fitness collection, and the breakdown of cooperation
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions. DOI: 10.1103/PhysRevE.87.04271
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Spatiotemporal establishment of dense bacterial colonies growing on hard agar.
The physical interactions of growing bacterial cells with each other and with their surroundings significantly affect the structure and dynamics of biofilms. Here a 3D agent-based model is formulated to describe the establishment of simple bacterial colonies expanding by the physical force of their growth. With a single set of parameters, the model captures key dynamical features of colony growth by non-motile, non EPS-producing E. coli cells on hard agar. The model, supported by experiment on colony growth in different types and concentrations of nutrients, suggests that radial colony expansion is not limited by nutrients as commonly believed, but by mechanical forces. Nutrient penetration instead governs vertical colony growth, through thin layers of vertically oriented cells lifting up their ancestors from the bottom. Overall, the model provides a versatile platform to investigate the influences of metabolic and environmental factors on the growth and morphology of bacterial colonies
Entropy production of cyclic population dynamics
Entropy serves as a central observable in equilibrium thermodynamics.
However, many biological and ecological systems operate far from thermal
equilibrium. Here we show that entropy production can characterize the behavior
of such nonequilibrium systems. To this end we calculate the entropy production
for a population model that displays nonequilibrium behavior resulting from
cyclic competition. At a critical point the dynamics exhibits a transition from
large, limit-cycle like oscillations to small, erratic oscillations. We show
that the entropy production peaks very close to the critical point and tends to
zero upon deviating from it. We further provide analytical methods for
computing the entropy production which agree excellently with numerical
simulations.Comment: 4 pages, 3 figures and Supplementary Material. To appear in Phys.
Rev. Lett.
A Traveling-Wave Solution for Bacterial Chemotaxis with Growth
Bacterial cells navigate around their environment by directing their movement
along chemical gradients. This process, known as chemotaxis, can promote the
rapid expansion of bacterial populations into previously unoccupied
territories. However, despite numerous experimental and theoretical studies on
this classical topic, chemotaxis-driven population expansion is not understood
in quantitative terms. Building on recent experimental progress, we here
present a detailed analytical study that provides a quantitative understanding
of how chemotaxis and cell growth lead to rapid and stable expansion of
bacterial populations. We provide analytical relations that accurately describe
the dependence of the expansion speed and density profile of the expanding
population on important molecular, cellular, and environmental parameters. In
particular, expansion speeds can be boosted by orders of magnitude when the
environmental availability of chemicals relative to the cellular limits of
chemical sensing is high. As analytical understanding of such complex
spatiotemporal dynamic processes is rare, the results derived here provide a
mathematical framework for further investigations of the different roles
chemotaxis plays in diverse ecological contexts.Comment: 27 pages main text, 34 pages Supplemental Informatio
Coordination of gene expression with cell size enables Escherichia coli to efficiently maintain motility across conditions
To swim and navigate, motile bacteria synthesize a complex motility machinery involving flagella, motors, and a sensory system. A myriad of studies has elucidated the molecular processes involved, but less is known about the coordination of motility expression with cellular physiology: In Escherichia coli, motility genes are strongly up-regulated in nutrient-poor conditions compared to nutrient-replete conditions; yet a quantitative link to cellular motility has not been developed. Here, we systematically investigated gene expression, swimming behavior, cell growth, and available proteomics data across a broad spectrum of exponential growth conditions. Our results suggest that cells up-regulate the expression of motility genes at slow growth to compensate for reduction in cell size, such that the number of flagella per cell is maintained across conditions. The observed four or five flagella per cell is the minimum number needed to keep the majority of cells motile. This simple regulatory objective allows E. coli cells to remain motile across a broad range of growth conditions, while keeping the biosynthetic and energetic demands to establish and drive the motility machinery at the minimum needed. Given the strong reduction in flagella synthesis resulting from cell size increases at fast growth, our findings also provide a different physiological perspective on bacterial cell size control: A larger cell size at fast growth is an efficient strategy to increase the allocation of cellular resources to the synthesis of those proteins required for biomass synthesis and growth, while maintaining processes such as motility that are only needed on a per-cell basis
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