Abstract
Classic experiments on the distribution of ducks around separated food sources found consistency with the "ideal free" distribution in which the local population is proportional to the local supply rate. Motivated by this experiment and others, we examine the analogous problem in the microbial world: the distribution of chemotactic bacteria around multiple nearby food sources. In contrast to the optimization of uptake rate that may hold at the level of a single cell in a spatially varying nutrient field, nutrient consumption by a population of chemotactic cells will modify the nutrient field, and the uptake rate will generally vary throughout the population. Through a simple model we study the distribution of resource uptake in the presence of chemotaxis, consumption, and diffusion of both bacteria and nutrients. Borrowing from the field of theoretical economics, we explore how the Gini index can be used as a means to quantify the inequalities of uptake. The redistributive effect of chemotaxis can lead to a phenomenon we term "chemotactic levelling," and the influence of these results on population fitness are briefly considered.
Highlights
In one of the more amusing, yet influential experiments on animal behavior, Harper [1] studied the distribution of mallards around two separated sources of standardized pieces of bread
In this paper we focus on three key questions in this area: What is the distribution of bacteria around spatially distinct nutrient sources and their associated impact on the resource field? What is the distribution of resource uptake rates within that population? What are the consequences of such distributions for cellular fitness?
Bacteria furthest from the source, and below the average uptake level in the nonchemotactic case, see their mean uptake decrease even further. Overall this corresponds to an increase of G: in higher dimensions, chemotaxis can bring the bacteria further away from the ideal free distribution, that is, it increases the inequalities among the population
Summary
In one of the more amusing, yet influential experiments on animal behavior, Harper [1] studied the distribution of mallards around two separated sources of standardized pieces of bread. Using the terminology of Fretwell and Lucas [2], “ideal” means that ducks can identify the source where their uptake is maximized, and “free” implies unfettered ability to access the source of choice This distribution, resulting from individual rational behaviors, achieves a population-wide uniformization of the probability of uptake and can be understood as a Nash equilibrium [3]. From the visually based searching of higher animals, and because of the diffusive behavior of nutrients and the cell populations, the microbial problem is distinct in character This feature motivates the present investigation of the consequences of a collection of individual chemotactic responses on the population-scale distribution of resources. We emphasize the fundamental difference between live microbial sources, such as Engelmann’s alga, and inert sources, such as lysis events; the former continuously release nutrients at low rates They are stable in time but can be significantly impacted by bacterial uptake. We explore the potential biological consequences of uptake redistribution through an example of growth at low nutrient levels
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical review. E, Statistical, nonlinear, and soft matter physics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
