Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Pattern formation along signaling gradients driven by active droplet behavior of cell swarms

Gradients of extracellular signals organize cells in tissues. Although there are several models for how gradients can pattern cell behavior, it is not clear how cells react to gradients when the population is undergoing 3D morphogenesis, in which cell-cell and cell-signal interactions are continually changing. Dictyostelium cells follow gradients of their nutritional source to feed and maintain their undifferentiated state. Using lightsheet imaging to simultaneously monitor signaling, single-cell, and population dynamics, we show that the cells migrate toward nutritional gradients in swarms. As swarms advance, they deposit clumps of cells at the rear, triggering differentiation. Clump deposition is explained by a physical model in which cell swarms behave as active droplets: cells proliferate within the swarm, with clump shedding occurring at a critical population size, at which cells at the rear no longer perceive the gradient and are not retained by the emergent surface tension of the swarm. The model predicts vortex motion of the cells within the swarm emerging from the local transfer of propulsion forces, a prediction validated by 3D tracking of single cells. This active fluid behavior reveals a developmental mechanism we term "musical chairs" decision-making, in which the decision to proliferate or differentiate is determined by the position of a cell within the group as it bifurcates.

Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods

Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc. Clearly, the phenotypic distribution - and how this changes over time and space - could be a major determinant of population-level dynamics. For instance, across a cancerous population, variations in movement, growth, and ability to evade death may determine its growth trajectory and response to therapy. In this review, we discuss how classical partial differential equation (PDE) approaches for modelling cellular systems and collective cell migration can be extended to include phenotypic structuring. The resulting non-local models - which we refer to as phenotype-structured partial differential equations (PS-PDEs) - form a sophisticated class of models with rich dynamics. We set the scene through a brief history of structured population modelling, and then review the extension of several classic movement models - including the Fisher-KPP and Keller-Segel equations - into a PS-PDE form. We proceed with a tutorial-style section on derivation, analysis, and simulation techniques. First, we show a method to formally derive these models from underlying agent-based models. Second, we recount travelling waves in PDE models of spatial spread dynamics and concentration phenomena in non-local PDE models of evolutionary dynamics, and combine the two to deduce phenotypic structuring across travelling waves in PS-PDE models. Third, we discuss numerical methods to simulate PS-PDEs, illustrating with a simple scheme based on the method of lines and noting the finer points of consideration. We conclude with a discussion of future modelling and mathematical challenges.

Chemotaxing E. coli do not count single molecules

Understanding biological functions requires identifying the physical limits and system-specific constraints that have shaped them. In Escherichia coli chemotaxis, gradient-climbing speed is information-limited, bounded by the sensory information they acquire from real-time measurements of their environment. However, it remains unclear what limits this information. Past work conjectured that E. coli's chemosensing is limited by the physics of molecule arrivals at their sensors. Here, we derive the physical limit on behaviorally-relevant information, and then perform single-cell experiments to quantify how much information E. coli's signaling pathway encodes. We find that E. coli encode two orders of magnitude less information than the physical limit due to their stochastic signal processing. Thus, system-specific constraints, rather than the physical limit, have shaped the evolution of this canonical sensory-motor behavior.

E. coli do not count single molecules

Organisms must perform sensory-motor behaviors to survive. What bounds or constraints limit behavioral performance? Previously, we found that the gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set by the limited information they acquire from their chemical environments (1). Here we ask what limits their sensory accuracy. Past theoretical analyses have shown that the stochasticity of single molecule arrivals sets a fundamental limit on the precision of chemical sensing (2). Although it has been argued that bacteria approach this limit, direct evidence is lacking. Here, using information theory and quantitative experiments, we find that E. coli's chemosensing is not limited by the physics of particle counting. First, we derive the physical limit on the behaviorally-relevant information that any sensor can get about a changing chemical concentration, assuming that every molecule arriving at the sensor is recorded. Then, we derive and measure how much information E. coli's signaling pathway encodes during chemotaxis. We find that E. coli encode two orders of magnitude less information than an ideal sensor limited only by shot noise in particle arrivals. These results strongly suggest that constraints other than particle arrival noise limit E. coli's sensory fidelity.

Microfluidic Ecology Unravels the Genetic and Ecological Drivers of T4r Bacteriophage Resistance in E. coli: Insights into Biofilm-Mediated Evolution

We use a microfluidic ecology which generates non-uniform phage concentration gradients and micro-ecological niches to reveal the importance of time, spatial population structure and collective population dynamics in the de novo evolution of T4r bacteriophage resistant motile E. coli. An insensitive bacterial population against T4r phage occurs within 20 hours in small interconnected population niches created by a gradient of phage virions, driven by evolution in transient biofilm patches. Sequencing of the resistant bacteria reveals mutations at the receptor site of bacteriophage T4r as expected but also in genes associated with biofilm formation and surface adhesion, supporting the hypothesis that evolution within transient biofilms drives de novo phage resistance.