Cellular Sensing Governs the Stability of Chemotactic Fronts

Fingering Instability Accelerates Population Growth of a Proliferating Cell Collective

During the growth of a cell collective, such as proliferating microbial colonies and epithelial tissues, the local cell growth increases the local pressure, which in turn suppresses cell growth. How this pressure-growth coupling affects the growth of a cell collective remains unclear. Here, we answer this question using a continuum model of a cell collective. We find that a fast-growing leading front and a slow-growing interior of the cell collective emerge due to the pressure-dependent growth rate. The leading front can exhibit fingering instability, and we confirm the predicted instability criteria numerically with the leading front explicitly simulated. Intriguingly, we find that fingering instability is not only a consequence of local cell growth but also enhances the entire population's growth rate as positive feedback. Our work unveils the fitness advantage of fingering formation and suggests that the ability to form protrusions can be evolutionarily selected.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Chemotactic Motility-Induced Phase Separation

Collectives of actively moving particles can spontaneously separate into dilute and dense phases-a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS-in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Metalearning Generalizable Dynamics from Trajectories

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical parameters. The iMODE method learns metaknowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bilevel optimization framework: an outer level capturing the common force field form among studied dynamical system instances and an inner level adapting to individual system instances. A priori physical knowledge can be conveniently embedded in the neural network architecture as inductive bias, such as conservative force field and Euclidean symmetry. With the learned metaknowledge, iMODE can model an unseen system within seconds, and inversely reveal knowledge on the physical parameters of a system, or as a neural gauge to "measure" the physical parameters of an unseen system with observed trajectories. iMODE can be generally applied to a dynamical system of an arbitrary type or number of physical parameters and is validated on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.

Morphological instability and roughening of growing 3D bacterial colonies

The morphogenesis of two-dimensional bacterial colonies has been well studied. However, little is known about the colony morphologies of bacteria growing in three dimensions, despite the prevalence of three-dimensional environments (e.g., soil, inside hosts) as natural bacterial habitats. Using experiments on bacteria in granular hydrogel matrices, we find that dense multicellular colonies growing in three dimensions undergo a common morphological instability and roughen, adopting a characteristic broccoli-like morphology when they exceed a critical size. Analysis of a continuum “active fluid” model of the expanding colony reveals that this behavior originates from an interplay of competition for nutrients with growth-driven colony expansion, both of which vary spatially. These results shed light on the fundamental biophysical principles underlying growth in three dimensions.

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.

Direct measurement of the aerotactic response in a bacterial suspension

Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration c. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling toward the oxygen source. We compute the aerotactic response χ(c) both at the population scale, from the drift velocity in the bacterial band, and at the bacterial scale, from the angular modulation of the run times. Both methods are consistent with a power-law χ∝c^{-2}, in good agreement with existing models based on the biochemistry of bacterial membrane receptors.

A biophysical threshold for biofilm formation

Bacteria are ubiquitous in our daily lives, either as motile planktonic cells or as immobilized surface-attached biofilms. These different phenotypic states play key roles in agriculture, environment, industry, and medicine; hence, it is critically important to be able to predict the conditions under which bacteria transition from one state to the other. Unfortunately, these transitions depend on a dizzyingly complex array of factors that are determined by the intrinsic properties of the individual cells as well as those of their surrounding environments, and are thus challenging to describe. To address this issue, here, we develop a generally-applicable biophysical model of the interplay between motility-mediated dispersal and biofilm formation under positive quorum sensing control. Using this model, we establish a universal rule predicting how the onset and extent of biofilm formation depend collectively on cell concentration and motility, nutrient diffusion and consumption, chemotactic sensing, and autoinducer production. Our work thus provides a key step toward quantitatively predicting and controlling biofilm formation in diverse and complex settings.