Session V14: Noise and Stochastic Fluctuations in Biological Systems

Excitable toxin-antitoxin modules coordinated through intracellular bottlenecks

Chronic infections and pathogenic biofilms present a serious threat to the health of humans by decreasing life expectancy and quality. The resilience of these microbial communities has been attributed to the spontaneous formation of persister cells, which constitute a small fraction of the population capable of surviving a wide range of environmental stressors. Gating of bacterial persistence has recently been linked to toxin-antitoxin (TA) modules, which are operons with an evolutionarily conserved motif that includes a toxin that halts cell growth and a corresponding antitoxin that neutralizes the toxin. While many such modules have been identified and studied in a wide range of organisms, little consideration of the interactions between multiple modules within a single host has been made. Moreover, the multitude of different antitoxin species are degraded by a relatively small number of proteolytic pathways, strongly suggesting competition between antitoxins for degradation machinery, i.e. queueing coupling. Here we present a theoretical understanding of the dynamics of multiple TA modules that are coupled through either proteolytic queueing, a toxic effect on cell growth rate, or both. We conclude that indirect queueing coordination between multiple TA modules may be central to controlling bacterial persistence.   

Ligand-Receptor Binding Kinetics in Surface Plasmon Resonance Cells: A Monte Carlo Analysis

Surface plasmon resonance (SPR) chips are widely used to measure association and dissociation rates for the binding kinetics between two species of chemicals, e.g., cell receptors and ligands. It is commonly assumed that ligands are spatially well mixed in the SPR region, and thus a mean-field rate equation description is appropriate. This approximation ignores the spatial fluctuations and temporal correlations induced by local rebinding events, which become prominent for slow diffusion rates and high binding rates. We report detailed Monte Carlo simulations of ligand binding kinetics in an SPR cell subject to laminar flow. We extract the binding dynamics by means of the techniques employed in experimental analysis that are motivated by the mean-field approximation. We find major discrepancies in a wide parameter range between the thus extracted rates and the known input simulation values. These results underscore the crucial quantitative importance of spatio-temporal correlations in binary reaction kinetics in SPR cell geometries, and demonstrate the failure of a mean-field analysis of SPR cells in the regime of high association rates, where the spatio-temporal correlations due to diffusive transport and ligand-receptor rebinding events dominate the dynamics of SPR systems.   

Calculating the mean time to capture for tethered ligands and its effect on the chemical equilibrium of bound ligand pairs

Cells interact with a number of extracellular proteins including growth factors, which are essential for e.g., wound healing and development. Some of these growth factors must form dimers on the cell surface to initiate their signaling pathway. This suggests one can more efficiently induce signaling via polymer-linked proteins. Motivated by experiments on a family of fibroblast growth factors linked by polymers of varying molecular weight [C.G. Decker et al., Biomaterials 81, 157 (2016)] we investigate theoretically the effect of the length of the linking polymer on the binding kinetics of the dimers to a receptor-covered surface. We show, through a first-passage time calculation, how the number of bound dimers in chemical equilibrium depends on the linker molecular weight. We discuss more broadly the implications for a variety of signaling molecules.   

The role of spatial dynamics in modulating metabolic interactions in biofilm development

Cell phenotypic expression is substantially affected by the presence of environmental stresses and cell-cell communication mechanisms. We study the metabolic interactions of the glutamate synthesis pathway to explain the oscillation of growth rate observed in a \textit{B. Subtilis} colony. Previous modelling schemes had failed in fully reproducing quantitative experimental observations as they did not explicitly address neither the diffusion of small metabolites nor the spatial distribution of phenotypically distinct bacteria inside the colony. We introduce a continuous space-temporal framework to explain how biofilm development dynamics is influenced by the metabolic interplay between two bacterial phenotypes composing the interior and the peripheral layer of the biofilm. Growth oscillations endorse the preservation of a high level of nutrients in the interior through diffusion and colony expansion in the periphery altogether. Our findings point out that perturbations of environmental conditions can result in the interruption of the interplay between cell populations and advocate alternative approaches to biofilm control strategies.   

Emergent simplicity in stochastic single-cell dynamics

TBA.   

Multicellular regulation of entropy, spatial order, and information

Many multicellular systems such as tissues and microbial biofilms consist of cells that secrete and sense signalling molecules. Understanding how collective behaviours of secrete-and-sense cells is an important challenge. We combined experimental and theoretical approaches to understand multicellular coordination of gene expression and spatial pattern formation among secrete-and-sense cells. We engineered secrete-and-sense yeast cells to show that cells can collectively and permanently remember a past event by reminding each other with their secreted signalling molecule. If one cell ``forgets'' then another cell can remind it. Cell-cell communication ensures a long-term (permanent) memory by overcoming common limitations of intracellular memory. We also established a new theoretical framework inspired by statistical mechanics to understand how fields of secrete-and-sense cells form spatial patterns. We introduce new metrics -- cellular entropy, cellular Hamiltonian, and spatial order index -- for dynamics of cellular automata that form spatial patterns. Our theory predicts how fast any spatial patterns form, how ordered they are, and establishes cellular Hamiltonian that, like energy for non-living systems, monotonically decreases towards a minimum over time.   

A stochastic moment based approach of the biochemical reaction networks

Biological systems are wonderfully complex. In order to gain a better understanding on how the complexity dictates the biological functions, it is important to investigate the underlying dynamic interactions of the biomolecular components. These interactions are governed by random events and thus stochastic models are needed to gain fundamental insight. However, stochastic models tend to be more difficult to fit to experimental data and are computationally demanding. We have developed a closure scheme method that calculates the stationary probability distribution of stochastic biochemical reaction networks. The method postulates that only a finite number of probability moments is necessary to capture all of the system's information, which can be achieved by maximizing the information entropy of the system. We attempt to provide useful information about the mesoscopic behavior of biochemical reaction networks with the help of the aforementioned closure scheme method. For our analysis, we study the Schl\"{o}gl model reaction network, a simple single component system that can exhibit bistability. Finally, we wonder whether the maximization of entropy can be a general criterion for establishing non-equilibrium steady state of biochemical reacting systems.   

Diffusion of a protein: the role of fluctuation-induced hydrodynamic coupling

The question of what determines the diffusion coefficient of a protein, or a macromolecular complex in general, is addressed by using a simple generic model of an asymmetric dumbbell that is made of two hydrodynamically coupled subunits. It is shown that equilibrium fluctuations can lead to an interplay between the internal and the external degrees of freedom and give rise to negative contributions to the overall diffusion coefficient. These fluctuation–induced contributions are controlled by the strength of the interactions between the subunits and their geometric characteristics. Our findings provide a significant step toward understanding the diffusion properties of proteins, which play a crucial role in their function and intracellular organization.   

Noise and the statistical mechanics of distributed transport in a colony of interacting agents

Inspired by the process of liquid food distribution between individuals in an ant colony, in this work we consider the statistical mechanics of resource dissemination between interacting agents with finite carrying capacity. The agents move inside a confined space (nest), pick up the food at the entrance of the nest and share it with other agents that they encounter. We calculate analytically and via a series of simulations the global food intake rate for the whole colony as well as observables describing how uniformly the food is distributed within the nest. Our model and predictions provide a useful benchmark to assess which strategies can lead to efficient food distribution within the nest and also to what level the observed food uptake rates and efficiency in food distribution are due to stochastic fluctuations or specific food exchange strategies by an actual ant colony.   

Regulation by a Critical Membrane

Many of the processes that underlie neural computation are carried out by ion channels embedded in the plasma membrane, a two-dimensional liquid that surrounds all cells. Recent experiments have demonstrated that this membrane is poised close to a liquid-liquid critical point in the Ising universality class. We use Monte Carlo simulations on the lattice Ising model to explore the ramifications of proximity to criticality for idealized ion channels that are allosterically coupled to Ising composition modes. Owing to diverging generalized susceptibilities, such a channel's activity becomes strongly influenced by perturbations that influence the membrane's critical temperature. In addition, the channel's kinetics acquire a range of time scales from its surrounding membrane, naturally leading to non-Markovian dynamics. Our model may account for the sensitivity of many diverse ion channels to chemically diverse anesthetics and other membrane perturbations.   

Exploring information transmission in gene networks using stochastic simulation and machine learning

How gene regulatory networks operate robustly despite environmental fluctuations and biochemical noise is a fundamental question in biology. Mathematically the stochastic dynamics of a gene regulatory network can be modeled using chemical master equation (CME), but nonlinearity and other challenges render analytical solutions of CMEs difficult to attain. While approaches of approximation and stochastic simulation have been devised for simple models, obtaining a more global picture of a system’s behaviors in high-dimensional parameter space without simplifying the system substantially remains a major challenge. Here we present a new framework for understanding and predicting the behaviors of gene regulatory networks in the context of information transmission among genes. Our approach uses stochastic simulation of the network followed by machine learning of the mapping between model parameters and network phenotypes such as information transmission behavior. We also devised ways to visualize high-dimensional phase spaces in intuitive and informative manners. We applied our approach to several gene regulatory circuit motifs, including both feedback and feedforward loops, to reveal underexplored aspects of their operational behaviors.