Department of Mathematics, University of Utah, Salt Lake City, Utah. Electronic address:
Published: November 2016
AI Article Synopsis
Article Abstract
The behavior of biochemical reactions requiring repeated enzymatic substrate modification depends critically on whether the enzymes act processively or distributively. Whereas processive enzymes bind only once to a substrate before carrying out a sequence of modifications, distributive enzymes release the substrate after each modification and thus require repeated bindings. Recent experimental and computational studies have revealed that distributive enzymes can act processively due to rapid rebindings (so-called quasi-processivity). In this study, we derive an analytical estimate of the probability of rapid rebinding and show that well-mixed ordinary differential equation models can use this probability to quantitatively replicate the behavior of spatial models. Importantly, rebinding requires that connections be added to the well-mixed reaction network; merely modifying rate constants is insufficient. We then use these well-mixed models to suggest experiments to 1) detect quasi-processivity and 2) test the theory. Finally, we show that rapid rebindings drastically alter the reaction's Michaelis-Menten rate equations.
Institute of Environmental Sciences, Department of Plant Pathology and Microbiology, Robert H. Smith Faculty of Agriculture, Food, and Environment, Hebrew University, Rehovot 76100, Israel.
Microbial communities thrive in virtually every habitat on Earth and are essential to the function of diverse ecosystems. Most microbial habitats are not spatially continuous and well-mixed, but rather composed, at the microscale, of many isolated or semi-isolated local patches of different sizes, resulting in partitioning of microbial populations into discrete local populations. The impact of this spatial fragmentation on population dynamics is not well-understood.
Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland; SIB Swiss Institute of Bioinformatics, Lausanne, CH-1015, Switzerland. Electronic address:
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model which bridges the Wright-Fisher and the Moran descriptions.
We show that the resolution-dependent loss of bimolecular reactions in spatiotemporal Reaction-Diffusion Master Equations (RDMEs) is in agreement with the mean-field Collins-Kimball (C-K) theory of diffusion-limited reaction kinetics. The RDME is a spatial generalization of the chemical master equation, which enables studying stochastic reaction dynamics in spatially heterogeneous systems. It uses a regular Cartesian grid to partition space into locally well-mixed reaction compartments and treats diffusion as a jump reaction between neighboring grid cells.
Unlabelled: Bacteria frequently inhabit surface-attached communities where rich "social" interactions can significantly alter their population-level behavior, including their response to antibiotics. Understanding these collective effects in spatially heterogeneous communities is an ongoing challenge. Here, we investigated the spatial organization that emerges from antibiotic exposure in initially randomly distributed communities containing antibiotic-resistant and -sensitive strains of , an opportunistic pathogen.
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie stochastic simulation algorithm (SSA) is often used to simulate these models; however, in many scenarios of interest, the computational cost quickly becomes prohibitive. This is further exacerbated in the Bayesian inference context when estimating parameters of chemical models, as the intractability of the likelihood requires multiple simulations of the underlying system.
