Ultrasensitivity and noise amplification in a model of<i>V. harveyi</i>quorum sensing

Bressloff, Paul C.

doi:10.1103/physreve.93.062418

Cited by 13 publications

(9 citation statements)

References 43 publications

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“…For non-oscillatory QS systems, it would be interesting to use the intracellular Lux-signaling pathways of [32] into our PDE-ODE model (1.0.1) to analyze sudden jumps between small and large amplitude steady-states for bistable QS systems as the cell density increases past a saddle-node bifurcation value. Moreover, (1.0.1) can be used to study the effect of spatial diffusion on the parallel QS signaling pathways associated with the marine bacterium V. harveyi, which were recently modeled in [5] through an ODE well-mixed limit. Our analysis in §3 has shown that the dimensionless PDE-ODE system (1.0.2) can be reduced to a limiting ODE system only when the bulk diffusivity satisfies D = O(− log ε), where ε is the dimensionless ratio of the cell radius to the length scale of the domain.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Iyaniwura,

Ward

2020

Preprint

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We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments or "cells" that have a permeable boundary. In this model, the cells are disks of a common radius ε 1 and they are spatially coupled through a passive extracellular bulk diffusion field with diffusivity D in a bounded 2-D domain. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit ε 1 of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. The analysis and computation of the nullspace of the GCEP as parameters are varied is central to the linear stability analysis. In the limit of large bulk diffusivity D = D0/ν 1, where ν ≡ −1/ log ε, an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation. The effect of the membrane permeability parameters, the reaction-kinetic parameters, the bulk diffusivity, and the spatial configuration of cells on both the emergence and synchronization of the oscillatory intracellular dynamics, as mediated by the bulk diffusion field, is analyzed in detail. The linear stability theory is validated from full numerical simulations of the PDE-ODE system, and from the reduced ODE model when D is large.

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Section: Discussion and Outlookmentioning

confidence: 99%

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Iyaniwura,

Ward

2020

Preprint

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“…Derive the contraction theory [2,27,28]. In general, we are considering dimension dynamical system: = ( , ), ∈ ℝ (1) Here, map : ℝ → ℝ is smooth nonlinear vector field, we then can define norms for vector and matrix and A.…”

Section: Global Convergencementioning

confidence: 99%

“…Quorum sensing [2][3][4] is important systematic stimulus and response that is sensitive to population density of interest. Functionally, ant is using quorum sensing to coordinate behaviors including foraging [5], house hunting [6,7], and cooperative transport [8].…”

Section: Introductionmentioning

confidence: 99%

Population model of Temnothorax albipennis as a distributed dynamical system: I. self-consistent threshold is an emergent property in combination of quorum sensing and chemical perception of limited resource

Qiu

2021

Preprint

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House hunting of ant, such as Temnothorax albipennis, has been shown to be a distributed dynamical system. Such a system includes agent-based algorithm [1], with agents in different roles including nest exploration, nest assessment, quorum sensing, and brood item transportation. Such an algorithm, if used properly, can be applied on artificial intelligent system, like robotic swarms. Despite of its complexity, we are focusing on the quorum sensing mechanism, which is also observed in bacteria model. In bacterial model, multiple biochemical networks co-exist within each cell, including binding of autoinducer and cognate receptors, and phosphorylation-dephosphorylation cycle. In ant hunting, we also have ant commitment to the nest, mimicking binding between autoinducer and cognate receptors. We also have assessment ant specific to one nest and information exchange between two assessment ants corresponding to different nests, which is similar process to the phosphorylation-dephosphorylation cycle in bacteria quorum sensing network. Due to the similarity between the two models, we borrow the idea from bacteria quorum sensing to clarify the definition of quorum threshold through biological plausible mechanism related to limited resource model. We further made use of the contraction analysis to explore the trade-off between decision split and decision consensus within ant population. Our work provides new generation model for understanding how ant adapt to the changing environment during quorum sensing.

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“…These linear equation can be analyzed along similar lines to the single-cell case using Fourier transforms and contour integration [55]. Here, we simply state the final results (for large N ).…”

Section: 32mentioning

confidence: 99%

Stochastic switching in biology: from genotype to phenotype

Bressloff¹

2017

J. Phys. A: Math. Theor.

126

116

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There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/ transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a systemsize expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this review is to provide a selfcontained survey of these mathematical methods, mainly within the context of biological switching processes at both the genotypic and phenotypic levels.

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Ultrasensitivity and noise amplification in a model ofV. harveyiquorum sensing

Cited by 13 publications

References 43 publications

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Population model of Temnothorax albipennis as a distributed dynamical system: I. self-consistent threshold is an emergent property in combination of quorum sensing and chemical perception of limited resource

Stochastic switching in biology: from genotype to phenotype

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