Protein concentration gradients and switching diffusions

Bressloff, Paul C.; Lawley, Sean D.; Murphy, Patrick

doi:10.1103/physreve.99.032409

Cited by 32 publications

(22 citation statements)

References 40 publications

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“…In light of this, we consider an alternative way of characterizing the approach to steady state that is based on the so-called accumulation time. The latter was originally developed within the context of diffusion-based morphogenesis [25][26][27][28], but has more recently been applied to intracellular protein gradient formation [29] and to diffusion processes with stochastic resetting [30].…”

Section: Introductionmentioning

confidence: 99%

Accumulation time of diffusion in a two-dimensional singularly perturbed domain

Bressloff

2022

Proc. R. Soc. A.

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A general problem of current interest is the analysis of diffusion problems in singularly perturbed domains, within which small subdomains are removed from the domain interior and boundary conditions imposed on the resulting holes. One major application is to intracellular diffusion, where the holes could represent organelles or biochemical substrates. In this paper, we use a combination of matched asymptotic analysis and Green’s function methods to calculate the so-called accumulation time for relaxation to steady state. The standard measure of the relaxation rate is in terms of the principal non-zero eigenvalue of the negative Laplacian. However, this global measure does not account for possible differences in the relaxation rate at different spatial locations, is independent of the initial conditions, and relies on the assumption that the eigenvalues have sufficiently large spectral gaps. As previously established for diffusion-based morphogen gradient formation, the accumulation time provides a better measure of the relaxation process.

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Section: Introductionmentioning

confidence: 99%

Accumulation time of diffusion in a two-dimensional singularly perturbed domain

Bressloff

2022

Proc. R. Soc. A.

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“…In this paper, rather than obtaining the full time-dependent solution, we focus on a particular characterization of the relaxation to steady state known as the local accumulation time. The latter has previously been developed within the context of diffusion-based morphogenesis [13,14,16,17], but has more recently been applied to intracellular protein gradient formation [18] and to diffusion processes with stochastic resetting [19]. The accumulation time is easier to calculate than the full time-dependent solution, and provides a more compact representation of the relaxation to steady state.…”

Section: A Pair Of Cells Coupled By a Single Gap Junctionmentioning

confidence: 99%

Local accumulation time for diffusion in cells with gap junction coupling

Bressloff

2022

Preprint

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In this paper we analyze the relaxation to steady-state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both electrical and chemical communication between cells. Most analytical models of gap junctions focus on the steady-state diffusive flux and the associated effective diffusivity. Here we investigate the relaxation to steady state in terms of the so-called local accumulation time. The latter is commonly used to estimate the time to form a protein concentration gradient during morphogenesis. The basic idea is to treat the fractional deviation from the steady-state concentration as a cumulative distribution for the local accumulation time. One of the useful features of the local accumulation time is that it takes into account the fact that different spatial regions can relax at different rates. We consider both static and dynamic gap junction models. The former treats the gap junction as a resistive channel with effective permeability µ, whereas the latter represents the gap junction as a stochastic gate that randomly switches between an open and closed state. The local accumulation time is calculated by solving the diffusion equation in Laplace space and then taking the small-s limit. We show that the accumulation time is a monotonically increasing function of spatial position, with a jump discontinuity at the gap junction. This discontinuity vanishes in the limit µ → ∞ for a static junction and β → 0 for a stochastically-gated junction, where β is the rate at which the gate closes. Finally, our results are generalized to the case of a linear array of cells with nearest neighbor gap junction coupling.

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“…Two key examples are (i) LFA-1 receptors that alternate between fast and slow diffusive states [34,81] and (ii) AMPA receptors on the postsynaptic membrane that alternate within seconds between rapid diffusive and stationary states [16]. To extend the present work to such heterogeneous diffusion, one could assume the receptor diffusivity fluctuates between discrete states, as in [27,28,61].…”

Section: Comparison To Zwanzig Correctionmentioning

confidence: 99%

How Receptor Surface Diffusion and Cell Rotation Increase Association Rates

Lawley¹,

Miles²

2019

SIAM J. Appl. Math.

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Many biological processes are initiated when diffusing extracellular reactants reach receptors on a cell membrane. Calculating this arrival rate has therefore attracted theoretical interest for decades. However, previous work has largely ignored the fact that receptors diffuse on the two-dimensional cell membrane in a process called surface or lateral diffusion. In this work, we derive an analytical formula for this arrival rate that takes into account receptor surface diffusion and cell rotational diffusion. Our theory predicts that the impact of these diffusive processes can be quantitatively described in terms of the relative size of the cell and the reactant. As applications, our theory predicts that surface and rotational diffusion have a negligible impact on bacterial chemoreception and a moderate impact on bacteriophage adsorption. Mathematically, our model is a three-dimensional anisotropic diffusion equation coupled to boundary conditions that are described by stochastic differential equations. We first apply matched asymptotic analysis to this stochastic partial differential equation and then use probabilistic methods to show that the solution can be represented by a Brownian particle in a stochastic environment. This representation enables efficient numerical computation of solution statistics and validation of our analytical results.

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Protein concentration gradients and switching diffusions

Cited by 32 publications

References 40 publications

Accumulation time of diffusion in a two-dimensional singularly perturbed domain

Accumulation time of diffusion in a two-dimensional singularly perturbed domain

Local accumulation time for diffusion in cells with gap junction coupling

How Receptor Surface Diffusion and Cell Rotation Increase Association Rates

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