We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form A + B ↔ C  . A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.

Samuel A. Isaacson

Ying Zhang

Bulletin of Mathematical Biology

BULLETIN OF MATHEMATICAL BIOLOGY 是数学生物学学会的官方期刊，传播原始研究成果和其他与生物学和数学科学接口相关的信息。贡献应该与这两个领域相关。为了适应广泛的新发展，该期刊接受各种投稿，包括：原创研究文章侧重于借助数学科学工具或新的数学工具和方法获得的新生物学见解，这些工具和方法已证明适用于生物学调查研究数学生物学教育评论评论观点，以及讨论对专业重要的问题的贡献所有贡献都经过同行评审。

The Bulletin of Mathematical Biology is the official journal of the Society for Mathematical Biology, dedicated to disseminating original research findings and information related to the interface between biology and mathematical sciences. Contributions should be relevant to both fields. The journal welcomes a variety of submissions, including original research articles that focus on new biological insights gained through mathematical tools or novel mathematical methods that have proven applicable to biological investigations; reviews on mathematical biology education; and discussions and viewpoints on issues of professional significance. All contributions undergo peer review.

《Bulletin of Mathematical Biology》是数学生物学学会的官方期刊，旨在传播原始研究成果及与生物学和数学科学交叉领域相关的信息。我们欢迎与这两个领域相关的各种投稿，包括：利用数学科学工具或新方法获得的新生物学见解的原创研究文章，这些工具和方法已被证明适用于生物学研究；数学生物学教育的评论；以及对专业重要问题的讨论和观点。所有投稿均经过同行评审。

Category	Quartile
数学	4
数学, 生物学	4
数学, 数学与计算生物学	4

An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions

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