# Stochastic Kinetics of mRNA Molecules in a General Transcription Model

Source: [Stochastic Kinetics of mRNA Molecules in a General Transcription Model](<https://www.sota2.com/research/paper/68fa4c051e209131ce949f67>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-18T05:02:43.517Z

Authors: Yuntao Lu, Yunxin Zhang

Published: 2025-02-12T00:06:51.000Z

## Abstract

Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined relevant research to some over-simplified special cases like the Telegraph model. This article establishes a general, unified and computationally efficient framework for studying stochastic transcription kinetics. We consider a chemical reaction model of transcription and construct the time-dependent solution to the corresponding chemical master equation. A well-known matrix-form expression for steady-state binomial moments is recovered by calculating the temporal limit of the time-dependent dynamics. Two novel inequalities for binomial moments and the probability mass function are derived using techniques from functional analysis. It follows that the distribution of mRNA counts is upper-bounded by a constant multiple of Poisson distribution, thus mathematically proving the main statement of the Heavy-Tailed Law. Additionally, the standard binomial moment method is analyzed from a numerical perspective, where truncation error is estimated using our inequalities. Compared with some widely-used numerical methods, a key advantage of this result is the significantly lower computational complexity.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2502.08028>)

[PDF](<https://arxiv.org/pdf/2502.08028.pdf>)