随机基因表达三阶段模型的近似解析蛋白质分布
Approximate Analytical Protein Distributions for the Three-stage Model of Stochastic Gene Expression
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中文总结 AI 辅助
针对难以获取精确蛋白质分布的基因表达三阶段模型，研究人员利用非齐次泊松过程的划分特性，将其映射到简化模型，构建出两个解析近似，验证了其在中间 regime 下的高准确性。
中文摘要 AI 辅助
基因表达本质上是一个随机过程，会在遗传上完全相同的细胞群体中产生表型异质性。虽然对于大量复杂模型，可以获得蛋白质数量的精确统计矩，但相应的分布却要难得多，且在许多情况下难以处理。经典的基因表达三阶段模型完美说明了这一点，该模型将蛋白质水平的波动预测为启动子切换、转录、翻译和降解事件的函数，所有这些事件都具有线性倾向；推导其精确蛋白质分布仍然难以实现。在此，利用非齐次泊松过程的划分特性，我们将三阶段模型精确映射到一个简化模型。该简化模型使我们能够基于更简单模型精确解的β混合表示，为三阶段模型的完整蛋白质分布构建两个解析近似。我们表明，这两个近似在不同极限情况下是渐近精确的，并针对广泛的参数范围通过模拟验证了它们的准确性。尽管是近似的，但这些是三阶段模型蛋白质分布的首个解析表达式，在中间 regime 中具有很高的准确性。
英文摘要
Gene expression is an intrinsically stochastic process that generates phenotypic heterogeneity within genetically identical cell populations. While the exact statistical moments of the protein count can be obtained for a broad range of complex models, the corresponding distributions are significantly harder to obtain and intractable in many cases. The classical three-stage model of gene expression, which predicts fluctuations in protein levels as a function of promoter switching, transcription, translation, and degradation events all occurring with linear propensities, illustrates this perfectly; deriving its exact protein distribution remains elusive. Here, using the partitioning property of time-inhomogeneous Poisson processes, we develop an exact mapping of the three-stage model onto a simplified model. The simplified model allows us to formulate two analytical approximations for the full protein distribution of the three-stage model based on a beta-mixture representation of the exact solution for a simpler model. We show that the two approximations are asymptotically exact in different limiting cases and verify their accuracy against simulations for a broad range of parameters. Although approximate, these are the first analytical expressions for protein distributions for the three-stage model that are highly accurate in intermediate regimes.
