School of Mathematics and Computers, Wuhan Textile University, Wuhan 430200, People's Republic of China.
Key Laboratory of Computational Mathematics, Guangdong Province, and School of Mathematics, Sun Yat-sen University, Guangzhou 510275, People's Republic of China.
Phys Rev E. 2019 Jul;100(1-1):012128. doi: 10.1103/PhysRevE.100.012128.
The activation of a gene is a complex biochemical process and could involve small steps, creating a memory between individual events. However, the effect of this molecular memory was often neglected in previous work. How the molecular memory affects gene expression remains not fully explored. We analyze a stochastic model of bursty gene expression, where the waiting time from inactivation to activation is assumed to follow a nonexponential (in fact, Erlang) distribution. We derive the analytical expression for the gene-product distribution, which explicitly traces the effect of molecule memory. Interestingly, we find that the effect of molecular memory is equivalent to the introduction of feedback. In addition, we analytically show that the stationary distribution is always super-Poissonian, independent of the detail of the waiting-time distribution, and there is the optimal step size that minimizes the Fano factor for any given mean burst size and is a decreasing function of the mean burst size. These analytical results indicate that molecular memory is an unneglectable factor affecting gene expression.
基因激活是一个复杂的生化过程，可能涉及小步骤，在单个事件之间产生记忆。然而，在以前的工作中，这种分子记忆的影响往往被忽视了。分子记忆如何影响基因表达仍未被充分探索。我们分析了一个突发基因表达的随机模型，其中从失活到激活的等待时间假设遵循非指数（实际上是爱尔朗）分布。我们推导出了基因产物分布的解析表达式，该表达式明确地追踪了分子记忆的影响。有趣的是，我们发现分子记忆的影响相当于引入了反馈。此外，我们还分析表明，无论等待时间分布的细节如何，固定分布总是超泊松分布，并且对于任何给定的平均爆发大小，都存在最小化 Fano 因子的最佳步长，并且是平均爆发大小的递减函数。这些分析结果表明，分子记忆是影响基因表达的一个不可忽视的因素。
