许多物理和生物系统依赖于材料通过多个独立阶段的进展。在病毒复制中,例如,病毒体进入细胞,经历一个复杂的过程,包括几个不同的阶段,然后最终积累和释放复制的病毒体。虽然这样的系统可能对构成这一进程的内部动力学有一些控制,许多人面临的一个挑战是在通常高度可变的外部环境下调节行为,作为系统输入。在这项工作中,我们通过线性多隔室模型研究了这个问题的简单模拟,该模型受到均值回复的Ornstein-Uhlenbeck过程形式的随机输入的影响,一种高斯过程。通过将系统表示为多维高斯过程,我们得出了几个与系统的协方差和自相关有关的闭式分析结果,量化平滑效应离散隔室提供多隔室系统。半分析结果表明,反馈和前馈回路可以增强系统的鲁棒性,模拟结果探讨了首次通过时间分布的棘手问题,这与病毒复制周期中的最终细胞裂解具有特定的相关性。最后,我们证明了在过程中看到的平滑是系统离散性的结果,并且不会在具有连续传输的系统中表现出来。虽然我们通过分析一个简单的线性问题取得了进展,我们的许多见解更普遍地适用,我们的工作使未来能够分析受到随机输入的多室过程。
Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behavior under what are often highly variable external environments acting as system inputs. In this work, we study a simple analog of this problem through a linear multicompartment model subject to a stochastic input in the form of a mean-reverting Ornstein-Uhlenbeck process, a type of Gaussian process. By expressing the system as a multidimensional Gaussian process, we derive several closed-form analytical results relating to the covariances and autocorrelations of the system, quantifying the smoothing effect discrete compartments afford multicompartment systems. Semianalytical results demonstrate that feedback and feedforward loops can enhance system robustness, and simulation results probe the intractable problem of the first passage time distribution, which has specific relevance to eventual cell lysis in the viral replication cycle. Finally, we demonstrate that the smoothing seen in the process is a consequence of the discreteness of the system, and does not manifest in systems with continuous transport. While we make progress through analysis of a simple linear problem, many of our insights are applicable more generally, and our work enables future analysis into multicompartment processes subject to stochastic inputs.