Coletti Anna, Newhall Katherine A, Walker Benjamin L, Bloom Kerry
University of North Carolina at Chapel Hill, Department of Mathematics, Chapel Hill, North Carolina 27510, USA.
University of California, Irvine, Department of Mathematics, Irvine, California 92697, USA.
Phys Rev E. 2025 Apr;111(4-1):044407. doi: 10.1103/PhysRevE.111.044407.
An example system of collective behavior in the presence of active agents is the structural maintenance of chromosome (SMC) protein complexes within the nucleus that create an architecture to facilitate the organization and proper function of the genome. Of the diverse functions these SMC proteins are capable of producing, we focus on the creation of localized clusters of chromatin in the nucleolus through transient cross-links. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow cross-linking leads to no clusters, fast cross-linking produces rigid slowly changing clusters, while intermediate timescales produce flexible clusters that mediate gene interaction. By mathematically analyzing different relative scalings of the two sources of stochasticity, thermal fluctuations, and the force induced by the transient cross-links, we predict these three distinct regimes of cluster behavior. Standard time averaging that takes the fluctuations of the transient cross-link force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the cross-links and thermal noise with an effective energy landscape predicts the timescale-dependent lifetimes of flexible clusters. No clusters are predicted when the fluctuations of the transient cross-link force are taken to be large relative to thermal fluctuations. This mathematical perturbation analysis illuminates the importance of accounting for stochasticity in local incoherent transient forces to predict emergent complex biological behavior.
在存在活性因子的情况下，集体行为的一个示例系统是细胞核内的染色体结构维持（SMC）蛋白复合物，它们构建了一种架构以促进基因组的组织和正常功能。在这些SMC蛋白能够产生的多种功能中，我们关注通过瞬时交联在核仁中形成局部染色质簇。大规模模拟揭示了作为时间尺度函数的三种不同动态行为：缓慢交联不会导致形成簇，快速交联产生刚性的缓慢变化的簇，而中间时间尺度产生介导基因相互作用的柔性簇。通过数学分析两种随机性来源（热涨落和瞬时交联诱导的力）的不同相对尺度，我们预测了簇行为的这三种不同状态。将瞬时交联力的涨落设为零的标准时间平均预测了刚性簇的存在。考虑交联涨落和热噪声与有效能量景观的相互作用，预测了柔性簇的时间尺度依赖性寿命。当瞬时交联力的涨落相对于热涨落较大时，预测不会形成簇。这种数学微扰分析阐明了在局部非相干瞬态力中考虑随机性以预测涌现的复杂生物行为的重要性。
