Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles ...has recently attracted attention especially in stochastic analysis and statistical physics of cellular biology, as novel experimental data is now available, but their interpretation remains challenging.} We derive here probability distribution functions for clusters that can either aggregate upon binding to form clusters of arbitrary sizes or a single cluster can dissociate into two sub-clusters. Using combinatorics properties and Markov chain representation, we compute steady-state distributions and moments for the number of particles per cluster in the case where the coagulation and fragmentation rates follow a detailed balance condition. We obtain explicit and asymptotic formulas for the cluster size and the number of clusters in terms of hypergeometric functions. To further characterize clustering, we introduce and discuss two mean times: one is time two particles spend together before they separate and other is the time they spend separated before they meet again for the first time. Finally we discuss applications of the present stochastic coagulation-fragmentation framework in cell biology.
Recovering a stochastic process from noisy ensembles of single particle trajectories (SPTs) is resolved here using the Langevin equation as a model. The massive redundancy contained in SPTs data ...allows recovering local parameters of the underlying physical model. We use several parametric and non-parametric estimators to compute the first and second moment of the process and to recover the local drift, its derivative and the diffusion tensor. Using a local asymptotic expansion of the estimators and computing the empirical transition probability function, we develop here a method to deconvolve the instrumental from the physical noise. We use numerical simulations to explore the range of validity for the estimators. The present analysis allows characterizing what can exactly be recovered from the statistics of super-resolution microscopy trajectories used in molecular trafficking and underlying cellular function.
We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of ...arbitrary sizes. A cluster can also dissociate into two subclusters with a uniform probability. To study the statistics of clusters, we combine a Markov chain analysis with a partition number approach. Interestingly, we obtain explicit formulas for the size and the number of clusters in terms of hypergeometric functions. Finally, we apply our analysis to study the statistical physics of telomeres (ends of chromosomes) clustering in the yeast nucleus and show that the diffusion-coagulation-fragmentation process can predict the organization of telomeres.
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