Bayesian parameter estimation in non-stationary semiflexible polymers from ensembles of trajectories

Abstract

During the cell-cycle and meiosis, during development, or in response to stress, chromosomes undertake dramatic programs of reorganisation, which can result in major changes to genomic architecture, as well as local changes to chromatin structure via chromatin remodelling and epigenetic modification. The biophysical properties of the genome may therefore vary significantly over time, from region to region, and from cell to cell.\n\nSemifleixble polymer models are frequently used to decipher the spatial and temporal aspects of chromosome organisation. Such models allow for parameter estimation from experimental observations (Bystricky et al., 2004, Ding et al., 2006, Koszul et al., 2008, Arbona et al., 2017), and so provide a concise quantification of the state of the system in terms of meaningful biophysical parameters, such as the compaction factor and bending-modulus. Simulation studies using appropriately parameterised models may also provide novel insights, and allow for predictions without confounding pleiotropic effects (Penfold et al., 2012), thus guiding future studies.\n\nMost semifleixble polymer models do not explicitly consider the spatial non-stationarity of chromosomes and chromatin. Furthermore, recent advances in chromosome conformation capture (3C)-based allow chromosome organisation to be (indirectly) measured in single cells (Belton et al., 2012, Nagano et al., 2013, 2016). The increasing availability of ensembles of trajectories sampled from potentially heterogeneous populations of cells means it is of interest to develop polymer statistic models that can capture both the spatial nonstationarity of the biophysical parameters, and the statistical relationships that exist within the population. Here we outline a statistical framework for non-stationary semiflexible polymers, and demonstrate how inference can be performed using ensembles of trajectories. For cells belonging to a homogenous population where the biophysical parameters are approximately identical in all cells, a (transformed) Gaussian process prior is assigned to the bending-modulus, and Markov chain Monte Carlo (MCMC) used to infer the posterior distribution of free parameters. For heterogeneous populations of cells, a transformed hierarchical GP (HGP) prior is assigned to the biophysical parameters, which naturally captures the statistical dependency of the parameters that exist across the population. Simulation studies demonstrate the accuracy of the model for homogenous and heterogeneous populations, while applications to yeast chromosome data demonstrates an improved ability to recapitulate trajectories of held out loci compared to related stationary models.\n\nCode used for these analyses, and a graphical user interface (GUI) for simulating non-stationary semifleixble polymer trajectories, have been implemented in MATLAB, and are available to download from: https://github.com/cap76/3MC.