Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes

Abstract

The spatiotemporal organization of chromatin influences many nuclear processes: from chromosome segregation to transcriptional regulation. To get a deeper understanding of these processes, it is essential to go beyond static viewpoints of chromosome structures, to accurately characterize chromatin’s diffusion properties. We present GP-FBM: a computational framework based on Gaussian processes and fractional Brownian motion to extract diffusion properties from stochastic trajectories of labeled chromatin loci. GP-FBM uses higher-order temporal correlations present in the data, therefore, outperforming existing methods. Furthermore, GP-FBM allows to interpolate incomplete trajectories and account for substrate movement when two or more particles are present. Using our method, we show that average chromatin diffusion properties are surprisingly similar in interphase and mitosis in mouse embryonic stem cells. We observe surprising heterogeneity in local chromatin dynamics, correlating with potential regulatory activity. We also present GP-Tool, a user-friendly graphical interface to facilitate usage of GP-FBM by the research community.

A quantitative modelling approach for DNA repair on a population scale

“…It is clear that more DNA-protein interactions are possible during longer time windows, since proteins have more time to travel longer distances to reach their target. The distance is denoted by the random variable R which has the expected squared displacement with diffusion constant [ 14 , 16 , 17 , 19 , 35 ]. Consequently, the searched volume is , where k ′ is a scaling constant.…”

“…Repair happens through the collective working of several proteins, which need to move through the environment and find their target. Nuclear diffusion has been studied and modelled in detail in different contexts such as chromatin [15][16][17] and protein movements [13,35], including the repair protein Rad4 [19]. It is clear that more DNA-protein interactions are possible during longer time windows, since proteins have more time to travel longer distances to reach their target.…”

“…Without assuming any specific molecular mechanism, we hypothesise that they are composed of two independent random variables namely accessibility to the lesion governing repair times and Brownian motions of proteins through the nucleus to find their target. It has been shown by several studies that proteins exhibit a range of different movements in the nucleus [13][14][15][16][17][18]. Diffusion has also been investigated and modelled in context of DNA repair for the Rad4-Rad23 complex [19].…”

Competition between transcription and loop extrusion modulates promoter and enhancer dynamics

“…For these two ESC lines, we imaged the labeled loci at high temporal resolution (500 ms per frame) in 2D with spinning disk confocal microscopy, using a set of optimized affine transformations to correct for chromatic aberrations and control for camera misalignment. Further enhancement of spot centroid localization was performed by fitting a 2D Gaussian shape to a precision of ~30 nm 25 . In line with previous high-throughput DNA FISH studies 52,53 , median inter-probe distances demonstrated a large cell-to-cell heterogeneity, varying from 69-286 nm (n = 72) for Sox2-SCR distances and from 71-426 nm (n = 49) for the control regions (Fig 1e; Table S1).…”

“…This is often characterized as subdiffusive movement, whereby the mean squared displacement (MSD) of the genomic element follows the relationship with time, t: MSD ∝ Dt α where D is the diffusion coefficient (a proxy for diffusive speed) and α, the anomalous exponent, is smaller than the value of 1 found in classical Brownian diffusion. Initial studies of randomly inserted tags suggested that heterochromatin was inherently less mobile than euchromatin in yeast 24 , but we recently reported significant locus-specific differences in chromatin diffusive properties at euchromatic regions in mouse embryonic stem cells (ESCs), suggesting finer-scale modulation of chromatin dynamics, potentially linked to underlying function 25 . As methods for tracking specific genomic regions in vivo has recently become available, researchers have asked whether the transcriptional activity of genes affects their mobility.…”