Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

Abstract

Understanding the spatial organisation of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical -or epigenetic -marks that are deposited along the genome are thought to play an important, yet poorly understood, role in determining genome organisation and cell identity. The physical principles underlying the interplay between epigenetic dynamics and genome folding remain elusive. Here we propose and study a theory that assumes a coupling between epigenetic mark and genome densities, and which can be applied at the scale of the whole nucleus. We show that equilibrium models are not compatible with experiments and a qualitative agreement is recovered by accounting for non-equilibrium processes which can stabilise microphase separated epigenomic domains. We finally discuss the potential biophysical origin of these terms.Establishing distinct and inheritable cellular identities in different tissues is crucial to the existence of complex multi-cellular organisms. Because all cells contain the same DNA, cellular fate cannot be directed by genetic cues alone. Instead, tissue-specific 3D genome organisation [1] and biochemical (also called epigenetic) patterns [2] are thought to be key regulators of cellular fate [3]. Epigenetic patterns are composed of biochemical marks on DNA and histones -the proteins which package DNA into chromatin [4] -and can be deposited or removed by a range of specialised proteins [2] often recruited by complexes such as RNA polymerase [5] and Polycomb Repressive Complex (PRC) [6].Investigating the interplay between genome organisation and epigenetic patterns can shed light into the mechanism underlying cell fate decision [7,8]. To study the dynamics of epigenetic patterns, Ising-like models have been proposed in the biophysics literature [9][10][11][12][13][14]. Yet, the genome is poorly represented by a 1D array of Ising spins. Instead, it is a fluctuating polymer which can assume distinct spatial organisations in 3D and also in response to stimuli [15,16] and epigenetic cues [3].In this Letter, and the companion paper [17], we aim to analyse the link between chromatin large-scale organisation and epigenetic dynamics by using models for chromatin folding inspired by the physics of magnetic polymers [18]. We study a Landau-Ginzburg field theory where the dynamics of epigenetic marks is linked to that of genome folding within the nucleus. Our theory considers a 1D chain of Potts-like spins which is allowed to fluctuate in 3D. It markedly departs from previous works [19,20] as we formalise and study a theory for the epigenomic organisation of a whole eukaryotic nucleus and investigate how non-equilibrium processes affect its thermodynamics and kinetics.We show that while an equilibrium theory for epigenomic organisation captures some features seen in vivo, such as segregation of different epigenetic marks, it fails to explain the experimentally observed coexistence of diverse epigenetic and genomic domains in eukaryotic nuclei [2,21]. In light of...

Inference of emergent spatio-temporal processes from single-cell sequencing reveals feedback betweende novoDNA methylation and chromatin condensates

“…3E, S1A). This is consistent with predictions from theoretical polymer models (33,34). On larger genomic scales, we therefore predict the emergence of heterogeneously sized, local DNAme level dependent chromatin clusters.…”

Phase separation of chromatin brush driven by enzymatic reaction dynamics of histone posttranslational modifications

“…The mechanism of phase separation, demonstrated by our theory, is very different from our previous theories 17,18 and other theories [8][9][10][11][12][13][14][15][16]20 . Our previous theories 17,18 predict that the applied pressure stabilizes a condensed chromatin phase due to the attractive interactions between nucleosomes and that RNA polymerase (which destabilizes the condensed phase) is excluded from this phase due to the excluded volume interactions between RNA polymerase and nucleosomes.…”

“…It is therefore of interest to theoretically predict the physical mechanism involved in the symmetry breaking during the development. Theoretical efforts have been made to predict the phase separation of chromatin [8][9][10][11][12][13][14][15][16][17][18][19][20][21] . In many cases, chromatin is theoretically treated as copolymers of euchromatin-and heterochromatin-like blocks [8][9][10][11][12][13][14][15][16] .…”

The domain-within-domain packing of euchromatin can be described as multiplicative cascades

“…Such an assessment is distinctly simpler than the comparison against full image data. Considering that microphase separation has been proposed as a mechanism for the organization of different chromatin types and chromatin in general (3,(31)(32)(33)(34)(35), such a testing approach that is based in concrete experimental data seems relevant.…”

“…Such scenarios further raise the question how such a scale-free organization of the block copolymers could be brought about. Here, recent theoretical work suggests that local, catalytically self-amplifying chromatin marks can establish microphase patterns (33,35). Seeing that self-amplifying processes are frequently implied in the formation of scale-free patterns, such models seem promising candidates.…”