Jeremy A. Owen

Cells remember their identities, in part, by using epigenetic marks—chemical modifications placed along the genome. How can mark patterns remain stable over cell generations despite their constant erosion by replication and other processes? We developed a theoretical model that reveals that three-dimensional (3D) genome organization can stabilize epigenetic memory as long as (i) there is a large density difference between chromatin compartments, (ii) modifying “reader-writer” enzymes spread marks in three dimensions, and (iii) the enzymes are limited in abundance relative to their histone substrates. Analogous to an associative memory that encodes memory in neuronal connectivity, mark patterns are encoded in a 3D network of chromosomal contacts. Our model provides a unified account of diverse observations and reveals a key role of 3D genome organization in epigenetic memory.

Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. We show how this bound sheds light on and unifies diverse sensitivity mechanisms, including kinetic proofreading and a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, representing in each case a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation and the function of biomolecular condensates.

The epigenetic state of a cell is associated with patterns of chemical modifications of histones (“marks”) across the genome, with different marks typical of active (euchromatic) and inactive (heterochromatic) genomic regions. These mark patterns can be stable over many cell generations—a form of epigenetic memory—despite their constant erosion due to replication and other processes. Enzymes that place histone marks are often stimulated by the same marks, as if “spreading” marks between neighboring histones. But this positive feedback may not be sufficient for stable memory, raising the question of what is. In this work, we show how 3D genome organization—in particular, the compartmental segregation of euchromatin and heterochromatin— could serve to stabilize an epigenetic memory, as long as (1) there is a large density difference between the compartments, (2) the modifying enzymes can spread marks in 3D, and (3) the enzymes are limited in abundance relative to their histone substrates. We introduce a biophysical model stylizing chromatin and its dynamics through the cell cycle, in which enzymes spread self-attracting marks on a polymer. We find that marks localize sharply and stably to the denser compartment, but over several cell generations, the model generically exhibits uncontrolled spread or global loss of marks. Strikingly, imposing limitation of the modifying enzymes—a plausible but oft-neglected element—totally changes this picture, yielding an epigenetic memory system, stable for hundreds of cell generations. Our model predicts a rich phenomenology to compare to experiments, and reveals basic design principles of putative epigenetic memory systems relying on compartmentalized 3D genome structure for their function.

Cell identity is governed by gene expression, regulated by transcription factor (TF) binding at cis-regulatory modules. Decoding the relationship between TF binding patterns and gene regulation is nontrivial, remaining a fundamental limitation in understanding cell decision-making. We developed the NetNC software to predict functionally active regulation of TF targets; demonstrated on nine datasets for the TFs Snail, Twist, and modENCODE Highly Occupied Target (HOT) regions. Snail and Twist are canonical drivers of epithelial to mesenchymal transition (EMT), a cell programme important in development, tumour progression and fibrosis. Predicted “neutral” (non-functional) TF binding always accounted for the majority (50% to 95%) of candidate target genes from statistically significant peaks and HOT regions had higher functional binding than most of the Snail and Twist datasets examined. Our results illuminated conserved gene networks that control epithelial plasticity in development and disease. We identified new gene functions and network modules including crosstalk with notch signalling and regulation of chromatin organisation, evidencing networks that reshape Waddington’s epigenetic landscape during epithelial remodelling. Expression of orthologous functional TF targets discriminated breast cancer molecular subtypes and predicted novel tumour biology, with implications for precision medicine. Predicted invasion roles were validated using a tractable cell model, supporting our approach.

Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of response by observing spontaneous equilibrium fluctuations. In this spirit, we derive here a collection of equalities and inequalities valid arbitrarily far from equilibrium that constrain the response of nonequilibrium steady states in terms of the strength of nonequilibrium driving. Our work opens new avenues for characterizing nonequilibrium response. As illustrations, we show how our results rationalize the energetic requirements of common biochemical motifs.

We consider the problem of how to construct a physical process over a finite state space X that applies some desired conditional distribution P to initial states to produce final states. This problem arises often in the thermodynamics of computation and nonequilibrium statistical physics more generally (e.g., when designing processes to implement some desired computation, feedback controller, or Maxwell demon). It was previously known that some conditional distributions cannot be implemented using any master equation that involves just the states in X. However, here we show that any conditional distribution P can in fact be implemented—if additional "hidden" states not in X are available. Moreover, we show that is always possible to implement P in a thermodynamically reversible manner. We then investigate a novel cost of the physical resources needed to implement a given distribution P: the minimal number of hidden states needed to do so. We calculate this cost exactly for the special case where P represents a single-valued function, and provide an upper bound for the general case, in terms of the nonnegative rank of P. These results show that having access to one extra binary degree of freedom, thus doubling the total number of states, is sufficient to implement any P with a master equation in a thermodynamically reversible way, if there are no constraints on the allowed form of the master equation. (Such constraints can greatly increase the minimal needed number of hidden states.) Our results also imply that for certain P that can be implemented without hidden states, having hidden states permits an implementation that generates less heat.