Epigenetic histone modifications play an important role in the maintenance of different cell phenotypes. The exact molecular mechanism for inheritance of the modification patterns over cell generations remains elusive. We construct a Potts-type model based on experimentally observed nearest-neighbor enzyme lateral interactions and nucleosome covalent modification state biased enzyme recruitment. The model can lead to effective nonlocal interactions among nucleosomes suggested in previous theoretical studies, and epigenetic memory is robustly inheritable against stochastic cellular processes.PACS numbers: 82.39. Rt, 87.17.Aa, 87.16.Yc, 87.16.A Nucleosomes are basic organizational units of chromatin in eukaryotic cells. A typical nucleosome has approximately 147 base pairs wrapped around a histone octamer and are interconnected by linker DNA of varying length (see Fig. 1) [1,2]. Covalent modifications of several amino acid residues on the histone core can lead to either active or repressive gene expression activities [3]. A dynamic equilibrium in the nucleosome modification state is attained due to a 'tug-of-war' between the associated covalent mark addition and removal enzymes [4]. The system may show a bistable behavior due to coexistence of repressive and active epigenetic states for different copies of a gene within the same cell [5].Experiments suggest that at least some of the nucleosome covalent patterns can be transmitted over a number of generations [1]. Although the actual mechanism for this epigenetic memory is unclear, a simple rule-based model by Dodd et al. [5] shows that robust bistability requires cooperative effects beyond neighboring nucleosomes, which they suggest is due to compact chromatin structures. Subsequent theoretical studies on yeast chromatin silencing [6], mouse stem cell differentiation [7], and plant flowering regulation [8] also conclude that this nonlocal cooperativity is necessary for generating stable epigenetic memory.In recent years molecular details on nucleosome covalent modification dynamics have been extensively studied. Measurements show that the typical residence time of a modification enzyme on chromatin is within sub-seconds to a few minutes [4]. Experimental observations also suggest that a modified nucleosome may have higher binding affinity for the corresponding enzymes [3,[9][10][11]. Another interesting observation is that a nucleosome bound modification enzyme complex laterally interacts with another bound to neighboring nucleosomes [10,12,13].Although the functional consequences of these interactions on epigenetic dynamics are unclear, recent work suggests that increased [14,15].In this work we construct a theoretical model aiming to bridge the gap between detailed molecular events occurring at the sub-second time scale, and the long-time scale epigenetic change dynamics that is typically in days or longer. To be specific we focus on lysine 4 (active) and lysine 9 (repressive) methylation on histone H3, although we expect the mechanism discussed here can be...

Osmosis through semi–permeable pores is a complex process by which solvent is driven by its free energy gradient towards a solute–rich reservoir. We have studied osmotic flow across a semi–permeable cylindrical pore using hard–sphere molecular dynamics which simulates osmosis in the absence of attractive forces between solute and solvent. In addition, we recorded the rates of pressure–driven solvent flow and the diffusive flow of labelled solvent under concentration gradients. It is apparent that there are differences, which are radius dependent, between viscous and diffusive solvent permeabilities in small pores. The osmotic flow rate is decreased by allowing solute entry into part of the pore, an effect which is not due to solute obstruction. The flow rate is dependent on the structure of the pore, which for asymmetric pores leads, surprisingly, to flow asymmetry or osmotic rectification. In the absence of any possible viscous rectification at these very low flow rates the effect correlates with changes between diffusive and pressure flows created by the presence of solute, an effect which has been predicted from thermodynamic arguments. The geometry of a semi–permeable pore in relation to the solute size is therefore required to predict the osmotic flow rate, a departure from the classical picture. Finally, by extracting transport parameters from simulations with pure solvent, we examine the departure of observed flow rate from that predicted by continuum mechanics, obtaining drag coefficients which we compare with those derived from hydrodynamics alone.

Particles that are embedded in fluid membranes or plates can induce bending if they impose a nonzero angle of contact. This bending mediates complicated effective particle-particle interactions. In the absence of tension, these interactions are nonpairwise additive and can result in clusters of particles with specific configurations that give rise to zero total membrane bending energy. Here, we consider an infinite periodic lattice of such membrane inclusions. Upon summing the nonpairwise interactions within a regular lattice, we find an unexpected infinite number of periodic lattices that preserve zero membrane bending energy. Elliptically shaped membrane inclusions further increase the phase space of this degeneracy.

A long-time fluctuation correlation function with a power-law form has been observed in recent single-molecule experiments by the Xie group. By analyzing the dynamics of an elastic network model (ENM) under white noise, we show that the observed long-time memory kernel can be explained by the discrepancy between the experimentally measured coordinate (or the coordinate directly coupled to protein function) and the minimum energy path of the system. Consequently, the dynamics of the measured collective coordinate has contributions from degrees of freedoms with a broad distribution of time scales. Our study also implies that the widely used ENM Hamiltonian should be viewed as a coarse-grained model of a protein over a rugged energy landscape. Large effective drag coefficients are needed to describe protein dynamics with the ENM's.