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...