Modeling of covalent modifications of histones to estimate the binding affinity.

Covalent histone modifications such as methylation, acetylation, phosphorylation, and other epigenetic modifications of the chromatin play an essential role in regulating eukaryotic cells of which most of these reactions are catalyzed by the enzymes. The binding energy of enzymes is often determined by experimental data via mathematical and statistical models due to specific modifications. Many theoretical models have been introduced to study histone modifications and reprogramming experiments in mammalian cells, in which all efforts in determining the affinity binding are essential part of the work. Here, we introduce a one-dimensional statistical Potts model to accurately determine the enzyme's binding free energy using the experimental data for various types of cells. We study the methylation of lysine 4 and 27 on histone H3 and suppose that each histone has one modification site with one of the seven states: H3K27me3, H3K27me2, H3K27me1, unmodified, H3K4me1, H3K4me2, and H3K4me3. Based on this model, the histone covalent modification is described. Moreover, by using simulation data, the histone's binding free energy and the energy of chromatin states are determined, when they are subject to changes from unmodified to active or repressive states, by finding the probability of the transition.