The human genome is arranged in the cell nucleus nonrandomly, and phase separation has been proposed as an important driving force for genome organization. However, the cell nucleus is an active system, and the contribution of nonequilibrium activities to phase separation and genome structure and dynamics remains to be explored. We simulated the genome using an energy function parametrized with chromosome conformation capture (Hi-C) data with the presence of active, nondirectional forces that break the detailed balance. We found that active forces that may arise from transcription and chromatin remodeling can dramatically impact the spatial localization of heterochromatin. When applied to euchromatin, active forces can drive heterochromatin to the nuclear envelope and compete with passive interactions among heterochromatin that tend to pull them in opposite directions. Furthermore, active forces induce long-range spatial correlations among genomic loci beyond single chromosome territories. We further showed that the impact of active forces could be understood from the effective temperature defined as the fluctuation–dissipation ratio. Our study suggests that nonequilibrium activities can significantly impact genome structure and dynamics, producing unexpected collective phenomena.
The three-dimensional (3D) organization of eukaryotic genomes plays an important role in genome function. While significant progress has been made in deciphering the folding mechanisms of individual chromosomes, the principles of the dynamic large-scale spatial arrangement of all chromosomes inside the nucleus are poorly understood. We use polymer simulations to model the diploid human genome compartmentalization relative to nuclear bodies such as nuclear lamina, nucleoli, and speckles. We show that a self-organization process based on a co-phase separation between chromosomes and nuclear bodies can capture various features of genome organization, including the formation of chromosome territories, phase separation of A/B compartments, and the liquid property of nuclear bodies. The simulated 3D structures quantitatively reproduce both sequencing-based genomic mapping and imaging assays that probe chromatin interaction with nuclear bodies. Importantly, our model captures the heterogeneous distribution of chromosome positioning across cells, while simultaneously producing well-defined distances between active chromatin and nuclear speckles. Such heterogeneity and preciseness of genome organization can coexist due to the non-specificity of phase separation and the slow chromosome dynamics. Together, our work reveals that the co-phase separation provides a robust mechanism for encoding functionally important 3D contacts without requiring thermodynamic equilibration that can be difficult to achieve.
Some of the most potent antifreeze proteins (AFPs) are approximately rigid helical structures that bind with one side in contact with the ice surface at specific orientations. These AFPs take random orientations in solution; however, most orientations become sterically inaccessible as the AFP approaches the ice surface. The effect of these inaccessible orientations on the rate of adsorption of AFP to ice has never been explored. Here, we present a diffusion-controlled theory of adsorption kinetics that accounts for these orientational restrictions to predict a rate constant for adsorption (k on, in m/s) as a function of the length and width of the AFP molecules. We find that k on decreases with length and diameter of the AFP and is almost proportional to the inverse of the area of the binding surface. We demonstrate that the restricted orientations create an entropic barrier to AFP adsorption, which we compute to be approximately 7 k BT for most AFPs and up to 9 k BT for Maxi, the largest known AFP. We compare the entropic resistance 1/k on to resistances for diffusion through boundary layers and across typical distances in the extracellular matrix and find that these entropic and diffusion resistances could become comparable in the small confined spaces of biological environments.
The adsorption of large rod-like molecules or crystallites on a flat crystal face, like Buffon's needle, requires the rods to "land" with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long helical antifreeze proteins (AFPs) that bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses towards the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule or explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.
Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.
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