Compartmentalization with nuclear landmarks yields random, yet precise, genome organization.

The 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 cophase 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 nonspecificity of phase separation and the slow chromosome dynamics. Together, our work reveals that the cophase separation provides a robust mechanism for us to produce functionally important 3D contacts without requiring thermodynamic equilibration that can be difficult to achieve.

Diffusion Attachment Model for Long Helical Antifreeze Proteins to Ice.

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 (kon, in m/s) as a function of the length and width of the AFP molecules. We find that kon 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 kBT for most AFPs and up to 9 kBT for Maxi, the largest known AFP. We compare the entropic resistance 1/kon 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.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale.

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to 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), which 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 toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor 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 the 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.

Diabat method for polymorph free energies: Extension to molecular crystals.

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.

The overdamped transmission coefficient: Recovering the true mean first passage time from an inaccurate reaction coordinate.

For inertial reaction dynamics, a transition state theory rate constant obtained from an inaccurate reaction coordinate can be a posteriori corrected with reactive flux methods. In contrast, reaction coordinate errors in overdamped mean first passage time calculations cannot be a posteriori corrected. This work develops an overdamped version of the transmission coefficient. The calculation requires information from committor analyses and an estimate of the diffusivity along the committor coordinate. We illustrate the calculation for a simple two-dimensional potential that admits exact solutions.

Gibbs free-energy differences between polymorphs via a diabat approach.

Polymorph free-energy differences are critical to several applications. A recently proposed diabat interpolation framework estimated free-energy differences between polymorphs by quadratic interpolation of diabats. This work extends the Zwanzig-Bennett relation to the NPT ensemble so that the diabats directly give Gibbs free-energy differences. We also demonstrate how the approach can be used in cases where the diabats are not parabolic. We illustrate the diabat method for Gibbs free-energy difference of zirconium (BCC and HCP phases) and compare it with the conventional lattice switch Monte Carlo approach.

OpenNucleome for high resolution nuclear structural and dynamical modeling.

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of "fixed points" within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

OpenNucleome for high-resolution nuclear structural and dynamical modeling.

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of 'fixed points' within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

Phase Separation and Correlated Motions in Motorized Genome.

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.

Diabat Interpolation for Polymorph Free-Energy Differences.

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.