Pairwise Contact Research Articles

Node features of chromosome structure networks and their connections to genome annotation

The 3D conformations of chromosomes can encode biological significance, and the implications of such structures have been increasingly appreciated recently. Certain chromosome structural features, such as A/B compartmentalization, are frequently extracted from Hi-C pairwise genome contact information (physical association between different regions of the genome) and compared with linear annotations of the genome, such as histone modifications and lamina association. We investigate how additional properties of chromosome structure can be deduced using an abstract graph representation of the contact heatmap, and describe specific network properties that can have a strong connection with some of these biological annotations. We constructed chromosome structure networks (CSNs) from bulk Hi-C data and calculated a set of site-resolved (node-based) network properties. These properties are useful for characterizing certain aspects of chromosomal structure. We examined the ability of network properties to differentiate several scenarios, such as haploid vs diploid cells, partially inverted nuclei vs conventional architecture, depletion of chromosome architectural proteins, and structural changes during cell development. We also examined the connection between network properties and a series of other linear annotations, such as histone modifications and chromatin states including poised promoter and enhancer labels. We found that semi-local network properties exhibit greater capability in characterizing genome annotations compared to diffusive or ultra-local node features. For example, the local square clustering coefficient can be a strong classifier of lamina-associated domains. We demonstrated that network properties can be useful for highlighting large-scale chromosome structure differences that emerge in different biological situations.

Simulating the rheology of dense suspensions using pairwise formulation of contact, lubrication and Brownian forces

Dense suspensions of solid particles in viscous liquid are ubiquitous in both industry and nature, and there is a clear need for efficient numerical routines to simulate their rheology and microstructure. Particles of micron size present a particular challenge: at low shear rates, colloidal interactions control their dynamics while at high rates, granular-like contacts dominate. While there are established particle-based simulation schemes for large-scale non-Brownian suspensions using only pairwise lubrication and contact forces, common schemes for colloidal suspensions generally are more computationally costly and thus restricted to relatively small system sizes. Here, we present a minimal particle-based numerical model for dense colloidal suspensions that incorporates Brownian forces in pairwise form alongside contact and lubrication forces. We show that this scheme reproduces key features of dense suspension rheology near the colloidal-to-granular transition, including both shear thinning due to entropic forces at low rates and shear thickening at high rates due to contact formation. This scheme is implemented in LAMMPS, a widely used open source code for parallelised particle-based simulations, with a runtime that scales linearly with the number of particles, making it amenable for large-scale simulations.

Computational predictions of 3D chromatin many-body interactions reveal roles of chromatin hubs in gene expression.

Chromatin 3D organization plays important roles in the regulation of gene expression. Hi-C measurements provide a projection of 3D chromatin organization onto a 2D heatmap, which depicts the population-averaged pairwise contact frequencies between all genomic elements. These 2D heatmaps highlight structural units of chromatin organization such as TADs. As distal cis-regulatory elements such as enhancers interact with promoters to increase the transcriptional output of target genes in a tissue-specific manner, quantifying cell-type specific chromatin spatial organization is therefore critical. However, TADs have been found to be largely invariant across cell types, suggesting that features of 2D Hi-C heatmaps are insufficient to gain understanding of tissue-specific gene expression. Another challenge is when multiple genomic elements are involved: It is not possible to obtain higher-order many-body interactions from Hi-C data. In order to address these problems, we apply CHROMATIX, a computational method which reconstructs ensembles of single-cell chromatin conformations by deconvolving Hi-C data. We reconstructed large ensembles (2×104) of independent 3D single-cell chromatin conformations which reproduce imaging, Dip-C, and 3D FISH single cell measurements. The reconstructed ensembles of single-cell chromatin structures further enable us to uncover statistically significant 3D hubs of higher-order many-body interactions. We uncovered chromatin hubs of many-bodies across hundreds of loci in B-lymphocyte cells. We illustrate the functional roles of these 3D hubs of many-body interactions in regulating gene expression. Using the example of eQTL associated genes, we show that higher-order 3D hubs provide the physical basis of differential gene expression, with detailed examples of hubs of 1-gene-to-many-eQTLs and many-genes-to-1-eQTL. Overall, our results show 3D chromatin many-body hubs are important for regulating gene expression, and they can be discovered through CHROMATIX computational modeling single-cell 3D chromatin conformations using population Hi-C data.

Coarse-grained model for simulating protein complexes: Folded vs. disordered proteins.

We develop a residue-level coarse-grained model for simulating multi-protein complexes. Contact potentials and distances between all pairs of residues are constructed via Boltzmann inversion of inter-molecular contacts of more than 22000 non-redundant unique interfaces of protein complexes. We show that the contact potentials between hydrophobic pairs are less sensitive to the residue identities when compared to the Miyazawa-Jernigan contact potentials derived from intra-molecular contacts. On the other hand, the contact potentials between hydrophilic pairs depend more strongly on the residue identities. These potentials and contact distances are adopted to the modified Wang-Frenkel potential for the short-range van der Waals (vdW) interactions and Deybe-Hückel electrostatics with a distance-dependent dielectric constant to simulate thermodynamic, kinetic, and structural properties of protein complexes of folded and disordered proteins. Upon parameterizing to fit the second virial coefficient of lysozyme and the binding affinities of the ubiquitin and ubiquitin-binding domains, we show that the potential form with a shorter cutoff distance performs best in predicting the binding affinities and structures for folded proteins. On the other hand, the structural properties of disordered proteins measured by the radius of gyration are in better agreement with experimental data at longer cutoff distances. Comparison between pairwise contact distributions for folded and disordered proteins shows that contacts between charged and polar residues are more prevalent in disordered proteins. The potentials are modified to account for this disparity. We show that the modified potentials perform well in predicting the binding affinities and structures for folded proteins as well as the radius of gyration for disordered proteins. The model can easily be implemented to many existing simulation packages to simulate multi-protein complexes containing disordered regions or proteins in order to gain insights into understanding many biological processes inside a cell.

Topologically designed electrospun peculiar three-sided walnut shaped microfiber array membrane exhibits superior poly-function

The designed microscopic structure partitions for poly-functional polymer composites are significant ways to accelerate the development of materials science. Herein, a novel flexible one-dimensional three-sided walnut shaped (abbreviated as TWS) microfiber is firstly designed and built via electrospinning by using an especial tri-axis spinneret. As a case research of expanding applications, the unique structured {[Tb(SSA)3(TPPO)2/polymethylmethacrylate (PMMA)]//[polyaniline (PANI)/PMMA]}//[CoFe2O4/PMMA] (marked as {[TST/P]//[P/P]}//[C/P]) photoluminescent-conductive-magnetic poly-functional TWS microfiber array membrane (abbreviated as PTMAM) are constructed by directional arrangement of the TWS microfibers. Through the elaborate topology design, the TWS microfiber realizes the division of three independent micro functional regions. By restricting the photoluminescent, conductive and magnetic media in their respective domains, the harmful interactions among the three functions are efficaciously avoided, thus enabling outstanding photoluminescent-conductive-magnetic poly-functions. By adjusting the concentrations of Tb(SSA)3(TPPO)2, PANI and CoFe2O4 NPs, PTMAM exhibits adjustable photoluminescence, aeolotropic conduction and magnetism. The photoluminescence can be used to detect whether PTMAM normally operates or abnormally operates in darkness. The formation mechanisms of TWS microfibers and array membrane are expounded. In addition, this unique TWS microfiber realizes the pairwise contact of each construction block, forming a unique heterostructure, which is expected to play a significant role in catalysis, energy storage and other fields.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions.

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

Resolving particle shape in DEM simulations from tabulated geometry information

DEM applications require versatile representations of the particle shapes. The downside of resolved shapes is the required computational effort. In this short communication, we propose new measures to reduce the computational effort needed to evaluate the pairwise contact of resolved polytopes in DEM simulations. Employing the Gilbert–Johnson–Keerthi (GJK) and Expanding Polytope algorithm (EPA) algorithm it is demonstrated that restricting the particle vertices to the actually required ones, which can be obtained from a directional tabulation prior to the simulation, reduces the computational effort drastically. The feasibility of this strategy is evaluated and discussed. Applicability is demonstrated by comparing the simulated granular outflow of regular polyhedrons with differently resolved edges from a hopper with experimental data. The results obtained disclose the strong effect of geometric features on particle discharge.

A unified statistical potential reveals that amino acid stickiness governs nonspecific recruitment of client proteins into condensates.

Membraneless organelles are cellular compartments that form by liquid–liquid phase separation of one or more components. Other molecules, such as proteins and nucleic acids, will distribute between the cytoplasm and the liquid compartment in accordance with the thermodynamic drive to lower the free energy of the system. The resulting distribution colocalizes molecular species to carry out a diversity of functions. Two factors could drive this partitioning: the difference in solvation between the dilute versus dense phase and intermolecular interactions between the client and scaffold proteins. Here, we develop a set of knowledge‐based potentials that allow for the direct comparison between stickiness, which is dominated by desolvation energy, and pairwise residue contact propensity terms. We use these scales to examine experimental data from two systems: protein cargo dissolving within phase‐separated droplets made from FG repeat proteins of the nuclear pore complex and client proteins dissolving within phase‐separated FUS droplets. These analyses reveal a close agreement between the stickiness of the client proteins and the experimentally determined values of the partition coefficients (R > 0.9), while pairwise residue contact propensities between client and scaffold show weaker correlations. Hence, the stickiness of client proteins is sufficient to explain their differential partitioning within these two phase‐separated systems without taking into account the composition of the condensate. This result implies that selective trafficking of client proteins to distinct membraneless organelles requires recognition elements beyond the client sequence composition.StatementEmpirical potentials for amino acid stickiness and pairwise residue contact propensities are derived. These scales are unique in that they enable direct comparison of desolvation versus contact terms. We find that partitioning of a client protein to a condensate is best explained by amino acid stickiness.

Identifying 3D Genome Organization in Diploid Organisms via Euclidean Distance Geometry

The spatial organization of the DNA in the cell nucleus plays an important role for gene regulation, DNA replication, and genomic integrity. Through the development of chromosome conformation capture experiments (such as 3C, 4C, Hi-C) it is now possible to obtain the contact frequencies of the DNA at the whole-genome level. In this paper, we study the problem of reconstructing the 3D organization of the genome from such whole-genome contact frequencies. A standard approach is to transform the contact frequencies into noisy distance measurements and then apply semidefinite programming (SDP) formulations to obtain the 3D configuration. However, neglected in such reconstructions is the fact that most eukaryotes including humans are diploid and therefore contain two copies of each genomic locus. We prove that the 3D organization of the DNA is not identifiable from distance measurements derived from contact frequencies in diploid organisms. In fact, there are infinitely many solutions even in the noise-free setting. We then discuss various additional biologically relevant and experimentally measurable constraints (including distances between neighboring genomic loci and higher-order interactions) and prove identifiability under these conditions. Furthermore, we provide SDP formulations for computing the 3D embedding of the DNA with these additional constraints and show that we can recover the true 3D embedding with high accuracy from both noiseless and noisy measurements. Finally, we apply our algorithm to real pairwise and higher-order contact frequency data and show that we can recover known genome organization patterns.

Circuit topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and scaling

SummaryReciprocal regulation of genome topology and function is a fundamental and enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers the opportunity to unravel this relationship. However, there is a need for a comprehensive theoretical framework in order to extract topological information for genome characterization and comparison. Here, we develop a toolbox for topological analysis based on Circuit Topology, allowing for the quantification of inter- and intracellular genomic heterogeneity, at various levels of fold complexity: pairwise contact arrangement, higher-order contact arrangement, and topological fractal dimension. Single-cell Hi-C data were analyzed and characterized based on topological content, revealing not only a strong multiscale heterogeneity but also highly conserved features such as a characteristic topological length scale and topological signature motifs in the genome. We propose that these motifs inform on the topological state of the nucleus and indicate the presence of active loop extrusion.

Extracting multi-way chromatin contacts from Hi-C data.

There is a growing realization that multi-way chromatin contacts formed in chromosome structures are fundamental units of gene regulation. However, due to the paucity and complexity of such contacts, it is challenging to detect and identify them using experiments. Based on an assumption that chromosome structures can be mapped onto a network of Gaussian polymer, here we derive analytic expressions for n-body contact probabilities (n > 2) among chromatin loci based on pairwise genomic contact frequencies available in Hi-C, and show that multi-way contact probability maps can in principle be extracted from Hi-C. The three-body (triplet) contact probabilities, calculated from our theory, are in good correlation with those from measurements including Tri-C, MC-4C and SPRITE. Maps of multi-way chromatin contacts calculated from our analytic expressions can not only complement experimental measurements, but also can offer better understanding of the related issues, such as cell-line dependent assemblies of multiple genes and enhancers to chromatin hubs, competition between long-range and short-range multi-way contacts, and condensates of multiple CTCF anchors.

Three-body crossover from a Cooper triple to a bound trimer state in three-component Fermi gases near a triatomic resonance

We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two- and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length $a_{-}$ for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.

Overcoming the Heuristic Nature of k‐means Clustering: Identification and Characterization of Binding Modes from Molecular Recognition Simulations

The accurate and reproducible detection and description of thermodynamic states in computational data is a nontrivial problem, particularly when the number of states is unknown a priori and for large, flexible chemical systems and complexes. To this end, we report a novel clustering protocol that combines high-resolution structural representation, brute-force repeat clustering, and optimization of clustering statistics to reproducibly identify the number of clusters present in a data set (k) for simulated ensembles of butyrylcholinesterase in complex with two previously studied organophosphate inhibitors. Each structure within our simulated ensembles was depicted as a high-dimensionality vector with components defined by specific protein−inhibitor contacts at the chemical group level and the magnitudes of these components defined by their respective extents of pair-wise atomic contact, thus allowing for algorithmic differentiation between varying degrees of interaction. These surface-weighted interaction fingerprints were tabulated for each of over 1 million structures from more than 100 μs of all atom molecular dynamics simulation per complex and used as the input for repetitive k-means clustering. Minimization of cluster population variance and range afforded accurate and reproducible identification of k, thereby allowing for the characterization of discrete binding modes from molecular simulation data in the form of contact tables that concisely encapsulate the observed intermolecular contact motifs. While the protocol presented herein to determine k and achieve non-heuristic clustering is demonstrated on data from massive atomistic simulation, our approach is generalizable to other data types and clustering algorithms, and is tractable with limited computational resources.

Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.

Inferring chromosome radial organization from Hi-C data

BackgroundThe nonrandom radial organization of eukaryotic chromosome territories (CTs) inside the nucleus plays an important role in nuclear functional compartmentalization. Increasingly, chromosome conformation capture (Hi-C) based approaches are being used to characterize the genome structure of many cell types and conditions. Computational methods to extract 3D arrangements of CTs from this type of pairwise contact data will thus increase our ability to analyze CT organization in a wider variety of biological situations.ResultsA number of full-scale polymer models have successfully reconstructed the 3D structure of chromosome territories from Hi-C. To supplement such methods, we explore alternative, direct, and less computationally intensive approaches to capture radial CT organization from Hi-C data. We show that we can infer relative chromosome ordering using PCA on a thresholded inter-chromosomal contact matrix. We simulate an ensemble of possible CT arrangements using a force-directed network layout algorithm and propose an approach to integrate additional chromosome properties into our predictions. Our CT radial organization predictions have a high correlation with microscopy imaging data for various cell nucleus geometries (lymphoblastoid, skin fibroblast, and breast epithelial cells), and we can capture previously documented changes in senescent and progeria cells.ConclusionsOur analysis approaches provide rapid and modular approaches to screen for alterations in CT organization across widely available Hi-C data. We demonstrate which stages of the approach can extract meaningful information, and also describe limitations of pairwise contacts alone to predict absolute 3D positions.

Multi- π+ systems in a finite volume

We present a formalism to describe two-$\pi^+$ and three-$\pi^+$ dynamics in finite volume, the formalism is based on combination of a variational approach and the Faddeev method. Both pair-wise and three-body interactions are included in the presentation. Impacts of finite lattice spacing and the cubic lattice symmetry are also discussed. To illustrate application of the formalism, the pair-wise contact interaction that resembles the leading order interaction terms in chiral effective theory is used to analyze recent lattice results.

Overcoming the Heuristic Nature of k-Means Clustering: Identification and Characterization of Binding Modes from Simulations of Molecular Recognition Complexes.

The accurate and reproducible detection and description of thermodynamic states in computational data is a nontrivial problem, particularly when the number of states is unknown a priori and for large, flexible chemical systems and complexes. To this end, we report a novel clustering protocol that combines high-resolution structural representation, brute-force repeat clustering, and optimization of clustering statistics to reproducibly identify the number of clusters present in a data set (k) for simulated ensembles of butyrylcholinesterase in complex with two previously studied organophosphate inhibitors. Each structure within our simulated ensembles was depicted as a high-dimensionality vector with components defined by specific protein-inhibitor contacts at the chemical group level and the magnitudes of these components defined by their respective extents of pair-wise atomic contact, thus allowing for algorithmic differentiation between varying degrees of interaction. These surface-weighted interaction fingerprints were tabulated for each of over 1 million structures from more than 100 μs of all-atom molecular dynamics simulation per complex and used as the input for repetitive k-means clustering. Minimization of cluster population variance and range afforded accurate and reproducible identification of k, thereby allowing for the characterization of discrete binding modes from molecular simulation data in the form of contact tables that concisely encapsulate the observed intermolecular contact motifs. While the protocol presented herein to determine k and achieve non-heuristic clustering is demonstrated on data from massive atomistic simulation, our approach is generalizable to other data types and clustering algorithms, and is tractable with limited computational resources.

Nonlinear diffusion and hyperuniformity from Poisson representation in systems with interaction mediated dynamics

We introduce a minimal model of interacting particles relying on conservation of the number of particles and interactions respecting conservation of the center of mass. The dynamics in our model is directly amenable to simple pairwise interactions between particles leading to particle displacements, ensues from this what we call interaction mediated dynamics. Inspired by binary reaction kinetics-like rules, we model systems of interacting agents activated upon pairwise contact. Using Poisson representations, our model is amenable to an exact nonlinear stochastic differential equation. We derive analytically its hydrodynamic limit, which turns out to be a nonlinear diffusion equation of porous medium type valid even far from steady state. We obtain exact self-similar solutions with subdiffusive scaling and compact support. The nonequilibrium steady state of our model in the dense phase displays hyperuniformity which we are able to predict from our analytical approach. We reinterpret hyperuniformity as stemming from correlations in particles displacements induced by the conservation of center of mass. Although quite simplistic, this model could in principle be realized experimentally at different scales by active particles systems.

Evolution of protein interfaces in multimers and fibrils.

A majority of cellular proteins function as part of multimeric complexes of two or more subunits. Multimer formation requires interactions between protein surfaces that lead to closed structures, such as dimers and tetramers. If proteins interact in an open-ended way, uncontrolled growth of fibrils can occur, which is likely to be detrimental in most cases. We present a statistical physics model that allows aggregation of proteins as either closed dimers or open fibrils of all lengths. We use pairwise amino-acid contact energies to calculate the energies of interacting protein surfaces. The probabilities of all possible aggregate configurations can be calculated for any given sequence of surface amino acids. We link the statistical physics model to a population genetics model that describes the evolution of the surface residues. When proteins evolve neutrally, without selection for or against multimer formation, we find that a majority of proteins remain as monomers at moderate concentrations, but strong dimer-forming or fibril-forming sequences are also possible. If selection is applied in favor of dimers or in favor of fibrils, then it is easy to select either dimer-forming or fibril-forming sequences. It is also possible to select for oriented fibrils with protein subunits all aligned in the same direction. We measure the propensities of amino acids to occur at interfaces relative to noninteracting surfaces and show that the propensities in our model are strongly correlated with those that have been measured in real protein structures. We also show that there are significant differences between amino acid frequencies at isologous and heterologous interfaces in our model, and we observe that similar effects occur in real protein structures.

A pairwise surface contact equation of state: COSMO-SAC-Phi

In this work a new method for inclusion of pressure effects in COSMO-type activity coefficient models is proposed. The extension consists in the direct combination of COSMO-SAC and lattice-fluid ideas by the inclusion of free volume in form of holes. The effort when computing pressure (given temperature, volume, and mole numbers) with the proposed model is similar to the cost for computing activity coefficients with any COSMO-type implementation. For given pressure, computational cost increases since an iterative method is needed. This concept was tested for representative substances and mixtures, ranging from light gases to molecules with up to 10 carbons. The proposed model was able to correlate experimental data of saturation pressure and saturated liquid volume of pure substances with deviations of 1.16% and 1.59%, respectively. In mixture vapor-liquid equilibria predictions, the resulting model was superior to Soave-Redlich-Kwong with Mathias-Copeman α-function and the classic van der Waals mixing rule in almost all cases tested and similar to PSRK method, from low pressures to over 100 bar. Good predictions of liquid-liquid equilibrium were also observed, performing similarly to UNIFAC-LLE, with improved responses at high temperatures and pressures.