ELViM: Exploring Biomolecular Energy Landscapes through Multidimensional Visualization

Molecular dynamics (MD) simulations provide a powerful means of exploring the dynamic behavior of biomolecular systems at the atomic level. However, analyzing the vast data sets generated by MD simulations poses significant challenges. This article discusses the energy landscape visualization method (ELViM), a multidimensional reduction technique inspired by the energy landscape theory. ELViM transcends one-dimensional representations, offering a comprehensive analysis of the effective conformational phase space without the need for predefined reaction coordinates. We apply the ELViM to study the folding landscape of the antimicrobial peptide Polybia-MP1, showcasing its versatility in capturing complex biomolecular dynamics. Using dissimilarity matrices and a force-scheme approach, the ELViM provides intuitive visualizations, revealing structural correlations and local conformational signatures. The method is demonstrated to be adaptable, robust, and applicable to various biomolecular systems.

PyMEGABASE: Predicting cell-type-specific structural annotations of chromosomes using the epigenome

The folding patterns of interphase genomes in higher eukaryotes, as obtained from DNA-proximity-ligation or Hi-C experiments, are used to classify loci into structural classes called compartments and subcompartments. These structurally annotated (sub)compartments are known to exhibit specific epigenomic characteristics and cell-type-specific variations. To explore the relationship between genome structure and the epigenome, we present PyMEGABASE (PYMB), a maximum-entropy-based neural network model that predicts (sub)compartment annotations of a locus based solely on the local epigenome, such as ChIP-Seq of histone post-translational modifications. PYMB builds upon our previous model while improving robustness, capability to handle diverse inputs and user-friendly implementation. We employed PYMB to predict subcompartments for over a hundred human cell types available in ENCODE, shedding light on the links between subcompartments, cell identity, and epigenomic signals. The fact that PYMB, trained on data for human cells, can accurately predict compartments in mice suggests that the model is learning underlying physicochemical principles transferable across cell types and species. Reliable at higher resolutions (up to 5 kbp), PYMB is used to investigate compartment-specific gene expression. Not only can PYMB generate (sub)compartment information without Hi-C experiments, but its predictions are also interpretable. Analyzing PYMB's trained parameters, we explore the importance of various epigenomic marks in each subcompartment prediction. Furthermore, the predictions of the model can be used as input for OpenMiChroM software, which has been calibrated to generate three-dimensional structures of the genome. Detailed documentation of PYMB is available at https://pymegabase.readthedocs.io, including an installation guide using pip or conda, and Jupyter/Colab notebook tutorials.

Structural reorganization and relaxation dynamics of axially stressed chromosomes

Chromosomes endure mechanical stresses throughout the cell cycle; for example, resulting from the pulling of chromosomes by spindle fibers during mitosis or deformation of the nucleus during cell migration. The response to physical stress is closely related to chromosome structure and function. Micromechanical studies of mitotic chromosomes have revealed them to be remarkably extensible objects and informed early models of mitotic chromosome organization. We use a data-driven, coarse-grained polymer modeling approach to explore the relationship between the spatial organization of individual chromosomes and their emergent mechanical properties. In particular, we investigate the mechanical properties of our model chromosomes by axially stretching them. Simulated stretching led to a linear force-extension curve for small strain, with mitotic chromosomes behaving about 10-fold stiffer than interphase chromosomes. Studying their relaxation dynamics, we found that chromosomes are viscoelastic solids with a highly liquid-like, viscous behavior in interphase that becomes solid-like in mitosis. This emergent mechanical stiffness originates from lengthwise compaction, an effective potential capturing the activity of loop-extruding SMC complexes. Chromosomes denature under large strains via unraveling, which is characterized by opening of large-scale folding patterns. By quantifying the effect of mechanical perturbations on the chromosome's structural features, our model provides a nuanced understanding of in vivo mechanics of chromosomes.

Chromosome Modeling on Downsampled Hi-C Maps Enhances the Compartmentalization Signal

The human genome is organized within a nucleus where chromosomes fold into an ensemble of different conformations. Chromosome conformation capture techniques such as Hi-C provide information about the genome architecture by creating a 2D heat map. Initially, Hi-C map experiments were performed in human interphase cell lines. Recently, efforts were expanded to several different organisms, cell lines, tissues, and cell cycle phases where obtaining high-quality maps is challenging. Poor sampled Hi-C maps present high sparse matrices where compartments located far from the main diagonal are difficult to observe. Aided by recently developed models for chromatin folding and dynamics investigation, we introduce a framework to enhance the compartments' information far from the diagonal observed in experimental sparse matrices. The simulations were performed using the Open-MiChroM platform aided by new trained parameters in the minimal chromatin model (MiChroM) energy function. The simulations optimized on a downsampled experimental map (10% of the original data) allow the prediction of a contact frequency similar to that of the complete (100%) experimental Hi-C. The modeling results open a discussion on how simulations and modeling can increase the statistics and help fill in some Hi-C regions not captured by poor sampling experiments. Open-MiChroM simulations allow us to explore the 3D genome organization of different organisms, cell lines, and cell phases that often do not produce high-quality Hi-C maps.

Exploring Energy Landscapes of Intrinsically Disordered Proteins: Insights into Functional Mechanisms

Intrinsically disordered proteins (IDPs) lack a rigid three-dimensional structure and populate a polymorphic ensemble of conformations. Because of the lack of a reference conformation, their energy landscape representation in terms of reaction coordinates presents a daunting challenge. Here, our newly developed energy landscape visualization method (ELViM), a reaction coordinate-free approach, shows its prime application to explore frustrated energy landscapes of an intrinsically disordered protein, prostate-associated gene 4 (PAGE4). PAGE4 is a transcriptional coactivator that potentiates the oncogene c-Jun. Two kinases, namely, HIPK1 and CLK2, phosphorylate PAGE4, generating variants phosphorylated at different serine/threonine residues (HIPK1-PAGE4 and CLK2-PAGE4, respectively) with opposing functions. While HIPK1-PAGE4 predominantly phosphorylates Thr51 and potentiates c-Jun, CLK2-PAGE4 hyperphosphorylates PAGE4 and attenuates transactivation. To understand the underlying mechanisms of conformational diversity among different phosphoforms, we have analyzed their atomistic trajectories simulated using AWSEM forcefield, and the energy landscapes were elucidated using ELViM. This method allows us to identify and compare the population distributions of different conformational ensembles of PAGE4 phosphoforms using the same effective phase space. The results reveal a predominant conformational ensemble with an extended C-terminal segment of WT PAGE4, which exposes a functional residue Thr51, implying its potential of undertaking a fly-casting mechanism while binding to its cognate partner. In contrast, for HIPK1-PAGE4, a compact conformational ensemble enhances its population sequestering phosphorylated-Thr51. This clearly explains the experimentally observed weaker affinity of HIPK1-PAGE4 for c-Jun. ELViM appears as a powerful tool, especially to analyze the highly frustrated energy landscape representation of IDPs where appropriate reaction coordinates are hard to apprehend.

A Scalable Computational Approach for Simulating Complexes of Multiple Chromosomes

Significant efforts have been recently made to obtain the three-dimensional (3D) structure of the genome with the goal of understanding how structures may affect gene regulation and expression. Chromosome conformational capture techniques such as Hi-C, have been key in uncovering the quantitative information needed to determine chromatin organization. Complementing these experimental tools, co-polymers theoretical methods are necessary to determine the ensemble of three-dimensional structures associated to the experimental data provided by Hi-C maps. Going beyond just structural information, these theoretical advances also start to provide an understanding of the underlying mechanisms governing genome assembly and function. Recent theoretical work, however, has been focused on single chromosome structures, missing the fact that, in the full nucleus, interactions between chromosomes play a central role in their organization. To overcome this limitation, MiChroM (Minimal Chromatin Model) has been modified to become capable of performing these multi-chromosome simulations. It has been upgraded into a fast and scalable software version, which is able to perform chromosome simulations using GPUs via OpenMM Python API, called Open-MiChroM. To validate the efficiency of this new version, analyses for GM12878 individual autosomes were performed and compared to earlier studies. This validation was followed by multi-chain simulations including the four largest human chromosomes (C1-C4). These simulations demonstrated the full power of this new approach. Comparison to Hi-C data shows that these multiple chromosome interactions are essential for a more accurate agreement with experimental results. Without any changes to the original MiChroM potential, it is now possible to predict experimentally observed inter-chromosome contacts. This scalability of Open-MiChroM allow for more audacious investigations, looking at interactions of multiple chains as well as moving towards higher resolution chromosomes models.