EXCOGITO, an Extensible Coarse-Graining Toolbox for the Investigation of Biomolecules by Means of Low-Resolution Representations.

Bottom-up coarse-grained (CG) models proved to be essential to complement and sometimes even replace all-atom representations of soft matter systems and biological macromolecules. The development of low-resolution models takes the moves from the reduction of the degrees of freedom employed, that is, the definition of a mapping between a system's high-resolution description and its simplified counterpart. Even in the absence of an explicit parametrization and simulation of a CG model, the observation of the atomistic system in simpler terms can be informative: this idea is leveraged by the mapping entropy, a measure of the information loss inherent to the process of coarsening. Mapping entropy lies at the heart of the extensible coarse-graining toolbox, EXCOGITO, developed to perform a number of operations and analyses on molecular systems pivoting around the properties of mappings. EXCOGITO can process an all-atom trajectory to compute the mapping entropy, identify the mapping that minimizes it, and establish quantitative relations between a low-resolution representation and the geometrical, structural, and energetic features of the system. Here, the software, which is available free of charge under an open-source license, is presented and showcased to introduce potential users to its capabilities and usage.

Quality assessment and community detection methods for anonymized mobility data in the Italian Covid context.

We discuss how to assess the reliability of partial, anonymized mobility data and compare two different methods to identify spatial communities based on movements: Greedy Modularity Clustering (GMC) and the novel Critical Variable Selection (CVS). These capture different aspects of mobility: direct population fluxes (GMC) and the probability for individuals to move between two nodes (CVS). As a test case, we consider movements of Italians before and during the SARS-Cov2 pandemic, using Facebook users' data and publicly available information from the Italian National Institute of Statistics (Istat) to construct daily mobility networks at the interprovincial level. Using the Perron-Frobenius (PF) theorem, we show how the mean stochastic network has a stationary population density state comparable with data from Istat, and how this ceases to be the case if even a moderate amount of pruning is applied to the network. We then identify the first two national lockdowns through temporal clustering of the mobility networks, define two representative graphs for the lockdown and non-lockdown conditions and perform optimal spatial community identification on both graphs using the GMC and CVS approaches. Despite the fundamental differences in the methods, the variation of information (VI) between them assesses that they return similar partitions of the Italian provincial networks in both situations. The information provided can be used to inform policy, for example, to define an optimal scale for lockdown measures. Our approach is general and can be applied to other countries or geographical scales.

Kinetics of radiation-induced DNA double-strand breaks through coarse-grained simulations.

Double-strand breaks (DSBs), i.e., the covalent cut of the DNA backbone over both strands, are a detrimental outcome of cell irradiation, bearing chromosomal aberrations and leading to cell apoptosis. In the early stages of the evolution of a DSB, the disruption of the residual interactions between the DNA moieties drives the fracture of the helical layout; in spite of its biological significance, the details of this process are still largely uncertain. Here, we address the mechanical rupture of DNA by DSBs via coarse-grained molecular dynamics simulations: the setup involves a 3855-bp DNA filament and diverse DSB motifs, i.e., within a range of distances between strand breaks (or DSB distance). By employing a coarse-grained model of DNA, we access the molecular details and characteristic timescales of the rupturing process. A sequence-nonspecific, linear correlation is observed between the DSB distance and the internal energy contribution to the disruption of the residual (Watson-Crick and stacking) contacts between DNA moieties, which is seemingly driven by an abrupt, cooperative process. Moreover, we infer an exponential dependence of the characteristic rupture times on the DSB distances, which we associate to an Arrhenius-like law of thermally-activated processes. This work lays the foundations of a detailed, mechanistic assessment of DSBs in silico as a benchmark to both numerical simulations and data from single-molecule experiments.

Gamma-Hemolysin Components: Computational Strategies for LukF-Hlg2 Dimer Reconstruction on a Model Membrane.

The gamma-hemolysin protein is one of the most common pore-forming toxins expressed by the pathogenic bacterium Staphylococcus aureus. The toxin is used by the pathogen to escape the immune system of the host organism, by assembling into octameric transmembrane pores on the surface of the target immune cell and leading to its death by leakage or apoptosis. Despite the high potential risks associated with Staphylococcus aureus infections and the urgent need for new treatments, several aspects of the pore-formation process from gamma-hemolysin are still unclear. These include the identification of the interactions between the individual monomers that lead to the formation of a dimer on the cell membrane, which represents the unit for further oligomerization. Here, we employed a combination of all-atom explicit solvent molecular dynamics simulations and protein-protein docking to determine the stabilizing contacts that guide the formation of a functional dimer. The simulations and the molecular modeling reveal the importance of the flexibility of specific protein domains, in particular the N-terminus, to drive the formation of the correct dimerization interface through functional contacts between the monomers. The results obtained are compared with the experimental data available in the literature.

Fast, Accurate, and System-Specific Variable-Resolution Modeling of Proteins.

In recent years, a few multiple-resolution modeling strategies have been proposed, in which functionally relevant parts of a biomolecule are described with atomistic resolution, with the remainder of the system being concurrently treated using a coarse-grained model. In most cases, the parametrization of the latter requires lengthy reference all-atom simulations and/or the usage of off-shelf coarse-grained force fields, whose interactions have to be refined to fit the specific system under examination. Here, we overcome these limitations through a novel multiresolution modeling scheme for proteins, dubbed coarse-grained anisotropic network model for variable resolution simulations, or CANVAS. This scheme enables a user-defined modulation of the resolution level throughout the system structure; a fast parametrization of the potential without the necessity of reference simulations; and the straightforward usage of the model on the most commonly used molecular dynamics platforms. The method is presented and validated with two case studies, the enzyme adenylate kinase and the therapeutic antibody pembrolizumab, by comparing the results obtained with the CANVAS model against fully atomistic simulations. The modeling software, implemented in Python, is made freely available for the community on a collaborative github repository.

Making sense of complex systems through resolution, relevance, and mapping entropy.

Complex systems are characterized by a tight, nontrivial interplay of their constituents, which gives rise to a multiscale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behavior of the system and separate them from less prominent players. Here, we tackle this problem making use of three measures of statistical information: Resolution, relevance, and mapping entropy. We address the links existing among them, taking the moves from the established relation between resolution and relevance and further developing novel connections between resolution and mapping entropy; by these means we can identify, in a quantitative manner, the number and selection of degrees of freedom of the system that preserve the largest information content about the generative process that underlies an empirical dataset. The method, which is implemented in a freely available software, is fully general, as it is shown through the application to three very diverse systems, namely, a toy model of independent binary spins, a coarse-grained representation of the financial stock market, and a fully atomistic simulation of a protein.

Information-theoretical measures identify accurate low-resolution representations of protein configurational space.

The steadily growing computational power employed to perform molecular dynamics simulations of biological macromolecules represents at the same time an immense opportunity and a formidable challenge. In fact, large amounts of data are produced, from which useful, synthetic, and intelligible information has to be extracted to make the crucial step from knowing to understanding. Here we tackled the problem of coarsening the conformational space sampled by proteins in the course of molecular dynamics simulations. We applied different schemes to cluster the frames of a dataset of protein simulations; we then employed an information-theoretical framework, based on the notion of resolution and relevance, to gauge how well the various clustering methods accomplish this simplification of the configurational space. Our approach allowed us to identify the level of resolution that optimally balances simplicity and informativeness; furthermore, we found that the most physically accurate clustering procedures are those that induce an ultrametric structure of the low-resolution space, consistently with the hypothesis that the protein conformational landscape has a self-similar organisation. The proposed strategy is general and its applicability extends beyond that of computational biophysics, making it a valuable tool to extract useful information from large datasets.

Structural Basis of Mutation-Dependent p53 Tetramerization Deficiency.

The formation of a tetrameric assembly is essential for the ability of the tumor suppressor protein p53 to act as a transcription factor. Such a quaternary conformation is driven by a specific tetramerization domain, separated from the central DNA-binding domain by a flexible linker. Despite the distance, functional crosstalk between the two domains has been reported. This phenomenon can explain the pathogenicity of some inherited or somatically acquired mutations in the tetramerization domain, including the widespread R337H missense mutation present in the population in south Brazil. In this work, we combined computational predictions through extended all-atom molecular dynamics simulations with functional assays in a genetically defined yeast-based model system to reveal structural features of p53 tetramerization domains and their transactivation capacity and specificity. In addition to the germline and cancer-associated R337H and R337C, other rationally designed missense mutations targeting a significant salt-bridge interaction that stabilizes the p53 tetramerization domain were studied (i.e., R337D, D352R, and the double-mutation R337D plus D352R). The simulations revealed a destabilizing effect of the pathogenic mutations within the p53 tetramerization domain and highlighted the importance of electrostatic interactions between residues 337 and 352. The transactivation assay, performed in yeast by tuning the expression of wild-type and mutant p53 proteins, revealed that p53 tetramerization mutations could decrease the transactivation potential and alter transactivation specificity, in particular by better tolerating negative features in weak DNA-binding sites. These results establish the effect of naturally occurring variations at positions 337 and 352 on p53's conformational stability and function.

Membrane binding of pore-forming γ-hemolysin components studied at different lipid compositions.

Methicillin-resistant Staphylococcus aureus is among those pathogens currently posing the highest threat to public health. Its host immune evasion strategy is mediated by pore-forming toxins (PFTs), among which the bi-component γ-hemolysin is one of the most common. The complexity of the porogenesis mechanism by γ-hemolysin poses difficulties in the development of antivirulence therapies targeting PFTs from S. aureus, and sparse and apparently contrasting experimental data have been produced. Here, through a large set of molecular dynamics simulations at different levels of resolution, we investigate the first step of pore formation, and in particular the effect of membrane composition on the ability of γ-hemolysin components, LukF and Hlg2, to steadily adhere to the lipid bilayer in the absence of proteinaceous receptors. Our simulations are in agreement with experimental data of γ-hemolysin pore formation on model membranes, which are here explained on the basis of the bilayer properties. Our computational investigation suggests a possible rationale to explain experimental data on phospholipid binding to the LukF component, and to hypothesise a mechanism by which, on purely lipidic bilayers, the stable anchoring of LukF to the cell surface facilitates Hlg2 binding, through the exposure of its N-terminal region. We expect that further insights on the mechanism of transition between soluble and membrane bound-forms and on the role played by the lipid molecules will contribute to the design of antivirulence agents with enhanced efficacy against methicillin-resistant S. aureus infections.

Communication pathways bridge local and global conformations in an IgG4 antibody.

The affinity of an antibody for its antigen is primarily determined by the specific sequence and structural arrangement of the complementarity-determining regions (CDRs). Recent evidence, however, points toward a nontrivial relation between the CDR and distal sites: variations in the binding strengths have been observed upon mutating residues separated from the paratope by several nanometers, thus suggesting the existence of a communication network within antibodies, whose extension and relevance might be deeper than insofar expected. In this work, we test this hypothesis by means of molecular dynamics (MD) simulations of the IgG4 monoclonal antibody pembrolizumab, an approved drug that targets the programmed cell death protein 1 (PD-1). The molecule is simulated in both the apo and holo states, totalling 4 µs of MD trajectory. The analysis of these simulations shows that the bound antibody explores a restricted range of conformations with respect to the apo one, and that the global conformation of the molecule correlates with that of the CDR. These results support the hypothesis that pembrolizumab featues a multi-scale hierarchy of intertwined global and local conformational changes. The analysis pipeline developed in this work is general, and it can help shed further light on the mechanistic aspects of antibody function.

A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules.

ABSTRACT: A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule.

Protein self-entanglement modulates successful folding to the native state: A multi-scale modeling study.

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules.

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

A Deep Graph Network-Enhanced Sampling Approach to Efficiently Explore the Space of Reduced Representations of Proteins.

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless development of computer architectures and algorithms. The consequent explosion in the number and extent of MD trajectories induces the need for automated methods to rationalize the raw data and make quantitative sense of them. Recently, an algorithmic approach was introduced by some of us to identify the subset of a protein's atoms, or mapping, that enables the most informative description of the system. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to such simplification; albeit relatively straightforward, this calculation can be time-consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. We rely on Deep Graph Networks, which provide extreme flexibility in handling structured input data and whose predictions prove to be accurate and-remarkably efficient. The trained network produces a speedup factor as large as 105 with respect to the algorithmic computation of the mapping entropy, enabling the reconstruction of its landscape by means of the Wang-Landau sampling scheme. Applications of this method reach much further than this, as the proposed pipeline is easily transferable to the computation of arbitrary properties of a molecular structure.

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators.

Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms-configuration assembly and hierarchical backmapping-to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an additional strong validation of their ability to equilibrate dense high-MW polymeric liquids. By demonstrating this consistency of knotting behaviour, our study opens the way for studying topological properties of polymer melts beyond time and length scales accessible to brute-force molecular dynamics simulations.

An Information-Theory-Based Approach for Optimal Model Reduction of Biomolecules.

In theoretical modeling of a physical system, a crucial step consists of the identification of those degrees of freedom that enable a synthetic yet informative representation of it. While in some cases this selection can be carried out on the basis of intuition and experience, straightforward discrimination of the important features from the negligible ones is difficult for many complex systems, most notably heteropolymers and large biomolecules. We here present a thermodynamics-based theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content. We employ this method to identify those reduced descriptions of proteins, in terms of a subset of their atoms, that retain the largest amount of information from the original model; we show that these highly informative representations share common features that are intrinsically related to the biological properties of the proteins under examination, thereby establishing a bridge between protein structure, energetics, and function.

Ligand-protein interactions in lysozyme investigated through a dual-resolution model.

A fully atomistic (AT) modeling of biological macromolecules at relevant length- and time-scales is often cumbersome or not even desirable, both in terms of computational effort required and a posteriori analysis. This difficulty can be overcome with the use of multiresolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive AT detail is crucial in the modeling of the active site in order to capture, for example, the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme with the inhibitor di-N-acetylchitotriose. Particular attention is payed to the impact of the mapping, that is, the selection of AT and coarse-grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.

Open-boundary Hamiltonian adaptive resolution. From grand canonical to non-equilibrium molecular dynamics simulations.

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume, and chemical potential. In practice, following the Hamiltonian adaptive resolution strategy, the system is partitioned into a domain of interest and a reservoir of non-interacting, ideal gas particles. An external potential, applied only in the interfacial region, balances the excess chemical potential of the system. To ensure that the size of the reservoir is infinite, we introduce a particle insertion/deletion algorithm to control the density in the ideal gas region. We show that it is possible to study non-equilibrium phenomena with this open-boundary molecular dynamics method. To this aim, we consider a prototypical confined liquid under the influence of an external constant density gradient. The resulting pressure-driven flow across the atomistic system exhibits a velocity profile consistent with the corresponding solution of the Navier-Stokes equation. This method conserves, on average, linear momentum and closely resembles experimental conditions. Moreover, it can be used to study various direct and indirect out-of-equilibrium conditions in complex molecular systems.

Tackling the Limitations of Copolymeric Small Interfering RNA Delivery Agents by a Combined Experimental-Computational Approach.

Despite the first successful applications of nonviral delivery vectors for small interfering RNA in the treatment of illnesses, such as the respiratory syncytial virus infection, the preparation of a clinically suitable, safe, and efficient delivery system still remains a challenge. In this study, we tackle the drawbacks of the existing systems by a combined experimental-computational in-depth investigation of the influence of the polymer architecture over the binding and transfection efficiency. For that purpose, a library of diblock copolymers with a molar mass of 30 kDa and a narrow dispersity (D < 1.12) was synthesized. We studied in detail the impact of an altered block size and/or composition of cationic diblock copolymers on the viability of each respective structure as a delivery agent for polynucleotides. The experimental investigation was further complemented by a computational study employing molecular simulations as well as an analytical description of systemic properties. This is the first report in which molecular dynamics simulations of RNA/cationic polymer complexes have been performed. Specifically, we developed and employed a coarse-grained model of the system at the molecular level to study the interactions between polymer chains and small interfering RNA. We were further able to confirm a threshold lengthbinding block/lengthnonbinding block ratio, which is required for efficient complexation of siRNA, and it was possible to find a correlation between the length of the cationic block and the size of the resulting polyplex. Hence, the combined insights from the experiments and the theoretical investigation resulted in a wealth of information about the properties of cationic diblock copolymers employed as RNA delivery agents, in particular regarding the molecular and mechanistic details of the interaction between the two components of a polyplex.

Steering a solute between coexisting solvation states: Revisiting nonequilibrium work relations and the calculation of free energy differences.

By analogy with single-molecule pulling experiments, we present a computational framework to obtain free energy differences between complex solvation states. To illustrate our approach, we focus on the calculation of solvation free energies (SFEs). However, the method can be readily extended to cases involving more complex solutes and solvation conditions as well as to the calculation of binding free energies. The main idea is to drag the solute across the simulation box where atomistic and ideal gas representations of the solvent coexist at constant temperature and chemical potential. At finite pulling speeds, the resulting work allows one to extract SFEs via nonequilibrium relations, whereas at infinitely slow pulling speeds, this process becomes equivalent to the thermodynamic integration method. Results for small molecules well agree with literature data and pave the way to systematic studies of arbitrarily large and complex molecules.