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.

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.

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.

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.

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.

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.

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.

Searching the Optimal Folding Routes of a Complex Lasso Protein.

Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Go-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.

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.

Concurrent coupling of realistic and ideal models of liquids and solids in Hamiltonian adaptive resolution simulations.

To understand the properties of a complex system it is often illuminating to perform a comparison with a simpler, even idealised one. A prototypical application of this approach is the calculation of free energies and chemical potentials in liquids, which can be decomposed in the sum of ideal and excess contributions. In the same spirit, in computer simulations it is possible to extract useful information on a given system making use of setups where two models, an accurate one and a simpler one, are concurrently employed and directly coupled. Here, we tackle the issue of coupling atomistic or, more in general, interacting models of a system with the corresponding idealised representations: for a liquid, this is the ideal gas, i.e. a collection of non-interacting particles; for a solid, we employ the ideal Einstein crystal, a construct in which particles are decoupled from one another and restrained by a harmonic, exactly integrable potential. We describe in detail the practical and technical aspects of these simulations, and suggest that the concurrent usage and coupling of realistic and ideal models represents a promising strategy to investigate liquids and solids in silico.

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method.

The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood-Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard-Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions.

Using force-based adaptive resolution simulations to calculate solvation free energies of amino acid sidechain analogues.

The calculation of free energy differences is a crucial step in the characterization and understanding of the physical properties of biological molecules. In the development of efficient methods to compute these quantities, a promising strategy is that of employing a dual-resolution representation of the solvent, specifically using an accurate model in the proximity of a molecule of interest and a simplified description elsewhere. One such concurrent multi-resolution simulation method is the Adaptive Resolution Scheme (AdResS), in which particles smoothly change their resolution on-the-fly as they move between different subregions. Before using this approach in the context of free energy calculations, however, it is necessary to make sure that the dual-resolution treatment of the solvent does not cause undesired effects on the computed quantities. Here, we show how AdResS can be used to calculate solvation free energies of small polar solutes using Thermodynamic Integration (TI). We discuss how the potential-energy-based TI approach combines with the force-based AdResS methodology, in which no global Hamiltonian is defined. The AdResS free energy values agree with those calculated from fully atomistic simulations to within a fraction of kBT. This is true even for small atomistic regions whose size is on the order of the correlation length, or when the properties of the coarse-grained region are extremely different from those of the atomistic region. These accurate free energy calculations are possible because AdResS allows the sampling of solvation shell configurations which are equivalent to those of fully atomistic simulations. The results of the present work thus demonstrate the viability of the use of adaptive resolution simulation methods to perform free energy calculations and pave the way for large-scale applications where a substantial computational gain can be attained.

From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics.

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

A multi-resolution model to capture both global fluctuations of an enzyme and molecular recognition in the ligand-binding site.

In multi-resolution simulations, different system components are simultaneously modeled at different levels of resolution, these being smoothly coupled together. In the case of enzyme systems, computationally expensive atomistic detail is needed in the active site to capture the chemistry of ligand binding. Global properties of the rest of the protein also play an essential role, determining the structure and fluctuations of the binding site; however, these can be modeled on a coarser level. Similarly, in the most computationally efficient scheme only the solvent hydrating the active site requires atomistic detail. We present a methodology to couple atomistic and coarse-grained protein models, while solvating the atomistic part of the protein in atomistic water. This allows a free choice of which protein and solvent degrees of freedom to include atomistically. This multi-resolution methodology can successfully model stable ligand binding, and we further confirm its validity by exploring the reproduction of system properties relevant to enzymatic function. In addition to a computational speedup, such an approach can allow the identification of the essential degrees of freedom playing a role in a given process, potentially yielding new insights into biomolecular function. Proteins 2016; 84:1902-1913. © 2016 Wiley Periodicals, Inc.

Discretized knot motion on a tensioned fiber induced by transverse waves.

Topological entanglement is a ubiquitous feature of many biological as well as artificial polymers and fibers. While the equilibrium properties of entangled chains have been the subject of several studies, little is known about their out-of-equilibrium behavior. Here, we address the problem of a stretched knotted fiber driven by a periodic force applied to one of its termini. We show that the onset of standing waves kinetically traps the knot in spatially localized states where the amplitude of the oscillations is maximal, while the knot normal diffusive dynamics is replaced by a discrete jump dynamics.

The relative entropy is fundamental to adaptive resolution simulations.

Adaptive resolution techniques are powerful methods for the efficient simulation of soft matter systems in which they simultaneously employ atomistic and coarse-grained (CG) force fields. In such simulations, two regions with different resolutions are coupled with each other via a hybrid transition region, and particles change their description on the fly when crossing this boundary. Here we show that the relative entropy, which provides a fundamental basis for many approaches in systematic coarse-graining, is also an effective instrument for the understanding of adaptive resolution simulation methodologies. We demonstrate that the use of coarse-grained potentials which minimize the relative entropy with respect to the atomistic system can help achieve a smoother transition between the different regions within the adaptive setup. Furthermore, we derive a quantitative relation between the width of the hybrid region and the seamlessness of the coupling. Our results do not only shed light on the what and how of adaptive resolution techniques but will also help setting up such simulations in an optimal manner.

Adaptive resolution simulation of oligonucleotides.

Nucleic acids are characterized by a complex hierarchical structure and a variety of interaction mechanisms with other molecules. These features suggest the need of multiscale simulation methods in order to grasp the relevant physical properties of deoxyribonucleic acid (DNA) and RNA using in silico experiments. Here we report an implementation of a dual-resolution modeling of a DNA oligonucleotide in physiological conditions; in the presented setup only the nucleotide molecule and the solvent and ions in its proximity are described at the atomistic level; in contrast, the water molecules and ions far from the DNA are represented as computationally less expensive coarse-grained particles. Through the analysis of several structural and dynamical parameters, we show that this setup reliably reproduces the physical properties of the DNA molecule as observed in reference atomistic simulations. These results represent a first step towards a realistic multiscale modeling of nucleic acids and provide a quantitatively solid ground for their simulation using dual-resolution methods.