Machine learning coarse-grained potentials of protein thermodynamics.

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

Binding-and-Folding Recognition of an Intrinsically Disordered Protein Using Online Learning Molecular Dynamics.

Intrinsically disordered proteins participate in many biological processes by folding upon binding to other proteins. However, coupled folding and binding processes are not well understood from an atomistic point of view. One of the main questions is whether folding occurs prior to or after binding. Here we use a novel, unbiased, high-throughput adaptive sampling approach to reconstruct the binding and folding between the disordered transactivation domain of c-Myb and the KIX domain of the CREB-binding protein. The reconstructed long-term dynamical process highlights the binding of a short stretch of amino acids on c-Myb as a folded α-helix. Leucine residues, especially Leu298-Leu302, establish initial native contacts that prime the binding and folding of the rest of the peptide, with a mixture of conformational selection on the N-terminal region with an induced fit of the C-terminal.

Validation of the Alchemical Transfer Method for the Estimation of Relative Binding Affinities of Molecular Series.

The accurate prediction of protein-ligand binding affinities is crucial for drug discovery. Alchemical free energy calculations have become a popular tool for this purpose. However, the accuracy and reliability of these methods can vary depending on the methodology. In this study, we evaluate the performance of a relative binding free energy protocol based on the alchemical transfer method (ATM), a novel approach based on a coordinate transformation that swaps the positions of two ligands. The results show that ATM matches the performance of more complex free energy perturbation (FEP) methods in terms of Pearson correlation but with marginally higher mean absolute errors. This study shows that the ATM method is competitive compared to more traditional methods in speed and accuracy and offers the advantage of being applicable with any potential energy function.

Validation of the Alchemical Transfer Method for the Estimation of Relative Binding Affinities of Molecular Series.

The accurate prediction of protein-ligand binding affinities is crucial for drug discovery. Alchemical free energy calculations have become a popular tool for this purpose. However, the accuracy and reliability of these methods can vary depending on the methodology. In this study, we evaluate the performance of a relative binding free energy protocol based on the alchemical transfer method (ATM), a novel approach based on a coordinate transformation that swaps the positions of two ligands. The results show that ATM matches the performance of more complex free energy perturbation (FEP) methods in terms of Pearson correlation, but with marginally higher mean absolute errors. This study shows that the ATM method is competitive compared to more traditional methods in speed and accuracy and offers the advantage of being applicable with any potential energy function.

The Role of Hydrophobic Nodes in the Dynamics of Class A ß-Lactamases.

Class A ß-lactamases are known for being able to rapidly gain broad spectrum catalytic efficiency against most ß-lactamase inhibitor combinations as a result of elusively minor point mutations. The evolution in class A ß-lactamases occurs through optimisation of their dynamic phenotypes at different timescales. At long-timescales, certain conformations are more catalytically permissive than others while at the short timescales, fine-grained optimisation of free energy barriers can improve efficiency in ligand processing by the active site. Free energy barriers, which define all coordinated movements, depend on the flexibility of the secondary structural elements. The most highly conserved residues in class A ß-lactamases are hydrophobic nodes that stabilize the core. To assess how the stable hydrophobic core is linked to the structural dynamics of the active site, we carried out adaptively sampled molecular dynamics (MD) simulations in four representative class A ß-lactamases (KPC-2, SME-1, TEM-1, and SHV-1). Using Markov State Models (MSM) and unsupervised deep learning, we show that the dynamics of the hydrophobic nodes is used as a metastable relay of kinetic information within the core and is coupled with the catalytically permissive conformation of the active site environment. Our results collectively demonstrate that the class A enzymes described here, share several important dynamic similarities and the hydrophobic nodes comprise of an informative set of dynamic variables in representative class A ß-lactamases.

TorchMD: A Deep Learning Framework for Molecular Simulations.

Molecular dynamics simulations provide a mechanistic description of molecules by relying on empirical potentials. The quality and transferability of such potentials can be improved leveraging data-driven models derived with machine learning approaches. Here, we present TorchMD, a framework for molecular simulations with mixed classical and machine learning potentials. All force computations including bond, angle, dihedral, Lennard-Jones, and Coulomb interactions are expressed as PyTorch arrays and operations. Moreover, TorchMD enables learning and simulating neural network potentials. We validate it using standard Amber all-atom simulations, learning an ab initio potential, performing an end-to-end training, and finally learning and simulating a coarse-grained model for protein folding. We believe that TorchMD provides a useful tool set to support molecular simulations of machine learning potentials. Code and data are freely available at github.com/torchmd.

Coarse graining molecular dynamics with graph neural networks.

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems.

Author Correction: Characterization of partially ordered states in the intrinsically disordered N-terminal domain of p53 using millisecond molecular dynamics simulations.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Small Molecule Modulation of Intrinsically Disordered Proteins Using Molecular Dynamics Simulations.

The extreme dynamic behavior of intrinsically disordered proteins hinders the development of drug-like compounds capable of modulating them. There are several examples of small molecules that specifically interact with disordered peptides. However, their mechanisms of action are still not well understood. Here, we use extensive molecular dynamics simulations combined with adaptive sampling algorithms to perform free ligand binding studies in the context of intrinsically disordered proteins. We tested this approach in the system composed by the D2 sub-domain of the disordered protein p27 and the small molecule SJ403. The results show several protein-ligand bound states characterized by the establishment of a loosely oriented interaction mediated by a limited number of contacts between the ligand and critical residues of p27. Finally, protein conformations in the bound state are likely to be explored by the isolated protein too, therefore supporting a model where the addition of the small molecule restricts the available conformational space.

Characterization of partially ordered states in the intrinsically disordered N-terminal domain of p53 using millisecond molecular dynamics simulations.

The exploration of intrinsically disordered proteins in isolation is a crucial step to understand their complex dynamical behavior. In particular, the emergence of partially ordered states has not been explored in depth. The experimental characterization of such partially ordered states remains elusive due to their transient nature. Molecular dynamics mitigates this limitation thanks to its capability to explore biologically relevant timescales while retaining atomistic resolution. Here, millisecond unbiased molecular dynamics simulations were performed in the exemplar N-terminal region of p53. In combination with state-of-the-art Markov state models, simulations revealed the existence of several partially ordered states accounting for [Formula: see text] 40% of the equilibrium population. Some of the most relevant states feature helical conformations similar to the bound structure of p53 to Mdm2, as well as novel [Formula: see text]-sheet elements. This highlights the potential complexity underlying the energy surface of intrinsically disordered proteins.

AdaptiveBandit: A Multi-armed Bandit Framework for Adaptive Sampling in Molecular Simulations.

Sampling from the equilibrium distribution has always been a major problem in molecular simulations due to the very high dimensionality of the conformational space. Over several decades, many approaches have been used to overcome the problem. In particular, we focus on unbiased simulation methods such as parallel and adaptive sampling. Here, we recast adaptive sampling schemes on the basis of multi-armed bandits and develop a novel adaptive sampling algorithm under this framework, AdaptiveBandit. We test it on multiple simplified potentials and in a protein folding scenario. We find that this framework performs similarly to or better than previous methods in every type of test potential. Furthermore, it provides a novel framework to develop new sampling algorithms with better asymptotic characteristics.

Synthesis, reactivity, X-ray characterization and docking studies of N7/N9-(2-pyrimidyl)-adenine derivatives.

The reaction of adenine with 2-chloropyrimidine yields as a major product the unexpected N7-(2-pyrimidyl)-adenine (1) and as a minor one N9-(2-pyrimidyl)-adenine (2). Both compounds have been characterized by X-ray diffraction analysis. Moreover, we report the formation of a 1:1 co-crystal (3) composed by compound (1) and adenine that was formed serendipitously during the synthesis of (1). Unexpectedly, the treatment of (1) with Brönsted acids like HCl or HNO3 causes the opening of the imidazole ring of the N7-substituted adenine, yielding N5-(pyrimidin-2-yl)pyrimidine-4,5,6-triamine (4-7) which we have X-ray characterized in its neutral, (4), monoprotonated [nitrate salt (6)] and diprotonated forms [hydrochloride salt (5) and, also, a tetrachlorozincate salt (7)]. Finally, we have used compound (5) as ligand to synthesize and X-ray characterize its complexes with Ir(III) and Ag(I) (compounds (8) and (9), respectively), where the latter is a 2D coordination polymer and the former is a discrete mononuclear complex. We have studied the supramolecular assemblies formed in the solid state by using density functional theory (DFT) calculations. Finally, DNA-docking studies of several compounds have been carried out in order to analyze their ability to interact with the DNA.

Machine Learning of Coarse-Grained Molecular Dynamics Force Fields.

Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.

Simulations meet machine learning in structural biology.

Classical molecular dynamics (MD) simulations will be able to reach sampling in the second timescale within five years, producing petabytes of simulation data at current force field accuracy. Notwithstanding this, MD will still be in the regime of low-throughput, high-latency predictions with average accuracy. We envisage that machine learning (ML) will be able to solve both the accuracy and time-to-prediction problem by learning predictive models using expensive simulation data. The synergies between classical, quantum simulations and ML methods, such as artificial neural networks, have the potential to drastically reshape the way we make predictions in computational structural biology and drug discovery.

Resultado de un estudio de casos múltiples con niños ciegos de edad temprana de la provincia Ciego de Ávila / Result of a study of multiple cases with blind children of early age from Ciego de Avila province

El juego es la actividad más importante del niño, porque propicia la estimulación de diversos procesos y cualidades psíquicas, tales como: la discriminación perceptual, la concentración de la atención, la generalización de relaciones, el razonamiento, las destrezas motrices, la sensibilidad táctil activa, la actividad motora gruesa, los movimientos finos de la mano y la percepción de la forma, lo que permite conocer el objeto, sus particularidades y propiedades; elementos esenciales a desarrollar en los invidentes. Es por eso que en el proceso de estimulación se requiere tener en cuenta la concepción del desarrollo físico y psíquico de este; y las potencialidades para alcanzarlo, a partir de las vivencias personales y del juego. Los resultados que emergieron del estudio de caso realizado permitieron corroborar la factibilidad de la estimulación temprana para el desarrollo armónico de los recursos compensatorio de los niños ciegos. Se apreciaron elocuentes logros en el desarrollo físico y psíquico de los mismos, también se logró una transformación en el modo de pensar y actuar de los adultos relacionados con el proceso de estimulación, se tornó más enternecedora la relación afectiva del adulto con el niño ciego, del niño ciego con el adulto y del niño ciego con otros niños (AU)

Game is the most important activity of a boy, because causes the psychic stimulation of diverse processes and qualities, such as: perceptual discrimination, concentration of attention, generalization of relations, reasoning, motor skills, active tactile sensitivity, gross motor activity, fine movements of the hand and the perception of the form, what allows to know the object, its particularitities and properties; essential elements to develop in blind persons. That is why in the stimulation process it is required to consider the conception of the physical and psychic development; and the potentialities to reach it, from personal experiences and the game. The results that emerged from the study of carried out case allowed to corroborate the feasibility of the early stimulation for the harmonic development of the compensatory resources of blind children. Eloquent profits in the physical and psychic development were appraised, also managed a transformation in the way of thinking and acting of adults related to the stimulation process, becoming more moving the affective relation of the adult with the blind child, the blind child with the adult and the blind child with other children (AU)