Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

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Machine Learning for Molecular Simulation.

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, coarse-grained molecular dynamics, the extraction of free energy surfaces and kinetics and generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into machine learning structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

Machine learning for molecular simulation

Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.

Enhanced sampling in molecular dynamics.

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

Unsupervised Learning Methods for Molecular Simulation Data.

Machine learning approaches for analyzing and enhancing molecular dynamics simulations.

Transition path sampling is a powerful tool in the study of rare events. Shooting trial trajectories from configurations along existing transition paths proved particularly efficient in the sampling of reactive trajectories. However, most shooting attempts tend not to result in transition paths, in particular in cases where the transition dynamics has diffusive character. To overcome the resulting efficiency problem, we developed an algorithm for "shooting from the top." We first define a shooting range through which all paths have to pass and then shoot off trial trajectories only from within this range. For a well chosen shooting range, nearly every shot is successful, resulting in an accepted transition path. To deal with multiple mechanisms, weighted shooting ranges can be used. To cope with the problem of unsuitably placed shooting ranges, we developed an algorithm that iteratively improves the location of the shooting range. The transition path sampling procedure is illustrated for models of diffusive and Langevin dynamics. The method should be particularly useful in cases where the transition paths are long so that only relatively few shots are possible, yet reasonable order parameters are known.

Transition path sampling of rare events by shooting from the top.

Exascale computing holds great opportunities for molecular dynamics (MD) simulations. However, to take full advantage of the new possibilities, we must learn how to focus computational power on the discovery of complex molecular mechanisms, and how to extract them from enormous amounts of data. Both aspects still rely heavily on human experts, which becomes a serious bottleneck when a large number of parallel simulations have to be orchestrated to take full advantage of the available computing power. Here, we use artificial intelligence (AI) both to guide the sampling and to extract the relevant mechanistic information. We combine advanced sampling schemes with statistical inference, artificial neural networks, and deep learning to discover molecular mechanisms from MD simulations. Our framework adaptively and autonomously initializes simulations and learns the sampled mechanism, and is thus suitable for massively parallel computing architectures. We propose practical solutions to make the neural networks interpretable, as illustrated in applications to molecular systems.

Artificial Intelligence Assists Discovery of Reaction Coordinates and Mechanisms from Molecular Dynamics Simulations

Na+/H+ antiporters exchange sodium ions and protons on opposite sides of lipid membranes. The electroneutral Na+/H+ antiporter NhaP from archaea Pyrococcus abyssi (PaNhaP) is a functional homolog of the human Na+/H+ exchanger NHE1, which is an important drug target. Here we resolve the Na+ and H+ transport cycle of PaNhaP by transition-path sampling. The resulting molecular dynamics trajectories of repeated ion transport events proceed without bias force, and overcome the enormous time-scale gap between seconds-scale ion exchange and microseconds simulations. The simulations reveal a hydrophobic gate to the extracellular side that opens and closes in response to the transporter domain motion. Weakening the gate by mutagenesis makes the transporter faster, suggesting that the gate balances competing demands of fidelity and efficiency. Transition-path sampling and a committor-based reaction coordinate optimization identify the essential motions and interactions that realize conformational alternation between the two access states in transporter function.

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Mechanism of the electroneutral sodium/proton antiporter PaNhaP from transition-path shooting

During infection the SARS-CoV-2 virus fuses its viral envelope with cellular membranes of its human host. The viral spike (S) protein mediates both the initial contact with the host cell and the subsequent membrane fusion. Proteolytic cleavage of S at the S2' site exposes its fusion peptide (FP) as the new N-terminus. By binding to the host membrane, the FP anchors the virus to the host cell. The reorganization of S2 between virus and host then pulls the two membranes together. Here we use molecular dynamics (MD) simulations to study the two core functions of the SARS-CoV-2 FP: to attach quickly to cellular membranes and to form an anchor strong enough to withstand the mechanical force during membrane fusion. In eight 10 μs long MD simulations of FP in proximity to endosomal and plasma membranes, we find that FP binds spontaneously to the membranes and that binding proceeds predominantly by insertion of two short amphipathic helices into the membrane interface. Connected via a flexible linker, the two helices can bind the membrane independently, yet binding of one promotes the binding of the other by tethering it close to the target membrane. By simulating mechanical pulling forces acting on the C-terminus of the FP, we then show that the bound FP can bear forces up to 250 pN before detaching from the membrane. This detachment force is more than 10-fold higher than an estimate of the force required to pull host and viral membranes together for fusion. We identify a fully conserved disulfide bridge in the FP as a major factor for the high mechanical stability of the FP membrane anchor. We conclude, first, that the sequential binding of two short amphipathic helices allows the SARS-CoV-2 FP to insert quickly into the target membrane, before the virion is swept away after shedding the S1 domain connecting it to the host cell receptor. Second, we conclude that the double attachment and the conserved disulfide bridge establish the strong anchoring required for subsequent membrane fusion. Multiple distinct membrane-anchoring elements ensure high avidity and high mechanical strength of FP-membrane binding.

Binding of SARS-CoV-2 Fusion Peptide to Host Endosome and Plasma Membrane.

During infection the SARS-CoV-2 virus fuses its viral envelope with cellular membranes of its human host. Initial contact with the host cell and membrane fusion are both mediated by the viral spike (S) protein. Proteolytic cleavage of S at the S2' site exposes its 40 amino acid long fusion peptide (FP). Binding of the FP to the host membrane anchors the S2 domain of S in both the viral and the host membrane. The reorganization of S2 then pulls the two membranes together. Here we use molecular dynamics (MD) simulations to study the two core functions of the SARS-CoV-2 FP: to attach quickly to cellular membranes and to form an anchor strong enough to withstand the mechanical force during membrane fusion. In eight 10 s-long MD simulations of FP in proximity to endosomal and plasma membranes, we find that FP binds spontaneously to the membranes and that binding proceeds predominantly by insertion of two short amphipathic helices into the membrane interface. Connected via a flexible linker, the two helices can bind the membrane independently, yet binding of one promotes the binding of the other by tethering it close to the target membrane. By simulating mechanical pulling forces acting on the C-terminus of the FP we then show that the bound FP can bear forces up to 250 pN before detaching from the membrane. This detachment force is more than ten-fold higher than an estimate of the force required to pull host and viral membranes together for fusion. We identify a fully conserved disulfide bridge in the FP as a major factor for the high mechanical stability of the FP membrane anchor. We conclude, first, that the sequential binding of two short amphipathic helices allows the SARS-CoV-2 FP to insert quickly into the target membrane, before the virion is swept away after shedding the S1 domain connecting it to the host cell receptor. Second, we conclude that the double attachment and the conserved disulfide bridge establish the strong anchoring required for subsequent membrane fusion. Multiple distinct membrane-anchoring elements ensure high avidity and high mechanical strength of FP-membrane binding.

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Hendrik Jung

Papers

Transition path sampling of rare events by shooting from the top.

Artificial Intelligence Assists Discovery of Reaction Coordinates and Mechanisms from Molecular Dynamics Simulations

Mechanism of the electroneutral sodium/proton antiporter PaNhaP from transition-path shooting

Binding of SARS-CoV-2 Fusion Peptide to Host Endosome and Plasma Membrane.

Binding of SARS-CoV-2 fusion peptide to host membranes