Free Energy Simulations of Receptor-Binding Domain Opening of the SARS-CoV-2 Spike Indicate a Barrierless Transition with Slow Conformational Motions.

Infection by sarbecoviruses begins with the attachment of the homotrimeric viral "spike" protein to the angiotensin-converting enzyme 2 receptor on the surface of mammalian cells. This requires one or more receptor-binding domains (RBDs) to be in the open (up) position. Here, we present the results of long molecular dynamics simulations with umbrella sampling (US) to compute a one-dimensional free energy profile of RBD opening/closing and the associated transition times. After ≃3.58µs of simulation time per US window (∼229 µs in total), which was required to approach trajectory decorrelation, the computed free energy profile was found to be without large barriers. This suggests that the RBD diffuses between the open and closed positions without significant energetic hindrance. This interpretation appears consistent with experiments but is at odds with some previous simulations. Modeling the RBD motion as diffusive dynamics along the computed free energy profile, we find that the overall time required for the transition is only about 2 µs, which is 5 orders of magnitude shorter than experimentally measured transition times. We speculate that the most likely reason for the transition time mismatch is our use of very short glycans, which was required to make the simulations performed here feasible. Despite the long simulation times, the final free energy profile is not fully converged with statistical errors of ≃1.16 kcal/mol, which were found to be consistent with the slow time decay in the autocorrelation of the conformational motions of the protein. The simulation lengths that would be required to obtain fully converged results remain unknown, but the present calculations would benefit from at least an order-of-magnitude extension.

Water dynamics around T0 vs R4 of hemoglobin from local hydrophobicity analysis.

The local hydration around tetrameric hemoglobin (Hb) in its T0 and R4 conformational substates is analyzed based on molecular dynamics simulations. Analysis of the local hydrophobicity (LH) for all residues at the α1ß2 and α2ß1 interfaces, responsible for the quaternary T → R transition, which is encoded in the Monod-Wyman-Changeux model, as well as comparison with earlier computations of the solvent accessible surface area, makes clear that the two quantities measure different aspects of hydration. Local hydrophobicity quantifies the presence and structure of water molecules at the interface, whereas "buried surface" reports on the available space for solvent. For simulations with Hb frozen in its T0 and R4 states, the correlation coefficient between LH and buried surface is 0.36 and 0.44, respectively, but it increases considerably if the 95% confidence interval is used. The LH with Hb frozen and flexible changes little for most residues at the interfaces but is significantly altered for a few select ones: Thr41α, Tyr42α, Tyr140α, Trp37ß, Glu101ß (for T0) and Thr38α, Tyr42α, Tyr140α (for R4). The number of water molecules at the interface is found to increase by ∼25% for T0 → R4, which is consistent with earlier measurements. Since hydration is found to be essential to protein function, it is clear that hydration also plays an essential role in allostery.

A Computational Framework for Determining the Breadth of Antibodies Against Highly Mutable Pathogens.

Highly mutable pathogens pose daunting challenges for antibody design. The usual criteria of high potency and specificity are often insufficient to design antibodies that provide long-lasting protection. This is due, in part, to the ability of the pathogen to rapidly acquire mutations that permit them to evade the designed antibodies. To overcome these limitations, design of antibodies with a larger neutralizing breadth can be pursued. Such broadly neutralizing antibodies (bnAbs) should remain targeted to a specific epitope, yet show robustness against pathogen mutability, thereby neutralizing a higher number of antigens. This is particularly important for highly mutable pathogens, like the influenza virus and the human immunodeficiency virus (HIV). The protocol describes a method for computing the "breadth" of a given antibody, an essential aspect of antibody design.

ppdx: Automated modeling of protein-protein interaction descriptors for use with machine learning.

This paper describes ppdx, a python workflow tool that combines protein sequence alignment, homology modeling, and structural refinement, to compute a broad array of descriptors for characterizing protein-protein interactions. The descriptors can be used to predict various properties of interest, such as protein-protein binding affinities, or inhibitory concentrations (IC50 ), using approaches that range from simple regression to more complex machine learning models. The software is highly modular. It supports different protocols for generating structures, and 95 descriptors can be currently computed. More protocols and descriptors can be easily added. The implementation is highly parallel and can fully exploit the available cores in a single workstation, or multiple nodes on a supercomputer, allowing many systems to be analyzed simultaneously. As an illustrative application, ppdx is used to parametrize a model that predicts the IC50 of a set of antigens and a class of antibodies directed to the influenza hemagglutinin stalk.

Multiscale affinity maturation simulations to elicit broadly neutralizing antibodies against HIV.

The design of vaccines against highly mutable pathogens, such as HIV and influenza, requires a detailed understanding of how the adaptive immune system responds to encountering multiple variant antigens (Ags). Here, we describe a multiscale model of B cell receptor (BCR) affinity maturation that employs actual BCR nucleotide sequences and treats BCR/Ag interactions in atomistic detail. We apply the model to simulate the maturation of a broadly neutralizing Ab (bnAb) against HIV. Starting from a germline precursor sequence of the VRC01 anti-HIV Ab, we simulate BCR evolution in response to different vaccination protocols and different Ags, which were previously designed by us. The simulation results provide qualitative guidelines for future vaccine design and reveal unique insights into bnAb evolution against the CD4 binding site of HIV. Our model makes possible direct comparisons of simulated BCR populations with results of deep sequencing data, which will be explored in future applications.

A Coarse-Grained Model of Affinity Maturation Indicates the Importance of B-Cell Receptor Avidity in Epitope Subdominance.

The elicitation of broadly neutralizing antibodies (bnAbs) is a major goal in the design of vaccines against rapidly-mutating viruses. In the case of influenza, many bnAbs that target conserved epitopes on the stem of the hemagglutinin protein (HA) have been discovered. However, these antibodies are rare, are not boosted well upon reinfection, and often have low neutralization potency, compared to strain-specific antibodies directed to the HA head. Different hypotheses have been proposed to explain this phenomenon. We use a coarse-grained computational model of the germinal center reaction to investigate how B-cell receptor binding valency affects the growth and affinity maturation of competing B-cells. We find that receptors that are unable to bind antigen bivalently, and also those that do not bind antigen cooperatively, have significantly slower rates of growth, memory B-cell production, and, under certain conditions, rates of affinity maturation. The corresponding B-cells are predicted to be outcompeted by B-cells that bind bivalently and cooperatively. We use the model to explore strategies for a universal influenza vaccine, e.g., how to boost the concentrations of the slower growing cross-reactive antibodies directed to the stem. The results suggest that, upon natural reinfections subsequent to vaccination, the protectiveness of such vaccines would erode, possibly requiring regular boosts. Collectively, our results strongly support the importance of bivalent antibody binding in immunodominance, and suggest guidelines for developing a universal influenza vaccine.

Molecular Simulation of Stapled Peptides.

Constrained peptides represent a relatively new class of biologic therapeutics, which have the potential to overcome several limitations of small-molecule drugs, and of designed antibodies. Because of their modest size, the rational design of such peptides is becoming increasingly amenable to computer simulation; multi-microsecond molecular dynamic (MD) simulations are now routinely possible on consumer-grade graphical processors (GPUs). Here, we describe the procedures for performing and analyzing MD simulations of hydrocarbon-stapled peptides using the CHARMM energy function, in isolation and in complex with a binding partner, to investigate their conformational properties and to compute changes in their binding affinity upon mutation.

The functional role of the hemoglobin-water interface.

The interface between hemoglobin (Hb) and its environment, in particular water, is of great physiological relevance. Here, results from in vitro, in vivo, and computational experiments (molecular dynamics simulations) are summarized and put into perspective. One of the main findings from the computations is that the stability of the deoxy, ligand-free T-state (T0) can be stabilized relative to the deoxy R-state (R0) only in sufficiently large simulation boxes for the hydrophobic effect to manifest itself. This effect directly influences protein stability and is operative also under physiological conditions. Furthermore, molecular simulations provide a dynamical interpretation of the Perutz model for Hb function. Results from experiments using higher protein concentrations and realistic cellular environments are also discussed. One of the next great challenges for computational studies, which as we show is likely to be taken up in the near future, is to provide a molecular-level understanding of the dynamics of proteins in such crowded environments.

Design of immunogens to elicit broadly neutralizing antibodies against HIV targeting the CD4 binding site.

A vaccine which is effective against the HIV virus is considered to be the best solution to the ongoing global HIV/AIDS epidemic. In the past thirty years, numerous attempts to develop an effective vaccine have been made with little or no success, due, in large part, to the high mutability of the virus. More recent studies showed that a vaccine able to elicit broadly neutralizing antibodies (bnAbs), that is, antibodies that can neutralize a high fraction of global virus variants, has promise to protect against HIV. Such a vaccine has been proposed to involve at least three separate stages: First, activate the appropriate precursor B cells; second, shepherd affinity maturation along pathways toward bnAbs; and, third, polish the Ab response to bind with high affinity to diverse HIV envelopes (Env). This final stage may require immunization with a mixture of Envs. In this paper, we set up a framework based on theory and modeling to design optimal panels of antigens to use in such a mixture. The designed antigens are characterized experimentally and are shown to be stable and to be recognized by known HIV antibodies.

A restrained locally enhanced sampling method (RLES) for finding free energy minima in complex systems.

We present an extension of the locally enhanced sampling method. A restraint potential is introduced to drive the many-replica system to the canonical ensemble corresponding to the physical, single-replica system. Convergence properties are demonstrated using a model rugged two-dimensional potential, for which sampling by conventional equilibrium molecular dynamics is inefficient. Restrained locally enhanced sampling (RLES) is found to explore the space of configurations with an efficiency comparable to that of temperature replica exchange. To demonstrate the potential of RLES for realistic applications, the method is used to fold the 12-residue tryptophan zipper miniprotein in explicit solvent. The RLES algorithm can be incorporated into existing LES implementations with minor code modifications.

The trajectory of intrahelical lesion recognition and extrusion by the human 8-oxoguanine DNA glycosylase.

Efficient search for DNA damage embedded in vast expanses of the DNA genome presents one of the greatest challenges to DNA repair enzymes. We report here crystal structures of human 8-oxoguanine (oxoG) DNA glycosylase, hOGG1, that interact with the DNA containing the damaged base oxoG and the normal base G while they are nested in the DNA helical stack. The structures reveal that hOGG1 engages the DNA using different protein-DNA contacts from those observed in the previously determined lesion recognition complex and other hOGG1-DNA complexes. By applying molecular dynamics simulations, we have determined the pathways taken by the lesion and normal bases when extruded from the DNA helix and their associated free energy profiles. These results reveal how the human oxoG DNA glycosylase hOGG1 locates the lesions inside the DNA helix and facilitates their extrusion for repair.

Water Dynamics Around Proteins: T- and R-States of Hemoglobin and Melittin.

The water dynamics, as characterized by the local hydrophobicity (LH), is investigated for tetrameric hemoglobin (Hb) and dimeric melittin. For the T0 to R0 transition in Hb, it is found that LH provides additional molecular-level insight into the Perutz mechanism, i.e., the breaking and formation of salt bridges at the α1/ß2 and α2/ß1 interface is accompanied by changes in LH. For Hb in cubic water boxes with 90 and 120 Å edge length it is observed that following a decrease in LH as a consequence of reduced water density or change of water orientation at the protein/water interface the α/ß interfaces are destabilized; this is a hallmark of the Perutz stereochemical model for the T to R transition in Hb. The present work thus provides a dynamical view of the classical structural model relevant to the molecular foundations of Hb function. For dimeric melittin, earlier results by Cheng and Rossky [ Nature 1998, 392, 696-699] are confirmed and interpreted on the basis of LH from simulations in which the protein structure is frozen. For the flexible melittin dimer, the changes in the local hydration can be as much as 30% greater than for the rigid dimer, reflecting the fact that protein and water dynamics are coupled.

Microsecond Molecular Dynamics Simulations of Proteins Using a Quasi-Equilibrium Solvation Shell Model.

We describe the development and implementation of a quasi-equilibrium hydration shell model of biomolecular solvation with adaptive boundaries. Applying the model to microsecond-long molecular dynamics simulations of several protein systems of varying complexity, we find that the model simulation results are of comparable quality to those obtained from simulations of fully solvated systems, but at a reduced computational cost. We discuss the dominant sources of error in the model and outline directions for future improvements.

Structural basis for power stroke vs. Brownian ratchet mechanisms of motor proteins.

Two mechanisms have been proposed for the function of motor proteins: The power stroke and the Brownian ratchet. The former refers to generation of a large downhill free energy gradient over which the motor protein moves nearly irreversibly in making a step, whereas the latter refers to biasing or rectifying the diffusive motion of the motor. Both mechanisms require input of free energy, which generally involves the processing of an ATP (adenosine 5'-triphosphate) molecule. Recent advances in experiments that reveal the details of the stepping motion of motor proteins, together with computer simulations of atomistic structures, have provided greater insights into the mechanisms. Here, we compare the various models of the power stroke and the Brownian ratchet that have been proposed. The 2 mechanisms are not mutually exclusive, and various motor proteins employ them to different extents to perform their biological function. As examples, we discuss linear motor proteins Kinesin-1 and myosin-V, and the rotary motor F1-ATPase, all of which involve a power stroke as the essential element of their stepping mechanism.

Insights into the origin of the high energy-conversion efficiency of F1-ATPase.

Our understanding of the rotary-coupling mechanism of F1-ATPase has been greatly enhanced in the last decade by advances in X-ray crystallography, single-molecular imaging, and theoretical models. Recently, Volkán-Kacsó and Marcus [S. Volkán-Kacsó, R. A. Marcus, Proc. Natl. Acad. Sci. U.S.A. 112, 14230 (2015)] presented an insightful thermodynamic model based on the Marcus reaction theory coupled with an elastic structural deformation term to explain the observed γ-rotation angle dependence of the adenosine triphosphate (ATP)/adenosine diphosphate (ADP) exchange rates of F1-ATPase. Although the model is successful in correlating single-molecule data, it is not in agreement with the available theoretical results. We describe a revision of the model, which leads to consistency with the simulation results and other experimental data on the F1-ATPase rotor compliance. Although the free energy liberated on ATP hydrolysis by F1-ATPase is rapidly dissipated as heat and so cannot contribute directly to the rotation, we show how, nevertheless, F1-ATPase functions near the maximum possible efficiency. This surprising result is a consequence of the differential binding of ATP and its hydrolysis products ADP and Pi along a well-defined pathway.

Response to comment on 'Valid molecular dynamics simulations of human hemoglobin require a surprisingly large box size'.

We recently reported that molecular dynamics simulations for hemoglobin require a surprisingly large box size to stabilize the T(0) state relative to R(0), as observed in experiments (El Hage et al., 2018). Gapsys and de Groot have commented on this work but do not provide convincing evidence that the conclusions of El Hage et al., 2018 are incorrect. Here we respond to these concerns, argue that our original conclusions remain valid, and raise our own concerns about some of the results reported in the comment by Gapsys and de Groot that require clarification.

Estimation of the breadth of CD4bs targeting HIV antibodies by molecular modeling and machine learning.

HIV is a highly mutable virus for which all attempts to develop a vaccine have been unsuccessful. Nevertheless, few long-infected patients develop antibodies, called broadly neutralizing antibodies (bnAbs), that have a high breadth and can neutralize multiple variants of the virus. This suggests that a universal HIV vaccine should be possible. A measure of the efficacy of a HIV vaccine is the neutralization breadth of the antibodies it generates. The breadth is defined as the fraction of viruses in the Seaman panel that are neutralized by the antibody. Experimentally the neutralization ability is measured as the half maximal inhibitory concentration of the antibody (IC50). To avoid such time-consuming experimental measurements, we developed a computational approach to estimate the IC50 and use it to determine the antibody breadth. Given that no direct method exists for calculating IC50 values, we resort to a combination of atomistic modeling and machine learning. For each antibody/virus complex, an all-atoms model is built using the amino acid sequence and a known structure of a related complex. Then a series of descriptors are derived from the atomistic models, and these are used to train a Multi-Layer Perceptron (an Artificial Neural Network) to predict the value of the IC50 (by regression), or if the antibody binds or not to the virus (by classification). The neural networks are trained by use of experimental IC50 values collected in the CATNAP database. The computed breadths obtained by regression and classification are reported and the importance of having some related information in the data set for obtaining accurate predictions is analyzed. This approach is expected to prove useful for the design of HIV bnAbs, where the computation of the potency must be accompanied by a computation of the breadth, and for evaluating the efficiency of potential vaccination schemes developed through modeling and simulation.

Cytosolic expression, solution structures, and molecular dynamics simulation of genetically encodable disulfide-rich de novo designed peptides.

Disulfide-rich peptides represent an important protein family with broad pharmacological potential. Recent advances in computational methods have made it possible to design new peptides which adopt a stable conformation de novo. Here, we describe a system to produce disulfide-rich de novo peptides using Escherichia coli as the expression host. The advantage of this system is that it enables production of uniformly 13 C- and 15 N-labeled peptides for solution nuclear magnetic resonance (NMR) studies. This expression system was used to isotopically label two previously reported de novo designed peptides, and to determine their solution structures using NMR. The ensemble of NMR structures calculated for both peptides agreed well with the design models, further confirming the accuracy of the design protocol. Collection of NMR data on the peptides under reducing conditions revealed a dependency on disulfide bonds to maintain stability. Furthermore, we performed long-time molecular dynamics (MD) simulations with tempering to assess the stability of two families of de novo designed peptides. Initial designs which exhibited a stable structure during simulations were more likely to adopt a stable structure in vitro, but attempts to utilize this method to redesign unstable peptides to fold into a stable state were unsuccessful. Further work is therefore needed to assess the utility of MD simulation techniques for de novo protein design.

Structure of the EmrE multidrug transporter and its use for inhibitor peptide design.

Small multidrug resistance (SMR) pumps represent a minimal paradigm of proton-coupled membrane transport in bacteria, yet no high-resolution structure of an SMR protein is available. Here, atomic-resolution structures of the Escherichia coli efflux-multidrug resistance E (EmrE) multidrug transporter in ligand-bound form are refined using microsecond molecular dynamics simulations biased using low-resolution data from X-ray crystallography. The structures are compatible with existing mutagenesis data as well as NMR and biochemical experiments, including pKas of the catalytic glutamate residues and the dissociation constant ([Formula: see text]) of the tetraphenylphosphonium+ cation. The refined structures show the arrangement of residue side chains in the EmrE active site occupied by two different ligands and in the absence of a ligand, illustrating how EmrE can adopt structurally diverse active site configurations. The structures also show a stable, well-packed binding interface between the helices H4 of the two monomers, which is believed to be crucial for EmrE dimerization. Guided by the atomic details of this interface, we design proteolysis-resistant stapled peptides that bind to helix H4 of an EmrE monomer. The peptides are expected to interfere with the dimerization and thereby inhibit drug transport. Optimal positions of the peptide staple were determined using free-energy simulations of peptide binding to monomeric EmrE Three of the four top-scoring peptides selected for experimental testing resulted in significant inhibition of proton-driven ethidium efflux in live cells without nonspecific toxicity. The approach described here is expected to be of general use for the design of peptide therapeutics.

Valid molecular dynamics simulations of human hemoglobin require a surprisingly large box size.

Recent molecular dynamics (MD) simulations of human hemoglobin (Hb) give results in disagreement with experiment. Although it is known that the unliganded (T[Formula: see text]) and liganded (R[Formula: see text]) tetramers are stable in solution, the published MD simulations of T[Formula: see text] undergo a rapid quaternary transition to an R-like structure. We show that T[Formula: see text] is stable only when the periodic solvent box contains ten times more water molecules than the standard size for such simulations. The results suggest that such a large box is required for the hydrophobic effect, which stabilizes the T[Formula: see text] tetramer, to be manifested. Even in the largest box, T[Formula: see text] is not stable unless His146 is protonated, providing an atomistic validation of the Perutz model. The possibility that extra large boxes are required to obtain meaningful results will have to be considered in evaluating existing and future simulations of a wide range of systems.