Dramatic Differences between the Structural Susceptibility of the S1 Pre- and S2 Postfusion States of the SARS-CoV-2 Spike Protein to External Electric Fields Revealed by Molecular Dynamics Simulations.

In its prefusion state, the SARS-CoV-2 spike protein (similarly to other class I viral fusion proteins) is metastable, which is considered to be an important feature for optimizing or regulating its functions. After the binding process of its S1 subunit (S1) with ACE2, the spike protein (S) undergoes a dramatic conformational change where S1 splits from the S2 subunit, which then penetrates the membrane of the host cell, promoting the fusion of the viral and cell membranes. This results in the infection of the host cell. In a previous work, we showed-using large-scale molecular dynamics simulations-that the application of external electric fields (EFs) induces drastic changes and damage in the receptor-binding domain (RBD) of the wild-type spike protein, as well of the Alpha, Beta, and Gamma variants, leaving a structure which cannot be recognized anymore by ACE2. In this work, we first extend the study to the Delta and Omicron variants and confirm the high sensitivity and extreme vulnerability of the RBD of the prefusion state of S to moderate EF (as weak as 104 V/m), but, more importantly, we also show that, in contrast, the S2 subunit of the postfusion state of the spike protein does not suffer structural damage even if electric field intensities four orders of magnitude higher are applied. These results provide a solid scientific basis to confirm the connection between the prefusion-state metastability of the SARS-CoV-2 spike protein and its susceptibility to be damaged by EF. After the virus docks to the ACE2 receptor, the stable and robust postfusion conformation develops, which exhibits a similar resistance to EF (damage threshold higher than 108 V/m) like most globular proteins.

Mechanistic Basis for a Connection between the Catalytic Step and Slow Opening Dynamics of Adenylate Kinase.

Escherichia coli adenylate kinase (AdK) is a small, monomeric enzyme that synchronizes the catalytic step with the enzyme's conformational dynamics to optimize a phosphoryl transfer reaction and the subsequent release of the product. Guided by experimental measurements of low catalytic activity in seven single-point mutation AdK variants (K13Q, R36A, R88A, R123A, R156K, R167A, and D158A), we utilized classical mechanical simulations to probe mutant dynamics linked to product release, and quantum mechanical and molecular mechanical calculations to compute a free energy barrier for the catalytic event. The goal was to establish a mechanistic connection between the two activities. Our calculations of the free energy barriers in AdK variants were in line with those from experiments, and conformational dynamics consistently demonstrated an enhanced tendency toward enzyme opening. This indicates that the catalytic residues in the wild-type AdK serve a dual role in this enzyme's function─one to lower the energy barrier for the phosphoryl transfer reaction and another to delay enzyme opening, maintaining it in a catalytically active, closed conformation for long enough to enable the subsequent chemical step. Our study also discovers that while each catalytic residue individually contributes to facilitating the catalysis, R36, R123, R156, R167, and D158 are organized in a tightly coordinated interaction network and collectively modulate AdK's conformational transitions. Unlike the existing notion of product release being rate-limiting, our results suggest a mechanistic interconnection between the chemical step and the enzyme's conformational dynamics acting as the bottleneck of the catalytic process. Our results also suggest that the enzyme's active site has evolved to optimize the chemical reaction step while slowing down the overall opening dynamics of the enzyme.

The SARS-CoV-2 spike protein is vulnerable to moderate electric fields.

Most of the ongoing projects aimed at the development of specific therapies and vaccines against COVID-19 use the SARS-CoV-2 spike (S) protein as the main target. The binding of the spike protein with the ACE2 receptor (ACE2) of the host cell constitutes the first and key step for virus entry. During this process, the receptor binding domain (RBD) of the S protein plays an essential role, since it contains the receptor binding motif (RBM), responsible for the docking to the receptor. So far, mostly biochemical methods are being tested in order to prevent binding of the virus to ACE2. Here we show, with the help of atomistic simulations, that external electric fields of easily achievable and moderate strengths can dramatically destabilise the S protein, inducing long-lasting structural damage. One striking field-induced conformational change occurs at the level of the recognition loop L3 of the RBD where two parallel beta sheets, believed to be responsible for a high affinity to ACE2, undergo a change into an unstructured coil, which exhibits almost no binding possibilities to the ACE2 receptor. We also show that these severe structural changes upon electric-field application also occur in the mutant RBDs corresponding to the variants of concern (VOC) B.1.1.7 (UK), B.1.351 (South Africa) and P.1 (Brazil). Remarkably, while the structural flexibility of S allows the virus to improve its probability of entering the cell, it is also the origin of the surprising vulnerability of S upon application of electric fields of strengths at least two orders of magnitude smaller than those required for damaging most proteins. Our findings suggest the existence of a clean physical method to weaken the SARS-CoV-2 virus without further biochemical processing. Moreover, the effect could be used for infection prevention purposes and also to develop technologies for in-vitro structural manipulation of S. Since the method is largely unspecific, it can be suitable for application to other mutations in S, to other proteins of SARS-CoV-2 and in general to membrane proteins of other virus types.

Dynamic Connection between Enzymatic Catalysis and Collective Protein Motions.

Enzymes employ a wide range of protein motions to achieve efficient catalysis of chemical reactions. While the role of collective protein motions in substrate binding, product release, and regulation of enzymatic activity is generally understood, their roles in catalytic steps per se remain uncertain. Here, molecular dynamics simulations, enzyme kinetics, X-ray crystallography, and nuclear magnetic resonance spectroscopy are combined to elucidate the catalytic mechanism of adenylate kinase and to delineate the roles of catalytic residues in catalysis and the conformational change in the enzyme. This study reveals that the motions in the active site, which occur on a time scale of picoseconds to nanoseconds, link the catalytic reaction to the slow conformational dynamics of the enzyme by modulating the free energy landscapes of subdomain motions. In particular, substantial conformational rearrangement occurs in the active site following the catalytic reaction. This rearrangement not only affects the reaction barrier but also promotes a more open conformation of the enzyme after the reaction, which then results in an accelerated opening of the enzyme compared to that of the reactant state. The results illustrate a linkage between enzymatic catalysis and collective protein motions, whereby the disparate time scales between the two processes are bridged by a cascade of intermediate-scale motion of catalytic residues modulating the free energy landscapes of the catalytic and conformational change processes.

Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force.

First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN2 reaction, NH3 + CH3Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B-matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method.

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Acceleration of Semiempirical QM/MM Methods through Message Passage Interface (MPI), Hybrid MPI/Open Multiprocessing, and Self-Consistent Field Accelerator Implementations.

The strategy and implementation of scalable and efficient semiempirical (SE) QM/MM methods in CHARMM are described. The serial version of the code was first profiled to identify routines that required parallelization. Afterward, the code was parallelized and accelerated with three approaches. The first approach was the parallelization of the entire QM/MM routines, including the Fock matrix diagonalization routines, using the CHARMM message passage interface (MPI) machinery. In the second approach, two different self-consistent field (SCF) energy convergence accelerators were implemented using density and Fock matrices as targets for their extrapolations in the SCF procedure. In the third approach, the entire QM/MM and MM energy routines were accelerated by implementing the hybrid MPI/open multiprocessing (OpenMP) model in which both the task- and loop-level parallelization strategies were adopted to balance loads between different OpenMP threads. The present implementation was tested on two solvated enzyme systems (including <100 QM atoms) and an SN2 symmetric reaction in water. The MPI version exceeded existing SE QM methods in CHARMM, which include the SCC-DFTB and SQUANTUM methods, by at least 4-fold. The use of SCF convergence accelerators further accelerated the code by ∼12-35% depending on the size of the QM region and the number of CPU cores used. Although the MPI version displayed good scalability, the performance was diminished for large numbers of MPI processes due to the overhead associated with MPI communications between nodes. This issue was partially overcome by the hybrid MPI/OpenMP approach which displayed a better scalability for a larger number of CPU cores (up to 64 CPUs in the tested systems).

Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations.

The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r(-1) term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN2 reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN2 reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical reactions.

Role of Protein Dynamics in Allosteric Control of the Catalytic Phosphoryl Transfer of Insulin Receptor Kinase.

The catalytic and allosteric mechanisms of insulin receptor kinase (IRK) are investigated by a combination of ab initio and semiempirical quantum mechanical and molecular mechanical (QM/MM) methods and classical molecular dynamics (MD) simulations. The simulations reveal that the catalytic reaction proceeds in two steps, starting with the transfer of a proton from substrate Tyr to the catalytic Asp1132, followed by the phosphoryl transfer from ATP to substrate Tyr. The enhancement of the catalytic rate of IRK upon phosphorylations in the enzyme's activation loop is found to occur mainly via changes to the free energy landscape of the proton transfer step, favoring the proton transfer in the fully phosphorylated enzyme. In contrast, the effects of the phosphorylations on the phosphoryl transfer are smaller. Equilibrium MD simulations show that IRK phosphorylations affect the protein dynamics of the enzyme before the proton transfer to Asp1132 with only a minor effect after the proton transfer. This finding is consistent with the large change in the proton transfer free energy and the smaller change in the free energy barrier of phosphoryl transfer found by QM/MM simulations. Taken together, the present results provide details on how IRK phosphorylation exerts allosteric control of the catalytic activity via modifications of protein dynamics and free energy landscape of catalytic reaction. The results also highlight the importance of protein dynamics in connecting protein allostery and catalysis to control catalytic activity of enzymes.

Assessing the accuracy of the isotropic periodic sum method through Madelung energy computation.

We tested the isotropic periodic sum (IPS) method for computing Madelung energies of ionic crystals. The performance of the method, both in its nonpolar (IPSn) and polar (IPSp) forms, was compared with that of the zero-charge and Wolf potentials [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. The results show that the IPSn and IPSp methods converge the Madelung energy to its reference value with an average deviation of ∼10(-4) and ∼10(-7) energy units, respectively, for a cutoff range of 18-24a (a/2 being the nearest-neighbor ion separation). However, minor oscillations were detected for the IPS methods when deviations of the computed Madelung energies were plotted on a logarithmic scale as a function of the cutoff distance. To remove such oscillations, we introduced a modified IPSn potential in which both the local-region and long-range electrostatic terms are damped, in analogy to the Wolf potential. With the damped-IPSn potential, a smoother convergence was achieved. In addition, we observed a better agreement between the damped-IPSn and IPSp methods, which suggests that damping the IPSn potential is in effect similar to adding a screening potential in IPSp.

Isotropic Periodic Sum Treatment of Long-Range Electrostatic Interactions in Combined Quantum Mechanical and Molecular Mechanical Calculations.

The isotropic periodic sum (IPS) method was extended to describe long-range electrostatic interactions in combined quantum mechanical and molecular mechanical (QM/MM) calculations. The resulting method, designated QM/MM-IPS, was tested for two ion association processes and a model SN2 reaction in aqueous solution. Potential of mean force (PMF) profiles and radial distribution functions computed from the QM/MM-IPS simulations were compared with those obtained by using the existing QM/MM-Ewald sum and cutoff (QM/MM-Cutoff) methods. In contrast to the QM/MM-Cutoff method, with which PMFs of ion separation tend to display a spurious linear drift, the QM/MM-IPS method successfully eliminates such artifacts, in excellent agreement with the QM/MM-Ewald results. The PMF obtained with the QM/MM-IPS method for the SN2 reaction that transfers an NH3 group between two chloride anions closely resembles that from the QM/MM-Ewald simulations. Compared with QM/MM-Ewald, the QM/MM-IPS method reduces the computational cost by 60-70% when a local region of 12 to 14 Å is used. These results suggest that the QM/MM-IPS method can be used as a reliable and efficient alternative to the QM/MM-Ewald method to incorporate long-range electrostatic effects in simulating solution-phase chemical reactions.

H-loop histidine catalyzes ATP hydrolysis in the E. coli ABC-transporter HlyB.

Adenosine triphosphate (ATP)-binding cassette (ABC) transporters form a family of molecular motor proteins that couple ATP hydrolysis to substrate translocation across cell membranes. Each nucleotide binding domain of ABC-transporters contains a highly conserved H-loop histidine residue, whose precise mechanistic role in motor functions has remained elusive. By using combined quantum mechanical and molecular mechanical (QM/MM) calculations, we showed that the conserved H-loop residue H662 in E. coli HlyB, a bacterial ABC-transporter, can act first as a general acid and then as a general base to facilitate proton transfer in ATP hydrolysis. Without the assistance of H662, direct proton transfer from the lytic water to ATP results in a substantially higher barrier height. Our findings suggest that the essential function of the H-loop residue H662 is to provide a "chemical linchpin" that shuttles protons between reactants through a relay mechanism, thereby catalyzing ATP hydrolysis in HlyB.

Selecting fast-folding proteins by their rate of convergence.

We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using only the very initial parts of the dynamical trajectories. It does not require any preliminary knowledge of the native state and can be applied to different kinds of models, including atomistic descriptions. We tested the method within both the lattice and off-lattice model frameworks and obtained several so far unknown good folders. The unbiased algorithm also allows one to determine the optimal folding temperature and takes at least 3-4 orders of magnitude fewer time steps than those needed to compute folding times.

Electric field-driven disruption of a native beta-sheet protein conformation and generation of a helix-structure.

We demonstrate that an external constant electric field is able to modify the secondary structure of a protein and induce a transition from a beta-sheet into a helix-like conformation. This dramatic change is driven by a global rearrangement of the dipole moments at the amide planes. We also predict electric-field-induced modifications of the intermediate states of the protein.