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The RNA-dependent RNA polymerase (RdRp) of norovirus is an attractive target of antiviral agents aimed at providing protection against norovirusassociated gastroenteritis. Here, we perform molecular dynamics simulations of the crystal structure of norovirus RdRp in complex with several known binders, as well as free-energy simulations by free-energy perturbation (FEP) to determine binding free energies of these molecules relative to the natural nucleotide substrates. We determine experimental EC(50) values and nucleotide incorporation efficiencies for several of these compounds. Moreover, we investigate the mechanism of inhibition of some of these ligands. Using FEP, we screened a virtual nucleotide library with 121 elements for binding to the polymerase and successfully identified two novel chain terminators.

A machine learning approach employing neural networks is developed to calculate the vibrational frequency shifts and transition dipole moments of the symmetric and antisymmetric OH stretch vibrations of a water molecule surrounded by water molecules. We employed the atom-centered symmetry functions (ACSFs), polynomial functions, and Gaussian-type orbital-based density vectors as descriptor functions and compared their performances in predicting vibrational frequency shifts using the trained neural networks. The ACSFs perform best in modeling the frequency shifts of the OH stretch vibration of water among the types of descriptor functions considered in this paper. However, the differences in performance among these three descriptors are not significant. We also tried a feature selection method called CUR matrix decomposition to assess the importance and leverage of the individual functions in the set of selected descriptor functions. We found that a significant number of those functions included in the set of descriptor functions give redundant information in describing the configuration of the water system. We here show that the predicted vibrational frequency shifts by trained neural networks successfully describe the solvent-solute interaction-induced fluctuations of OH stretch frequencies.

Memristors represent the fourth electrical circuit element complementing resistors, capacitors and inductors. Hallmarks of memristive behavior include pinched and frequency-dependent I–V hysteresis loops and most importantly a functional dependence of the magnetic flux passing through an ideal memristor on its electrical charge. Microtubules (MTs), cylindrical protein polymers composed of tubulin dimers are key components of the cytoskeleton. They have been shown to increase solution’s ionic conductance and re-orient in the presence of electric fields. It has been hypothesized that MTs also possess intrinsic capacitive and inductive properties, leading to transistor-like behavior. Here, we show a theoretical basis and experimental support for the assertion that MTs under specific circumstances behave consistently with the definition of a memristor. Their biophysical properties lead to pinched hysteretic current–voltage dependence as well a classic dependence of magnetic flux on electric charge. Based on the information about the structure of MTs we provide an estimate of their memristance. We discuss its significance for biology, especially neuroscience, and potential for nanotechnology applications.

We apply several mixed quantum–classical Liouville-based methods and Ehrenfest (mean-field) dynamics to the simulation of vibrational energy flow between amide I modes in a one-dimensional model of a hydrogen-bonded polypeptide. Three solutions of the mixed quantum–classical Liouville (MQCL) equation are implemented: a surface-hopping solution, an adiabatic solution, and a mean-field-like method known as the Poisson Bracket Mapping Equation (PBME) solution. The energy transport is investigated by calculating the time-dependent populations of the subsystem states localized on the different amide I modes following excitation at one end of the chain. In the cases of surface-hopping and adiabatic dynamics, the excitation delocalizes on a timescale of a few hundred femtoseconds, while for PBME and Ehrenfest dynamics it delocalizes on a timescale of picoseconds. When hydrogen bond distortions are introduced at each end of the chain, surface-hopping and adiabatic dynamics predict energy hopping between these distal sites, while no transfer occurs if PBME and Ehrenfest dynamics are used. Given the more accurate nature of the surface-hopping solution, these results demonstrate that the mean-field dynamics generated by the PBME and Ehrenfest approaches fail for modelling this energy transfer process, as they yield a very different picture of the quantum dynamics. The insights gained from this study set the stage for simulations of vibrational energy flow in more realistic models of peptides via the surface-hopping and adiabatic dynamics solutions of the MQCL equation.

The hepatitis C virus (HCV) envelope glycoproteins E1 and E2 are critical in viral attachment and cell fusion, and studies of these proteins may provide valuable insights into their potential uses in vaccines and antiviral strategies. Progress has included elucidating the crystal structures of portions of their ectodomains, as well as many other studies of hypervariable regions, stem regions, glycosylation sites, and the participation of E1/E2 in viral fusion with the endosomal membrane. The available structural data have shed light on the binding sites of cross-neutralizing antibodies. A large amount of information has been discovered concerning heterodimerization, including the roles of transmembrane domains, disulfide bonding, and heptad repeat regions. The possible organization of higher order oligomers within the HCV virion has also been evaluated on the basis of experimental data. In this review, E1/E2 structure and function is discussed, and some important issues requiring further study are highlighted.

In the development of antiviral drugs that target viral RNA-dependent RNA polymerases, off-target toxicity caused by the inhibition of the human mitochondrial RNA polymerase (POLRMT) is a major liability. Therefore, it is essential that all new ribonucleoside analogue drugs be accurately screened for POLRMT inhibition. A computational tool that can accurately predict NTP binding to POLRMT could assist in evaluating any potential toxicity and in designing possible salvaging strategies. Using the available crystal structure of POLRMT bound to an RNA transcript, here we created a model of POLRMT with an NTP molecule bound in the active site. Furthermore, we implemented a computational screening procedure that determines the relative binding free energy of an NTP analogue to POLRMT by free energy perturbation (FEP), i.e. a simulation in which the natural NTP molecule is slowly transformed into the analogue and back. In each direction, the transformation was performed over 40 ns of simulation on our IBM Blue Gene Q supercomputer. This procedure was validated across a panel of drugs for which experimental dissociation constants were available, showing that NTP relative binding free energies could be predicted to within 0.97 kcal/mol of the experimental values on average. These results demonstrate for the first time that free-energy simulation can be a useful tool for predicting binding affinities of NTP analogues to a polymerase. We expect that our model, together with similar models of viral polymerases, will be very useful in the screening and future design of NTP inhibitors of viral polymerases that have no mitochondrial toxicity.

Despite the recent success of newly developed direct-acting antivirals against hepatitis C, the disease continues to be a global health threat due to the lack of diagnosis of most carriers and the high cost of treatment. The heterodimer formed by glycoproteins E1 and E2 within the hepatitis C virus (HCV) lipid envelope is a potential vaccine candidate and antiviral target. While the structure of E1/E2 has not yet been resolved, partial crystal structures of the E1 and E2 ectodomains have been determined. The unresolved parts of the structure are within the realm of what can be modeled with current computational modeling tools. Furthermore, a variety of additional experimental data is available to support computational predictions of E1/E2 structure, such as data from antibody binding studies, cryo-electron microscopy (cryo-EM), mutational analyses, peptide binding analysis, linker-scanning mutagenesis, and nuclear magnetic resonance (NMR) studies. In accordance with these rich experimental data, we have built an in silico model of the full-length E1/E2 heterodimer. Our model supports that E1/E2 assembles into a trimer, which was previously suggested from a study by Falson and coworkers (P. Falson, B. Bartosch, K. Alsaleh, B. A. Tews, A. Loquet, Y. Ciczora, L. Riva, C. Montigny, C. Montpellier, G. Duverlie, E. I. Pecheur, M. le Maire, F. L. Cosset, J. Dubuisson, and F. Penin, J. Virol. 89:10333–10346, 2015, https://doi.org/10.1128/JVI.00991-15 ). Size exclusion chromatography and Western blotting data obtained by using purified recombinant E1/E2 support our hypothesis. Our model suggests that during virus assembly, the trimer of E1/E2 may be further assembled into a pentamer, with 12 pentamers comprising a single HCV virion. We anticipate that this new model will provide a useful framework for HCV envelope structure and the development of antiviral strategies. IMPORTANCE One hundred fifty million people have been estimated to be infected with hepatitis C virus, and many more are at risk for infection. A better understanding of the structure of the HCV envelope, which is responsible for attachment and fusion, could aid in the development of a vaccine and/or new treatments for this disease. We draw upon computational techniques to predict a full-length model of the E1/E2 heterodimer based on the partial crystal structures of the envelope glycoproteins E1 and E2. E1/E2 has been widely studied experimentally, and this provides valuable data, which has assisted us in our modeling. Our proposed structure is used to suggest the organization of the HCV envelope. We also present new experimental data from size exclusion chromatography that support our computational prediction of a trimeric oligomeric state of E1/E2.

Tubulin, an α/β heterodimer, has had most of its 3D structure analyzed; however, the carboxy (C)-termini remain elusive. Importantly, the C-termini play critical roles in regulating microtubule structure and function. They are sites of most of the post-translational modifications of tubulin and interaction sites with molecular motors and microtubule-associated proteins. Simulated annealing was used in our molecular dynamics modeling to predict the interactions of the C-terminal tails with the tubulin dimer. We examined differences in their flexibility, interactions with the body of tubulin, and the existence of structural motifs. We found that the α-tubulin tail interacts with the H11 helix of β-tubulin, and the β-tubulin tail interacts with the H11 helix of α-tubulin. Tail domains and H10/B9 loops interact with each other and compete for interactions with positively-charged residues of the H11 helix on the neighboring monomer. In a simulation in which α-tubulin's H10/B9 loop switches on sub-nanosecond intervals between interactions with the C-terminal tail of α-tubulin and the H11 helix of β-tubulin, the intermediate domain of α-tubulin showed more fluctuations compared to those in the other simulations, indicating that tail domains may cause shifts in the position of this domain. This suggests that C-termini may affect the conformation of the tubulin dimer which may explain their essential function in microtubule formation and effects on ligand binding to microtubules. Our modeling also provides evidence for a disordered-helical/helical double-state system of the T3/H3 region of the microtubule, which could be linked to depolymerization following GTP hydrolysis. Proteins 2011; © 2011 Wiley-Liss, Inc.

The neuronal cytoskeleton has been hypothesized to play a role in higher cognitive functions including learning, memory and consciousness. Experimental evidence suggests that both microtubules and actin filaments act as biological electrical wires that can transmit and amplify electric signals via the flow of condensed ion clouds. The potential transmission of electrical signals via the cytoskeleton is of extreme importance to the electrical activity of neurons in general. In this regard, the unique structure, geometry and electrostatics of microtubules are discussed with the expected impact on their specific functions within the neuron. Electric circuit models of ionic flow along microtubules are discussed in the context of experimental data, and the specific importance of both the tubulin C-terminal tail regions, and the nano-pore openings lining the microtubule wall is elucidated. Overall, these recent results suggest that ions, condensed around the surface of the major filaments of the cytoskeleton, flow along and through microtubules in the presence of potential differences, thus acting as transmission lines propagating intracellular signals in a given cell. The significance of this conductance to the functioning of the electrically active neuron, and to higher cognitive function is also discussed.

Microtubules are involved in numerous cellular processes including chromosome segregation during mitosis and, as a result, their constituent protein, tubulin, has become a successful target of several chemotherapeutic drugs. In general, these drugs bind indiscriminately to tubulin within both cancerous and healthy cells, resulting in unwanted side effects. However, differences between β-tubulin isotypes expressed in a wide range of cell types may aid in the development of anti-tubulin drugs having increased specificity for only certain types of cells. Here, we describe a digital signal processing (DSP) method that is capable of predicting hot spots for the tubulin family of proteins as well as determining relative differences in binding affinities to these hot spots based only on the primary sequence of 10 human tubulin isotypes. Due to the fact that several drug binding sites have already been characterized within β-tubulin, we are able to correlate hot spots with the binding sites for known chemotherapy drugs. We have also verified the accuracy of this method using the correlation between the binding affinities of characterized drugs and the tubulin isotypes. Additionally, the DSP method enables the rapid estimation of relative differences in binding affinities within the binding sites of tubulin isotypes that are yet to be experimentally determined.

Microtubules are significant therapeutic targets for the treatment of cancer, where suppression of microtubule dynamicity by drugs such as paclitaxel forms the basis of clinical efficacy. Peloruside A, a macrolide isolated from New Zealand marine sponge Mycale hentscheli, is a microtubule-stabilizing agent that synergizes with taxoid drugs through a unique site and is an attractive lead compound in the development of combination therapies. We report here unique allosteric properties of microtubule stabilization via peloruside A and present a structural model of the peloruside-binding site. Using a strategy involving comparative hydrogen-deuterium exchange mass spectrometry of different microtubule-stabilizing agents, we suggest that taxoid-site ligands epothilone A and docetaxel stabilize microtubules primarily through improved longitudinal interactions centered on the interdimer interface, with no observable contributions from lateral interactions between protofilaments. The mode by which peloruside A achieves microtubule stabilization also involves the interdimer interface, but includes contributions from the alpha/beta-tubulin intradimer interface and protofilament contacts, both in the form of destabilizations. Using data-directed molecular docking simulations, we propose that peloruside A binds within a pocket on the exterior of beta-tubulin at a previously unknown ligand site, rather than on alpha-tubulin as suggested in earlier studies.

The coupled reference interaction site model-hyper-netted chain (RISM-HNC)/ simulation methodology determines solvation free energies as a function of the set of all radial distribution functions of solvent atoms about atomic solute sites. These functions are determined from molecular dynamics (MD) or Monte Carlo (MC) simulations rather than from solving the RISM and HNC equations iteratively. Previous applications of the method showed that it can predict relative free energies of solvation for small solutes accurately. However, the errors scale with the system size. In this study, we propose the use of the hard-sphere free energy as the reference and a linear response approximation to improve the performance, i.e., accuracy and robustness, of the method, particularly removing the size dependency of the error. The details of the new formalism are presented. To validate the proposed formalism, solvation free energies of N-methylacetamide and methylamine are computed using the new RISM-HNC-based expressions in addition to a linear response expression, which are compared to previous thermodynamic integration and thermodynamic perturbation results performed with the same force field. Additionally, free energies of solvation for cyclohexane, pyridine, benzene and derivatives, and other small organic molecules are calculated and compared to experimental values.

Energy released by the hydrolysis of the high-energy phosphate bond of nucleoside triphosphate (NTP) cofactors is the driving force behind most biological processes. To understand how this energy is used to induce differences in protein structure and function, we examine the transfer of vibrational energy into the nucleotide-bound actin active site immediately after reaction activation. To this end, we perform Born-Oppenheimer molecular dynamics simulations of the active site at the level of density functional theory (DFT) starting at the calculated transition state (TS) structure. Similarly to the mechanism determined in many nucleotide-bound protein systems, the Os-Pγ bond is first elongated. Then, nucleophilic attack of the lytic water on Pγ occurs. Subsequently, protons are transferred in a cycle formed by water molecules, a protein residue, Asp154, and the γ-phosphate group, resulting in the formation of H2PO4(-). To investigate the possible creation of excited vibrational states in the products, power spectra of bond-length autocorrelation functions for relevant bonds within the active site are compared for simulations that start at the TS, at reactants, and at reaction end products. The hydroxyl bond formed in the final proton transfer to the phosphate molecule is observed to exhibit relatively high kinetic energies and large oscillations during reaction. It is also likely that some of the energy released by the reaction is captured by the low-energy stretching vibrations of the phosphoryl bonds of orthophosphate, which oscillate with large amplitudes in nonequilibrium simulations of end products.

An application of the coupled reference interaction site model (RISM)/simulation methodology to the calculation of the potential of mean force (PMF) curve in aqueous solution for the identity nucleophilic substitution reaction Cl(-) + CH(3)Cl is performed. The free energy of activation is calculated to be 27.1 kcal/mol which compares very well with the experimentally determined barrier height of 26.6 kcal/mol. Furthermore, the calculated PMF is almost superimposed with that previously calculated using the computationally rigorous Monte Carlo with importance sampling method (Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J. Am. Chem. Soc. 1985, 107, 154). Using the calculated PMF, a crude estimate of the solvated kinetic transmission coefficient also compares well with that of previous more accurate simulations. These results indicate that the coupled RISM/simulation method provides a cost-effective methodology for studying reactions in solution.

We present an application of the recently proposed coupled reference interation site model (RISM)/molecular dynamics (MD) solvation free-energy method (Freedman, H.; Truong, T. N. Chem. Phys. Lett. 2003, 381, 362; J. Chem. Phys. 2004, 121, 2187) to study the hydration effect upon the tautomeric equilibria of 2-hydroxypyridine and 2-oxopyridine and of cytosine in water. In this methodology, simulation trajectories of solvated systems are computed and averaged to determine radial distribution functions, which are then inserted into a RISM expression for the solvation free energy. The computed differences in free energy of hydration for the two tautomerizations agree well with the experimental data as well as results from previous free-energy simulations. This is particularly encouraging since the coupled RISM/MD method requires a single MD simulation as compared to the more complicated and computationally demanding free-energy simulation methods.

We present a new methodology for computing solvation free energy, which is based upon the reference interaction site model (RISM)/hypernetted chain (HNC) solvation free energy expression, but which substitutes radial distribution functions taken from simulations for those calculated by simultaneous solution of the RISM and HNC equations. Consequently, solvation free energy can be obtained from a single molecular dynamics or Monte Carlo simulation. Here we describe in detail the coupled RISM/simulation approach, and offer some error analysis. Finally we give the results of its application to a set of small test molecules in aqueous solution. The success shown in some of our results demonstrates that the coupled RISM/simulation approach is worth considering further as a potentially useful tool in studies of solvated systems, such as aqueous molecular biosystems.

We propose a new computational methodology that couples reference interaction site model (RISM) and molecular dynamics (MD) or Monte Carlo (MC) simulation methods for determination of solvation free energies. We employ the RISM formulation of solvation free energy. The correlation functions entering this expression are derived from radial distribution functions supplied by MD or MC simulations, instead of coming from simultaneous solution of the RISM and hyper-netted chain equations. We apply this approach to determining free energies of solvation for several small molecules. Our results are in good agreement with experimental values, demonstrating the potential of this method for applications to larger systems.

We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.

Tubulin, an α/β heterodimer, has had most of its 3D structure analyzed; however, the carboxy (C)-termini remain elusive. Importantly, the C-termini play critical roles in regulating microtubule structure and function. They are sites of most of the post-translational modifications of tubulin and interaction sites with molecular motors and microtubule-associated proteins. Simulated annealing was used in our molecular dynamics modeling to predict the interactions of the C-terminal tails with the tubulin dimer. We examined differences in their flexibility, interactions with the body of tubulin, and the existence of structural motifs. We found that the α-tubulin tail interacts with the H11 helix of β-tubulin, and the β-tubulin tail interacts with the H11 helix of α-tubulin. Tail domains and H10/B9 loops interact with each other and compete for interactions with positively-charged residues of the H11 helix on the neighboring monomer. In a simulation in which α-tubulin's H10/B9 loop switches on sub-nanosecond intervals between interactions with the C-terminal tail of α-tubulin and the H11 helix of β-tubulin, the intermediate domain of α-tubulin showed more fluctuations compared to those in the other simulations, indicating that tail domains may cause shifts in the position of this domain. This suggests that C-termini may affect the conformation of the tubulin dimer which may explain their essential function in microtubule formation and effects on ligand binding to microtubules. Our modeling also provides evidence for a disordered-helical/helical double-state system of the T3/H3 region of the microtubule, which could be linked to depolymerization following GTP hydrolysis.

To provide more accurate computational estimates of binding free energies in solution from molecular dynamics (MD) simulations, a separate solvation contribution for the binding ligand is determined from a linear response treatment. We use explicit water coordinates for this term and combine with MM-PBSA (molecular mechanics, Poisson-Boltzmann, and surface area contributions) in a new approach (MM-PB/LRA-SA). To assess this method, application to the binding between theophylline and its derivatives to an RNA aptamer was performed and compared with experimental binding affinities. Explicitly solvated MD trajectories were generated with the same parameter set used in the previous work by Gouda et al., who compared the relative binding of these molecules by both the MM-PBSA and thermodynamic integration methods. Substituting the linear response term for the ligand in the MM-PB/LRA-SA approach led to an improvement upon MM-PBSA when compared with experimental and thermodynamic integration results at approximately twice the computational cost. The balance between accuracy and computational expense achieved using this method suggests potential advantages in applying it in the virtual drug-screening process.

Tubulin, the primary subunit of microtubules, is remarkable for the variety of small molecules to which it binds. Many of these are very useful or promising agents in cancer chemotherapy. One of the most useful of these is paclitaxel. The tubulin molecule is itself an alpha/beta heterodimer, both alpha- and beta-tubulin monomers existing as multiple isotypes. Despite the success of paclitaxel as an anticancer drug, resistance often occurs in cancer cells and has been associated with variations in tubulin isotype expression, most notably with the increased expression of betaIII-tubulin. Paclitaxel is thought to reach its binding site on beta-tubulin by diffusion through nanopores in the microtubule wall. It has been suggested that a transitional step in this process may be the binding of paclitaxel to an intermediate site within a nanopore, from which it moves directly to its binding site in the microtubule interior facing the lumen. To test this hypothesis, we have computationally docked paclitaxel within a microtubule nanopore and simulated its passage to the intermediate binding site. Targeted molecular dynamics was then used to test the hypothesis that paclitaxel utilizes the H6/H7 loop as a hinge to move directly from this intermediate binding site to its final position in the luminal binding site. We observed that this motion appears to be stabilized by the formation of a hydrogen bond involving serine 275 in beta-tubulin isotypes I, IIa, IIb, IVa, IVb, V, VII, and VIII. Interestingly, this residue is replaced by alanine in the betaIII and VI isotypes. This observation raises the possibility that the observed isotype difference in paclitaxel binding may be a kinetic effect arising from the isotype difference at this residue. We are now able to suggest derivatives of paclitaxel that may reverse the isotype-specificity or lead to an alternate stabilizing hydrogen-bond interaction with tubulin, thus increasing the rate of passage to the luminal binding site and hopefully offering a therapeutic advantage in paclitaxel resistant cases.