From short‐time molecular dynamics to long‐time stochastic dynamics of proteins

Future directions for combining molecular and continuum models in protein simulations

In order to perform useful computer simulations on protein molecules, models that combine atomistic and continuum approaches will be necessary. The use of continuum models will reduce the number of system variables and allow studies of longer time scales. On the other hand, one will still need to retain atomic detail in certain parts of the protein molecule, such as an enzyme active site. Most of the important advances to date have been continuum models of the surrounding solvent, but simplified descriptions of the protein itself also are being developed. Finally, in order to study these several different levels of complexity simultaneously in a single simulation, it will be necessary to use modern software engineering techniques.

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

Distribution of the iron-heme displacement as resulting from myoglobin conformational substrates: an AOM approach to the interpretation of the EPR spectra

The electron paramagnetic resonance (EPR) low-temperature spectra of high spin ferric myoglobin samples in different solvent composition have been analyzed in terms of a distribution of the energy differences delta 1 and delta 2 for the iron low-lying electronic states. The widths of these distributions, which are found to be dependent on the solvent composition, have been correlated to the presence of a frozen ensemble of conformational substrates. A dedicated analysis based on the angular overlap method (AOM) has allowed us to work out a quantitative relationship between the delta 1 and delta 2 distributions and the spread of the iron-heme displacement; this being a structural parameter relevant for the biological functionality of the protein. The observed dependence of the iron-heme displacement distribution on the solvent composition is discussed.

Rotamer interconversion and its influence on the fluorescence decay of tyrosine: a molecular dynamics study

To test the hypothesis of charge-transfer quenching between an electrophile in the alanyl sidechain (carbonyl carbon or protonated amino group) and the excited aromatic phenol-subunit, which leads to a bi-exponential fluorescence decay of tyrosine in acidic aqueous solution, we investigated the dynamics of this amino acid and of the peptide Gly-Tyr-Gly in vacuo and in water with classical molecular dynamics (MD) and with stochastic dynamics (SD) computer simulation. The proposed low-frequency of interconversions between sidechain rotamers on a fluorescence time-scale could not be confirmed. Instead, frequent transitions for both, chi 1 and chi 2, dihedrals were observed. Simulating a low pH situation (protonated carboxylate group) did not significantly affect the transition frequency. Rotamer interconversions in the peptide Gly-Tyr-Gly, though significantly less, were also observed although the fluorescence decay of this compound could be described by a uni-modal lifetime distribution centered at 0.8 ns. The results obtained from simulations in vacuo and in solution were critically compared with those of stochastic simulations. We found the stochastic simulation in a better agreement to full MD (water explicitly included), which is highly time consuming, whereas the in vacuo simulations clearly deviated from both. We conclude from our results that, since the rotamers do frequently interconvert within the fluorescence lifetime of tyrosine, their contribution to the non-exponential fluorescence decay should be negligible.

Binding of an antiviral agent to a sensitive and a resistant human rhinovirus. Computer simulation studies with sampling of amino acid side-chain conformation. I. Mapping the rotamers of residue 188 of viral protein 1

The mutation of valine 188 to leucine in the viral protein 1 of human rhinovirus 14 renders the virus resistant to certain antiviral compounds. Thermodynamic-cycle perturbation theory provides a means of calculating the difference in the binding free energies of an antiviral compound to the wild-type virus and to the mutant virus. In calculating the relevant free-energy differences in molecular dynamics simulations, it is important to sample the multiple rotational isomers of residue 188 correctly. In general, these rotamers will not be fully sampled during a single molecular dynamics simulation. However, the contributions of all the rotamers to the free-energy differences associated with mutation of residue 188 may be considered explicitly once they have been identified and their relative free energies determined. Therefore, we describe here the mapping of the rotamers of residue 188 by steric-bump search and energy minimization techniques, and by the computation of potentials of mean force (p.m.f.s.) using umbrella sampling. The usefulness, validity and efficiency of these methods of examining rotameric states is discussed. Adiabatic mapping by energy minimization was found to be unreliable for this residue due to the small magnitude of its interactions with the surrounding protein atoms. Ambiguities in the adiabatic maps were resolved by computing p.m.f.s. The p.m.f. for valine 188 in the unliganded wild-type virus shows a minimum corresponding to the crystallographically observed conformation of valine 188. The p.m.f.s. for valine 188 in the liganded virus and for leucine 188 in the unliganded mutant virus suggest that the experimentally observed conformations may be interpreted as averages of a number of conformations corresponding to those at the minima in the p.m.f.s. The calculations suggest also that the conformation of leucine 188 may change when the ligand binds. The use of the calculated p.m.f.s. to compute the difference in the free energy of binding of an antiviral compound to the wild-type and mutant rhinoviruses is described in the accompanying article.

Critical analysis of objections against the biological molecular energy machines

In the past, two important objections against McClare's idea of biological molecular energy machines were raised. One of the criticisms was concerned with the origin of energy gained in ATP cleavage and with an interpretation of McClare's "excited vibrational state." The former argument reveals a failure of the critics to comprehend McClare's approach. As to the excited vibrational state, it can be identified with nonequilibrium conformational states of the unit rather than with a single vibrational mode. The other criticism based on Brillouin's energy cost of measurement argued that reversible operation of biological molecular energy machines would be virtually impossible. Using propagation velocities of deformations of the unit's structure (instead of velocity of light), the objections against reversibility are invalidated even in the framework of the critic's approach. McClare's idea and relevant definitions are thus physically correct.

Plausible view on the biological molecular energy machines

A qualitative picture of operation modes of biological molecular energy machines is presented. It is suggested that there is mutual control between the flow of molecular energy stored in a biological molecular energy machine and the sequence of nonequilibrium conformational states through which the machine passes in doing work. If the structure of the conformational space is favorable, the set of trajectories in this space decomposes into two families, each of which accomplishes another task. This divergence of trajectories enables to distinguish molecular objects according to differences in interaction between the machine and the object, i.e., to perform a measurement on a molecular object and process the object according to the result of that measurement.