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Enzymes control chemical reactions that are key to life processes, and allow them to take place on the time scale needed for synchronization between the relevant reaction cycles. In addition to general interest in their biological roles, these proteins present a fundamental scientific puzzle, since the origin of their tremendous catalytic power is still unclear. While many different hypotheses have been put forward to rationalize this, one of the proposals that has become particularly popular in recent years is the idea that dynamical effects contribute to catalysis. Here, we present a critical review of the dynamical idea, considering all reasonable definitions of what does and does not qualify as a dynamical effect. We demonstrate that no dynamical effect (according to these definitions) has ever been experimentally shown to contribute to catalysis. Furthermore, the existence of non-negligible dynamical contributions to catalysis is not supported by consistent theoretical studies. Our review is aimed, in part, at readers with a background in chemical physics and biophysics, and illustrates that despite a substantial body of experimental effort, there has not yet been any study that consistently established a connection between an enzyme's conformational dynamics and a significant increase in the catalytic contribution of the chemical step. We also make the point that the dynamical proposal is not a semantic issue but a well-defined scientific hypothesis with well-defined conclusions. [ABSTRACT FROM AUTHOR]

One of the major problems in molecular-dynamics simulations of polar fluids or macromolecular systems is the evaluation of electrostatic interactions. A system of N atoms demands an amount of work proportional to N2 for such calculations. Truncation procedures that neglect a significant part of the long-range effects are often necessary for computational feasibility, though such procedures may introduce serious errors in the simulations. This work introduces a simple and very effective approach for treating the long-range electrostatic forces. The present method, which is referred to as the local reaction field method, follows some of the ideas of the previously developed generalized Ewald method but then develops into a much simpler method. This is done by dividing the system into M groups of atoms and evaluating separately the short- and long-range contributions to the potential of each group. The short-range potential is evaluated explicitly as in any standard truncation method, while the long-range potential is approximated by the first four terms in a multipole expansion. In addition, the long-range potential is updated only once in every L time steps leading to a method of the order of N×M×q/L+N×P where q is related to the number of expansion terms and P is the average number of atoms inside the cutoff range. The speed, accuracy, and precision of the present method is assessed by evaluating the self-energy of a sodium ion in water and the self-energies of the acidic residues of bovine pancreatic trypsin inhibitor using an adiabatic charging free-energy perturbation approach. It is found that the present method reproduces accurately the corresponding results obtained without any cutoff but an order of magnitude faster. Furthermore, at the limit of very large systems, the speed of this method can be 2 orders of magnitude faster than that of the no-cutoff method even when each group contains only a small number of atoms. It is also found that... [ABSTRACT FROM AUTHOR]

The free energy functions for electron transfer reactions in solution are explored using a previously developed microscopic simulation approach that provides a clear definition of these functions and the variable (the reaction coordinate) used as their argument. The issue of whether the curvatures of the two functions (which correspond to states with nonpolar and polar solutes) are different is given special attention. It is found, in contrast to some previous suggestions, that the curvatures of the two functions are quite similar, even when one would expect differences due to dielectric saturation effects, and that Marcus’ approximation (and, in fact, the linear response theory inherent in this approximation) provides a valid description of the solvent’s role in electron transfer reactions over a wide range of conditions. The present study demonstrates that direct simulations of the reactant and product states do not provide the data needed for determination of the free energy functions in high energy regions. On the other hand, a free energy perturbation approach developed in our early studies does allow one to obtain statistically significant data for these regions of high free energy. Inclusion of the solvent electronic polarizabilities in the potential results in a marked lowering of the solvent reorganization energy, but does not change the ratio of the curvatures of the free energy functions for the nonpolar and polar states. Finally, the effect of solvent tunneling is evaluated with the dispersed polaron method and shown to be rather small, and it is argued that the observed deviations from the classical Marcus theory in the inverted region are due to quantum mechanical tunneling associated with the solute vibrations, rather than to differences in the curvatures of the solvent free energy functions. [ABSTRACT FROM AUTHOR]

A consistent simulation of ionic or strongly polar solutes in polar solvents presents a major challenge from both fundamental and practical aspects. The frequently used method of periodic boundary conditions (PBC) does not correctly take into account the symmetry of the solute field. Instead of using PBC, it is natural to model this type of system as a sphere (with the solute at the origin), but the boundary conditions to be used in such a model are not obvious. Early calculations performed with our surface constrained soft sphere dipoles (SCSSD) model indicated that the dipoles near the surface of the sphere will show unusual orientational preferences (they will overpolarize) unless a corrective force is included in the model, and thus we implemented polarization constraints in this spherical model of polar solutions. More recent approaches that treated the surface with stochastic dynamics, but did not take into account the surface polarization effects, were also found to exhibit these nonphysical orientational preferences. The present work develops a surface constrained all-atom solvent (SCAAS) model in order to consistently treat the surface polarization effects in all-atom molecular dynamics simulations. The SCAAS model, which was presented in a preliminary way in previous works, introduces surface constraints as boundary conditions in order to make the necessarily finite system behave as if it was part of an infinite system. The performance of the model with regard to various properties of bulk water is examined by comparing its results to those obtained by PBC simulations. The results obtained from SCAAS models of different sizes are found to be similar to each other and to the corresponding PBC results. The performance of the model in simulations of solvated ions is emphasized and a comparison of the results obtained with spheres of different sizes demonstrates that the model does not possess significant size dependence. This indicates that the model can... [ABSTRACT FROM AUTHOR]

The Ewald method, which is known as a method for evaluating electrostatic interactions in periodic systems, is extended to nonperiodic systems. A general way of applying the Ewald method to nonperiodic systems is described and a detailed application is demonstrated for the treatment of ions immersed in dipolar solvent molecules. As a preliminary test, electric fields produced by point dipoles forming a simple cubic lattice are calculated, both by the new Ewald treatment and by the conventional cutoff (truncation) method. These test calculations not only demonstrate the advantage of the new Ewald method but also reveal inherent problems associated with the cutoff method. [ABSTRACT FROM AUTHOR]

Examines the stability of the surface constrained all-atom solvent (SCAAS) model. Use of periodic boundary condition and Ewald treatment yield size dependent simulations; Implication of the SCAAS model for calculating the dielectric constants of protein; Benefits of the SCAAS model.

Studies the optimum cavity size in Langevin dipole lattices and Brownian dipole lattices. Dielectric constants of the dipole lattices; Cavity radius; Variation in the effective cavity size.

Simulation methods for exploring the microscopic aspects of electron transfer (ET) reactions are developed. For the high temperature limit, where anharmonicity effects are crucial, we develop a semiclassical trajectory (ST) method. This method treats the reaction by considering the time dependence of the electronic energy gap along the classical trajectories of the solvent molecules. The ST approach, which appears as an ad hoc approach, might be at present the most rigorous practical models for simulating ET reactions. That is, this method reproduces the results of the quantum mechanical harmonic test case in the high temperature statistical limit. More importantly, for anharmonic systems it provides a rate constant which depends on the proper activation free energy; this dependence cannot be evaluated by any of the current quantum mechanical methods. For the low temperature range we develop a ‘‘dispersed polaron’’ model that uses the Fourier transform of the microscopic energy gap to evaluate the harmonic Franck–Condon factors of the system. These Franck–Condon factors are then used to evaluate the quantum mechanical harmonic rate constant. The potential of our approach is outlined by considering its implementation in studies of several key problems. This includes: (i) Studies of the effect of solvent dynamics and the role of dielectric relaxation times. (ii) Studies of the actual microscopic activation free energy. (iii) Exploration of the role of vibronic channels in the inverted region. (iv) Transition between the adiabatic and diabatic limits. [ABSTRACT FROM AUTHOR]

Significant progress has been made in recent years in simulation of molecular spectra. It appears, however, that the available methods do not offer a reliable and practical way for simulation of the vibronic line shapes of large anharmonic molecules. As a step in the effort of attacking this problem we develop a semiclassical approach that generates quantized vibronic transitions between electronic surfaces of anharmonic molecules. The method evaluates vibronic transition probabilities by using the energy representation (Green’s functions) of the corresponding semiclassical propagators. The resulting expression generates automatically interference effects for nonquantized actions and gives significant intensity only for quantized vibronic transitions. The method is demonstrated in several test cases including the simulation of the line shape for the X→B transition in I2. The agreement between the quantum mechanical and classical results is excellent. The powerful physical insight provided by the method and its potential use in fundamental studies of line broadening in anharmonic molecules is outlined. [ABSTRACT FROM AUTHOR]

A practical ab initio quantum-mechanical approach for calculations of free energies of molecules in solutions is developed. This approach treats the solute molecules by an explicit ab initio self-consistent-field approach while representing the solvent molecules by a pseudopotential. The solvation energies are evaluated by a free-energy perturbation approach that uses the distribution function associated with a classical force field as a reference state for the quantum-mechanical calculations. The performance of the method is examined by evaluating the solvation energy of an Li+ ion. It is found that the calculation times are not much longer than that of the corresponding classical free-energy perturbation calculations. [ABSTRACT FROM AUTHOR]

Microscopic simulation of solvated proteins are used to evaluate the relationship between the macroscopic field and macroscopic polarization, thus providing the corresponding dielectric constant, ε. This parameter is evaluated by two different methods which are first examined and calibrated by calculating the dielectric constant of bulk water. These calculations indicate that the reaction field, which represents the effect of the missing solvent around the given explicit region, must be included in the simulations in order to obtain a reasonable value for ε. The corresponding effect is not related to the reduction of the effective interactions between charges in the reference region but to the intrinsic value of ε in that region. This means that vacuum calculations of ε in proteins might underestimate its actual value. Or in other words, calculations of ε in proteins must include the effect of the reaction field or a sufficiently large number of surrounding solvent molecules. Having included the surrounding solvent in simulations of trypsin, we find that ε depends on the actual protein site. In particular, we find that ε can be as large as 10 in sites of catalytic importance. It is pointed out that the dielectric constant that should be used in calculations of protein properties depends on the part of the system which is not treated explicitly and is not necessarily the macroscopic ε. For example, using ε in electrostatic calculations that consider the protein polar groups explicitly accounts twice for some aspects of the protein polarity. Finally, possible ways to use microscopically determined dielectric constants for electrostatic calculations in protein are considered. [ABSTRACT FROM AUTHOR]