Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs

Different microscopic and semimicroscopic approaches for calculations of electrostatic energies in macromolecules are examined. This includes the Protein Dipoles Langevin Dipoles (PDLD) method, the semimicroscopic PDLD (PDLD/S) method, and a free energy perturbation (FEP) method. The incorporation of these approaches in the POLARIS and ENZYMIX modules of the MOLARIS package is described in detail. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions, as well as the effects of the ionic strength and external pH. Determination of the hydrophobic energy involves an approach that considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. Ionic strength effects are studied by modeling the ionic environment around the given system using a grid of residual charges and evaluating the relevant interaction using Coulomb's law with the dielectric constant of water. The performance of the FEP calculations is significantly enhanced by using special boundary conditions and evaluating the long-range electrostatic contributions using the Local Reaction Field (LRF) model. A diverse set of electrostatic effects are examined, including the solvation energies of charges in proteins and solutions, energetics of ion pairs in proteins and solutions, interaction between surface charges in proteins, and effect of ionic strength on such interactions, as well as electrostatic contributions to binding and catalysis in solvated proteins. Encouraging results are obtained by the microscopic and semimicroscopic approaches and the problems associated with some macroscopic models are illustrated. The PDLD and PDLD/S methods appear to be much faster than the FEP approach and still give reasonable results. In particular, the speed and simplicity of the PDLD/S method make it an effective strategy for calculations of electrostatic free energies in interactive docking studies. Nevertheless, comparing the results of the three approaches can provide a useful estimate of the accuracy of the calculated energies. © 1993 John Wiley & Sons, Inc.     

Thermodynamics of unstable DNA structures from the kinetics of the microgene PCR

The microgene polymerization reaction (MPR) generates head-to-tail tandem repeats from homoduplexes (HDs). In MPR initiation, one HD putatively aligns two others in the proximity required to form a nucleation complex, thus allowing the DNA polymerase to skip the intertemplate gap and generate an initial doublet (ID) prone to repeat propagation. The current investigation refines this stage by additional thermodynamic considerations and elucidates the fundamental mechanism underlying propagation. Four different HD types were designed to extend the range of melting temperatures and to simultaneously modify the stabilities of their secondary structures. Following the propagation kinetics with these, using real-time PCR at different temperatures revealed a new stage in the MPR, amplification of an ID by an original HD, and enabled us to decipher the biphasic kinetics of the process. This amplification merges with the propagation stage if the lifetime of the staggered conformation of the ID is sufficiently long for DNA polymerase to fill in the overhangs. The observed increase with temperature of thermodynamically unfavorable conformations of singlet and doublet HDs that underlies, respectively, MPR initiation and propagation is well correlated with simulations by UNAFold.     

Simulation of tunneling in enzyme catalysis by combining a biased propagation approach and the quantum classical path method: application to lipoxygenase

The ability of using wave function propagation approaches to simulate isotope effects in enzymes is explored, focusing on the large H/D kinetic isotope effect of soybean lipoxygenase-1 (SLO-1). The H/D kinetic isotope effect (KIE) is calculated as the ratio of the rate constants for hydrogen and deuterium transfer. The rate constants are calculated from the time course of the H and D nuclear wave functions. The propagations are done using one-dimensional proton potentials generated as sections from the full multidimensional surface of the reacting system in the protein. The sections are obtained during a classical empirical valence bond (EVB) molecular dynamics simulation of SLO-1. Since the propagations require an extremely long time for treating realistic activation barriers, it is essential to use an effective biasing approach. Thus, we develop here an approach that uses the classical quantum path (QCP) method to evaluate the quantum free energy change associated with the biasing potential. This approach provides an interesting alternative to full QCP simulations and to other current approaches for simulating isotope effects in proteins. In particular, this approach can be used to evaluate the quantum mechanical transmission factor or other dynamical effects, while still obtaining reliable quantized activation free energies due to the QCP correction.     

Pair correlation functions in mixtures of Lennard-Jones particles

The pair correlation functions for a mixture of two Lennard-Jones particles were computed by both the Percus-Yevick equations and by molecular dynamics. The changes in the pair correlation function resulting from changes in the composition of the mixtures are quite unexpected. Essentially, identical changes are obtained from the Percus-Yevick equations and from molecular dynamics simulations. The molecular reason for this unexpected behavior is discussed.     

Numerical solution of isospectral flows

In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation

where is a symmetric matrix, is a skew-symmetric matrix function of and is the Lie bracket operator. We show that standard Runge-Kutta schemes fail in recovering the main qualitative feature of these flows, that is isospectrality, since they cannot recover arbitrary cubic conservation laws. This failure motivates us to introduce an alternative approach and establish a framework for generation of isospectral methods of arbitrarily high order.

     

On zero-sum partitions and anti-magic trees

We study zero-sum partitions of subsets in abelian groups, and apply the results to the study of anti-magic trees. Extension to the nonabelian case is also given.     

Solvent-induced forces in protein folding reflections on the protein folding problem

It is shown that the solvent induced forces on hydrophilic groups are the strongest ones. The relevance of this finding to protein folding is discussed.     

Water’s contribution in providing strong solvent-induced forces in protein folding

It is commonly accepted that water plays an essential role in determining both the stability of the 3D structure of protein, as well as speed of the protein folding process. How exactly water does that, is still very controversial. Until recently it was believed that various hydrophobic effects, which originate from the solvent, are the dominant factors. In the first part of this article we discuss the paradigm shift from hydrophobic (H?O), to a hydrophilic (H?I) based theory of protein folding. Next, we analyze the types of solvent-induced forces that are exerted on various groups on the protein. We find that the H?I–H?I solvent-induced forces are likely to be the strongest. These forces originate from water molecules forming hydrogen-bonded-bridges between two, or more hydrophilic groups attached to the protein. Therefore, it is argued that these forces are also the forces that force the protein to fold, in a short time, along a narrow range of pathways. This paradigm shift brings us, as close as we can hope for, to a solution to the general problem of protein folding.     

Multiscale modeling of biological functions

Recent years have witnessed a tremendous explosion in computational power, which in turn has resulted in great progress in the complexity of the biological and chemical problems that can be addressed by means of all-atom simulations. Despite this, however, our computational time is not infinite, and in fact many of the key problems of the field were resolved long before the existence of the current levels of computational power. This review will start by presenting a brief historical overview of the use of multiscale simulations in biology, and then present some key developments in the field, highlighting several cases where the use of a physically sound simplification is clearly superior to a brute-force approach. Finally, some potential future directions will be discussed.