Donald Hamelberg

Accelerated molecular dynamics: A promising and efficient simulation method for biomolecules

Many interesting dynamic properties of biological molecules cannot be simulated directly using molecular dynamics because of nanosecond time scale limitations. These systems are trapped in potential energy minima with high free energy barriers for large numbers of computational steps. The dynamic evolution of many molecular systems occurs through a series of rare events as the system moves from one potential energy basin to another. Therefore, we have proposed a robust bias potential function that can be used in an efficient accelerated molecular dynamics approach to simulate the transition of high energy barriers without any advance knowledge of the location of either the potential energy wells or saddle points. In this method, the potential energy landscape is altered by adding a bias potential to the true potential such that the escape rates from potential wells are enhanced, which accelerates and extends the time scale in molecular dynamics simulations. Our definition of the bias potential echoes the underlying shape of the potential energy landscape on the modified surface, thus allowing for the potential energy minima to be well defined, and hence properly sampled during the simulation. We have shown that our approach, which can be extended to biomolecules, samples the conformational space more efficiently than normal molecular dynamics simulations, and converges to the correct canonical distribution.

Sampling of slow diffusive conformational transitions with accelerated molecular dynamics

Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an accelerated molecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.

Characterization of a Novel DNA Minor-Groove Complex

Many dicationic amidine compounds bind in the DNA minor groove and have excellent biological activity against a range of infectious diseases. Para-substituted aromatic diamidines such as furamidine, which is currently being tested against trypanosomiasis in humans, and berenil, which is used in animals, are typical examples of this class. Recently, a meta-substituted diamidine, CGP 40215A, has been found to have excellent antitrypanosomal activity. The compound has a linear, conjugated linking group that can be protonated under physiological conditions when the compound interacts with DNA. Structural and molecular dynamics analysis of the DNA complex indicated an unusual AT-specific complex that involved water-mediated H-bonds between one amidine of the compound and DNA bases at the floor of the minor groove. To investigate this unique system in more detail DNase I footprinting, surface plasmon resonance biosensor techniques, linear dichroism, circular dichroism, ultraviolet-visible spectroscopy, and additional molecular dynamics simulations have been conducted. Spectrophotometric titrations of CGP 40215A binding to poly(dAT)(2) have characteristics of DNA-binding-induced spectral changes as well as effects due to binding-induced protonation of the compound linker. Both footprinting and surface plasmon resonance results show that this compound has a high affinity for AT-rich sequences of DNA but very weak binding to GC sequences. The dissociation kinetics of the CGP 40215A-DNA complex are much slower than with similar diamidines such as berenil. The linear dichroism results support a minor-groove complex for the compound in AT DNA sequences. Molecular dynamics studies complement the structural analysis and provide a clear picture of the importance of water in mediating the dynamic interactions between the ligand and the DNA bases in the minor groove.

A dry ligand-binding cavity in a solvated protein

Ligands usually bind to proteins by displacing water from the binding site. The affinity and kinetics of binding therefore depend on the hydration characteristics of the site. Here, we show that the extreme case of a completely dehydrated free binding site is realized for the large nonpolar binding cavity in bovine β-lactoglobulin. Because spatially delocalized water molecules may escape detection by x-ray diffraction, we use water 17O and 2H magnetic relaxation dispersion (MRD), 13C NMR spectroscopy, molecular dynamics simulations, and free energy calculations to establish the absence of water from the binding cavity. Whereas carbon nanotubes of the same diameter are filled by a hydrogen-bonded water chain, the MRD data show that the binding pore in the apo protein is either empty or contains water molecules with subnanosecond residence times. However, the latter possibility is ruled out by the computed hydration free energies, so we conclude that the 315 Å3 binding pore is completely empty. The apo protein is thus poised for efficient binding of fatty acids and other nonpolar ligands. The qualitatively different hydration of the β-lactoglobulin pore and carbon nanotubes is caused by subtle differences in water–wall interactions and water entropy.

A statistical analysis of the precision of reweighting-based simulations

Various advanced simulation techniques, which are used to sample the statistical ensemble of systems with complex Hamiltonians, such as those displayed in condensed matters and biomolecular systems, rely heavily on successfully reweighting the sampled configurations. The sampled points of a system from an elevated thermal environment or on a modified Hamiltonian are reused with different statistical weights to evaluate its properties at the initial desired temperature or of the original Hamiltonian. Often, the decrease of accuracy induced by this procedure is ignored and the final results can be far from what is expected. We have addressed the reasons behind such a phenomenon and have provided a quantitative method to estimate the number of sampled points required in the crucial step of reweighting of these advanced simulation methods. We also provided examples from temperature histogram reweighting and accelerated molecular dynamics reweighting to illustrate this idea, which can be generalized to the dynamic reweighting as well. The study shows that this analysis may provide a priori guidance for the strategy of setting up the parameters of advanced simulations before a lengthy one is carried out. The method can therefore provide insights for optimizing the parameters for high accuracy simulations with finite amount of computational resources.

Relating kinetic rates and local energetic roughness by accelerated molecular-dynamics simulations

We show that our accelerated molecular-dynamics (MD) approach can extend the time scale in all-atom MD simulations of biopolymers. We also show that this technique allows for the kinetic rate information to be recaptured. In deducing the kinetic rates, the relationship between the local energetic roughness of the potential-energy landscape and the effective diffusion coefficient is established. These are demonstrated on a very slow but important biomolecular process: the dynamics of cis-trans-isomerization of Ser-Pro motifs. We do not only recapture the slow kinetic rates, which is difficult in traditional MD, but also obtain the underlying roughness of the energy landscape of proteins at atomistic resolution.

Resolving the complex role of enzyme conformational dynamics in catalytic function

Despite growing evidence suggesting the importance of enzyme conformational dynamics (ECD) in catalysis, a consensus on how precisely ECD influences the chemical step and reaction rates is yet to be reached. Here, we characterize ECD in Cyclophilin A, a well-studied peptidyl-prolyl cis-trans isomerase, using normal and accelerated, atomistic molecular dynamics simulations. Kinetics and free energy landscape of the isomerization reaction in solution and enzyme are explored in unconstrained simulations by allowing significantly lower torsional barriers, but in no way compromising the atomistic description of the system or the explicit solvent. We reveal that the reaction dynamics is intricately coupled to enzymatic motions that span multiple timescales and the enzyme modes are selected based on the energy barrier of the chemical step. We show that Kramers’ rate theory can be used to present a clear rationale of how ECD affects the reaction dynamics and catalytic rates. The effects of ECD can be incorporated into the effective diffusion coefficient, which we estimate to be about ten times slower in enzyme than in solution. ECD thereby alters the preexponential factor, effectively impeding the rate enhancement. From our analyses, the trend observed for lower torsional barriers can be extrapolated to actual isomerization barriers, allowing successful prediction of the speedup in rates in the presence of CypA, which is in notable agreement with experimental estimates. Our results further reaffirm transition state stabilization as the main effect in enhancing chemical rates and provide a unified view of ECD’s role in catalysis from an atomistic perspective.

Protein conformational dynamics in the mechanism of HIV-1 protease catalysis

We have used chemical protein synthesis and advanced physical methods to probe dynamics-function correlations for the HIV-1 protease, an enzyme that has received considerable attention as a target for the treatment of AIDS. Chemical synthesis was used to prepare a series of unique analogues of the HIV-1 protease in which the flexibility of the “flap” structures (residues 37–61 in each monomer of the homodimeric protein molecule) was systematically varied. These analogue enzymes were further studied by X-ray crystallography, NMR relaxation, and pulse-EPR methods, in conjunction with molecular dynamics simulations. We show that conformational isomerization in the flaps is correlated with structural reorganization of residues in the active site, and that it is preorganization of the active site that is a rate-limiting factor in catalysis.

Reoptimization of the AMBER force field parameters for peptide bond (Omega) torsions using accelerated molecular dynamics.

Improving the accuracy of molecular mechanics force field parameters for atomistic simulations of proteins and nucleic acids has been an ongoing effort. The availability of computer power and improved methodologies for conformational sampling has allowed the assessment of these parameters by comparing the free energies calculated from molecular dynamic (MD) simulations and those measured from thermodynamic experiments. Here, we focus on testing and optimizing the AMBER force field parameters for the omega dihedral, which represents rotation around the peptide bond of proteins. Due to the very slow isomerization rate of the peptide bond, it is not possible to sample the phase space with standard MD simulations. We therefore employed an accelerated MD method in explicit water in which the original Hamiltonian is modified to speed up conformational sampling and the correct canonical distribution is recaptured. Using well-studied model systems for the peptide and peptidyl prolyl bonds, we discovered that the AMBER omega dihedral parameters underestimated experimentally measured activation free energy barriers for cis/trans conversion as well as failed to reproduce the free energy difference between the two isomers. We reoptimized the original AMBER omega dihedral parameters and further validated their transferability on several experimentally studied dipeptides. The revised set of parameters successfully reproduced the cis/trans equilibria and free energy barriers within experimental and simulation errors. We also investigated the structures of the transition state and cis/trans isomers of prolyl peptide bonds in terms of pyramidality, a measure of the puckering of the prolyl ring. We observed, as expected from quantum mechanical studies, significant bidirectional, out-of-plane motions of prolyl nitrogen in the transition state.

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study.

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.