Biomedical subjects

Vijay S Pande

Publications and source records attributed to Vijay S Pande.

At least 19 recordsLinked to original sources

PubMed2006

Local structure formation in simulations of two small proteins.

Massively parallel all-atom, explicit solvent molecular dynamics simulations were used to explore the formation and existence of local structure in two small alpha-helical proteins, the villin headpiece and the helical fragment B of protein A. We report on the existence of transient helices and combinations of helices in the unfolded ensemble, and on the order of formation of helices, which appears to largely agree with previous experimental results. Transient local structure is observed even in the absence of overall native structure. We also calculate sets of residue-residue pairs that are statistically predictive of the formation of given local structures in our simulations.

Computer Simulation↗

PubMed2006

Simulated unfolded-state ensemble and the experimental NMR structures of villin headpiece yield similar wide-angle solution X-ray scattering profiles.

With the advent of powerful synchrotron sources, solution X-ray scattering is being increasingly used to get basic information about the structure of polypeptides. The solution scattering technique essentially provides one-dimensional data, which are then interpreted in terms of a three-dimensional structure through model building. Here we calculate wide-angle solution scattering patterns for an ensemble of simulated unfolded structures of villin headpiece, which differ from the native structure by rmsd = 8.8 +/- 1.0 A and have only negligible amounts of native secondary structure. We show that the wide-angle solution scattering pattern of such an ensemble shares significant similarity with the one based on the experimental NMR structures of the molecule. Our results suggest that solution scattering in the wide-angle limit, by itself, provides very little information about the secondary structure content of a polypeptide or its side-chain packing.

Computer Simulation↗

PubMed2006

Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics.

We present a technique for biomolecular free energy calculations that exploits highly parallelized sampling to significantly reduce the time to results. The technique combines free energies for multiple, nonoverlapping configurational macrostates and is naturally suited to distributed computing. We describe a methodology that uses this technique with docking, molecular dynamics, and free energy perturbation to compute absolute free energies of binding quickly compared to previous methods. The method does not require a priori knowledge of the binding pose as long as the docking technique used can generate reasonable binding modes. We demonstrate the method on the protein FKBP12 and eight of its inhibitors.

Biophysics↗

PubMed2006

Ensemble molecular dynamics yields submillisecond kinetics and intermediates of membrane fusion.

Lipid membrane fusion is critical to cellular transport and signaling processes such as constitutive secretion, neurotransmitter release, and infection by enveloped viruses. Here, we introduce a powerful computational methodology for simulating membrane fusion from a starting configuration designed to approximate activated prefusion assemblies from neuronal and viral fusion, producing results on a time scale and degree of mechanistic detail not previously possible to our knowledge. We use an approach to the long time scale simulation of fusion by constructing a Markovian state model with large-scale distributed computing, yielding an understanding of fusion mechanisms on time scales previously impossible to simulate to our knowledge. Our simulation data suggest a branched pathway for fusion, in which a common stalk-like intermediate can either rapidly form a fusion pore or remain in a metastable hemifused state that slowly forms fully fused vesicles. This branched reaction pathway provides a mechanistic explanation both for the biphasic fusion kinetics and the stable hemifused intermediates previously observed experimentally. Our distributed computing and Markovian state model approaches provide sufficient sampling to detect rare transitions, a systematic process for analyzing reaction pathways, and the ability to develop quantitative approximations of reaction kinetics for fusion.

Algorithms↗

PubMed2006

Electric fields at the active site of an enzyme: direct comparison of experiment with theory.

The electric fields produced in folded proteins influence nearly every aspect of protein function. We present a vibrational spectroscopy technique that measures changes in electric field at a specific site of a protein as shifts in frequency (Stark shifts) of a calibrated nitrile vibration. A nitrile-containing inhibitor is used to deliver a unique probe vibration to the active site of human aldose reductase, and the response of the nitrile stretch frequency is measured for a series of mutations in the enzyme active site. These shifts yield quantitative information on electric fields that can be directly compared with electrostatics calculations. We show that extensive molecular dynamics simulations and ensemble averaging are required to reproduce the observed changes in field.

Aldehyde Reductase↗

PubMed2006

Nanotube confinement denatures protein helices.

In striking contrast to simple polymer physics theory, which does not account for solvent effects, we find that physical confinement of solvated biopolymers decreases solvent entropy, which in turn leads to a reduction in the organized structural content of the polymer. Since our theory is based on a fundamental property of water-protein statistical mechanics, we expect it to have broad implications in many biological and material science contexts.

Entropy↗

PubMed2006

Using massively parallel simulation and Markovian models to study protein folding: examining the dynamics of the villin headpiece.

We report on the use of large-scale distributed computing simulation and novel analysis techniques for examining the dynamics of a small protein. Matters addressed include folding rate, very long time scale kinetics, ensemble properties, and interaction with water. The target system for the study, the villin headpiece, has been of great interest to experimentalists and theorists both. Sampling totaled nearly 500 mus-the most extensive published to date for a system of villin's size in explicit solvent with all atom detail-and was in the form of tens of thousands of independent molecular dynamics trajectories, each several tens of nanoseconds in length. We report on kinetics sensitivity analyses that, using a set of short simulations, probed the role of water in villin's folding and sensitivity to the simulation's electrostatics treatment. By constructing Markovian state models (MSMs) from the collected data, we were able to propagate dynamics to times far beyond those directly simulated and to rapidly compute mean first passage times, long time kinetics (tens of microseconds), and evolution of ensemble property distributions over long times, otherwise currently impossible. We also tested our MSM by using it to predict the structure of villin de novo.

Algorithms↗

PubMed2006

Kinetic definition of protein folding transition state ensembles and reaction coordinates.

Using distributed molecular dynamics simulations we located four distinct folding transitions for a 39-residue betabetaalphabeta protein fold. To characterize the nature of each room temperature transition, we calculated the probability of transmission for 500 points along each free energy barrier. We introduced a method for determining transition states by employing the transmission probability, Ptrans, and determined which conformations were transition state ensemble members (Ptrans approximately 0.5). The transmission probability may be used to characterize the barrier in several ways. For example, we ran simulations at 82 degrees C, determined the change in Ptrans with temperature for all 2,000 conformations, and quantified Hammond behavior directly using Ptrans correlation. Additionally, we propose that diffusion along Ptrans may provide the configurational diffusion rate at the top of the barrier. Specifically, given a transition state conformation x0 with estimated Ptrans=0.5, we selected a large set of subsequent conformations from independent trajectories, each exactly a small time deltat after x0 (250 ps). Calculating Ptrans for the new trial conformations, we generated the P(Ptrans|deltat=250 ps) distribution that reflected diffusion. This approach provides a novel perspective on the diffusive nature of a protein folding transition and provides a framework for a quantitative study of activated relaxation kinetics.

Computer Simulation↗

PubMed2006

Validation of Markov state models using Shannon's entropy.

Markov state models are kinetic models built from the dynamics of molecular simulation trajectories by grouping similar configurations into states and examining the transition probabilities between states. Here we present a procedure for validating the underlying Markov assumption in Markov state models based on information theory using Shannon's entropy. This entropy method is applied to a simple system and is compared with the previous eigenvalue method. The entropy method also provides a way to identify states that are least Markovian, which can then be divided into finer states to improve the model.

Bayes Theorem↗

PubMed2006

Kinetic computational alanine scanning: application to p53 oligomerization.

We have developed a novel computational alanine scanning approach that involves analysis of ensemble unfolding kinetics at high temperature to identify residues that are critical for the stability of a given protein. This approach has been applied to dimerization of the oligomerization domain (residues 326-355) of tumor suppressor p53. As validated by experimental results, our approach has reasonable success in identifying deleterious mutations, including mutations that have been linked to cancer. We discuss a method for determining the effect of mutations on the location of the dimerization transition state.

Alanine↗

PubMed2005

Can conformational change be described by only a few normal modes?

We suggest a simple method to assess how many normal modes are needed to map a conformational change. By projecting the conformational change onto a subspace of the normal-mode vectors and using root mean square deviation as a test of accuracy, we find that the first 20 modes only contribute 50% or less of the total conformational change in four test cases (myosin, calmodulin, NtrC, and hemoglobin). In some allosteric systems, like the molecular switch NtrC, the conformational change is localized to a limited number of residues. We find that many more modes are necessary to accurately map this collective displacement. In addition, the normal-mode "spectra" can provide useful information about the details of the conformational change, especially when comparing structures with different bound ligands, in this case, calmodulin. Indeed, this approach presents normal-mode analysis as a useful basis in which to capture the mechanism of conformational change, and shows that the number of normal modes needed to capture the essential collective motions of atoms should be chosen according to the required accuracy.

Amino Acids↗

PubMed2005

The solvation interface is a determining factor in peptide conformational preferences.

The 21 residue polyalanine-based F(s) peptide was studied using thousands of long, explicit solvent, atomistic molecular dynamics simulations that reached equilibrium at the ensemble level. Peptide conformational preference as a function of hydrophobicity was examined using a spectrum of explicit solvent models, and the peptide length-dependence of the hydrophilic and hydrophobic components of solvent-accessible surface area for several ideal conformational types was considered. Our results demonstrate how the character of the solvation interface induces several conformational preferences, including a decrease in mean helical content with increased hydrophilicity, which occurs predominantly through reduced nucleation tendency and, to a lesser extent, destabilization of helical propagation. Interestingly, an opposing effect occurs through increased propensity for 3(10)-helix conformations, as well as increased polyproline structure. Our observations provide a framework for understanding previous reports of conformational preferences in polyalanine-based peptides including (i) terminal 3(10)-helix prominence, (ii) low pi-helix propensity, (iii) increased polyproline conformations in short and unfolded peptides, and (iv) membrane helix stability in the presence and absence of water. These observations provide physical insight into the role of water in peptide conformational equilibria at the atomic level, and expand our view of the complexity of even the most "simple" of biopolymers. Whereas previous studies have focused predominantly on hydrophobic effects with respect to tertiary structure, this work highlights the need for consideration of such effects at the secondary structural level.

Hydrophobic and Hydrophilic Interactions↗

PubMed2005

A new set of molecular mechanics parameters for hydroxyproline and its use in molecular dynamics simulations of collagen-like peptides.

Recently, the importance of proline ring pucker conformations in collagen has been suggested in the context of hydroxylation of prolines. The previous molecular mechanics parameters for hydroxyproline, however, do not reproduce the correct pucker preference. We have developed a new set of parameters that reproduces the correct pucker preference. Our molecular dynamics simulations of proline and hydroxyproline monomers as well as collagen-like peptides, using the new parameters, support the theory that the role of hydroxylation in collagen is to stabilize the triple helix by adjusting to the right pucker conformation (and thus the right phi angle) in the Y position.

Collagen↗

PubMed2005

Error analysis and efficient sampling in Markovian state models for molecular dynamics.

In previous work, we described a Markovian state model (MSM) for analyzing molecular-dynamics trajectories, which involved grouping conformations into states and estimating the transition probabilities between states. In this paper, we analyze the errors in this model caused by finite sampling. We give different methods with various approximations to determine the precision of the reported mean first passage times. These approximations are validated on an 87 state toy Markovian system. In addition, we propose an efficient and practical sampling algorithm that uses these error calculations to build a MSM that has the same precision in mean first passage time values but requires an order of magnitude fewer samples. We also show how these methods can be scaled to large systems using sparse matrix methods.

Algorithms↗

PubMed2005

How large is an alpha-helix? Studies of the radii of gyration of helical peptides by small-angle X-ray scattering and molecular dynamics.

Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alanine-based alpha-helix-forming peptides of the composition Ace-(AAKAA)(n)-GY-NH(2), n=2-7, in aqueous solvent at 10(+/-1) degrees C. In contrast to other techniques typically used to study alpha-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal alpha-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(+/-0.6)A, which is to be compared with the radius of gyration of an ideal 37-mer alpha-helix of 17.6A. Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (< or =37 amino acid residues), these alpha-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.

Circular Dichroism↗

PubMed2005

Foldamer dynamics expressed via Markov state models. I. Explicit solvent molecular-dynamics simulations in acetonitrile, chloroform, methanol, and water.

In this article, we analyze the folding dynamics of an all-atom model of a polyphenylacetylene (pPA) 12-mer in explicit solvent for four common organic and aqueous solvents: acetonitrile, chloroform, methanol, and water. The solvent quality has a dramatic effect on the time scales in which pPA 12-mers fold. Acetonitrile was found to manifest ideal folding conditions as suggested by optimal folding times on the order of approximately 100-200 ns, depending on temperature. In contrast, chloroform and water were observed to hinder the folding of the pPA 12-mer due to extreme solvation conditions relative to acetonitrile; chloroform denatures the oligomer, whereas water promotes aggregation and traps. The pPA 12-mer in a pure methanol solution folded in approximately 400 ns at 300 K, compared relative to the experimental 12-mer folding time of approximately 160 ns measured in a 1:1 v/v THF/methanol solution. Requisite in drawing the aforementioned conclusions, analysis techniques based on Markov state models are applied to multiple short independent trajectories to extrapolate the long-time scale dynamics of the 12-mer in each respective solvent. We review the theory of Markov chains and derive a method to impose detailed balance on a transition-probability matrix computed from simulation data.

Acetonitriles↗

PubMed2005

Foldamer dynamics expressed via Markov state models. II. State space decomposition.

The structural landscape of poly-phenylacetylene (pPA), otherwise known as m-phenylene ethynylene oligomers, has been shown to consist of a very diverse set of conformations, including helices, turns, and knots. Defining a state space decomposition to classify these conformations into easily identifiable states is an important step in understanding the dynamics in relation to Markov state models. We define the state decomposition of pPA oligomers in terms of the sequence of discretized dihedral angles between adjacent phenyl rings along the oligomer backbone. Furthermore, we derive in mathematical detail an approach to further reduce the number of states by grouping symmetrically equivalent states into a single parent state. A more challenging problem requires a formal definition for knotted states in the structural landscape. Assuming that the oligomer chain can only cross the ideal helix path once, we propose a technique to define a knotted state derived from a helical state determined by the position along the helical nucleus where the chain crosses the ideal helix path. Several examples of helical states and knotted states from the pPA 12-mer illustrate the principles outlined in this article.

Acetylene↗

PubMed2005

Direct calculation of the binding free energies of FKBP ligands.

Direct calculations of the absolute free energies of binding for eight ligands to FKBP protein were performed using the Fujitsu BioServer massively parallel computer. Using the latest version of the general assisted model building with energy refinement (AMBER) force field for ligand model parameters and the Bennett acceptance ratio for computing free-energy differences, we obtained an excellent linear fit between the calculated and experimental binding free energies. The rms error from a linear fit is 0.4 kcal/mol for eight ligand complexes. In comparison with a previous study of the binding energies of these same eight ligand complexes, these results suggest that the use of improved model parameters can lead to more predictive binding estimates, and that these estimates can be obtained with significantly less computer time than previously thought. These findings make such direct methods more attractive for use in rational drug design.

Biophysics↗