Biomedical subjects

Bojan Zagrovic

Publications and source records attributed to Bojan Zagrovic.

13 recordsLinked to original sources

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

Comparing atomistic simulation data with the NMR experiment: how much can NOEs actually tell us?

Simulated molecular dynamics trajectories of proteins and nucleic acids are often compared with nuclear magnetic resonance (NMR) data for the purposes of assessing the quality of the force field used or, equally important, trying to interpret ambiguous experimental data. In particular, nuclear Overhauser enhancement (NOE) intensities or atom-atom distances derived from them are frequently calculated from the simulated ensembles because the distance restraints derived from NOEs are the key ingredient in NMR-based protein structure determination. In this study, we ask how diverse and nonnative-like an ensemble of structures can be and still match the experimental NOE distance upper bounds well. We present two examples in which simulated ensembles of highly nonnative polypeptide structures (an unfolded state ensemble of the villin headpiece and a high-temperature denatured ensemble of lysozyme) are shown to match fairly well the experimental NOE distance upper bounds from which the corresponding native structures were derived. For example, the unfolded ensemble of villin headpiece, which is on average 0.90 +/- 0.13 nm root-mean-square deviation away from the native NMR structure, deviates from the experimental restraints by only 0.027 nm on average. However, this artificially good agreement is largely a consequence of 1) the highly nonlinear effects of r(-6) (or r(-3)) averaging and 2) focusing only on the experimentally observed set of NOE bounds. Namely, in addition to the experimentally observed NOEs, both simulated ensembles (especially the villin ensemble) also predict a large number of NOEs, which are not seen in the experiment. If these are taken into account, the agreement between simulation and experiment gets markedly worse, as it should, given the nonnative nature of the underlying simulated ensembles. In light of the examples given, we conclude that comparing experimental NOE distance restraints with large simulated ensembles provides just by itself only limited information about the quality of simulation.

Animals↗

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

Unusual compactness of a polyproline type II structure.

Polyproline type II (PPII) helix has emerged recently as the dominant paradigm for describing the conformation of unfolded polypeptides. However, most experimental observables used to characterize unfolded proteins typically provide only short-range, sequence-local structural information that is both time- and ensemble-averaged, giving limited detail about the long-range structure of the chain. Here, we report a study of a long-range property: the radius of gyration of an alanine-based peptide, Ace-(diaminobutyric acid)2-(Ala)7-(ornithine)2-NH2. This molecule has previously been studied as a model for the unfolded state of proteins under folding conditions and is believed to adopt a PPII fold based on short-range techniques such as NMR and CD. By using synchrotron radiation and small-angle x-ray scattering, we have determined the radius of gyration of this peptide to be 7.4 +/- 0.5 angstroms, which is significantly less than the value expected from an ideal PPII helix in solution (13.1 angstroms). To further study this contradiction, we have used molecular dynamics simulations using six variants of the AMBER force field and the GROMOS 53A6 force field. However, in all cases, the simulated ensembles underestimate the PPII content while overestimating the experimental radius of gyration. The conformational model that we propose, based on our small angle x-ray scattering results and what is known about this molecule from before, is that of a very flexible, fluctuating structure that on the level of individual residues explores a wide basin around the ideal PPII geometry but is never, or only rarely, in the ideal extended PPII helical conformation.

Circular Dichroism↗

PubMed2004

Random-coil behavior and the dimensions of chemically unfolded proteins.

Spectroscopic studies have identified a number of proteins that appear to retain significant residual structure under even strongly denaturing conditions. Intrinsic viscosity, hydrodynamic radii, and small-angle x-ray scattering studies, in contrast, indicate that the dimensions of most chemically denatured proteins scale with polypeptide length by means of the power-law relationship expected for random-coil behavior. Here we further explore this discrepancy by expanding the length range of characterized denatured-state radii of gyration (R(G)) and by reexamining proteins that reportedly do not fit the expected dimensional scaling. We find that only 2 of 28 crosslink-free, prosthetic-group-free, chemically denatured polypeptides deviate significantly from a power-law relationship with polymer length. The R(G) of the remaining 26 polypeptides, which range from 16 to 549 residues, are well fitted (r(2) = 0.988) by a power-law relationship with a best-fit exponent, 0.598 +/- 0.028, coinciding closely with the 0.588 predicted for an excluded volume random coil. Therefore, it appears that the mean dimensions of the large majority of chemically denatured proteins are effectively indistinguishable from the mean dimensions of a random-coil ensemble.

Guanidine↗

PubMed2004

Folding probabilities: a novel approach to folding transitions and the two-dimensional Ising-model.

The theoretical concept of folding probability, p(fold), has proven to be a useful means to characterize the kinetics of protein folding. Here, we illustrate the practical importance of p(fold) and demonstrate how it can be determined theoretically. We derive a general analytical expression for p(fold) and show how it can be estimated from simulations for systems where the transition rates between the relevant microstates are not known. By analyzing the Ising model we are able to determine the scaling behavior of the numerical error in the p(fold) estimate as function of the number of analyzed Monte Carlo runs. We apply our method to a simple, newly developed protein folding model for the formation of alpha helices. It is demonstrated that our technique highly parallelizes the calculation of p(fold) and that it is orders of magnitude more efficient than conventional approaches.

Algorithms↗

PubMed2004

How does averaging affect protein structure comparison on the ensemble level?

Recent algorithmic advances and continual increase in computational power have made it possible to simulate protein folding and dynamics on the level of ensembles. Furthermore, analyzing protein structure by using ensemble representation is intrinsic to certain experimental techniques, such as nuclear magnetic resonance. This creates a problem of how to compare an ensemble of molecules with a given reference structure. Recently, we used distance-based root-mean-square deviation (dRMS) to compare the native structure of a protein with its unfolded-state ensemble. We showed that for small, mostly alpha-helical proteins, the mean unfolded-state Calpha-Calpha distance matrix is significantly more nativelike than the Calpha-Calpha matrices corresponding to the individual members of the unfolded ensemble. Here, we give a mathematical derivation that shows that, for any ensemble of structures, the dRMS deviation between the ensemble-averaged distance matrix and any given reference distance matrix is always less than or equal to the average dRMS deviation of the individual members of the ensemble from the same reference matrix. This holds regardless of the nature of the reference structure or the structural ensemble in question. In other words, averaging of distance matrices can only increase their level of similarity to a given reference matrix, relative to the individual matrices comprising the ensemble. Furthermore, we show that the above inequality holds in the case of Cartesian coordinate-based root-mean-square deviation as well. We discuss this in the context of our proposal that the average structure of the unfolded ensemble of small helical proteins is close to the native structure, and demonstrate that this finding goes beyond the above mathematical fact.

Computer Simulation↗

PubMed2003

Structural correspondence between the alpha-helix and the random-flight chain resolves how unfolded proteins can have native-like properties.

Recently, we have proposed that, on average, the structure of the unfolded state of small, mostly alpha-helical proteins may be similar to the native structure (the 'mean-structure' hypothesis). After examining thousands of simulations of both the folded and the unfolded states of five polypeptides in atomistic detail at room temperature, we report here a result that seems at odds with the mean-structure hypothesis. Specifically, the average inter-residue distances in the collapsed unfolded structures agree well with the statistics of the ideal random-flight chain with link length of 3.8 A (the length of one amino acid). A possible resolution of this apparent contradiction is offered by the observation that the inter-residue distances in a typical alpha-helix over short stretches are close to the average distances in an ideal random-flight chain.

Computer Simulation↗

PubMed2003

Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing.

Atomistic simulations of protein folding have the potential to be a great complement to experimental studies, but have been severely limited by the time scales accessible with current computer hardware and algorithms. By employing a worldwide distributed computing network of tens of thousands of PCs and algorithms designed to efficiently utilize this new many-processor, highly heterogeneous, loosely coupled distributed computing paradigm, we have been able to simulate hundreds of microseconds of atomistic molecular dynamics. This has allowed us to directly simulate the folding mechanism and to accurately predict the folding rate of several fast-folding proteins and polymers, including a nonbiological helix, polypeptide alpha-helices, a beta-hairpin, and a three-helix bundle protein from the villin headpiece. Our results demonstrate that one can reach the time scales needed to simulate fast folding using distributed computing, and that potential sets used to describe interatomic interactions are sufficiently accurate to reach the folded state with experimentally validated rates, at least for small proteins.

Algorithms↗

PubMed2003

Solvent viscosity dependence of the folding rate of a small protein: distributed computing study.

By using distributed computing techniques and a supercluster of more than 20,000 processors we simulated folding of a 20-residue Trp Cage miniprotein in atomistic detail with implicit GB/SA solvent at a variety of solvent viscosities (gamma). This allowed us to analyze the dependence of folding rates on viscosity. In particular, we focused on the low-viscosity regime (values below the viscosity of water). In accordance with Kramers' theory, we observe approximately linear dependence of the folding rate on 1/gamma for values from 1-10(-1)x that of water viscosity. However, for the regime between 10(-4)-10(-1)x that of water viscosity we observe power-law dependence of the form k approximately gamma(-1/5). These results suggest that estimating folding rates from molecular simulations run at low viscosity under the assumption of linear dependence of rate on inverse viscosity may lead to erroneous results.

Algorithms↗

PubMed2002

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations.

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.

Amino Acid Sequence↗

PubMed2002

Simulation of folding of a small alpha-helical protein in atomistic detail using worldwide-distributed computing.

By employing thousands of PCs and new worldwide-distributed computing techniques, we have simulated in atomistic detail the folding of a fast-folding 36-residue alpha-helical protein from the villin headpiece. The total simulated time exceeds 300 micros, orders of magnitude more than previous simulations of a molecule of this size. Starting from an extended state, we obtained an ensemble of folded structures, which is on average 1.7A and 1.9A away from the native state in C(alpha) distance-based root-mean-square deviation (dRMS) and C(beta) dRMS sense, respectively. The folding mechanism of villin is most consistent with the hydrophobic collapse view of folding: the molecule collapses non-specifically very quickly ( approximately 20ns), which greatly reduces the size of the conformational space that needs to be explored in search of the native state. The conformational search in the collapsed state appears to be rate-limited by the formation of the aromatic core: in a significant fraction of our simulations, the C-terminal phenylalanine residue packs improperly with the rest of the hydrophobic core. We suggest that the breaking of this interaction may be the rate-determining step in the course of folding. On the basis of our simulations we estimate the folding rate of villin to be approximately 5micros. By analyzing the average features of the folded ensemble obtained by simulation, we see that the mean folded structure is more similar to the native fold than any individual folded structure. This finding highlights the need for simulating ensembles of molecules and averaging the results in an experiment-like fashion if meaningful comparison between simulation and experiment is to be attempted. Moreover, our results demonstrate that (1) the computational methodology exists to simulate the multi-microsecond regime using distributed computing and (2) that potential sets used to describe interatomic interactions may be sufficiently accurate to reach the folded state, at least for small proteins. We conclude with a comparison between our results and current protein-folding theory.

Amino Acid Sequence↗

PubMed2002

Native-like mean structure in the unfolded ensemble of small proteins.

The nature of the unfolded state plays a great role in our understanding of proteins. However, accurately studying the unfolded state with computer simulation is difficult, due to its complexity and the great deal of sampling required. Using a supercluster of over 10,000 processors we have performed close to 800 micros of molecular dynamics simulation in atomistic detail of the folded and unfolded states of three polypeptides from a range of structural classes: the all-alpha villin headpiece molecule, the beta hairpin tryptophan zipper, and a designed alpha-beta zinc finger mimic. A comparison between the folded and the unfolded ensembles reveals that, even though virtually none of the individual members of the unfolded ensemble exhibits native-like features, the mean unfolded structure (averaged over the entire unfolded ensemble) has a native-like geometry. This suggests several novel implications for protein folding and structure prediction as well as new interpretations for experiments which find structure in ensemble-averaged measurements.

Amino Acid Sequence↗