ABSTRACT Simulating protein folding thermodynamics starting purely from a protein sequence is a grand challenge of computational biology. Here, we present an algorithm to calculate a canonical distribution from molecular dynamics simulation of protein folding. This algorithm is based on the replica exchange method where the kinetic trapping problem is overcome by exchanging noninteracting replicas simulated at different temperatures. Our algorithm uses multiplexed-replicas with a number of independent molecular dynamics runs at each temperature. Exchanges of configurations between these multiplexed-replicas are also tried, rendering the algorithm applicable to large-scale distributed computing (i.e., highly heterogeneous parallel computers with processors having different computational power). We demonstrate the enhanced sampling of this algorithm by simulating the folding thermodynamics of a 23 amino acid miniprotein. We show that better convergence is achieved compared to constant temperature molecular dynamics simulation, with an efficient scaling to large number of computer processors. Indeed, this enhanced sampling results in (to our knowledge) the first example of a replica exchange algorithm that samples a folded structure starting from a completely unfolded state.

By employing thousands of PCs and new worldwide-distributed computing techniques, we have simulated in atomistic detail the folding of a fastfolding 36-residue a-helical protein from the villin headpiece. The total simulated time exceeds 300 ms, 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 1.7 A ˚ and 1.9 A ˚ away from the native state in Ca distance-based root-meansquare deviation (dRMS) and Cb 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 (,20 ns), 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

Amyotrophic lateral sclerosis (ALS) is the most common motor neuron disease in human adults that is characterized by selective motor neuron death. 1–4 In approximately 10 % of the cases of

Experimental observations suggest that proteins follow different pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature —the temperature for which the SH3 domain undergoes a rapid folding transition with minimal kinetic barriers — and observe that below this temperature the model protein may undergo a folding transition via multiple folding pathways. The folding kinetics is characterized by slow and fast pathways and the presence of only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediates states under extreme experimental conditions, such as very low temperatures. A very recent report (Viguera et al., Proc. Natl. Acad. Sci. USA, 100:5730–5735, 2003) of an intermediate in the folding transition of the Bergerac mutant of the α-spectrin SH3 domain protein supports this hypothesis.

The exquisite reliability of proteins in recognizing their targets has been intensely studied for more than a century. Several paradigms for protein recognition have emerged, varying in the degree

ABSTRACT 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 a-helical proteins, the mean unfolded-state Ca-Ca distance matrix is significantly more nativelike than the Ca-Ca 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.

ABSTRACT 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

ABSTRACT: Previously, we identified the protein BBL as a downhill folder. This conclusion was based on the statistical mechanical analysis of equilibrium experiments performed in two variants of BBL, one with a fluorescent label at the N-terminus, and another one labeled at both ends. A recent report has claimed that our results are an artifact of label-induced aggregation and that BBL with no fluorescent labels and a longer N-terminal tail folds in a two-state fashion. Here, we show that singly and doubly labeled BBL do not aggregate, unfold reversibly, and have the same thermodynamic properties when studied under appropriate experimental conditions (e.g., our original conditions (1)). With an elementary analysis of the available data on the nonlabeled BBL (2), we also show that this slightly more stable BBL variant is not a two-state folder. We discuss the problems that led to its previous misclassification and how they can be avoided. Finally, we investigate the equilibrium unfolding of the singly labeled BBL with both ends protected by acetylation and amidation. This variant has the same thermodynamic stability of the nonlabeled BBL and displays all the equilibrium signatures of downhill folding. From all these observations, we conclude that fluorescent labels do not perturb the thermodynamic properties of BBL, which consistently folds downhill regardless of its stability and specific protein tails. The work on BBL illustrates the shortcomings of applying conventional procedures intended to distinguish between twostate

The dimensions and secondary structure content of two proteins which fold in a two-state manner are measured within milliseconds of denatur-ant dilution using synchrotron-based, stopped-flow small-angle X-ray scattering and far-UV circular dichroism spectroscopy. Even upon a jump to strongly native conditions, neither ubiquitin nor common-type acyl-phosphatase contract prior to the major folding event. Circular dichroism and fluorescence indicate that negligible amounts of secondary and tertiary structures form in the burst phase. Thus, for these two denatured states, collapse and secondary structure formation are not energetically downhill processes even under aqueous, low-denaturant conditions. In addition, water appears to be as good a solvent as that with high concen-trations of denaturant, when considering the over-all dimensions of the denatured state. However, the removal of denaturant does subtly alter the distribution of backbone dihedral f,c angles, most likely resulting in a shift from the polyproline II region to the helical region of the Ramachandran map. We consider the thermodynamic origins of these behaviors along with implications for folding mechanisms and computer simulations thereof.

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