Perspective: Markov models for long-timescale biomolecular dynamics.

Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is insufficient, as researchers must be able to transform the data in a simulation trajectory into specific scientific insights. Although this analysis step has often been taken for granted, it deserves further attention as large-scale simulations become increasingly routine. In this perspective, we discuss the application of Markov models to the analysis of large-scale biomolecular simulations. We draw attention to recent improvements in the construction of these models as well as several important open issues. In addition, we highlight recent theoretical advances that pave the way for a new generation of models of molecular kinetics.

COMPUTING: Screen Savers of the World Unite!

Unused CPU time on desktop computers could be put to good use, if distributed computing succeeds in capturing people's imagination. In their Perspective, Shirts and Pande describe existing distributed computing projects and recent efforts to overcome parallelization problems. This vast underused resource could raise biological and other scientific computation to fundamentally new predictive levels.

Pathways for protein folding: is a new view needed?

Theoretical studies using simplified models of proteins have shed light on the general heteropolymeric aspects of the folding problem. Recent work has emphasized the statistical aspects of folding pathways. In particular, progress has been made in characterizing the ensemble of transition state conformations and elucidating the role of intermediates. These advances suggest a reconciliation between the new ensemble approaches and the classical view of a folding pathway.

Free energy landscape of activation in a signalling protein at atomic resolution.

The interconversion between inactive and active protein states, traditionally described by two static structures, is at the heart of signalling. However, how folded states interconvert is largely unknown due to the inability to experimentally observe transition pathways. Here we explore the free energy landscape of the bacterial response regulator NtrC by combining computation and nuclear magnetic resonance, and discover unexpected features underlying efficient signalling. We find that functional states are defined purely in kinetic and not structural terms. The need of a well-defined conformer, crucial to the active state, is absent in the inactive state, which comprises a heterogeneous collection of conformers. The transition between active and inactive states occurs through multiple pathways, facilitated by a number of nonnative transient hydrogen bonds, thus lowering the transition barrier through both entropic and enthalpic contributions. These findings may represent general features for functional conformational transitions within the folded state.

Multiscale dynamics of macromolecules using normal mode Langevin.

Proteins and other macromolecules have coupled dynamics over multiple time scales (from femtosecond to millisecond and beyond) that make resolving molecular dynamics challenging. We present an approach based on periodically decomposing the dynamics of a macromolecule into slow and fast modes based on a scalable coarse-grained normal mode analysis. A Langevin equation is used to propagate the slowest degrees of freedom while minimizing the nearly instantaneous degrees of freedom. We present numerical results showing that time steps of up to 1000 fs can be used, with real speedups of up to 200 times over plain molecular dynamics. We present results of successfully folding the Fip35 mutant of WW domain.

A multiscale approach to sampling nascent peptide chains in the ribosomal exit tunnel.

We present a new multiscale method that combines all-atom molecular dynamics with coarse-grained sampling, towards the aim of bridging two levels of physiology: the atomic scale of protein side chains and small molecules, and the huge scale of macromolecular complexes like the ribosome. Our approach uses all-atom simulations of peptide (or other ligand) fragments to calculate local 3D spatial potentials of mean force (PMF). The individual fragment PMFs are then used as a potential for a coarse-grained chain representation of the entire molecule. Conformational space and sequence space are sampled efficiently using generalized ensemble Monte Carlo. Here, we apply this method to the study of nascent polypeptides inside the cavity of the ribosome exit tunnel. We show how the method can be used to explore the accessible conformational and sequence space of nascent polypeptide chains near the ribosome peptidyl transfer center (PTC), with the eventual aim of understanding the basis of specificity for co-translational regulation. The method has many potential applications to predicting binding specificity and design, and is sufficiently general to allow even greater separation of scales in future work.

On the theory of folding kinetics for short proteins.

BACKGROUND: Recent data have suggested two principles that are central to the work we describe here. First, proteins are the result of evolutionary 'sequence selection' to optimize the energy of the native state. Second, the overlap with the native state is a qualitatively suitable reaction coordinate for modeling folding kinetics. The former principle is bolder and better established. RESULTS: Employing only these two principles, we have constructed a non-phenomenological, correlated energy landscape theory that predicts single barrier protein folding kinetics. Moreover, we are able to analytically describe the nature of the free energetic barrier between the denatured and native states of a protein and to detail the nature of folding kinetics for short proteins. Our model predicts Hammond behavior and also describes how mutations can lead to drastic differences in folding times. CONCLUSIONS: We find that folding and unfolding kinetics can be characterized by a single thermodynamic parameter and, moreover, that Monte Carlo simulation data on folding and unfolding rates with different temperatures and mutations collapse with this characterization. Our results also delineate a regime in which kinetics may proceed via a single unique nucleus.

Molecular dynamics simulations of unfolding and refolding of a beta-hairpin fragment of protein G.

We have studied the unfolding and refolding pathway of a beta-hairpin fragment of protein G by using molecular dynamics. Although this fragment is small, it possesses several of the qualities ascribed to small proteins: cooperatively formed beta-sheet secondary structure and a hydrophobic "core" of packed side chains. At high temperatures, we find that the beta-hairpin unfolds through a series of sudden, discrete conformational changes. These changes occur between states that are identified with the folded state, a pair of partially unfolded kinetic intermediates, and the unfolded state. To study refolding at low temperatures, we perform a series of short simulations starting from the transition states of the discrete transitions determined by the unfolding simulations.

Mathematical analysis of coupled parallel simulations.

A set of parallel replicas of a single simulation can be statistically coupled to closely approximate long trajectories. In many cases, this produces nearly linear speedup over a single simulation ( M times faster with M simulations), rendering previously intractable problems within reach of large computer clusters. Interestingly, by varying the coupling of the parallel simulations, it is possible in some systems to obtain greater than linear speedup. The methods are generalizable to any search algorithm with long residence times in intermediate states.

Is the molten globule a third phase of proteins?

The equilibrium properties of proteins are studied by Monte Carlo simulation of two simplified models of protein-like heteropolymers. These models emphasize the polymeric entropy of the fluctuating polypeptide chain. Our calculations suggest a generic phase diagram that contains a thermodynamically distinct "molten globule" state in addition to a rigid native state and a nontrivial unfolded state. The roles of side-chain packing and loop entropy are discussed.

Folding pathway of a lattice model for proteins.

The folding of a protein-like heteropolymer is studied by using direct simulation of a lattice model that folds rapidly to a well-defined "native" structure. The details of each molecular folding event depend on the random initial conformation as well as the random thermal fluctuations of the polymer. By analyzing the statistical properties of hundreds of folding events, a classical folding "pathway" for such a polymer is found that includes partially folded, on-pathway intermediates that are shown to be metastable equilibrium states of the polymer. These results are discussed in the context of the "classical" and "new" views of folding.

Mechanical unfolding of a beta-hairpin using molecular dynamics.

Single-molecule mechanical unfolding experiments have the potential to provide insights into the details of protein folding pathways. To investigate the relationship between force-extension unfolding curves and microscopic events, we performed molecular dynamics simulations of the mechanical unfolding of the C-terminal hairpin of protein G. We have studied the dependence of the unfolding pathway on pulling speed, cantilever stiffness, and attachment points. Under conditions that generate low forces, the unfolding trajectory mimics the untethered, thermally accessible pathway previously proposed based on high-temperature studies. In this stepwise pathway, complete breakdown of backbone hydrogen bonds precedes dissociation of the hydrophobic cluster. Under more extreme conditions, the cluster and hydrogen bonds break simultaneously. Transitions between folding intermediates can be identified in our simulations as features of the calculated force-extension curves.

Statistical mechanics of simple models of protein folding and design.

It is now believed that the primary equilibrium aspects of simple models of protein folding are understood theoretically. However, current theories often resort to rather heavy mathematics to overcome some technical difficulties inherent in the problem or start from a phenomenological model. To this end, we take a new approach in this pedagogical review of the statistical mechanics of protein folding. The benefit of our approach is a drastic mathematical simplification of the theory, without resort to any new approximations or phenomenological prescriptions. Indeed, the results we obtain agree precisely with previous calculations. Because of this simplification, we are able to present here a thorough and self contained treatment of the problem. Topics discussed include the statistical mechanics of the random energy model (REM), tests of the validity of REM as a model for heteropolymer freezing, freezing transition of random sequences, phase diagram of designed ("minimally frustrated") sequences, and the degree to which errors in the interactions employed in simulations of either folding and design can still lead to correct folding behavior.

Nonrandomness in protein sequences: evidence for a physically driven stage of evolution?

The sequences, or primary structures, of existing biopolymers--in particular, proteins--are believed to be a product of evolution. Are the sequences random? If not, what is the character of this nonrandomness? To explore the statistics of protein sequences, we use the idea of mapping the sequence onto the trajectory of a random walk, originally proposed by Peng et al. [Peng, C.-K., Buldyrev, S. V., Goldberger, A. L., Havlin, S., Sciortino, F., Simons, M. & Stanley, H. E. (1992) Nature (London) 356, 168-170] in their analysis of DNA sequences. Using three different mappings, corresponding to three basic physical interactions between amino acids, we found pronounced deviations from pure randomness, and these deviations seem directed toward minimization of the energy of the three-dimensional structure. We consider this result as evidence for a physically driven stage of evolution.

Thermodynamic procedure to synthesize heteropolymers that can renature to recognize a given target molecule.

We suggest a procedure to synthesize polymers with characteristics similar to those observed in globular proteins: renaturability and the existence of an "active site" capable of specifically recognizing a given target molecule. This procedure is investigated by computer simulation, which finds a yield of up to 65%. We believe that, in principle, this scheme can be realized in vitro. The applicability of this approach as a model of prebiotic synthesis in vivo is also discussed.

Simulation of biomimetic recognition between polymers and surfaces.

Many biological processes, such as transmembrane signaling and pathogen-host interactions, are initiated by a protein recognizing a specific pattern of binding sites on part of a membrane or cell surface. By recognition, we imply that the polymer quickly finds and then adsorbs strongly on the pattern-matched region and not on others. The development of synthetic systems that can mimic such recognition between polymers and surfaces could have significant impact on advanced applications such as the development of sensors, molecular-scale separation processes, and synthetic viral inhibition agents. Attempting to affect recognition in synthetic systems by copying the detailed chemistries to which nature has been led over millenia of evolution does not seem practical for most applications. This leads us to the following question: Are there any universal strategies that can affect recognition between polymers and surfaces? Such generic strategies may be easier to implement in abiotic applications. We describe results that suggest that biomimetic recognition between synthetic polymers and surfaces is possible by exploiting certain generic strategies, and we elucidate the kinetic mechanisms by which this occurs. Our results suggest convenient model systems for experimental studies of dynamics in free energy landscapes characteristic of frustrated systems.