Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 2. Example Applications to Alanine Dipeptide and a β-Hairpin Peptide † (original) (raw)
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In this work we demonstrate the use of a rigorous formalism for the extraction of state-to-state transition functions as a way to study the kinetics of protein folding in the context of a Markov chain. The approach is illustrated by its application to two different systems: a blocked alanine dipeptide in a vacuum and the C-terminal â-hairpin motif from protein G in water. The first system displays some of the desired features of the approach, whereas the second illustrates some of the challenges that must be overcome to apply the method to more complex biomolecular systems. For both example systems, Boltzmann weighted conformations produced by a replica exchange Monte Carlo procedure were used as starting states for kinetic trajectories. The alanine dipeptide displays Markovian behavior in a state space defined with respect to -ã torsion angles. In contrast, Markovian behavior was not observed for the â-hairpin in a state space where all possible native hydrogen bonding patterns were resolved. This may be due to our choice of state definitions or sampling limitations. Furthermore, the use of different criteria for hydrogen bonding results in the apparent observation of different mechanisms from the same underlying data: one set of criteria indicate a zipping type of process, but another indicates more of a collapse followed by almost simultaneous formation of a large number of contacts. Analysis of long-lived states observed during the simulations of the â-hairpin suggests that important aspects of the folding process that are not captured by order parameters in common use include the formation of non-native hydrogen bonds and the degree and nature of salt bridge formation.
Describing protein folding kinetics by molecular dynamics simulations
2004
In this work we demonstrate the use of a rigorous formalism for the extraction of state-to-state transition functions as a way to study the kinetics of protein folding in the context of a Markov chain. The approach is illustrated by its application to two different systems: a blocked alanine dipeptide in a vacuum and the C-terminal â-hairpin motif from protein G in water. The first system displays some of the desired features of the approach, whereas the second illustrates some of the challenges that must be overcome to apply the method to more complex biomolecular systems. For both example systems, Boltzmann weighted conformations produced by a replica exchange Monte Carlo procedure were used as starting states for kinetic trajectories. The alanine dipeptide displays Markovian behavior in a state space defined with respect to -ª torsion angles. In contrast, Markovian behavior was not observed for the â-hairpin in a state space where all possible native hydrogen bonding patterns wer...
The Journal of Physical Chemistry B, 2011
way to identify the relevant macrostates of the system and their exchange rates. The procedures usually require an initial discretization of the trajectory into microstates that have to satisfy certain criteria; e.g., conformations separated by free energy barriers have to belong to different microstates, 13 and the size of the microstates has to be sufficient to provide a statistically significant estimate of the transition probabilities into the other microstates. These requirements cannot always be enforced from the beginning of the analysis. Although MSMs provide tools to check a posteriori the Markovianity of the system, other ways to cross-check the results and identify possible weaknesses in the model can improve the overall description and understanding of the biopolymer dynamics.
Proceedings of The National Academy of Sciences, 2005
We report the application of Langevin dynamics to the physicsbased united-residue (UNRES) force field developed in our laboratory. Ten trajectories were run on seven proteins [PDB ID codes 1BDD (␣; 46 residues), 1GAB (␣; 47 residues), 1LQ7 (␣; 67 residues), 1CLB (␣; 75 residues), 1E0L (; 28 residues), and 1E0G (␣؉; 48 residues), and 1IGD (␣؉; 61 residues)] with the UNRES force field parameterized by using our recently developed method for obtaining a hierarchical structure of the energy landscape. All ␣helical proteins and 1E0G folded to the native-like structures, whereas 1IGD and 1E0L yielded mostly nonnative ␣-helical folds although the native-like structures are lowest in energy for these two proteins, which can be attributed to neglecting the entropy factor in the current parameterization of UNRES. Average folding times for successful folding simulations were of the order of nanoseconds, whereas even the ultrafast-folding proteins fold only in microseconds, which implies that the UNRES time scale is approximately three orders of magnitude larger than the experimental time scale because the fast motions of the secondary degrees of freedom are averaged out. Folding with Langevin dynamics required 2-10 h of CPU time on average with a single AMD Athlon MP 2800؉ processor depending on the size of the protein. With the advantage of parallel processing, this process leads to the possibility to explore thousands of folding pathways and to predict not only the native structure but also the folding scenario of a protein together with its quantitative kinetic and thermodynamic characteristics.
Molecular dynamics simulations of protein folding from the transition state
Proceedings of the National Academy of Sciences, 2002
Putative transition-state ensemble (TSE) conformations of src SH3 were identified by monitoring the deviation from the experimental values along molecular dynamics (MD) simulations of unfolding. Sixty MD trajectories (for a total of about 7 s) were then started from the putative TSE. About one-half of the 60 runs reached the folded state while unfolding was observed in the remaining half of the runs. This result validates -value analysis as an approach to obtain structural information on the transition state. It also demonstrates that an atomic resolution description of the TSE can be extracted from MD simulations. All conformations in the TSE have the central three-stranded -sheet formed in agreement with experimental data. An elongation of strand 2 as well as nonnative side-chain interactions between the diverging turn and the distal hairpin are observed. The simulation results indicate that the tight packing of the side chains between the diverging turn and the distal hairpin is a necessary condition for rapid folding. Contacts between residues in the most structured element of the TSE, the central -sheet, are kinetically more important than those between the N-and C-terminal strands.
Molecular Dynamics Simulations of Protein Folding
Protein Structure Prediction, 2008
Putative transition-state ensemble (TSE) conformations of src SH3 were identified by monitoring the deviation from the experimental values along molecular dynamics (MD) simulations of unfolding. Sixty MD trajectories (for a total of about 7 s) were then started from the putative TSE. About one-half of the 60 runs reached the folded state while unfolding was observed in the remaining half of the runs. This result validates -value analysis as an approach to obtain structural information on the transition state. It also demonstrates that an atomic resolution description of the TSE can be extracted from MD simulations. All conformations in the TSE have the central three-stranded -sheet formed in agreement with experimental data. An elongation of strand 2 as well as nonnative side-chain interactions between the diverging turn and the distal hairpin are observed. The simulation results indicate that the tight packing of the side chains between the diverging turn and the distal hairpin is a necessary condition for rapid folding. Contacts between residues in the most structured element of the TSE, the central -sheet, are kinetically more important than those between the N-and C-terminal strands.
Molecular Dynamics Simulations of Proteins and Peptides: From Folding to Drug Design
Current Protein & Peptide Science, 2008
Computer simulations of proteins, lipids and nucleic acids at equilibrium have become essentially routine. However, the fact remains that complete sampling of conformational space continues to be a bottleneck in the field. The challenge for the future is to overcome such problems and use computational approaches to understand recognition and spontaneous self-organization in biomolecular systems (folding, aggregation and assembly of complexes), processes that cannot be directly observed experimentally. In this review, examples illustrating the extent to which simulations can be used to understand these phenomena in biomolecular systems will be presented along with examples of methodological developments to increase our physical understanding of the processes. The study cases will cover the problems of peptidereceptor recognition and the use of the information obtained for the design of new non-peptidic ligands; the study of the folding mechanism of small proteins and finally the study of the initial stages of peptide self-aggregation.
Protein folding pathways and kinetics: molecular dynamics simulations of beta-strand motifs
Biophysical journal, 2002
The folding pathways and the kinetic properties for three different types of off-lattice four-strand antiparallel -strand protein models interacting via a hybrid Go-type potential have been investigated using discontinuous molecular dynamics simulations. The kinetic study of protein folding was conducted by temperature quenching from a denatured or random coil state to a native state. The progress parameters used in the kinetic study include the squared radius of gyration R g 2 , the fraction of native contacts within the protein as a whole Q, and between specific strands Q ab . In the time series of folding, the denatured proteins undergo a conformational change toward the native state. The model proteins exhibit a variety of kinetic folding pathways that include a fast-track folding pathway without passing through an intermediate and multiple pathways with trapping into more than one intermediate. The kinetic folding behavior of the -strand proteins strongly depends on the native-state geometry of the model proteins and the size of the bias gap g, an artificial measure of a model protein's preference for its native state.
Protein-Folding Dynamics: Overview of Molecular Simulation Techniques
Annual Review of Physical Chemistry, 2007
Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study protein-folding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.
Protein folding kinetics and thermodynamics from atomistic simulation
Proceedings of the National Academy of Sciences, 2012
Advances in simulation techniques and computing hardware have created a substantial overlap between the timescales accessible to atomic-level simulations and those on which the fastest-folding proteins fold. Here we demonstrate, using simulations of four variants of the human villin headpiece, how simulations of spontaneous folding and unfolding can provide direct access to thermodynamic and kinetic quantities such as folding rates, free energies, folding enthalpies, heat capacities, Φ-values, and temperaturejump relaxation profiles. The quantitative comparison of simulation results with various forms of experimental data probing different aspects of the folding process can facilitate robust assessment of the accuracy of the calculations while providing a detailed structural interpretation for the experimental observations. In the example studied here, the analysis of folding rates, Φ-values, and folding pathways provides support for the notion that a norleucine double mutant of villin folds five times faster than the wild-type sequence, but following a slightly different pathway. This work showcases how computer simulation has now developed into a mature tool for the quantitative computational study of protein folding and dynamics that can provide a valuable complement to experimental techniques.