Discrete molecular dynamics studies of the folding of a protein-like model

Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical properties of the proteins (lattice models), while others are computationally heavy (traditional MD). Results: We use a recently-proposed approach of Zhou and Karplus to study the folding of the protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding --- unfolding transition. In addition, we demonstrate the ability to study the coreof the model protein. Conclusion: The algorithm along with the model of inter-residue interactions can serve as a tool to study the thermodynamics and kinetics of protein models.Comment: 15 pages including 20 figures (Folding & Design in press

Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example during chromosome organization. Describing phenomena that cover such diverse length, and also time scales, requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA, and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure

Dissecting Ubiquitin Folding Using the Self-Organized Polymer Model

Folding of Ubiquitin (Ub) is investigated at low and neutral pH at different temperatures using simulations of the coarse-grained Self-Organized-Polymer model with side chains. The calculated radius of gyration, showing dramatic variations with pH, is in excellent agreement with scattering experiments. At $T_m$ Ub folds in a two-state manner at low and neutral pH. Clustering analysis of the conformations sampled in equilibrium folding trajectories at $T_m$, with multiple transitions between the folded and unfolded states, show a network of metastable states connecting the native and unfolded states. At low and neutral pH, Ub folds with high probability through a preferred set of conformations resulting in a pH-dependent dominant folding pathway. Folding kinetics reveal that Ub assembly at low pH occurs by multiple pathways involving a combination of nucleation-collapse and diffusion collision mechanism. The mechanism by which Ub folds is dictated by the stability of the key secondary structural elements responsible for establishing long range contacts and collapse of Ub. Nucleation collapse mechanism holds if the stability of these elements are marginal, as would be the case at elevated temperatures. If the lifetimes associated with these structured microdomains are on the order of hundreds of $\mu sec$ then Ub folding follows the diffusion-collision mechanism with intermediates many of which coincide with those found in equilibrium. Folding at neutral pH is a sequential process with a populated intermediate resembling that sampled at equilibrium. The transition state structures, obtained using a $P_{fold}$ analysis, are homogeneous and globular with most of the secondary and tertiary structures being native-like. Many of our findings are not only in agreement with experiments but also provide missing details not resolvable in standard experiments

Unfolding simulations reveal the mechanism of extreme unfolding cooperativity in the kinetically stable alpha-lytic protease.

Kinetically stable proteins, those whose stability is derived from their slow unfolding kinetics and not thermodynamics, are examples of evolution's best attempts at suppressing unfolding. Especially in highly proteolytic environments, both partially and fully unfolded proteins face potential inactivation through degradation and/or aggregation, hence, slowing unfolding can greatly extend a protein's functional lifetime. The prokaryotic serine protease alpha-lytic protease (alphaLP) has done just that, as its unfolding is both very slow (t(1/2) approximately 1 year) and so cooperative that partial unfolding is negligible, providing a functional advantage over its thermodynamically stable homologs, such as trypsin. Previous studies have identified regions of the domain interface as critical to alphaLP unfolding, though a complete description of the unfolding pathway is missing. In order to identify the alphaLP unfolding pathway and the mechanism for its extreme cooperativity, we performed high temperature molecular dynamics unfolding simulations of both alphaLP and trypsin. The simulated alphaLP unfolding pathway produces a robust transition state ensemble consistent with prior biochemical experiments and clearly shows that unfolding proceeds through a preferential disruption of the domain interface. Through a novel method of calculating unfolding cooperativity, we show that alphaLP unfolds extremely cooperatively while trypsin unfolds gradually. Finally, by examining the behavior of both domain interfaces, we propose a model for the differential unfolding cooperativity of alphaLP and trypsin involving three key regions that differ between the kinetically stable and thermodynamically stable classes of serine proteases

Folding of Cu, Zn superoxide dismutase and Familial Amyotrophic Lateral Sclerosis

Cu,Zn superoxide dismutase (SOD1) has been implicated in the familial form of the neurodegenerative disease Amyotrophic Lateral Sclerosis (ALS). It has been suggested that mutant mediated SOD1 misfolding/aggregation is an integral part of the pathology of ALS. We study the folding thermodynamics and kinetics of SOD1 using a hybrid molecular dynamics approach. We reproduce the experimentally observed SOD1 folding thermodynamics and find that the residues which contribute the most to SOD1 thermal stability are also crucial for apparent two-state folding kinetics. Surprisingly, we find that these residues are located on the surface of the protein and not in the hydrophobic core. Mutations in some of the identified residues are found in patients with the disease. We argue that the identified residues may play an important role in aggregation. To further characterize the folding of SOD1, we study the role of cysteine residues in folding and find that non-native disulfide bond formation may significantly alter SOD1 folding dynamics and aggregation propensity.Comment: 16 pages, 5 figure

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations suggest that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By mean of molecular dynamics simulations around the native conformation, which simulate the protein and the surrounding solvent at full--atom level, we generate an energetic map of the equilibrium state of the protein and simplify it with an Eigenvalue decomposition. The components of the Eigenvector associated with the lowest Eigenvalue indicate which are the "hot" sites responsible for the stability and for the fast folding of the protein. Comparison of these predictions with the results of mutatgenesis experiments, performed for five small proteins, provide an excellent agreement

Single-domain protein folding: a multi-faceted problem

We review theoretical approaches, experiments and numerical simulations that have been recently proposed to investigate the folding problem in single-domain proteins. From a theoretical point of view, we emphasize the energy landscape approach. As far as experiments are concerned, we focus on the recent development of single-molecule techniques. In particular, we compare the results obtained with two main techniques: single protein force measurements with optical tweezers and single-molecule fluorescence in studies on the same protein (RNase H). This allows us to point out some controversial issues such as the nature of the denatured and intermediate states and possible folding pathways. After reviewing the various numerical simulation techniques, we show that on-lattice protein-like models can help to understand many controversial issues.Comment: 26 pages, AIP Conference Proceeding

Critical examination of the inherent-structure-landscape analysis of two-state folding proteins

Recent studies attracted the attention on the inherent structure landscape (ISL) approach as a reduced description of proteins allowing to map their full thermodynamic properties. However, the analysis has been so far limited to a single topology of a two-state folding protein, and the simplifying assumptions of the method have not been examined. In this work, we construct the thermodynamics of four two-state folding proteins of different sizes and secondary structure by MD simulations using the ISL method, and critically examine possible limitations of the method. Our results show that the ISL approach correctly describes the thermodynamics function, such as the specific heat, on a qualitative level. Using both analytical and numerical methods, we show that some quantitative limitations cannot be overcome with enhanced sampling or the inclusion of harmonic corrections.Comment: published Physical Review E, vol. 80, 061907-1-11 (2009