Two center multipole expansion method: application to macromolecular systems

We propose a new theoretical method for the calculation of the interaction energy between macromolecular systems at large distances. The method provides a linear scaling of the computing time with the system size and is considered as an alternative to the well known fast multipole method. Its efficiency, accuracy and applicability to macromolecular systems is analyzed and discussed in detail.Comment: 23 pages, 7 figures, 1 tabl

A Vulnerability in Popular Molecular Dynamics Packages Concerning Langevin and Andersen Dynamics

We report a serious problem associated with a number of current implementations of Andersen and Langevin dynamics algorithms. When long simulations are run in many segments, it is sometimes possible to have a repeating sequence of pseudorandom numbers enter the calcuation. We show that, if the sequence repeats rapidly, the resulting artifacts can quickly denature biomolecules and are then easily detectable. However, if the sequence repeats less frequently, the artifacts become subtle and easily overlooked. We derive a formula for the underlying cause of artifacts in the case of the Langevin thermostat, and find it vanishes slowly as the inverse square root of the number of time steps per simulation segment. Numerous examples of simulation artifacts are presented, including dissociation of a tetrameric protein after 110 ns of dynamics, reductions in atomic fluctuations for a small protein in implicit solvent, altered thermodynamic properties of a box of water molecules, and changes in the transition free energies between dihedral angle conformations. Finally, in the case of strong thermocoupling, we link the observed artifacts to previous work in nonlinear dynamics and show that it is possible to drive a 20-residue, implicitly solvated protein into periodic trajectories if the thermostat is not used properly. Our findings should help other investigators re-evaluate simulations that may have been corrupted and obtain more accurate results

Order through Disorder: Hyper-Mobile C-Terminal Residues Stabilize the Folded State of a Helical Peptide. A Molecular Dynamics Study

Conventional wisdom has it that the presence of disordered regions in the three-dimensional structures of polypeptides not only does not contribute significantly to the thermodynamic stability of their folded state, but, on the contrary, that the presence of disorder leads to a decrease of the corresponding proteins' stability. We have performed extensive 3.4 µs long folding simulations (in explicit solvent and with full electrostatics) of an undecamer peptide of experimentally known helical structure, both with and without its disordered (four residue long) C-terminal tail. Our simulations clearly indicate that the presence of the apparently disordered (in structural terms) C-terminal tail, increases the thermodynamic stability of the peptide's folded (helical) state. These results show that at least for the case of relatively short peptides, the interplay between thermodynamic stability and the apparent structural stability can be rather subtle, with even disordered regions contributing significantly to the stability of the folded state. Our results have clear implications for the understanding of peptide energetics and the design of foldable peptides

Modulation of a protein free-energy landscape by circular permutation

Circular permutations usually retain the native structure and function of a protein while inevitably perturb its folding dynamics. By using simulations with a structure-based model and a rigorous methodology to determine free-energy surfaces from trajectories we evaluate the effect of a circular permutation on the free-energy landscape of the protein T4 lysozyme. We observe changes which, while subtle, largely affect the cooperativity between the two subdomains. Such a change in cooperativity has been previously experimentally observed and recently also characterized using single molecule optical tweezers and the Crooks relation. The free-energy landscapes show that both the wild type and circular permutant have an on-pathway intermediate, previously experimentally characterized, where one of the subdomains is completely formed. The landscapes, however, differ in the position of the rate-limiting step for folding, which occurs before the intermediate in the wild-type and after in the circular permutant. This shift of transition state explains the observed change in the cooperativity. The underlying free-energy landscape thus provides a microscopic description of the folding dynamics and the connection between circular permutation and the loss of cooperativity experimentally observed

The Energy Computation Paradox and ab initio Protein Folding

The routine prediction of three-dimensional protein structure from sequence remains a challenge in computational biochemistry. It has been intuited that calculated energies from physics-based scoring functions are able to distinguish native from nonnative folds based on previous performance with small proteins and that conformational sampling is the fundamental bottleneck to successful folding. We demonstrate that as protein size increases, errors in the computed energies become a significant problem. We show, by using error probability density functions, that physics-based scores contain significant systematic and random errors relative to accurate reference energies. These errors propagate throughout an entire protein and distort its energy landscape to such an extent that modern scoring functions should have little chance of success in finding the free energy minima of large proteins. Nonetheless, by understanding errors in physics-based score functions, they can be reduced in a post-hoc manner, improving accuracy in energy computation and fold discrimination

Multiscale Coarse-Graining of the Protein Energy Landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states

First-Step Mutations for Adaptation at Elevated Temperature Increase Capsid Stability in a Virus

The relationship between mutation, protein stability and protein function plays a central role in molecular evolution. Mutations tend to be destabilizing, including those that would confer novel functions such as host-switching or antibiotic resistance. Elevated temperature may play an important role in preadapting a protein for such novel functions by selecting for stabilizing mutations. In this study, we test the stability change conferred by single mutations that arise in a G4-like bacteriophage adapting to elevated temperature. The vast majority of these mutations map to interfaces between viral coat proteins, suggesting they affect protein-protein interactions. We assess their effects by estimating thermodynamic stability using molecular dynamic simulations and measuring kinetic stability using experimental decay assays. The results indicate that most, though not all, of the observed mutations are stabilizing

Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations

Accelerated molecular dynamics (aMD) has been shown to enhance conformational space sampling relative to classical molecular dynamics; however, the exponential reweighting of aMD trajectories, which is necessary for the calculation of free energies relating to the classical system, is oftentimes problematic, especially for systems larger than small poly peptides. Here, we propose a method of accelerating only the degrees of freedom most pertinent to sampling, thereby reducing the total acceleration added to the system and improving the convergence of calculated ensemble averages, which we term selective aMD. Its application is highlighted in two biomolecular cases. First, the model system alanine dipeptide is simulated with classical MD, all-dihedral aMD, and selective aMD, and these results are compared to the infinite sampling limit as calculated with metadynamics. We show that both forms of aMD enhance the convergence of the underlying free energy landscape by 5-fold relative to classical MD; however, selective aMD can produce improved statistics over all-dihedral aMD due to the improved reweighting. Then we focus on the pharmaceutically relevant case of computing the free energy of the decoupling of oseltamivir in the active site of neuraminidase. Results show that selective aMD greatly reduces the cost of this alchemical free energy transformation, whereas all-dihedral aMD produces unreliable free energy estimates

Determining Peptide Partitioning Properties via Computer Simulation

The transfer of polypeptide segments into lipid bilayers to form transmembrane helices represents the crucial first step in cellular membrane protein folding and assembly. This process is driven by complex and poorly understood atomic interactions of peptides with the lipid bilayer environment. The lack of suitable experimental techniques that can resolve these processes both at atomic resolution and nanosecond timescales has spurred the development of computational techniques. In this review, we summarize the significant progress achieved in the last few years in elucidating the partitioning of peptides into lipid bilayer membranes using atomic detail molecular dynamics simulations. Indeed, partitioning simulations can now provide a wealth of structural and dynamic information. Furthermore, we show that peptide-induced bilayer distortions, insertion pathways, transfer free energies, and kinetic insertion barriers are now accurate enough to complement experiments. Further advances in simulation methods and force field parameter accuracy promise to turn molecular dynamics simulations into a powerful tool for investigating a wide range of membrane active peptide phenomena