Why are MD simulated protein folding times wrong?

The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that in the framework of Markov State Model (MSM) describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples, we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care

Virus Capsid Dissolution Studied by Microsecond Molecular Dynamics Simulations

Dissolution of many plant viruses is thought to start with swelling of the capsid caused by calcium removal following infection, but no high-resolution structures of swollen capsids exist. Here we have used microsecond all-atom molecular simulations to describe the dynamics of the capsid of satellite tobacco necrosis virus with and without the 92 structural calcium ions. The capsid expanded 2.5% upon removal of the calcium, in good agreement with experimental estimates. The water permeability of the native capsid was similar to that of a phospholipid membrane, but the permeability increased 10-fold after removing the calcium, predominantly between the 2-fold and 3-fold related subunits. The two calcium binding sites close to the icosahedral 3-fold symmetry axis were pivotal in the expansion and capsid-opening process, while the binding site on the 5-fold axis changed little structurally. These findings suggest that the dissociation of the capsid is initiated at the 3-fold axis

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

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

Combining Optimal Control Theory and Molecular Dynamics for Protein Folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages

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

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

Mechanical and Assembly Units of Viral Capsids Identified via Quasi-Rigid Domain Decomposition

Key steps in a viral life-cycle, such as self-assembly of a protective protein container or in some cases also subsequent maturation events, are governed by the interplay of physico-chemical mechanisms involving various spatial and temporal scales. These salient aspects of a viral life cycle are hence well described and rationalised from a mesoscopic perspective. Accordingly, various experimental and computational efforts have been directed towards identifying the fundamental building blocks that are instrumental for the mechanical response, or constitute the assembly units, of a few specific viral shells. Motivated by these earlier studies we introduce and apply a general and efficient computational scheme for identifying the stable domains of a given viral capsid. The method is based on elastic network models and quasi-rigid domain decomposition. It is first applied to a heterogeneous set of well-characterized viruses (CCMV, MS2, STNV, STMV) for which the known mechanical or assembly domains are correctly identified. The validated method is next applied to other viral particles such as L-A, Pariacoto and polyoma viruses, whose fundamental functional domains are still unknown or debated and for which we formulate verifiable predictions. The numerical code implementing the domain decomposition strategy is made freely available