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

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

Three-Dimensional Stochastic Off-Lattice Model of Binding Chemistry in Crowded Environments

Molecular crowding is one of the characteristic features of the intracellular environment, defined by a dense mixture of varying kinds of proteins and other molecules. Interaction with these molecules significantly alters the rates and equilibria of chemical reactions in the crowded environment. Numerous fundamental activities of a living cell are strongly influenced by the crowding effect, such as protein folding, protein assembly and disassembly, enzyme activity, and signal transduction. Quantitatively predicting how crowding will affect any particular process is, however, a very challenging problem because many physical and chemical parameters act synergistically in ways that defy easy analysis. To build a more realistic model for this problem, we extend a prior stochastic off-lattice model from two-dimensional (2D) to three-dimensional (3D) space and examine how the 3D results compare to those found in 2D. We show that both models exhibit qualitatively similar crowding effects and similar parameter dependence, particularly with respect to a set of parameters previously shown to act linearly on total reaction equilibrium. There are quantitative differences between 2D and 3D models, although with a generally gradual nonlinear interpolation as a system is extended from 2D to 3D. However, the additional freedom of movement allowed to particles as thickness of the simulation box increases can produce significant quantitative change as a system moves from 2D to 3D. Simulation results over broader parameter ranges further show that the impact of molecular crowding is highly dependent on the specific reaction system examined

PIP2-Binding Site in Kir Channels: Definition by Multiscale Biomolecular Simulations†

Phosphatidylinositol bisphosphate (PIP(2)) is an activator of mammalian inwardly rectifying potassium (Kir) channels. Multiscale simulations, via a sequential combination of coarse-grained and atomistic molecular dynamics, enabled exploration of the interactions of PIP(2) molecules within the inner leaflet of a lipid bilayer membrane with possible binding sites on Kir channels. Three Kir channel structures were investigated: X-ray structures of KirBac1.1 and of a Kir3.1-KirBac1.3 chimera and a homology model of Kir6.2. Coarse-grained simulations of the Kir channels in PIP(2)-containing lipid bilayers identified the PIP(2)-binding site on each channel. These models of the PIP(2)-channel complexes were refined by conversion to an atomistic representation followed by molecular dynamics simulation in a lipid bilayer. All three channels were revealed to contain a conserved binding site at the N-terminal end of the slide (M0) helix, at the interface between adjacent subunits of the channel. This binding site agrees with mutagenesis data and is in the proximity of the site occupied by a detergent molecule in the Kir chimera channel crystal. Polar contacts in the coarse-grained simulations corresponded to long-lived electrostatic and H-bonding interactions between the channel and PIP(2) in the atomistic simulations, enabling identification of key side chains

The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes

A new coarse-grain model for molecular dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid molecules are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielectric constant of unity (). Second, water molecules are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water molecule is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main physical properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liquid crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liquid crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or experimental methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 microseconds were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodology's inherent multiscale capabilities

Enhanced Lipid Diffusion and Mixing in Accelerated Molecular Dynamics

Accelerated molecular dynamics (aMD) is an enhanced sampling technique that expedites conformational space sampling by reducing the barriers separating various low-energy states of a system. Here, we present the first application of the aMD method on lipid membranes. Altogether, ∼1.5 μs simulations were performed on three systems: a pure POPC bilayer, a pure DMPC bilayer, and a mixed POPC:DMPC bilayer. Overall, the aMD simulations are found to produce significant speedup in trans–gauche isomerization and lipid lateral diffusion versus those in conventional MD (cMD) simulations. Further comparison of a 70-ns aMD run and a 300-ns cMD run of the mixed POPC:DMPC bilayer shows that the two simulations yield similar lipid mixing behaviors, with aMD generating a 2–3-fold speedup compared to cMD. Our results demonstrate that the aMD method is an efficient approach for the study of bilayer structural and dynamic properties. On the basis of simulations of the three bilayer systems, we also discuss the impact of aMD parameters on various lipid properties, which can be used as a guideline for future aMD simulations of membrane systems

Parameterization of a coarse-grained model of cholesterol with point-dipole electrostatics

© 2018, Springer Nature Switzerland AG. We present a new coarse-grained (CG) model of cholesterol (CHOL) for the electrostatic-based ELBA force field. A distinguishing feature of our CHOL model is that the electrostatics is modeled by an explicit point dipole which interacts through an ideal vacuum permittivity. The CHOL model parameters were optimized in a systematic fashion, reproducing the electrostatic and nonpolar partitioning free energies of CHOL in lipid/water mixtures predicted by full-detailed atomistic molecular dynamics simulations. The CHOL model has been validated by comparison to structural, dynamic and thermodynamic properties with experimental and atomistic simulation reference data. The simulation of binary DPPC/cholesterol mixtures covering the relevant biological content of CHOL in mammalian membranes is shown to correctly predict the main lipid behavior as observed experimentally

Синдром Мэя - Тернера: современные методы диагностики и лечения

May-Turner syndrome is a condition where the left common iliac vein is compressed between the lumbar spine and the overlying right common iliac artery. Left iliac vein compression is common (up to 24%) in the general population, but clinical manifestations occur in a few patients. This syndrome should be considered in case of unexplained edema of the left lower extremity since routine duplex ultrasound does not possess optimal sensitivity and specificity in the study of the iliac veins and the inferior vena cava. Intravascular ultrasound is the most accurate diagnostic method. However, the advent of computed tomography angiography and magnetic resonance angiography providing high-quality images of the vasculature have become a promising alternative to invasive intravascular ultrasound. Treatment for May-Turner syndrome usually involves stenting of the left common iliac vein along with medical therapy, including antithrombotic (anticoagulant and antiplatelet) therapy combined with phlebotonics. Our review reports modern methods of diagnosis and treatment of May-Turner syndrome.Синдром Мэя - Тернера (СМТ) является симптомокомплексом, который возникает при сдавлении левой общей подвздошной вены между поясничным отделом позвоночника и правой общей подвздошной артерией. Компрессия левой общей подвздошной вены распространена в общей популяции (24%), однако клинические проявления наступают у значительно меньшего количества пациентов. Заподозрить данный синдром следует при необъяснимом отеке левой нижней конечности, так как классическое ультразвуковое дуплексное сканирование не обладает необходимыми чувствительностью и специфичностью при исследовании подвздошных вен и нижней полой вены. Внутрисосудистое ультразвуковое исследование (ВСУЗИ) является наиболее точным методом диагностики, однако компьютерная томографическая и магнитно-резонансная ангиографии с высоким качеством изображения представляют эффективную альтернативу инвазивному ВСУЗИ. Основным методом лечения СМТ является стентирование левой общей подвздошной вены на фоне приема медикаментозной терапии, включающей антитромбо-тическую (антикоагулянтную и антиагрегантную) терапию в комбинации с флеботонизирующими препаратами. Цель данного обзора состоит в описании современных методов диагностики и лечения синдрома Мэя - Тернера