Anton V. Sinitskiy

Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method

The variational two-electron reduced-density-matrix (2-RDM) method, scaling polynomially with the size of the system, was applied to linear chains and three-dimensional clusters of atomic hydrogen as large as H(64). In the case of the 4x4x4 hydrogen lattice of 64 hydrogen atoms, a correct description of the dissociation requires about 10(18) equally weighted determinants in the wave function, which is too large for traditional multireference methods. The correct energy in the dissociation limit was obtained from the variational 2-RDM method in contrast to Hartree-Fock and single-reference methods. Analysis of the occupation numbers demonstrates that even for 1.0 A bond distances the presence of strong electron correlation requires a multireference method. Three-dimensional systems exhibit a marked increase in electron correlation from one-dimensional systems regardless of size. The metal-to-insulator transition upon expansion of the clusters was studied using the decay of the 1-RDM off-diagonal elements. The variational 2-RDM method was shown to capture the metal-to-insulator transition and dissociation behavior accurately for all systems.

Optimal Number of Coarse-Grained Sites in Different Components of Large Biomolecular Complexes

The computational study of large biomolecular complexes (molecular machines, cytoskeletal filaments, etc.) is a formidable challenge facing computational biophysics and biology. To achieve biologically relevant length and time scales, coarse-grained (CG) models of such complexes usually must be built and employed. One of the important early stages in this approach is to determine an optimal number of CG sites in different constituents of a complex. This work presents a systematic approach to this problem. First, a universal scaling law is derived and numerically corroborated for the intensity of the intrasite (intradomain) thermal fluctuations as a function of the number of CG sites. Second, this result is used for derivation of the criterion for the optimal number of CG sites in different parts of a large multibiomolecule complex. In the zeroth-order approximation, this approach validates the empirical rule of taking one CG site per fixed number of atoms or residues in each biomolecule, previously widely used for smaller systems (e.g., individual biomolecules). The first-order corrections to this rule are derived and numerically checked by the case studies of the Escherichia coli ribosome and Arp2/3 actin filament junction. In different ribosomal proteins, the optimal number of amino acids per CG site is shown to differ by a factor of 3.5, and an even wider spread may exist in other large biomolecular complexes. Therefore, the method proposed in this paper is valuable for the optimal construction of CG models of such complexes.

The Theory of Ultra-Coarse-Graining. 2. Numerical Implementation.

The increasing interest in the modeling of complex macromolecular systems in recent years has spurred the development of numerous coarse-graining (CG) techniques. However, many of the CG models are constructed assuming that all details beneath the resolution of CG degrees of freedom are fast and average out, which sets limits on the resolution of feasible coarse-grainings and on the range of applications of the CG models. Ultra-coarse-graining (UCG) makes it possible to construct models at any desired resolution while accounting for discrete conformational or chemical changes within the CG sites that can modulate the interactions between them. Here, we discuss the UCG methodology and its numerical implementation. We pay particular attention to the numerical mechanism for including state transitions between different conformations within CG sites because this has not been discussed previously. Using a simple example of 1,2-dichloroethane, we demonstrate the ability of the UCG model to reproduce the multiconfigurational behavior of this molecular liquid, even when each molecule is modeled with only one CG site. The methodology can also be applied to other molecular liquids and macromolecular systems with time scale separation between conformational transitions and other intramolecular motions and rotations.

Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics

The ring polymer molecular dynamics (RPMD) method has gained popularity in recent years as a simple approximation for calculating real time quantum correlation functions in condensed media. However, the extent to which RPMD captures real dynamical quantum effects and why it fails under certain situations have not been clearly understood. Addressing this issue has been difficult in the absence of a genuine justification for the RPMD algorithm starting from the quantum Liouville equation. To this end, a new and exact path integral formalism for the calculation of real time quantum correlation functions is presented in this work, which can serve as a rigorous foundation for the analysis of the RPMD method as well as providing an alternative derivation of the well established centroid molecular dynamics method. The new formalism utilizes the cyclic symmetry of the imaginary time path integral in the most general sense and enables the expression of Kubo-transformed quantum time correlation functions as that of physical observables pre-averaged over the imaginary time path. Upon filtering with a centroid constraint function, the formulation results in the centroid dynamics formalism. Upon filtering with the position representation of the imaginary time path integral, we obtain an exact quantum dynamics formalism involving the same variables as the RPMD method. The analysis of the RPMD approximation based on this approach clarifies that an explicit quantum dynamical justification does not exist for the use of the ring polymer harmonic potential term (imaginary time kinetic energy) as implemented in the RPMD method. It is analyzed why this can cause substantial errors in nonlinear correlation functions of harmonic oscillators. Such errors can be significant for general correlation functions of anharmonic systems. We also demonstrate that the short time accuracy of the exact path integral limit of RPMD is of lower order than those for finite discretization of path. The present quantum dynamics formulation also serves as the basis for developing new quantum dynamical methods that utilize the cyclic nature of the imaginary time path integral.

Cations Stiffen Actin Filaments by Adhering a Key Structural Element to Adjacent Subunits

Ions regulate the assembly and mechanical properties of actin filaments. Recent work using structural bioinformatics and site-specific mutagenesis favors the existence of two discrete and specific divalent cation binding sites on actin filaments, positioned in the long axis between actin subunits. Cation binding at one site drives polymerization, while the other modulates filament stiffness and plays a role in filament severing by the regulatory protein, cofilin. Existing structural methods have not been able to resolve filament-associated cations, and so in this work we turn to molecular dynamics simulations to suggest a candidate binding pocket geometry for each site and to elucidate the mechanism by which occupancy of the “stiffness site” affects filament mechanical properties. Incorporating a magnesium ion in the “polymerization site” does not seem to require any large-scale change to an actin subunit’s conformation. Binding of a magnesium ion in the “stiffness site” adheres the actin DNase-binding loop (D-loop) to its long-axis neighbor, which increases the filament torsional stiffness and bending persistence length. Our analysis shows that bound D-loops occupy a smaller region of accessible conformational space. Cation occupancy buries key conserved residues of the D-loop, restricting accessibility to regulatory proteins and enzymes that target these amino acids.

Simulated Dynamics of Glycans on Ligand-Binding Domain of NMDA Receptors Reveals Strong Dynamic Coupling between Glycans and Protein Core

N-Methyl-d-aspartate (NMDA) receptors, key neuronal receptors playing the central role in learning and memory, are heavily glycosylated in vivo. Astonishingly little is known about the structure, dynamics, and physiological relevance of glycans attached to them. We recently demonstrated that certain glycans on the ligand binding domain (LBD) of NMDA receptors (NMDARs) can serve as intramolecular potentiators, changing EC50 of NMDAR coagonists. In this work, we use molecular dynamics trajectories, in aggregate 86.5 μs long, of the glycosylated LBD of the GluN1 subunit of the NMDAR to investigate the behavior of glycans on NMDARs. Though all glycans in our simulations were structurally the same (Man5), the dynamics of glycans at different locations on NMDARs was surprisingly different. The slowest-time scale motions that we detected in various glycans in some cases corresponded to a flipping of parts of glycans relative to each other, while in other cases they reduced to a head-to-tail bending of a glycan. We predict that time scales of conformational changes in glycans on the GluN1 LBD of NMDARs range from nanoseconds to at least hundreds of microseconds. Some of the conformational changes in the glycans correlate with the physiologically important clamshell-like opening and closing of the GluN1 LBD domain. Thus, glycans are an integral part of NMDARs, and computational models of NMDARs should include glycans to faithfully represent the structure and the dynamics of these receptors.

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynmans imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

Highly Coarse-Grained Representations of Transmembrane Proteins

Numerous biomolecules and biomolecular complexes, including transmembrane proteins (TMPs), are symmetric or at least have approximate symmetries. Highly coarse-grained models of such biomolecules, aiming at capturing the essential structural and dynamical properties on resolution levels coarser than the residue scale, must preserve the underlying symmetry. However, making these models obey the correct physics is in general not straightforward, especially at the highly coarse-grained resolution where multiple (∼3–30 in the current study) amino acid residues are represented by a single coarse-grained site. In this paper, we propose a simple and fast method of coarse-graining TMPs obeying this condition. The procedure involves partitioning transmembrane domains into contiguous segments of equal length along the primary sequence. For the coarsest (lowest-resolution) mappings, it turns out to be most important to satisfy the symmetry in a coarse-grained model. As the resolution is increased to capture more detail, however, it becomes gradually more important to match modular repeats in the secondary structure (such as helix-loop repeats) instead. A set of eight TMPs of various complexity, functionality, structural topology, and internal symmetry, representing different classes of TMPs (ion channels, transporters, receptors, adhesion, and invasion proteins), has been examined. The present approach can be generalized to other systems possessing exact or approximate symmetry, allowing for reliable and fast creation of multiscale, highly coarse-grained mappings of large biomolecular assemblies.