Martin McCullagh

The Theory of Ultra-Coarse-Graining. 1. General Principles.

Coarse-grained (CG) models provide a computationally efficient means to study biomolecular and other soft matter processes involving large numbers of atoms correlated over distance scales of many covalent bond lengths and long time scales. Variational methods based on information from simulations of finer-grained (e.g., all-atom) models, for example the multiscale coarse-graining (MS-CG) and relative entropy minimization methods, provide attractive tools for the systematic development of CG models. However, these methods have important drawbacks when used in the ultra-coarse-grained (UCG) regime, e.g., at a resolution level coarser or much coarser than one amino acid residue per effective CG particle in proteins. This is due to the possible existence of multiple metastable states within the CG sites for a given UCG model configuration. In this work, systematic variational UCG methods are presented that are specifically designed to CG entire protein domains and subdomains into single effective CG particles. This is accomplished by augmenting existing effective particle CG schemes to allow for discrete state transitions and configuration-dependent resolution. Additionally, certain conclusions of this work connect back to single-state force matching and open up new avenues for method development in that area. These results provide a formal statistical mechanical basis for UCG methods related to force matching and relative entropy CG methods and suggest practical algorithms for constructing optimal approximate UCG models from fine-grained simulation data.

Unraveling the mystery of ATP hydrolysis in actin filaments.

Actin performs its myriad cellular functions by the growth and disassembly of its filamentous form. The hydrolysis of ATP in the actin filament has been shown to modulate properties of the filament, thus making it a pivotal regulator of the actin life cycle. Actin has evolved to selectively hydrolyze ATP in the filamentous form, F-actin, with an experimentally observed rate increase over the monomeric form, G-actin, of 4.3 × 104. The cause of this dramatic increase in rate is investigated in this paper using extensive QM/MM simulations of both G- and F-actin. To compute the free energy of hydrolysis in both systems, metadynamics is employed along two collective variables chosen to describe the reaction coordinates of hydrolysis. F-actin is modeled as a monomer with restraints applied to coarse-grained variables enforced to keep it in a filament-like conformation. The simulations reveal a barrier height reduction for ATP hydrolysis in F-actin as compared to G-actin of 8 ± 1 kcal/mol, in good agreement with the experimentally measured barrier height reduction of 7 ± 1 kcal/mol. The barrier height reduction is influenced by an enhanced rotational diffusion of water in F-actin as compared to G-actin and shorter water wires between Asp154 and the nucleophilic water in F-actin, leading to more rapid proton transport.

Electrostatic interactions between the Bni1p formin FH2 domain and actin influence actin filament nucleation

Formins catalyze nucleation and growth of actin filaments. Here, we study the structure and interactions of actin with the FH2 domain of budding yeast formin Bni1p. We built an all-atom model of the formin dimer on an Oda actin filament 7-mer and studied structural relaxation and interprotein interactions by molecular dynamics simulations. These simulations produced a refined model for the FH2 dimer associated with the barbed end of the filament and showed electrostatic interactions between the formin knob and actin target-binding cleft. Mutations of two formin residues contributing to these interactions (R1423N, K1467L, or both) reduced the interaction energies between the proteins, and in coarse-grained simulations, the formin lost more interprotein contacts with an actin dimer than with an actin 7-mer. Biochemical experiments confirmed a strong influence of these mutations on Bni1p-mediated actin filament nucleation, but not elongation, suggesting that different interactions contribute to these two functions of formins.

Self-assembly of perylenediimide-single strand DNA conjugates: Employing hydrophobic interactions and DNA base pairing to create a diverse structural space

The self-assembly behavior of DNA conjugates possessing a perylenediimide (PDI) head group and an N-oligonucleotide tail has been investigated using a combination of optical spectroscopy and cryogenic transmission electron microscopy (cryo-TEM) imaging. To obtain insight into the interplay between PDI hydrophobic interactions and DNA base-pairing we employed systematic variation in the length and composition of the oligo tails. Conjugates with short (TA)n or (CG)n oligo tails (n≤3) form helical or nonhelical fibers constructed from π-stacked PDI head groups with pendent oligo tails in aqueous solution. Conjugates with longer (TA)n oligo tails also form stacks of PDI head groups, which are further aggregated by base-pairing between their oligo tails, leading to fiber bundling and formation of bilayers. The longer (CG)n conjugates form PDI end-capped duplexes, which further assemble into PDI-stacked arrays of duplexes leading to large scale ordered assemblies. Cryo-TEM imaging reveals that (CG)3 gives rise to both fibers and large assemblies, whereas (CG)5 assembles preferentially into large ordered structures.

Implicit Solvation Using the Superposition Approximation (IS-SPA): An Implicit Treatment of the Nonpolar Component to Solvation for Simulating Molecular Aggregation

Nonpolar solute-solvent interactions are the driving force for aggregation in important chemical and biological phenomena including protein folding, peptide self-assembly, and oil-water emulsion formation. Currently, the most accurate and computationally efficient description of these processes requires an explicit treatment of all solvent and solute atoms. Previous computationally feasible implicit solvent models, such as solute surface area approaches, are unsuccessful at capturing aggregation features including both structural and energetic trends while more theoretically rigorous approaches, such as Reference Interaction Site Model (RISM), are accurate but extremely computationally demanding. Our approach, denoted Implicit Solvation using the Superposition Approximation (IS-SPA), builds on previous theory utilizing the Kirkwood superposition approximation to approximate the mean force of the solvent from solute parameters. We introduce and verify a parabolic first solvation shell truncation of atomic solvation, fitting water distributions around a molecule, and a Monte Carlo integration of the mean solvent force. These extensions allow this method to be implemented as an efficient nonpolar implicit solvent model for molecular simulation. The approximations in IS-SPA are first explored and justified for the homodimerization of an array of different sized Lennard-Jones spheres. The accuracy and transferability of the approach are demonstrated by its ability to capture the position and relative energies of the desolvation barrier and free energy minimum of alkane homodimers. The model is then shown to reproduce the phase separation and solubility of cyclohexane and water. These promising results, coupled with 2 orders of magnitude speed-up for dilute systems as compared to explicit solvent simulations, demonstrate that IS-SPA is an appealing approach to boost the time- and length-scale of molecular aggregation simulations.

Deriving Coarse-Grained Charges from All-Atom Systems: An Analytic Solution

An analytic method to assign optimal coarse-grained charges based on electrostatic potential matching is presented. This solution is the infinite size and density limit of grid-integration charge-fitting and is computationally more efficient by several orders of magnitude. The solution is also minimized with respect to coarse-grained positions which proves to be an extremely important step in reproducing the all-atom electrostatic potential. The joint optimal-charge optimal-position coarse-graining procedure is applied to a number of aggregating proteins using single-site per amino acid resolution. These models provide a good estimate of both the vacuum and Debye-Hückel screened all-atom electrostatic potentials in the vicinity and in the far-field of the protein. Additionally, these coarse-grained models are shown to approximate the all-atom dimerization electrostatic potential energy of 10 aggregating proteins with good accuracy.

Allostery in the dengue virus NS3 helicase: Insights into the NTPase cycle from molecular simulations

The C-terminus domain of non-structural 3 (NS3) protein of the Flaviviridae viruses (e.g. HCV, dengue, West Nile, Zika) is a nucleotide triphosphatase (NTPase) -dependent superfamily 2 (SF2) helicase that unwinds double-stranded RNA while translocating along the nucleic polymer. Due to these functions, NS3 is an important target for antiviral development yet the biophysics of this enzyme are poorly understood. Microsecond-long molecular dynamic simulations of the dengue NS3 helicase domain are reported from which allosteric effects of RNA and NTPase substrates are observed. The presence of a bound single-stranded RNA catalytically enhances the phosphate hydrolysis reaction by affecting the dynamics and positioning of waters within the hydrolysis active site. Coupled with results from the simulations, electronic structure calculations of the reaction are used to quantify this enhancement to be a 150-fold increase, in qualitative agreement with the experimental enhancement factor of 10–100. Additionally, protein-RNA interactions exhibit NTPase substrate-induced allostery, where the presence of a nucleotide (e.g. ATP or ADP) structurally perturbs residues in direct contact with the phosphodiester backbone of the RNA. Residue-residue network analyses highlight pathways of short ranged interactions that connect the two active sites. These analyses identify motif V as a highly connected region of protein structure through which energy released from either active site is hypothesized to move, thereby inducing the observed allosteric effects. These results lay the foundation for the design of novel allosteric inhibitors of NS3.

Elucidating Structural Evolution of Perylene Diimide Aggregates Using Vibrational Spectroscopy and Molecular Dynamics Simulations

Perylene diimides (PDIs) are a family of molecules that have potential applications to organic photovoltaics. These systems typically aggregate cofacially due to π-stacking interactions between the aromatic perylene cores. In this study, the structure and characteristics of aggregated N, N-bis(2,6-diisopropylphenyl)-3,4,9,10-perylenetetracarboxylic diimide (common name lumogen orange), a perylene diimide (PDI) with sterically bulky imide functional groups, were investigated using both experimental vibrational spectroscopy and molecular dynamics (MD) simulations. Samples of lumogen orange dispersed in chloroform exhibited complex aggregation behavior, as evidenced by the evolution of the FTIR spectrum over a period of several hours. While for many PDI systems with less bulky imide functional groups aggregation is dominated by π-stacking interactions between perylene cores, MD simulations of lumogen orange dimers indicated a second, more energetically favorable aggregate structure mediated by edge-to-edge interactions between PDI units. Two-dimensional infrared spectroscopy together with orientational statistics obtained from MD simulations were employed to identify and rationalize aggregation-induced coupling between vibrational modes.