Showing papers by "Guo-Wei Wei published in 2013"

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Abstract: The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the Poisson-Boltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of O(N2) at most, where N is the number of atoms or residues, in contrast to O(N3) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

Abstract: This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors, and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e. electrostatic) solvation, non-polar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics, and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace–Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson–Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst–Planck (NP) equations for the dynamics of charged solvent species, generalized Navier–Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent–solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent–solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

Abstract: Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR, and cryo-electron microscopy, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation, and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger's functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, whereas our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions.

Parameterization of a geometric flow implicit solvation model

Abstract: Implicit solvent models are popular for their high computational efficiency and simplicity over explicit solvent models and are extensively used for computing molecular solvation properties. The accuracy of implicit solvent models depends on the geometric description of the solute-solvent interface and the solvent dielectric profile that is defined near the surface of the solute molecule. Typically, it is assumed that the dielectric profile is spatially homogeneous in the bulk solvent medium and varies sharply across the solute-solvent interface. However, the specific form of this profile is often described by ad hoc geometric models rather than physical solute-solvent interactions. Hence, it is of significant interest to improve the accuracy of these implicit solvent models by more realistically defining the solute-solvent boundary within a continuum setting. Recently, a differential geometry-based geometric flow solvation model was developed, in which the polar and nonpolar free energies are coupled through a characteristic function that describes a smooth dielectric interface profile across the solvent-solute boundary in a thermodynamically self-consistent fashion. The main parameters of the model are the solute/solvent dielectric coefficients, solvent pressure on the solute, microscopic surface tension, solvent density, and molecular force-field parameters. In this work, we investigate how changes in the pressure, surface tension, solute dielectric coefficient, and choice of different force-field charge and radii parameters affect the prediction accuracy for hydration free energies of 17 small organic molecules based on the geometric flow solvation model. The results of our study provide insights on the parameterization, accuracy, and predictive power of this new implicit solvent model.

Stochastic model for protein flexibility analysis.

Abstract: Protein flexibility is an intrinsic property and plays a fundamental role in protein functions. Computational analysis of protein flexibility is crucial to protein function prediction, macromolecular flexible docking, and rational drug design. Most current approaches for protein flexibility analysis are based on Hamiltonian mechanics. We introduce a stochastic model to study protein flexibility. The essential idea is to analyze the free induction decay of a perturbed protein structural probability, which satisfies the master equation. The transition probability matrix is constructed by using probability density estimators including monotonically decreasing radial basis functions. We show that the proposed stochastic model gives rise to some of the best predictions of Debye-Waller factors or B factors for three sets of protein data introduced in the literature.

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation

Abstract: Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Origin of parameter degeneracy and molecular shape relationships in geometric-flow calculations of solvation free energies.

Abstract: Implicit solvent models are important tools for calculating solvation free energies for chemical and biophysical studies since they require fewer computational resources but can achieve accuracy comparable to that of explicit-solvent models. In past papers, geometric flow-based solvation models have been established for solvation analysis of small and large compounds. In the present work, the use of realistic experiment-based parameter choices for the geometric flow models is studied. We find that the experimental parameters of solvent internal pressure p = 172 MPa and surface tension γ = 72 mN/m produce solvation free energies within 1 RT of the global minimum root-mean-squared deviation from experimental data over the expanded set. Our results demonstrate that experimental values can be used for geometric flow solvent model parameters, thus eliminating the need for additional parameterization. We also examine the correlations between optimal values of p and γ which are strongly anti-correlated. Geometric analysis of the small molecule test set shows that these results are inter-connected with an approximately linear relationship between area and volume in the range of molecular sizes spanned by the data set. In spite of this considerable degeneracy between the surface tension and pressure terms in the model, both terms are important for the broader applicability of the model.

A molecular level prototype for mechanoelectrical transducer in mammalian hair cells

Abstract: The mechanoelectrical transducer (MET) is a crucial component of mammalian auditory system. The gating mechanism of the MET channel remains a puzzling issue, though there are many speculations, due to the lack of essential molecular building blocks. To understand the working principle of mammalian MET, we propose a molecular level prototype which constitutes a charged blocker, a realistic ion channel and its surrounding membrane. To validate the proposed prototype, we make use of a well-established ion channel theory, the Poisson---Nernst---Planck equations, for three-dimensional (3D) numerical simulations. A wide variety of model parameters, including bulk ion concentration, applied external voltage, blocker charge and blocker displacement, are explored to understand the basic function of the proposed MET prototype. We show that our prototype prediction of channel open probability in response to blocker relative displacement is in remarkable accordance with experimental observation of rat cochlea outer hair cells. Our results appear to suggest that tip links which connect hair bundles gate MET channels.