Theoretical and in silico modeling of biological systems : from protein structure prediction to cellular dynamics

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Title from PDF of title page (University of Missouri--Columbia, viewed on January 28, 2011).Thesis advisor: Dr. Ioan Kosztin.Vita.Ph. D. University of Missouri--Columbia 2009.This thesis describes four distinct studies (involving a variety of concepts and methods from the physical sciences) of complex biological systems and processes that cover a wide range of time and length scales (extending from the molecular to the multi-cellular level), namely: 1) identification of near-native structures from a large set of in silico predicted structures for a given target protein by probing the stability of the structures against simulated heating using Molecular Dynamics (MD) simulations; 2) all atom MD simulatio study of protein-cell membrane interactions designed to elucidate the relation between the conformational structure of the GP41 fusion peptide of HIV-1 virus and the density of the lipid membrane; 3) calculation of the potential of mean force for water transport through single wall carbon nanotubes from nonequilibrium MD simulations; and 4) development and application of a novel computational method, referred to as the cellularparticle dynamics (CPD) method, for the simulation of the dynamics of multicellular systems.Includes bibliographical reference

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski's equality

doi:10.1063/1.2166379In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular-dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many-particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crooks [ Phys. Rev. E 61, 2361 (2000) ] transient fluctuation theorem (that is more general than JE) and the stiff-spring approximation, we show that (i) the mean dissipative work mathd in the F and R pullings is the same, (ii) both U(z) and mathd can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of mathd. To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.This work was supported in part by grants from the University of Missouri Research Board, the Institute for Theoretical Sciences, a joint institute of Notre Dame University and Argonne National Laboratory, the U.S. Department of Energy, Office of Science through Contract No. W-31-109-ENG-38, and NSF through FIBR-0526854

Calculating potentials of mean force and diffusion coefficients from nonequilibirum processes without Jarzynski's equality

In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories, that transiently violate the second law, are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crook's transient fluctuation theorem (that is more general than JE) and the stiff spring approximation, we show that: (i) the mean dissipative work W_d in the F and R pullings are equal, (ii) both U(z) and W_d can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of W_d. To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.Comment: ReVTeX4, 13 pages, 6 EPS figures, Submitted to Journal of Chemical Physic

Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Computer simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in explaining and predicting the resulting stationary structures (corresponding to the lowest adhesion energy state). Here we present two alternatives to the MMC approach for modeling cellular motion and self-assembly: (1) a kinetic Monte Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC, both KMC and CPD methods are capable of simulating the dynamics of the cellular system in real time. In the KMC approach a transition rate is associated with possible rearrangements of the cellular system, and the corresponding time evolution is expressed in terms of these rates. In the CPD approach cells are modeled as interacting cellular particles (CPs) and the time evolution of the multicellular system is determined by integrating the equations of motion of all CPs. The KMC and CPD methods are tested and compared by simulating two experimentally well known phenomena: (1) cell-sorting within an aggregate formed by two types of cells with different adhesivities, and (2) fusion of two spherical aggregates of living cells.Comment: 11 pages, 7 figures; submitted to Phys Rev

Dimer Formation Enhances Structural Differences between Amyloid β-Protein (1–40) and (1–42): An Explicit-Solvent Molecular Dynamics Study

Amyloid -protein (A) is central to the pathology of Alzheimer's disease. A 5% difference in the primary structure of the two predominant alloforms, A and A, results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD) studies of A and A assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD–derived A and A monomers and dimers was subjected to fully atomistic molecular dynamics (MD) simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower -strand propensities than those predicted by DMD. Fully atomistic A and A monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of A dimers indicated a larger conformational variability in comparison to that of A dimers. A dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to A dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of A dimers and was significantly lower than in A dimers. The potential relevance of the three positively charged amino acids in mediating the A oligomer toxicity is discussed in the light of available experimental data

Large-scale, dynamin-like motions of the human guanylate binding protein 1 revealed by multi-resolution simulations

Guanylate binding proteins (GBPs) belong to the dynamin-related superfamily and exhibit various functions in the fight against infections. The functions of the human guanylate binding protein 1 (hGBP1) are tightly coupled to GTP hydrolysis and dimerization. Despite known crystal structures of the hGBP1 monomer and GTPase domain dimer, little is known about the dynamics of hGBP1. To gain a mechanistic understanding of hGBP1, we performed sub-millisecond multi-resolution molecular dynamics simulations of both the hGBP1 monomer and dimer. We found that hGBP1 is a highly flexible protein that undergoes a hinge motion similar to the movements observed for other dynamin-like proteins. Another large-scale motion was observed for the C-terminal helix α13, providing a molecular view for the α13–α13 distances previously reported for the hGBP1 dimer. Most of the loops of the GTPase domain were found to be flexible, revealing why GTP binding is needed for hGBP1 dimerization to occur

Early amyloid β-protein aggregation precedes conformational change

The aggregation of amyloid-β protein (1–42) is studied at experimental concentrations using all-atom molecular dynamics simulations. We observe a fast aggregation into oligomers without significant changes in the internal structure of individual proteins. The aggregation process is characterized in terms of transition networks

Histograms of salt bridge propensities.

<p> <i>Total salt bridge propensities of the three positively charged amino acids: R5, K16, and K28 in A</i><i> and A</i><i> monomers and dimers are displayed as histograms for each of the two water models.</i></p