Multiscale modeling of biomolecular systems

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on February 14, 2008)Vita.Thesis (Ph. D.) University of Missouri-Columbia 2007.Studies of structure-function relationships in biomolecular systems require to follow nanometersize systems on time scales spanning from pico- to micro-seconds, while maintaining atomic scale spatial resolution in all-atom molecular dynamics (MD) simulations. In this work we propose new methods to investigate the following, intrinsically multiscale problems: (i) theoretical prediction of optical and spectral properties of pigment-protein complexes, (ii) reconstruction of potential of mean force and its corresponding diffusion coefficient from non-equilibrium molecular dynamics simulations, (iii) transport of potassium ion through the Gramicidin A channel and of glycerol through the GlpF channel, and (iv) prediction of the species-dependent oligomerization state of the light harvesting antenna complexes. The main novelty of these methods is that they rely only on the high resolution atomic structure of the biomolecular system. Therefore, they have not only explanatory, but predictive power as well.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

Theoretical prediction of spectral and optical properties of bacteriochlorophylls in thermally disordered LH2 antenna complexes

doi:10.1063/1.2210481A general approach for calculating spectral and optical properties of pigment-protein complexes of known atomic structure is presented. The method, that combines molecular dynamics simulations, quantum chemistry calculations, and statistical mechanical modeling, is demonstrated by calculating the absorption and circular dichroism spectra of the B800-B850 bacteriochlorophylls of the LH2 antenna complex from Rs. molischianum at room temperature. The calculated spectra are found to be in good agreement with the available experimental results. The calculations reveal that the broadening of the B800 band is mainly caused by the interactions with the polar protein environment, while the broadening of the B850 band is due to the excitonic interactions. Since it contains no fitting parameters, in principle, the proposed method can be used to predict optical spectra of arbitrary pigment-protein complexes of known structure.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 Grant No. FIBR-0526854. One of the authors (A.D.) acknowledges support from the Burroughs Welcome Fund. The authors also acknowledge computer time provided by NCSA Allocations Board grant MCB020036

Calculating free-energy profiles in biomolecular systems from fast nonequilibrium processes

Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate RC on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics MD simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force PMF due to the rest of the system. By employing the recently proposed FR method I. Kosztin et al., J. Chem. Phys. 124, 064106 2006 , which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: 1 of deca-alanine as a function of its end-to-end distance, and 2 that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the positiondependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in an overdamped Brownian model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.This work was supported in part by grants from 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 Contract No. W-31-109-ENG-38 , and the National Science Foundation Grant No. FIBR-0526854 . We gratefully acknowledge the generous computational resources provided by the University of Missouri Bioinformatics Consortium. M.W.F. gratefully acknowledges support from the University of Missouri Undergraduate Research Scholars Program

Using stochastic models calibrated from nanosecond nonequilibrium simulations to approximate mesoscale information

doi:10.1063/1.3106225We demonstrate how the surrogate process approximation (SPA) method can be used to compute both the potential of mean force along a reaction coordinate and the associated diffusion coefficient using a relatively small number (10-20) of bidirectional nonequilibrium trajectories coming from a complex system. Our method provides confidence bands which take the variability of the initial configuration of the high-dimensional system, continuous nature of the work paths, and thermal fluctuations into account. Maximum-likelihood-type methods are used to estimate a stochastic differential equation (SDE) approximating the dynamics. For each observed time series, we estimate a new SDE resulting in a collection of SPA models. The physical significance of the collection of SPA models is discussed and methods for exploiting information in the population of estimated SPA models are demonstrated and suggested. Molecular dynamics simulations of potassium ion dynamics inside a gramicidin A channel are used to demonstrate the methodology, although SPA-type modeling has also proven useful in analyzing single-molecule experimental time series.C.P.C. thanks Benoît Roux for providing comments on this paper, Riccardo Chelli for helpful discussions related to PMF computations, a referee for helpful comments on the first version, and NIH Grant No. T90 DK070121-04. L.J. and I.K. gratefully acknowledge the computer time provided by the University of Missouri Bioinformatics Consortium. Partial computational support was obtained from the Rice Computational Research Cluster funded by NSF under Grant No. CNS-0421109 and a partnership between Rice University, AMD, and Cray

Influence of subunit structure on the oligomerization state of light harvesting complexes: a free energy calculation study

DOI:10.1016/j.chemphys.2005.08.038Light harvesting complexes 2 (LH2) from Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila form ring complexes out of eight or nine identical subunits, respectively. Here, we investigate computationally what factors govern the different ring sizes. Starting from the crystal structure geometries, we embed two subunits of each species into their native lipid-bilayer/water environment. Using molecular dynamics simulations with umbrella sampling and steered molecular dynamics, we probe the free energy profiles along two reaction coordinates, the angle and the distance between two subunits. We find that two subunits prefer to arrange at distinctly different angles, depending on the species, at about 42.5 deg for Rs. molischianum and at about 38.5 deg for Rps. acidophila, which is likely to be an important factor contributing to the assembly into different ring sizes. Our calculations suggest a key role of surface contacts within the transmembrane domain in constraining these angles, whereas the strongest interactions stabilizing the subunit dimers are found in the C-, and to a lesser extent, N-terminal domains. The presented computational approach provides a promising starting point to investigate the factors contributing to the assembly of protein complexes, in particular if combined with modeling of genetic variants.This work was supported by grants from the University of Missouri Research Board (LJ and IK), the Institute for Theoretical Sciences, a joint institute of Notre Dame University and Argonne National Laboratory, and the U.S. Department of Energy, Office of Science through contract No.W-31-109-ENG-38 (IK and TR)

Reconstruction of free energy profiles from fast non-equilibrium processes [abstract]

Abstract only availableOften, gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing a small number of fast nonequilibrium MD simulations in both forward and time reversed directions we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in very good agreement with previous results obtained by different methods. Compared to these PMF calculation methods our approach is about one order of magnitude faster and, in addition, also provides the position dependent diffusion coefficient along the RC. Thus, by employing the computed PMF and diffusion coefficient in a suitable stochastic model we could estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.MU Undergraduate Research Scholars Progra