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- Creators: Hindemith, Paul, 1895-1963
Description
The properties of materials depend heavily on the spatial distribution and connectivity of their constituent parts. This applies equally to materials such as diamond and glasses as it does to biomolecules that are the product of billions of years of evolution. In science, insight is often gained through simple models with characteristics that are the result of the few features that have purposely been retained. Common to all research within in this thesis is the use of network-based models to describe the properties of materials. This work begins with the description of a technique for decoupling boundary effects from intrinsic properties of nanomaterials that maps the atomic distribution of nanomaterials of diverse shape and size but common atomic geometry onto a universal curve. This is followed by an investigation of correlated density fluctuations in the large length scale limit in amorphous materials through the analysis of large continuous random network models. The difficulty of estimating this limit from finite models is overcome by the development of a technique that uses the variance in the number of atoms in finite subregions to perform the extrapolation to large length scales. The technique is applied to models of amorphous silicon and vitreous silica and compared with results from recent experiments. The latter part this work applies network-based models to biological systems. The first application models force-induced protein unfolding as crack propagation on a constraint network consisting of interactions such as hydrogen bonds that cross-link and stabilize a folded polypeptide chain. Unfolding pathways generated by the model are compared with molecular dynamics simulation and experiment for a diverse set of proteins, demonstrating that the model is able to capture not only native state behavior but also partially unfolded intermediates far from the native state. This study concludes with the extension of the latter model in the development of an efficient algorithm for predicting protein structure through the flexible fitting of atomic models to low-resolution cryo-electron microscopy data. By optimizing the fit to synthetic data through directed sampling and context-dependent constraint removal, predictions are made with accuracies within the expected variability of the native state.
ContributorsDe Graff, Adam (Author) / Thorpe, Michael F. (Thesis advisor) / Ghirlanda, Giovanna (Committee member) / Matyushov, Dmitry (Committee member) / Ozkan, Sefika B. (Committee member) / Treacy, Michael M. J. (Committee member) / Arizona State University (Publisher)
Created2011
Description
Conformational changes in biomolecules often take place on longer timescales than are easily accessible with unbiased molecular dynamics simulations, necessitating the use of enhanced sampling techniques, such as adaptive umbrella sampling. In this technique, the conformational free energy is calculated in terms of a designated set of reaction coordinates. At the same time, estimates of this free energy are subtracted from the potential energy in order to remove free energy barriers and cause conformational changes to take place more rapidly. This dissertation presents applications of adaptive umbrella sampling to a variety of biomolecular systems. The first study investigated the effects of glycosylation in GalNAc2-MM1, an analog of glycosylated macrophage activating factor. It was found that glycosylation destabilizes the protein by increasing the solvent exposure of hydrophobic residues. The second study examined the role of bound calcium ions in promoting the isomerization of a cis peptide bond in the collagen-binding domain of Clostridium histolyticum collagenase. This study determined that the bound calcium ions reduced the barrier to the isomerization of this peptide bond as well as stabilizing the cis conformation thermodynamically, and identified some of the reasons for this. The third study represents the application of GAMUS (Gaussian mixture adaptive umbrella sampling) to on the conformational dynamics of the fluorescent dye Cy3 attached to the 5' end of DNA, and made predictions concerning the affinity of Cy3 for different base pairs, which were subsequently verified experimentally. Finally, the adaptive umbrella sampling method is extended to make use of the roll angle between adjacent base pairs as a reaction coordinate in order to examine the bending both of free DNA and of DNA bound to the archaeal protein Sac7d. It is found that when DNA bends significantly, cations from the surrounding solution congregate on the concave side, which increases the flexibility of the DNA by screening the repulsion between phosphate backbones. The flexibility of DNA on short length scales is compared to the worm-like chain model, and the contribution of cooperativity in DNA bending to protein-DNA binding is assessed.
ContributorsSpiriti, Justin Matthew (Author) / van der Vaart, Arjan (Thesis advisor) / Chizmeshya, Andrew (Thesis advisor) / Matyushov, Dmitry (Committee member) / Fromme, Petra (Committee member) / Arizona State University (Publisher)
Created2011
Description
Molecular dynamics (MD) simulations provide a particularly useful approach to understanding conformational change in biomolecular systems. MD simulations provide an atomistic, physics-based description of the motions accessible to biomolecular systems on the pico- to micro-second timescale, yielding important insight into the free energy of the system, the dynamical stability of contacts and the role of correlated motions in directing the motions of the system. In this thesis, I use molecular dynamics simulations to provide molecular mechanisms that rationalize structural, thermodynamic, and mutation data on the interactions between the lac repressor headpiece and its O1 operator DNA as well as the ERK2 protein kinase. I performed molecular dynamics simulations of the lac repressor headpiece - O1 operator complex at the natural angle as well as at under- and overbent angles to assess the factors that determine the natural DNA bending angle. I find both energetic and entropic factors contribute to recognition of the natural angle. At the natural angle the energy of the system is minimized by optimization of protein-DNA contacts and the entropy of the system is maximized by release of water from the protein-DNA interface and decorrelation of protein motions. To identify the mechanism by which mutations lead to auto-activation of ERK2, I performed a series of molecular dynamics simulations of ERK1/2 in various stages of activation as well as the constitutively active Q103A, I84A, L73P and R65S ERK2 mutants. My simulations indicate the importance of domain closure for auto-activation and activity regulation. My results enable me to predict two loss-of-function mutants of ERK2, G83A and Q64C, that have been confirmed in experiments by collaborators. One of the powerful capabilities of MD simulations in biochemistry is the ability to find low free energy pathways that connect and explain disparate structural data on biomolecular systems. An extention of the targeted molecular dynamics technique using constraints on internal coordinates will be presented and evaluated. The method gives good results for the alanine dipeptide, but breaks down when applied to study conformational changes in GroEL and adenylate kinase.
ContributorsBarr, Daniel Alan (Author) / van der Vaart, Arjan (Thesis advisor) / Matyushov, Dmitry (Committee member) / Wolf, George (Committee member) / Shumway, John (Committee member) / Arizona State University (Publisher)
Created2011
ContributorsHindemith, Paul, 1895-1963 (Composer)
Description
In a typical living cell, millions to billions of proteins—nanomachines that fluctuate and cycle among many conformational states—convert available free energy into mechanochemical work. A fundamental goal of biophysics is to ascertain how 3D protein structures encode specific functions, such as catalyzing chemical reactions or transporting nutrients into a cell. Protein dynamics span femtosecond timescales (i.e., covalent bond oscillations) to large conformational transition timescales in, and beyond, the millisecond regime (e.g., glucose transport across a phospholipid bilayer). Actual transition events are fast but rare, occurring orders of magnitude faster than typical metastable equilibrium waiting times. Equilibrium molecular dynamics (EqMD) can capture atomistic detail and solute-solvent interactions, but even microseconds of sampling attainable nowadays still falls orders of magnitude short of transition timescales, especially for large systems, rendering observations of such "rare events" difficult or effectively impossible.
Advanced path-sampling methods exploit reduced physical models or biasing to produce plausible transitions while balancing accuracy and efficiency, but quantifying their accuracy relative to other numerical and experimental data has been challenging. Indeed, new horizons in elucidating protein function necessitate that present methodologies be revised to more seamlessly and quantitatively integrate a spectrum of methods, both numerical and experimental. In this dissertation, experimental and computational methods are put into perspective using the enzyme adenylate kinase (AdK) as an illustrative example. We introduce Path Similarity Analysis (PSA)—an integrative computational framework developed to quantify transition path similarity. PSA not only reliably distinguished AdK transitions by the originating method, but also traced pathway differences between two methods back to charge-charge interactions (neglected by the stereochemical model, but not the all-atom force field) in several conserved salt bridges. Cryo-electron microscopy maps of the transporter Bor1p are directly incorporated into EqMD simulations using MD flexible fitting to produce viable structural models and infer a plausible transport mechanism. Conforming to the theme of integration, a short compendium of an exploratory project—developing a hybrid atomistic-continuum method—is presented, including initial results and a novel fluctuating hydrodynamics model and corresponding numerical code.
Advanced path-sampling methods exploit reduced physical models or biasing to produce plausible transitions while balancing accuracy and efficiency, but quantifying their accuracy relative to other numerical and experimental data has been challenging. Indeed, new horizons in elucidating protein function necessitate that present methodologies be revised to more seamlessly and quantitatively integrate a spectrum of methods, both numerical and experimental. In this dissertation, experimental and computational methods are put into perspective using the enzyme adenylate kinase (AdK) as an illustrative example. We introduce Path Similarity Analysis (PSA)—an integrative computational framework developed to quantify transition path similarity. PSA not only reliably distinguished AdK transitions by the originating method, but also traced pathway differences between two methods back to charge-charge interactions (neglected by the stereochemical model, but not the all-atom force field) in several conserved salt bridges. Cryo-electron microscopy maps of the transporter Bor1p are directly incorporated into EqMD simulations using MD flexible fitting to produce viable structural models and infer a plausible transport mechanism. Conforming to the theme of integration, a short compendium of an exploratory project—developing a hybrid atomistic-continuum method—is presented, including initial results and a novel fluctuating hydrodynamics model and corresponding numerical code.
ContributorsSeyler, Sean L (Author) / Beckstein, Oliver (Thesis advisor) / Chamberlin, Ralph (Committee member) / Matyushov, Dmitry (Committee member) / Thorpe, Michael F (Committee member) / Vaiana, Sara (Committee member) / Arizona State University (Publisher)
Created2017
Description
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
ContributorsLanfear, Nathan A (Author) / Suslov, Sergei (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Platte, Rodrigo (Committee member) / Matyushov, Dmitry (Committee member) / Kuiper, Hendrik (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016
Description
The relation between water and protein physics is a topic of much interest. Molecular dynamics (MD) simulations of biomolecules are a common computational technique to obtain atomistic insight into the physical behavior of biomolecules, including the nature of the interaction between water and the protein. In order to model biomolecules at the highest level of accuracy, an explicit, atomistic representation of the water is typically necessary. The number of water molecules that need to be simulated is normally on the order of thousands. The high dimensional MD dataset is then expanded with considerably more dimensions. We describe here a set of tools which can be used to extract general features of the water behavior, which can then be utilized to build simplified models of the water kinetics which make quantitative predictions, such as the flux rate through a pore.
ContributorsWelland, Ian (Author) / Beckstein, Oliver (Committee member) / Matyushov, Dmitry (Committee member) / Barrett, The Honors College (Contributor)
Created2015-12
ContributorsHindemith, Paul, 1895-1963 (Composer)
ContributorsHindemith, Paul, 1895-1963 (Composer)
ContributorsHindemith, Paul, 1895-1963 (Composer)