Matching Items (30)
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
Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
With the advent of the X-ray free-electron laser (XFEL), an opportunity has arisen to break the nexus between radiation dose and spatial resolution in diffractive imaging, by outrunning radiation damage altogether when using single X-ray pulses so brief that they terminate before atomic motion commences. This dissertation concerns the application of XFELs to biomolecular imaging in an effort to overcome the severe challenges associated with radiation damage and macroscopic protein crystal growth. The method of femtosecond protein nanocrystallography (fsPNX) is investigated, and a new method for extracting crystallographic structure factors is demonstrated on simulated data and on the first experimental fsPNX data obtained at an XFEL. Errors are assessed based on standard metrics familiar to the crystallography community. It is shown that resulting structure factors match the quality of those measured conventionally, at least to 9 angstrom resolution. A new method for ab-initio phasing of coherently-illuminated nanocrystals is then demonstrated on simulated data. The method of correlated fluctuation small-angle X-ray scattering (CFSAXS) is also investigated as an alternative route to biomolecular structure determination, without the use of crystals. It is demonstrated that, for a constrained two-dimensional geometry, a projection image of a single particle can be formed, ab-initio and without modeling parameters, from measured diffracted intensity correlations arising from disordered ensembles of identical particles illuminated simultaneously. The method is demonstrated experimentally, based on soft X-ray diffraction from disordered but identical nanoparticles, providing the first experimental proof-of-principle result. Finally, the fundamental limitations of CFSAXS is investigated through both theory and simulations. It is found that the signal-to-noise ratio (SNR) for CFSAXS data is essentially independent of the number of particles exposed in each diffraction pattern. The dependence of SNR on particle size and resolution is considered, and realistic estimates are made (with the inclusion of solvent scatter) of the SNR for protein solution scattering experiments utilizing an XFEL source.
ContributorsKirian, Richard A (Author) / Spence, John C. H. (Committee member) / Doak, R. Bruce (Committee member) / Weierstall, Uwe (Committee member) / Bennett, Peter (Committee member) / Treacy, Michael M. J. (Committee member) / Arizona State University (Publisher)
Created2011
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
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (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
Zeolites are a class of microporous materials that are immensely useful as molecular sieves and catalysts. While there exist millions of hypothetical zeolite topologies, only 206 have been recognized to exist in nature, and the question remains: What distinguishes known zeolite topologies from their hypothetical counterparts? It has been found that all 206 of the known zeolites can be represented as networks of rigid perfect tetrahedra that hinge freely at the connected corners. The range of configurations over which the corresponding geometric constraints can be met has been termed the "flexibility window". Only a small percentage of hypothetical types exhibit a flexibility window, and it is thus proposed that this simple geometric property, the existence of a flexibility window, provides a reliable benchmark for distinguishing potentially realizable hypothetical structures from their infeasible counterparts. As a first approximation of the behavior of real zeolite materials, the flexibility window provides additional useful insights into structure and composition. In this thesis, various methods for locating and exploring the flexibility window are discussed. Also examined is the assumption that the tetrahedral corners are force-free. This is a reasonable approximation in silicates for Si-O-Si angles above ~135°. However, the approximation is poor for germanates, where Ge-O-Ge angles are constrained to the range ~120°-145°. Lastly, a class of interesting low-density hypothetical zeolites is evaluated based on the feasibility criteria introduced.
ContributorsDawson, Colby (Author) / Treacy, Michael M. J. (Thesis advisor) / O'Keeffe, Michael (Committee member) / Thorpe, Michael F. (Committee member) / Rez, Peter (Committee member) / Bennett, Peter (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2012
Description
In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrödinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrödinger equation in R^n with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrödinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
ContributorsCordero-Soto, Ricardo J (Author) / Suslov, Sergei (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Engman, Martin (Committee member) / Herrera-Valdez, Marco (Committee member) / Arizona State University (Publisher)
Created2011
Description
In translating the Russian-language math paper “On Applications of Graph Theory for the Description and Analysis of Information Flow Diagrams in Control Systems” (V.L. Epstein, 1964) we endeavor not only to analyze the specific applications of this paper’s analysis of adjacency matrices to current topics of interest in graph theory, but also to demonstrate in general the value of translating foreign language papers.
ContributorsSaarinen, Emma Catherine (Author) / Inozemtseva, Julia (Thesis director) / Suslov, Sergei (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12