Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

Computer simulations of slowly relaxing systems in external fields

Eine der offenen Fragen der aktuellen Physik ist das Verständnis von Systemen im Nichtgleichgewicht. Im Gegensatz zu der Gleichgewichtsphysik ist in diesem Bereich aktuell kein Formalismus bekannt der ein systematisches Beschreiben der unterschiedlichen Systeme ermöglicht. Um das Verständnis über diese Systeme zu vergrößern werden in dieser Arbeit zwei unterschiedliche Systeme studiert, die unter einem externen Feld ein starkes nichtlineares Verhalten zeigen. Hierbei handelt es sich zum einen um das Verhalten von Teilchen unter dem Einfluss einer extern angelegten Kraft und zum anderen um das Verhalten eines Systems in der Nähe des kritischen Punktes unter Scherung. Das Modellsystem in dem ersten Teil der Arbeit ist eine binäre Yukawa Mischung, die bei tiefen Temperaturen einen Glassübergang zeigt. Dies führt zu einer stark ansteigenden Relaxationszeit des Systems, so dass man auch bei kleinen Kräften relativ schnell ein nichtlineares Verhalten beobachtet. In Abhängigkeit der angelegten konstanten Kraft können in dieser Arbeit drei Regime, mit stark unterschiedlichem Teilchenverhalten, identifiziert werden. In dem zweiten Teil der Arbeit wird das Ising-Modell unter Scherung betrachtet. In der Nähe des kritischen Punkts kommt es in diesem Modell zu einer Beeinflussung der Fluktuationen in dem System durch das angelegte Scherfeld. Dies hat zur Folge, dass das System stark anisotrop wird und man zwei unterschiedliche Korrelationslängen vorfindet, die mit unterschiedlichen Exponenten divergieren. Infolgedessen lässt sich der normale isotrope Formalismus des "finite-size scaling" nicht mehr auf dieses System anwenden. In dieser Arbeit wird gezeigt, wie dieser auf den anisotropen Fall zu verallgemeinern ist und wie damit die kritischen Punkte, sowie die dazu gehörenden kritischen Exponenten berechnet werden können.

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments. (C) 2004 American Institute of Physics.

Progressive loss of ferroelectricity under bipolar pulsed fields and experimental determination of non-switchable polarization in Au/Ba0.5Sr0.5TiO3/SrRuO3 thin-film capacitors

175 nm-thick Ba0.5Sr0.5TiO3 (BST) thin film fabricated by pulsed laser deposition (PLD) technique is found to be a mixture of two distributions of material. We discuss whether these two components are nano-regions of paraelectric and ferroelectric phases, or a bimodal grain-size distribution, or an effect of oxygen vacancy gradient from the electrode interface. The fraction of switchable ferroelectric phase decreases under bipolar pulsed fields, but it recovers after removal of the external fields. The plot of capacitance in decreasing dc voltage (C(Vdown arrow) versus that in increasing dc 61 voltage C(Vup arrow) is a superposition of overlapping of two triangles, in contrast to one well-defined triangle for typical ferroelectric SrBi2Ta2O9 thin films.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Exact static polarizabilities of correlated finite model systems

A finite-field method for calculating exact polarizabilities of correlated conjugated model systems within the valence bond (VB) framework is presented. The correlations reduce the polarizabilities from their noninteracting values and extend the range of linearity to higher external fields. The large nonlinear polarizabilities observed in strongly correlated conjugated organic molecules cannot be directly attributed to electron correlations. The method described can be employed to calculate static polarizabilities for any desired state of a correlated system.

Directional grain growth from anisotropic kinetic roughening of grain boundaries in sheared colloidal crystals

The fabrication of functional materials via grain growth engineering implicitly relies on altering the mobilities of grain boundaries (GBs) by applying external fields. Although computer simulations have alluded to kinetic roughening as a potential mechanism for modifying GB mobilities, its implications for grain growth have remained largely unexplored owing to difficulties in bridging the widely separated length and time scales. Here, by imaging GB particle dynamics as well as grain network evolution under shear, we present direct evidence for kinetic roughening of GBs and unravel its connection to grain growth in driven colloidal polycrystals. The capillary fluctuation method allows us to quantitatively extract shear-dependent effective mobilities. Remarkably, our experiments reveal that for sufficiently large strains, GBs with normals parallel to shear undergo preferential kinetic roughening, resulting in anisotropic enhancement of effective mobilities and hence directional grain growth. Single-particle level analysis shows that the mobility anisotropy emerges from strain-induced directional enhancement of activated particle hops normal to the GB plane. We expect our results to influence materials fabrication strategies for atomic and block copolymeric polycrystals as well.

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Ferromagnetic Resonance Force Microscopy

A new approach to magnetic resonance was introduced in 1992 based upon detection of spin-induced forces by J. Sidles [1]. This technique, now called magnetic resonance force microscopy (MRFM), was first demonstrated that same year via electron paramagnetic resonance (EPR) by D. Rugar et al. [2]. This new method combines principles of magnetic resonance with those of scanned probe technology to detect spin resonance through mechanical, rather than inductive, means. In this thesis the development and use of ferromagnetic resonance force microscopy (FMRFM) is described. This variant of MRFM, which allows investigation of ferromagnetic samples, was first demonstrated in 1996 by Z. Zhang et al. [3]. FMRFM enables characterization of (a) the dynamic magnetic properties of microscale magnetic devices, and (b) the spatial dependence of ferromagnetic resonance within a sample. Both are impossible with conventional ferromagnetic resonance techniques.

Ferromagnetically coupled systems, however, pose unique challenges for force detection. In this thesis the attainable spatial resolution - and the underlying physical mechanisms that determine it - are established. We analyze the dependence of the magnetostatic modes upon sample dimensions using a series of microscale yttrium iron garnet (YIG) samples. Mapping of mode amplitudes within these sample is attained with an unprecedented spatial resolution of 15μm. The modes, never before analyzed on this scale, fit simple models developed in this thesis for samples of micron dimensions. The application of stronger gradient fields induces localized perturbation of the ferromagnetic resonance modes. The first demonstrations of this effect are presented in this study, and a simple theoretical model is developed to explain our observations. The results indicate that the characteristics of the locally-detected ferromagnetic modes are still largely determined by the external fields and dimensions of the entire sample, rather than by the localized interaction volume (i.e., the locale most strongly affected by the local gradient field). Establishing this is a crucial first step toward understanding FMRFM in the high gradient field limit where the dispersion relations become locally determined. In this high gradient field regime, FMRFM imaging becomes analogous with that of EPR MRFM.

FMRFM has also been employed to characterize magnetic multilayers, similar to those utilized in giant magnetoresistance (GMR) devices, on a lateral scale 40 x 40μm. This is orders of magnitude smaller than possible via conventional methods. Anisotropy energies, thickness, and interface qualities of individual layers have been resolved.

This initial work clearly demonstrates the immense and unique potential that FMRFM offers for characterizing advanced magnetic nanostructures and magnetic devices.

Produção de oscillons durante restaurações e quebras espontâneas de simetrias

Na natureza há vários fenômenos envolvendo transições de fase com quebra ou restauração de simetrias. Tipicamente, mudanças de fase, são associadas com uma quebra ou restauração de simetria, que acontecem quando um determinado parâmetro de controle é variado, como por exemplo temperatura, densidade, campos externos, ou de forma dinâmica. Essas mudanças que os sistemas sofrem podem levar a formação de defeitos topológicos, tais como paredes de domínios, vórtices ou monopolos magnéticos. Nesse trabalho estudamos particularmente mudanças de fase associadas com quebras ou restaurações dinâmicas de simetria que estão associadas com formação ou destruição de defeitos do tipo paredes de domínio em modelos de campos escalares com simetria discreta. Nesses processos dinâmicos com formação ou destruição de domínios, estudamos a possibilidade de formação de estruturas do tipo oscillons, que são soluções não homogêneas e instáveis de campo, mas que podem concentrar nelas uma quantidade apreciável de energia e terem uma vida (duração) suficientemente grande para serem de importância física. Estudamos a possibilidade de formação dessas soluções em modelos de dois campos escalares interagentes em que o sistema é preparado em diferentes situações, com a dinâmica resultante nesses sistemas estudada numa rede discreta.

Photonics and lasing in liquid crystal materials

Owing to fundamental reasons of symmetry, liquid crystals are soft materials. This softness allows long length-scales, large susceptibilities and the existence of modulated phases, which respond readily to external fields. Liquid crystals with such phases are tunable, self-assembled, photonic band gap materials; they offer exciting opportunities both in basic science and in technology. Since the density of photon states is suppressed in the stop band and is enhanced at the band edges, these materials may be used as switchable filters or as mirrorless lasers. Disordered periodic liquid crystal structures can show random lasing. We highlight recent advances in this rapidly growing area, and discuss future prospects in emerging liquid crystal materials. Liquid crystal elastomers and orientationally ordered nanoparticle assemblies are of particular interest. © 2006 The Royal Society.

Electronic states of a hydrogenic donor impurity in semiconductor nano-structures

We propose a method for uniformly calculating the electronic states of a hydrogenic donor impurity in low-dimensional semiconductor nano-structures in the framework of effective-mass envelope-function theory, and we study the electronic structures of this systems. Compared to previous methods, our method has the following merits: (a) It can be widely applied in the calculation of the electronic states of hydrogenic donor impurities in nano-structures of various shapes; (b) It can easily be extended to study the effects of external fields and other complex cases; (c) The excited states are more easily calculated than with the variational method; (d) It is convenient to calculate the change of the electronic states with the position of a hydrogenic donor impurity in nano-structures; (e) The binding energy can be calculated explicitly. (c) 2007 Elsevier B.V. All rights reserved.