Statistical mechanics models in protein association problems

Doctor of PhilosophyDepartment of PhysicsJeremy D. SchmitProtein-Protein interactions can lead to disordered states such as precipitates or gels, or to ordered states such as crystals or microtubules. In order to study the different natures of protein-protein interactions we have developed statistical mechanics models in order to interpret the varied behavior of different protein systems. The main point will be to develop theoretical models that infer the time a length scales that characterize the dynamics of the systems analyzed. This approach seek to facilitate a connection to simulations and experiments, where a high resolution analysis in length and time is possible, since the theories can provide insights about the relevant time and length scales, and also about issues that can appear when studying these systems. The first system studied is monoclonal antibodies in solution. Antibody solutions deviate from the dynamical and rheological response expected for globular proteins, especially as volume fraction is increased. Experimental evidence shows that antibodies can reversibly bind to each other via F[subscript]ab and F[subscript]c domains, and form larger structures (clusters) of several antibodies. Here we present a microscopic equilibrium model to account for the distribution of cluster sizes. Antibody clusters are modeled as polymers that can grow via reversible bonds either between two F[subscript]ab domains or between a F[subscript]ab and a F[subscript]c. We propose that the dynamical and rheological behavior is determined by molecular entanglements of the clusters. This entanglement does not occur at low concentrations where antibody-antibody binding contributes to the viscosity by increasing the effective size of the particles. The model explains the observed shear-thinning behavior of antibody solutions. The second system is protein condensates inside living cells. Biomolecule condensates appear throughout the cell serving a wide variety of functions, but it is not clear how functional properties show in the concentrated network inside the condensate droplets. Here we model disordered proteins as linear polymers formed by "stickers" evenly spaced by "spacers". The spacing between stickers gives rise to different network toplogies inside the condensate droplet, determining distinguishing properties such us density and client binding. The third system is protein-protein binding in a salt solutions. Biomolecular simulations are typically performed in an aqueous environment where the number of ions remains fixed for the duration of the simulation, generally with a number of salt pairs intended to match the macroscopic salt concentration. In contrast, real biomolecules experience local ion environments where the salt concentration is dynamic and may differ from bulk. We develop a statistical mechanics model to account for fluctuations of ions concentrations, and study how it affects the free energy of protein-protein binding

Giant Gravitons with NSNS B field

We study the motion of a D(8-p)-brane probe in the background created by a stack of non-threshold (D(p-2), Dp) bound states for $2\le p\le 6$. The brane probe and the branes of the background have two common directions. We show that for a particular value of the worldvolume gauge field there exist configurations of the probe brane which behave as massless particles and can be interpreted as gravitons blown up into a fuzzy sphere and a noncommutative plane. We check this behaviour by studying the motion and energy of the brane and by determining how supersymmetry is broken by the probe as it moves under the action of the background.Comment: 24 pages, LaTe

Flux Stabilization of D-branes in a non-threshold bound state background

We study some configurations of brane probes which are partially wrapped on spheres transverse to a stack of non-threshold bound states. The latter are represented by the corresponding supergravity background. Two cases are studied: D(10-p)-branes in the background of (D(p-2), Dp) bound states and D(8-p)-branes in the (NS5, Dp) geometry. By using suitable flux quantization rules of the worldvolume gauge field, we determine the stable configurations of the probe. The analysis of the energy and supersymmetry of these configurations reveals that they can be interpreted as bound states of lower dimensional objects polarized into a D-brane.Comment: 11 pages, LaTe

Magnetic catalysis in flavored ABJM

We study the magnetic catalysis of chiral symmetry breaking in the ABJM Chern-Simons matter theory with unquenched flavors in the Veneziano limit. We consider a magnetized D6-brane probe in the background of a flavored black hole which includes the backreaction of massless smeared flavors in the ABJM geometry. We find a holographic realization for the running of the quark mass due to the dynamical flavors. We compute several thermodynamic quantities of the brane probe and analyze the effects of the dynamical quarks on the fundamental condensate and on the phase diagram of the model. The dynamical flavors have an interesting effect on the magnetic catalysis. At zero temperature and fixed magnetic field, the magnetic catalysis is suppressed for small bare quark masses whereas it is enhanced for large values of the mass. When the temperature is non-zero there is a critical magnetic field, above which the magnetic catalysis takes place. This critical magnetic field decreases with the number of flavors, which we interpret as an enhancement of the catalysis.Comment: 33 pages, 11 figures; v2: refs added; v3: revised version, new subsection on running mass added, discussion clarifie

Flavoring the gravity dual of N=1 Yang-Mills with probes

We study two related problems in the context of a supergravity dual to N=1 SYM. One of the problems is finding kappa symmetric D5-brane probes in this particular background. The other is the use of these probes to add flavors to the gauge theory. We find a rich and mathematically appealing structure of the supersymmetric embeddings of a D5-brane probe in this background. Besides, we compute the mass spectrum of the low energy excitations of N=1 SQCD (mesons) and match our results with some field theory aspects known from the study of supersymmetric gauge theories with a small number of flavors.Comment: 55 pages, 7 figures, LaTeX; v2: typos corrected, references added; v3: typos correcte

On the energy saved by interlayer interactions in the superconducting state of cuprates

A Ginzburg-Landau-like functional is proposed reproducing the main low-energy features of various possible high-Tc superconducting mechanisms involving energy savings due to interlayer interactions. The functional may be used to relate these savings to experimental quantities. Two examples are given, involving the mean-field specific heat jump at Tc and the superconducting fluctuations above Tc. Comparison with existing data suggests, e.g., that the increase of Tc due to the so-called interlayer tunneling (ILT) mechanism of interlayer kinetic-energy savings is negligible in optimally-doped Bi-2212.Comment: 12 pages, no figures. Version history: 21-aug-2003, first version (available on http://arxiv.org/abs/cond-mat/0308423v1); 15-jan-2004, update to match Europhys. Lett. publication (minor grammar changes, updates in bibliography - e.g., refs. 5 and 26