The purpose of this investigation was to develop and validate mathematical models of the sprint relay race. Two approaches, a classical exponential approach and a "new" polynomial approach, were chosen for implementation. Archival film of a 100 m sprint was used to gather displacement data for the first 60 m of the race. Filming had been performed with a single highspeed 16 mm cine camera (LOCAM) at 50 fps. The coordinates were digitized, scaled and filtered using a low pass, critically damped, 4$\sp{\rm th}$ order, zero-lag Butterworth digital filter with a 1 Hz cutoff frequency. Linear velocities were calculated using finite differences. A sprinter was modelled in two ways. The first was an Exponential Model which required as input a personal best time for the 100 m race and the sprinter's maximum constant velocity. The second was a Polynomial Model which required as input the parameters mentioned in the Exponential Model and, additionally, the displacement coefficients for the first 60 m of the 100 m sprint. Relay software was developed to piece the sprint relay together using the corresponding exponential or polynomial approach. The results indicated that the relay software reasonably simulated the kinematic and temporal quantities of a 4 x 100 m relay and can be used by coaches to gain insight into the sprint relay without risking injury to their athletes. Furthermore, the Exponential Model, using less information, described the sprinter's kinematics better than the Polynomial Model.

Solid-state nuclear magnetic resonance (NMR) techniques were applied to the study of the phase behavior and to the determination of the headgroup conformation of phosphonolipids, both natural and synthetic. The results are compared with those for analogous phospholipids in biological and model membranes. $\sp{31}$P NMR was used to characterize the phase behavior of phospho- and phosphonolipids present in polar and total lipid extracts of the protozoa Tetrahymena thermophila. The $\sp{31}$P NMR spectra of aqueous dispersions of polar and total lipids consist in the partial superposition of two powder patterns, one for each phosphorus-containing lipid class. At low temperature, both lipid extracts give rise to lineshapes characteristic of the lamellar structure. Spectra of the polar lipids show that between 15 and 40$\sp\circ$C, a broad, reversible transition from bilayer to hexagonal phase takes place. On the other hand, the phase behavior for total lipids is different: no hexagonal phase is formed, the lipids remain in the bilayer phase at a higher temperature, and a transition to an isotropic phase occurs between 35 and 40$\sp\circ$C, which is not easily reversible. A large proportion of ethanolamine-containing lipids, both phosphate and phosphonate analogs, is responsible for the hexagonal phase formation observed with the polar lipids. When neutral lipids are present with the polar lipids, the bilayer is stabilized up to a higher temperature. One of the neutral lipid components, tetrahymanol, a pentacyclic triterpenoid, is believed to be responsible for this stabilization. The results show that the conformation of the headgroup up to the phosphorus atom is very similar in phospho- and phosphonolipids, i.e. the C2-C3-O-P torsion angle is nearly trans and the C3-O-P-C1 angle variable over the range of values investigated, with a bend at the phosphorus atom. Contrary to the phosphodiester moiety in analogous phospholipids which adopts a gauche-gauche conformation, two solutions for the next torsion angle O-P-C1-C2 were found around 100 and 130$\sp\circ$. The last segment P-C1-C2-N is nearly trans, whereas the corresponding O-C1-C2-N segment in phospholipids is gauche. Despite the differences in the torsion angle values, the overall appearance of the headgroup is similar for both phospho- and phosphonolipids. The headgroup first extends out of the bilayer plane, bending at the phosphorus atom and the terminal portion lies nearly parallel to the membrane surface. (Abstract shortened by UMI.)

In the last few years, a new physics field is gaining much attention: biophysics. Physicists are especially well prepared to study and model some of the most complicated biological mechanisms. For example, many studies are now focused on better understanding the behavior of polymers such as DNA, RNA, and proteins to help develop techniques to manipulate and analyze these molecules. This thesis contains two such studies that were conducted using molecular dynamics simulations. The first concentrates on tethered polyelectrolytes under electrophoresis in free-solution. It presents results that, for the first time, directly confirm the equivalence principle as established by Didier Long, Jean-Louis Viovy, and Armand Ajdari. The second centers on confined polyelectrolytes under electrophoresis in free-solution where the radial confinement force is mechanical of origin and transverse to the net motion of the molecules. It redefines "free-draining", a most fundamental property of polyelectrolytes in free-solution, and points towards a new method for separating charged chains by size. One will also find, at the beginning of the thesis, two entire chapters dedicated to first, put the two studies in the proper context, and second, allow a better comprehension of the theory of polyelectrolytes in free-solution undergoing electrophoresis.

The idea that non-specific DNA-binding proteins are capable of finding their cognate sites on DNA much faster than the time calculated via three-dimensional diffusion theory has been proposed in recent years as an important mechanism for the activity of DNA enzymes and transcription factors. The goal of this study was to investigate, using Brownian dynamics simulation methods, the fundamental mechanisms involved in facilitated diffusion of DNA-binding proteins near and on DNA chains, and the relative roles these mechanisms play in determining the mean time proteins require to find their specific targets on a DNA chain. Two different scenarios were investigated. In the first scenario, the DNA was an extended chain aligned on a surface with a cognate site located at one end of the DNA, exposed to a homogenous solution of proteins with attractive interactions for the DNA monomers. The dynamics of these proteins were characterized and mean time required for proteins to find their specific target DNA monomer was studied as a function of protein concentration in the bulk and the strength of the non-specific binding energy between DNA and proteins. An optimal binding energy was identified corresponding to the most efficient search process. In the second scenario, the DNA also had a coiled conformation. The effect of DNA conformation on protein transport and the mean first passage time was studied. Here, it was discovered that proteins found their target on a coiled DNA much faster that on partially extended DNA chains. The occurrence of inter-segmental transfers, where proteins moved a large distance in sequence space by short hops across loops, was confirmed and correlated with the enhanced target search efficiency observed in coiled DNA. The results of this simulation study reproduced some of the previous predictions of kinetic models and experimental observations, and extended the knowledge about the target search process of DNA-binding proteins to aspects not easily studied using available theoretical and experimental methods.

Now that the human genome project has been completed, the race is on to improve the existing sequencing techniques, or develop new ones, to allow affordable and reasonably quick personal DNA testing. This would help predict personal response to drugs and disease predisposition. The standard sequencing method is based on electrophoresis, which allows a sorting of molecules according to their size. In the first part of this thesis, I develop a new numerical method to rapidly obtain the continuum limit mobility of a migrating molecule, using results obtained on a lattice. I then use this technique to re-examine the theoretical foundation of the current model (the Ogston-Morris-Rodbard-Chrambach or OMRC model) used to describe the molecular size dependence of the electrophoresic mobility of small molecules during gel electrophoresis. I consider three-dimensional gels and electric field lines similar to the ones used in electrophoresis and show that the OMRC model could not reliably predict the mobility of a molecule in a gel. In the second part of this thesis, I present a computational study of a new technique that could be used to provide alternatives to electrophoresis-based sequencing. This technique, named solid phase DNA amplification, allows for the parallelization of DNA amplification (and ultimately, a new sequencing method). I use Monte Carlo and Brownian Dynamics simulations to model this new experimental technique. I show that it leads to a geometrical amplification of DNA molecules and sharp population size distributions.

A simple structure-based mechanism explaining how membrane lipid composition influences the ability of the nicotinic acetylcholine receptor (nAChR) to convert agonist binding into opening of its transmembrane ion channel is proposed. This mechanism is based both on a recent atomic model of the nAChR, as well as extensive characterization of affinity purified nAChRs reconstituted into a number of different model membranes. Biophysical characterization of the nAChR upon reconstitution into membranes of defined lipid composition identifies the receptor's specific lipid requirements, and highlights the structural consequences of its reconstitution into membranes lacking these essential lipids. Infrared measurements show that while membrane lipid composition has no effect on nAChR secondary structure, it influences the ability of the nAChR to undergo agonist induced conformational change. In the absence of specific lipids the nAChR appears locked in a non-conducting conformation in which the binding of agonist fails to trigger a response. Hydrogen-deuterium exchange studies show that these non-functional nAChRs also exhibit increased 1H/2H exchange kinetics, while thermal denaturation data shows that they display reduced thermal stability. Interpreted in light of the new nAChR atomic model (PDB ID: 2BG9), these data provide insight into the lipid-dependent structural rearrangements resulting in an uncoupling of the nAChR's ligand binding and channel gating functions.

We study the sensory processing features of a network built of ON and OFF cells with global delayed feedback. We investigate the response of neural populations to spatio-temporal forcing, mimicking that found in most sensory systems. The network architecture is inspired from the physiology of the electrosensory lateral-line lobe (ELL) of the weakly electric fish, where we describe the collective behavior of populations in the pyramidal cell layer. ON pyramidal cells receive sensory inputs directly, while OFF cells receive a mirror image of the stimuli via an interneuron, inverting their response. The two opposed responses propagate upstream where they recruit the inhibitory feedback pathways. To enhance the distinction between the sub-populations, different baseline firing rates are implemented (to which we refer as asymmetry). As a novel approach to this problem, we model the neural circuit using a system of neural field equations, where the connectivity is determined solely by all-to-all and non-topographic inhibitory recurrent connections. Motivated by numerical and experimental results on the electrosensory system, we determine the conditions for which global rhythmic activity states appear in response to spatially organized stimuli. Novel responses to localized pulses are shown in the steady state regime, where the feedback connections interfere with local ON and OFF activities. These effects are systematically compared to the dynamics of a noisy Integrate-And-Fire network sharing the same architecture and parameters with the neural field formulation. Lastly, we investigate the impact of intrinsic cellular adaptation on oscillatory dynamics. Together these results establish the theoretical basis for input driven transitions to rhythmic states in delayed feedback networks with realistic neural populations.

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No description available.

No description available.