Hard spheres within classical density functional theory and Min proteins in Escherichia coli

by Jeff B. Schulte

Institution: Oregon State University
Department: Physics
Degree: PhD
Year: 2015
Keywords: Classical Density Functional Theory; Density functionals
Record ID: 2057921
Full text PDF: http://hdl.handle.net/1957/55645


This thesis reports on computational research in two different areas. I first discuss the Min-protein system found within Escherichia coli. Following this I discuss an extended investigation into improving free energy functionals that are used within Classical Density Functional Theory in order to model water. Chapter 2 examines the dynamics of the Min-protein system within E. Coli, which aid in regulating the process of cell division by identifying the center of the cell. While this system usually exhibits robust bipolar oscillations in a variety of cell shapes, recent experiments have shown that when the cells are mechanically deformed into wide, flattened out, irregular shapes, the spatial regularity of these oscillations breaks down. We employ widely used stochastic and deterministic models of the Min system to simulate cells with flattened shapes. The deterministic model predicts regular bipolar oscillations, in contradiction with the experimentally observed behavior, while the single molecule nature of the stochastic model, which is based on the same reaction-diffusion equations, leads to the disruption of the regular patterns of protein concentration. We further report on simulations of symmetric but flattened cell shapes, and find that it is the flattening and accompanying lateral expansion rather than the asymmetry of the cell shapes that causes the irregular oscillation behavior. Chapter 3 begins our discussion of Classical Density Functional Theory research by introducing many of the key concepts used in the following chapters. Chapter 4 investigates the value of the distribution function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in statistical associating fluid theory, which is the basis of a number of recently developed classical density functionals, including ones developed within my research group. We define two averaged values for the distribution function at contact and derive formulas for each of them from the White Bear version of the fundamental measure theory functional, using an assumption of thermodynamic consistency. We test these formulas, as well as two existing formulas, against Monte Carlo simulations and find excellent agreement between the Monte Carlo data and one of our averaged distribution functions. Chapter 5 details our modifications of our recently published statistical associating fluid theory-based classical density functional theory for water, incorporating this improved distribution function at contact. We examine the effect of this alteration by studying two hard-sphere solutes and a Lennard-Jones approximation of a krypton-atom solute, and find improvement. Finally, Chapter 6 introduces an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of the new distribution function at contact referred to above. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions, which allows for an…