Regulation of cellular pH: From molecules to membranes

The vacuolar H+-ATPase (V-ATPase) is a universal class of proton pumps responsible for creating and maintaining acidic milieus in both intracellular and extracellular spaces. In the first chapter, I develop a mechanochemical model of this enzyme based upon the counter-rotation of adjacent subunits. The mathematical approach details a general integrated method for describing the mechanical and chemical reactions that occur in motor systems. A novel escapement is proposed for how the protons cross the protein-bilayer interface, and it is shown how this movement couples to ATP hydrolysis. This model reproduces a variety of experimental data while providing a framework for understanding the function of the enzyme's subunits. Specifically, it explains how ATP hydrolysis can uncouple from proton movement, which has important consequences for cellular energetics and pH regulation.;Until now only an equilibrium theory of organelle acidification has been proposed; however, recent experiments show that large proton leaks prevent many cellular compartments from reaching thermodynamic equilibrium. The characterization of the V-ATPase is used in the second chapter in order to develop a unified model of organelle acidification based on the interplay of ion pumps and channels and the physical characteristics of the organelle. This model successfully describes the time dependent acidification of many different organelle systems. It accurately predicts both the electrical and concentration dependent terms of the chemical potential. In conjunction with fluorescence experiments, I determined the first measurements of the proton permeability of organelles along the secretory pathway. These measurements allowed me to make the first estimates of the number of V-ATPases in each compartment by analyzing the resting pH's of the respective organelles. I found a decrease in permeability from the endoplasmic reticulum (ER) (51 x 10-4 cm/s) to the Golgi (21 x 10-4 cm/s) to the mature secretory granules (MSGs) (3 x 10 -4 cm/s). This drop in permeability is accompanied by an increase in the V-ATPase density.;An elastic energy model of in cubo protein crystallization is presented in the third chapter. I identify the relevant energetics involved in this process and calculate the elastic energy cost of implanting membrane proteins into the highly curved Pn3m cubic phase. The dependence of this energy on the geometry of the Pn3m phase was understood through the D minimal surface, a mathematical surface thought to model the interface geometry of the Pn3m phase. I show that salt-induced shrinkage of the cubic phase increases the energetic cost of proteins in the bulk cubic phase. This energy drives the growth of protein crystals in the flattened lamellar regions where the membrane can accommodate the presence of proteins without creating elastic deformations. A statistical model of this process is developed, and kinetic equations for crystal growth are obtained. Key model parameters were determined by analyzing the growth of bacteriorhodopsin crystals at different lattice parameters. I show how the time required for crystal growth depends on the physical characteristics of the protein and the state of the cubic phase. Thus, the model provides a rational basis for optimizing the experimental procedure for proteins that have not been crystallized.