Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

Oxy anion-accelerated rearrangements

The alkali metal salts of 1,5-hexadien-3-ols undergo accelerated Cope rearrangements to the enolates of δ, ε-unsaturated carbonyl compounds. The generality of the rearrangement was investigated in numerous systems, particularly acyclic cases, and the effect of changes in substituents, counterions, solvents, and geometrical structures were noted and discussed. Applications of this methodology in synthesis included the synthesis of the insect pheromone frontalin, the preparation of selectively monoprotected 1,6-dicarbonyl compounds from 4-methoxy- and 4-phenylthio-1,5-hexadien-3-ols, and the construction of complex ring structures such as a D-homo-estratetraenone derivative.

Thermochemical estimates of the energetics of anionpromoted alkoxide fragmentations were made, and in all cases heterolytic cleavage was favored over hemolytic cleavage by 8.5-53 kcal/mol. The implication of these and other thermochemical estimates is that the anionic oxy-Cope rearrangement occurs via a concerted mechanism rather than a dissociation-recombination process. The concepts of anion-induced bond weakening were successfully applied to an accelerated [1,3]-shift of a dithiane fragment in a cyclohexenyl system. Trapping experiments demonstrated that > 85% of the [1,3]-shift occurred within a solvent cage. Attempts at promoting an intramolecular ene reaction using the potassium salts of 2,7-octadien-1-o1 and 2,8-nonadien-1-o1 were unsuccessful. A general review of anion-promoted bond reorganizations and anion substituent effects is also presented.