I. Quantal effects in biochemical cooperativity and a proposed mechanism for the differentiation of calcium signaling in synaptic plasticity. II. Evolutionary algorithms for the optimization of methods in computational chemistry

In Part 1 of this thesis, we propose that biochemical cooperativity is a fundamentally non-ideal process. We show quantal effects underlying biochemical cooperativity and highlight apparent ergodic breaking at small volumes. The apparent ergodic breaking manifests itself in a divergence of deterministic and stochastic models. We further predict that this divergence of deterministic and stochastic results is a failure of the deterministic methods rather than an issue of stochastic simulations.

Ergodic breaking at small volumes may allow these molecular complexes to function as switches to a greater degree than has previously been shown. We propose that this ergodic breaking is a phenomenon that the synapse might exploit to differentiate Ca$^{2+}$ signaling that would lead to either the strengthening or weakening of a synapse. Techniques such as lattice-based statistics and rule-based modeling are tools that allow us to directly confront this non-ideality. A natural next step to understanding the chemical physics that underlies these processes is to consider \textit{in silico} specifically atomistic simulation methods that might augment our modeling efforts.

In the second part of this thesis, we use evolutionary algorithms to optimize \textit{in silico} methods that might be used to describe biochemical processes at the subcellular and molecular levels. While we have applied evolutionary algorithms to several methods, this thesis will focus on the optimization of charge equilibration methods. Accurate charges are essential to understanding the electrostatic interactions that are involved in ligand binding, as frequently discussed in the first part of this thesis.

I. Synthetic Studies Toward the Total Synthesis of Polycyclic Natural Products – Communesin F, Perophoramidine and Ineleganolide. II. Nickel Catalyzed Intramolecular C–O Bond Formation

Expedient synthetic approaches to the highly functionalized polycyclic alkaloids communesin F and perophoramidine are described using a unified approach featuring a key decarboxylative allylic alkylation to access a crucial and highly congested 3,3-disubstituted oxindole. Described are two distinct, stereoselective alkylations that produce structures in divergent diastereomeric series possessing the critical vicinal all-carbon quaternary centers needed for each synthesis. Synthetic studies toward these challenging core structures have revealed a number of unanticipated modes of reactivity inherent to these complex alkaloid scaffolds. Finally, a previously unknown mild and efficient deprotection protocol for the o-nitrobenzyl group is disclosed – this serendipitous discovery permitted a concise endgame for the formal syntheses of both communesin F and perophoramidine.

In addition, the atroposelective synthesis of PINAP ligands has been accomplished via a palladium-catalyzed C–P coupling process through dynamic kinetic resolution. These catalytic conditions allow access to a wide variety of alkoxy- and benzyloxy-substituted PINAP ligands in high enantiomeric excess.

An efficient and exceptionally mild intramolecular nickel-catalyzed carbon–oxygen bond-forming reaction between vinyl halides and primary, secondary, and tertiary alcohols has been achieved. This operationally simple method allows direct access to cyclic vinyl ethers in high yields in a single step.

Finally, synthetic studies toward polycyclic ineleganolide are described. The entire fragmented carbon framework has been constructed from this work. Highly (Z)-selective olefination was achieved by the method by the Ando group.