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.

Insights into Neural Crest Evolution

Neural crest cells are unique to vertebrates and essential to the development and evolution of the craniofacial skeleton. Using a combination of DiI cell lineage tracing, transcriptomics, and analysis of key transcription factors of the Sox Family, I examined neural crest development in the sea lamprey, Petromyzon marinus, as the most basal extant vertebrate from which it is possible to get embryos. The results have uncovered distinct cranial and trunk neural crest subpopulations along the anterior-posterior axis of the lamprey embryo, with a clear separation between the two. However, no evidence of the presence of an intermediate vagal neural crest population was uncovered. Comparing cranial neural crest genes between lamprey and chick, either by examining individual candidate genes or whole genome transcriptome analysis, reveals significant changes in the cranial neural crest gene regulatory network of lamprey compared with chick. In particular, the lamprey cranial neural crest is "missing" several gnathostome cranial crest genes. We speculate that these may underlie the evolutionary divergence of craniofacial development between jawed and jawless vertebrates. Despite the absence of vagal neural crest, DiI-labeling shows that trunk neural crest-derived cells, likely homologous to mammalian Schwann cell precursors, contribute to the lamprey enteric nervous system, potentially representing the most primitive form of neural crest cells contribution to the ENS. Finally, I characterized key members of the Sox Family (Sox B-F) due to their importance in neural crest specification in other species. In comparative studies of the SoxC genes (Sox4, Sox11, and Sox12) in both lamprey and Xenopus, I found similar expression patterns and a novel key role in early neural crest specification, suggesting a conserved role of the SoxC genes amongst vertebrates. Taken together, this work represents important progress in characterizing the early evolution of the neural crest in vertebrates and its role in the transition from jawless to jawed vertebrates.