Bifurcation and singularity analysis of a molecular network for the induction of long-term memory.

Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis.

Structure-function analyses of {\it PAX6\/} and the molecular bases of aniridia

PAX6 is a transcription activator that regulates eye development in animals ranging from Drosophila to human. The C-terminal region of PAX6 is proline/serine/threonine-rich (PST) and functions as a potent transactivation domain when attached to a heterologous DNA-binding domain of the yeast transcription factor, GAL4. The PST region comprises 152 amino acids encoded by four exons. The transactivation function of the PST region has not been defined and characterized in detail by in vitro mutagenesis. I dissected the PST domain in two independent systems, a heterologous system using a GAL4 DNA-binding site and the native system of PAX6. In both systems, the results show consistently that all four constituent exons of the PST domain are responsible for the transactivation function. The four exon fragments act cooperatively to stimulate transcription, although none of them can function individually as an independent transactivation domain. Combinations of two or more exon fragments can reconstitute substantial transactivation activity when fused to the DNA-binding domain of GAL4, but they surprisingly do not produce much activity in the context of native PAX6 even though the mutant PAX6 proteins are stable and their DNA-binding function remains unaffected. I conclude that the PAX6 protein contains an unusually large transactivation domain that is evolutionarily conserved to a high degree, and that its full transactivation activity relies on the cooperative action of the four exon fragments.^ Most PAX6 mutations detected in patients with aniridia result in truncations of the protein. Some of the truncation mutations occur in the PST region of PAX6, resulting in mutant proteins that retain their DNA-binding ability but have no significant transactivation activity. It is not clear whether such mutants are true loss-of-function or dominant-negative mutants. I show that these mutants are dominant-negative if they are coexpressed with wild-type PAX6 in cultured cells and that the dominant-negative effects result from enhanced DNA-binding ability of these mutants due to removal of the PST domain. These mutants are able to repress the wild-type PAX6 activity not only at target genes with paired domain binding sites but also at target genes with homeodomain binding sites.^ Mutations in the human PAX6 gene produce various phenotypes, including aniridia, Peters' anomaly, autosomal dominant keratitis, and familial foveal dysplasia. The various phenotypes may arise from different mutations in the same gene. To test this theory, I performed a functional analysis of two missense mutations in the paired domain: the R26G mutation reported in a case of Peters' anomaly, and the I87R mutation identified in a patient with aniridia. While both the R26 and the I87 positions are conserved in the paired boxes of all known PAX genes, X-ray crystallography has shown that only R26 makes contact with DNA. I found that the R26G mutant failed to bind a subset of paired domain binding sites but, surprisingly, bound other sites and successfully transactivated promoters containing those sites. In contrast, the I87R mutant had lost the ability to bind DNA at all tested sites and failed to transactivate promoters. My data support the haploinsufficiency hypothesis of aniridia, and the hypothesis that R26G is a hypomorphic allele. ^

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^