Evolutionary expansion and specialization of the PDZ domains.

PDZ domains are protein-protein interaction modules widely used to assemble membranous signaling complexes including those found in the neuronal synapse. PDZ-containing genes encoded in metazoan genomes vastly outnumber those in prokaryotes, plants, and fungi. By comparing 40 proteomes to track the evolutionary history of the PDZ domain, we observed that the variety of associations between PDZ and other domains expands greatly along the stem leading to metazoans and choanoflagellates. We asked whether the expansion of PDZ domains was due to random or specific sequence changes. Studying the sequence signatures of 58 PDZ lineages that are common to bilaterian animals, we showed that six common amino acid residues are able to classify 96% of PDZ domains to their correct evolutionary lineage. In PDZ domain-ligand cocrystals, four of these "classifying positions" lie in direct contact with the -1 and -3 residues of the ligand. This suggests coevolution of the more flexible regions of the binding interaction as a central mechanism of specialization inherent within the PDZ domain. To identify these positions, we devised two independent algorithms--a metric termed within-clade entropy (WCE) and an average mutual information (AvgMI) score--that both reached similar results. Extending these tools to the choanoflagellate, Monosiga brevicollis, we compared its PDZ domains with their putative metazoan orthologs. Interestingly, the M. brevicollis genes lack conservation at the classifying positions suggesting dissociation between domain organization in multidomain proteins and specific changes within the PDZ domain.

Amplification in the auditory periphery: the effect of coupling tuning mechanisms.

A mathematical model describing the coupling between two independent amplification mechanisms in auditory hair cells is proposed and analyzed. Hair cells are cells in the inner ear responsible for translating sound-induced mechanical stimuli into an electrical signal that can then be recorded by the auditory nerve. In nonmammals, two separate mechanisms have been postulated to contribute to the amplification and tuning properties of the hair cells. Models of each of these mechanisms have been shown to be poised near a Hopf bifurcation. Through a weakly nonlinear analysis that assumes weak periodic forcing, weak damping, and weak coupling, the physiologically based models of the two mechanisms are reduced to a system of two coupled amplitude equations describing the resonant response. The predictions that follow from an analysis of the reduced equations, as well as performance benefits due to the coupling of the two mechanisms, are discussed and compared with published experimental auditory nerve data.

Multi-locus nonparametric linkage analysis of complex trait loci with neural networks.

Complex traits are generally taken to be under the influence of multiple genes, which may interact with each other to confer susceptibility to disease. Statistical methods in current use for localizing such genes essentially work under single-gene models, either implicitly or explicitly. In genomic screens for complex disease genes, some of the marker loci must be in tight linkage with disease susceptibility genes. We developed a general multi-locus approach to identify sets of such marker loci. Our approach focuses on affected sib pair data and employs a nonparametric pattern recognition technique using artificial neural networks. This technique analyzes all markers simultaneously in order to detect patterns of locus interactions. When applied to previously published sib pair data on type I diabetes, our approach finds the same genes as in the published report in addition to some new loci. For a specific two-locus model of inheritance, the power of our approach is higher than that of the currently used analysis standard.

Universal distribution of saliencies for pruning in layered neural networks.

A better understanding of pruning methods based on a ranking of weights according to their saliency in a trained network requires further information on the statistical properties of such saliencies. We focus on two-layer networks with either a linear or nonlinear output unit, and obtain analytic expressions for the distribution of saliencies and their logarithms. Our results reveal unexpected universal properties of the log-saliency distribution and suggest a novel algorithm for saliency-based weight ranking that avoids the numerical cost of second derivative evaluations.

Building a hierarchy with neural networks: an example-image vector quantization.

Electronic neural networks can perform the function of associative memory. Given an input pattern, the network searches through its stored memories to find which of them best matches the input. Thus the network does a combination of content-addressable search and error correction. The number of random memories that a network can store is limited to a fraction of the number of electronic neurons in the circuit. We propose a method for building a hierarchy of networks that allows the fast parallel search through a list of memories that is too large to store in a single network. We have demonstrated the principle of this approach by an example in image vector quantization.