On the Combination of Game-Theoretic Learning and Multi Model Adaptive Filters

This paper casts coordination of a team of robots within the framework of game theoretic learning algorithms. In particular a novel variant of fictitious play is proposed, by considering multi-model adaptive filters as a method to estimate other players’ strategies. The proposed algorithm can be used as a coordination mechanism between players when they should take decisions under uncertainty. Each player chooses an action after taking into account the actions of the other players and also the uncertainty. Uncertainty can occur either in terms of noisy observations or various types of other players. In addition, in contrast to other game-theoretic and heuristic algorithms for distributed optimisation, it is not necessary to find the optimal parameters a priori. Various parameter values can be used initially as inputs to different models. Therefore, the resulting decisions will be aggregate results of all the parameter values. Simulations are used to test the performance of the proposed methodology against other game-theoretic learning algorithms.</p

Structural and Biophysical Studies of Hair Cell Mechanotransduction Proteins

Our senses of hearing, balance, and motion are the result of hair cells that act as cellular accelerometers to transmute mechanical forces into electrical signals for decoding by the central nervous system. To accomplish this task of mechanoelectrical transduction (MET), hair cells use an array of stereocilia that conduct electrical currents in response to mechanical stimuli. At the tips of these stereocilia, hair cells assemble over a dozen protein components to construct a sophisticated nanomachine that couples the movement of their stereocilia with the opening of mechanically gated ion channels. When forces impinge on stereocilia, they pivot at their base, slide past each other, and impart tension on the tip link, a protein linkage that connects the side of one stereocilium to the mechanically gated ion channel of an adjacent, shorter stereocilium. While this conceptual framework of hair cell of mechanoelectrical transduction has been established, a precise molecular description of the proteins that comprise the machinery is still lacking. A structural understanding of the molecular components of the MET complex and how they function in mechanoelectrical transduction are limited. While previous structural studies on MET-related molecules have been performed, they have not yet produced a clear understanding of the molecular mechanisms underlying MET. The work presented in this thesis seeks to expand our structural descriptions of different components of the transduction machinery, and to validate the functional mechanisms suggested by these descriptions. The tip link that couples adjacent stereocilia is composed of two large proteins – cadherin 23 and protocadherin 15 (PCDH15). It had previously been demonstrated that the extracellular region of the tip link protein PCDH15 was cis-dimeric, yet the molecular details of PCDH15 self-interaction remained elusive despite the existence of structural information for two-thirds of the molecule. Using a series of biophysical experiments and electron microscopy, we revealed that dimerization of the PCDH15 ectodomain is mediated by two distinct interfaces at opposite ends of the molecule. We determined the crystal structure of one of these interfaces, allowing us to engineer monomeric versions of PCDH15 through structure-guided mutations. By expressing these monomeric versions of PCDH15 in hair cells, we were able to demonstrate the functional importance of PCDH15 cis-dimerization for transduction. Within the MET machinery is an elastic element that is in series with the mechanically gated ion channel. While some have postulated the molecular identity of this so-called gating spring to be the tip link proteins, others have cast doubts on this idea due to an apparent mismatch in their stiffness. Along with our collaborators, we performed single-molecule photonic force microscopy studies to directly measure the elasticity of monomeric PCDH15. By analyzing unfolding events observed in these single-molecule experiments, we determined the unfolding behavior of PCDH15 domains. Our results suggested that individual domains of PCDH15 unfold in the force regime of native sound response, and suggest that the domains of PCDH15 and CDH23 can be unfolded in functional hair bundles. On the cytoplasmic side of the MET machinery, it was recently shown that the cytosolic calcium and integrin-binding proteins CIB2 and CIB3 interact with the MET associated membrane protein TMC1. This interaction has been shown to be critical for MET, but the molecular functions of these proteins remained unknown. Using a series of co- immunoprecipitation experiments and peptide binding assays, we defined the CIB2 binding region of TMC1. By determining the crystal structures of CIB3 and its complex with a TMC1- peptide, we were able to visualize the molecular determinants that allow CIB3 to interact with itself and TMC1. We demonstrate that CIB2 mutations affect the single channel conductance of the MET channel, indicating that CIB2 is a regulator of the MET complex. Lastly, I sought to develop methods and protocols for producing samples of MET associated membrane proteins TMIE and TMC1 for structural studies, ultimately producing milligram quantities of TMIE. Using multi-angle light scattering, I found evidence that TMIE forms a hexamer. I also explored the potential of using Caenorhabditis elegans to generate a sample of native-like TMC protein. Both of these lines of work require continuing experimentation. Overall, the works presented here provide molecular descriptions of various MET related proteins. Our structural and biophysical studies of PCDH15 revealed the molecular determinates of PCDH15 cis-dimerization and enabled us to engineer PCDH15 mutants with novel properties. The helical nature of PCDH15 suggests a mechanism for tip link extension through helical unwinding. Our single molecule investigations of PCDH15 strongly implicate it and CDH23 as the gating spring molecules. Our work with CIB2 establishes it as regulator of TMC1 function, and thus MET properties. The crystal structure of the CIB3:TMC1-peptide complex suggests potential mechanisms for this regulation that need to be investigated further