Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

State equation for shape-memory alloys. Aplication to Cu-Zn-Al

We deal with the hysteretic behavior of partial cycles in the two¿phase region associated with the martensitic transformation of shape¿memory alloys. We consider the problem from a thermodynamic point of view and adopt a local equilibrium formalism, based on the idea of thermoelastic balance, from which a formal writing follows a state equation for the material in terms of its temperature T, external applied stress ¿, and transformed volume fraction x. To describe the striking memory properties exhibited by partial transformation cycles, state variables (x,¿,T) corresponding to the current state of the system have to be supplemented with variables (x,¿,T) corresponding to points where the transformation control parameter (¿¿ and/or T) had reached a maximum or a minimum in the previous thermodynamic history of the system. We restrict our study to simple partial cycles resulting from a single maximum or minimum of the control parameter. Several common features displayed by such partial cycles and repeatedly observed in experiments lead to a set of analytic restrictions, listed explicitly in the paper, to be verified by the dissipative term of the state equation, responsible for hysteresis. Finally, using calorimetric data of thermally induced partial cycles through the martensitic transformation in a Cu¿Zn¿Al alloy, we have fitted a given functional form of the dissipative term consistent with the analytic restrictions mentioned above.

Functional EF-hands in neuronal calcium sensor GCAP2 determine its phosphorylation state and subcellular distribution in vivo, and are essential for photoreceptor cell integrity

The neuronal calcium sensor proteins GCAPs (guanylate cyclase activating proteins) switch between Ca2+-free and Ca2+-bound conformational states and confer calcium sensitivity to guanylate cyclase at retinal photoreceptor cells. They play a fundamental role in light adaptation by coupling the rate of cGMP synthesis to the intracellular concentration of calcium. Mutations in GCAPs lead to blindness. The importance of functional EF-hands in GCAP1 for photoreceptor cell integrity has been well established. Mutations in GCAP1 that diminish its Ca2+ binding affinity lead to cell damage by causing unabated cGMP synthesis and accumulation of toxic levels of free cGMP and Ca2+. We here investigate the relevance of GCAP2 functional EF-hands for photoreceptor cell integrity. By characterizing transgenic mice expressing a mutant form of GCAP2 with all EF-hands inactivated (EF(-)GCAP2), we show that GCAP2 locked in its Ca2+-free conformation leads to a rapid retinal degeneration that is not due to unabated cGMP synthesis. We unveil that when locked in its Ca2+-free conformation in vivo, GCAP2 is phosphorylated at Ser201 and results in phospho-dependent binding to the chaperone 14-3-3 and retention at the inner segment and proximal cell compartments. Accumulation of phosphorylated EF(-)GCAP2 at the inner segment results in severe toxicity. We show that in wildtype mice under physiological conditions, 50% of GCAP2 is phosphorylated correlating with the 50% of the protein being retained at the inner segment. Raising mice under constant light exposure, however, drastically increases the retention of GCAP2 in its Ca2+-free form at the inner segment. This study identifies a new mechanism governing GCAP2 subcellular distribution in vivo, closely related to disease. It also identifies a pathway by which a sustained reduction in intracellular free Ca2+ could result in photoreceptor damage, relevant for light damage and for those genetic disorders resulting in 'equivalent-light'' scenarios.