Spike-type contrast structures

Construction of an Asymptotic Expansion for the Parabolic Problem Other Problems with Corner Boundary Layers Nonisothermal Fast Chemical Reactions Contrast Structures in Partial Differential Equations A. Step-Type Solutions in the Noncritical Case Step-Type Solutions in the Critical Case Spike-Type Solutions Applications... 

Thus we see that these solutions have not only boundary layers, but also interior layers. Solutions having such interior layers are called contrast structures. A contrast structure of the type represented in Fig. 8 is called a spike, and a contrast structure of the type represented in Fig. 9 is called a step (or threshold). 

Contrast structures of step type and spike t) pe were considered in Section V for ordinary differential equations. In this section, we construct asymptotics for step-type and spike-type solutions of partial differential equations. 

We retain condition III from Section VIII.A, which is required for the construction of the boundary functions. Under conditions I-III we construct an asymptotic expansion for a spike-type solution or, in other words, for a contrast spike-type structure. This is a solution of problem (8.1), (8.2), which is close to the solution u = closed curve F where the solution has a spike. The location of the curve r is not known a priori just as in Section VIII.B. This curve is defined during the construction of the asymptotics. 

It is now widely believed that in skeletal muscle a depolarization-induced change in the structure of the DHPR a 1 subunit directly influences the RyR in such a way as to markedly increase its conductance for Ca +. Since the resulting increase in [Ca +]i can open other RyR channels, this produces a surge of Ca + release. In contrast, cardiac muscle expresses a different a 1 DHPR subunit than skeletal muscle. The cardiac subunit has much higher channel conductance and faster kinetics than the skeletal muscle type, and so admits much more extracellular calcium during the action potential. Thus, CICR does play an important role in cardiac muscle. In both cases, high [Ca +]i reduces RyR conductance, by direct binding of Ca + (or Ca +-calmodulin) to RyR, by activation of a kinase that phosphorylates RyR, and probably both. At the same time, Ca-calmodulin (Ca-CaM) activates a protein kinase that phosphorylates the SR Ca-ATPase, which increases its activity 10- to 100-fold. These two mechanisms combine to terminate the Ca " " spike. 

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