ATP depletion results inMitochondria are central to the apoptosis activation pathway in many physiological and pathological conditions. Members of the Bcl-2 family of proteins are known to affect mitochondrial function and regulate the release of apoptosis-activating factors (2-5). Anti-apoptotic members of Bcl-2 family (e.g. Bcl-2 and Bcl-x L ) act primarily to preserve mitochondrial integrity by suppressing the release of cytochrome c (5). In contrast, proapoptotic members (Bax, Bid, etc.) induce the release of cytochrome c and cause mitochondrial dysfunction (1, 6 -8). The pro-apoptotic protein, Bax, which normally resides in the cytosol, translocates to mitochondria when triggered by certain stimuli (6, 9). Translocated Bax has been shown to induce cytochrome c release both in vivo (1, 6, 10) and in vitro (11) and this is followed by caspase activation (10, 12). The mitochondrial permeability transition, an event that results in disruption of the mitochondrial potential gradient, has been reported to induce cytochrome c release and apoptosis (13). However, our observations and several other reports suggest that the effects of Bax are targeted at the outer mitochondrial membrane and that the mitochondrial inner membrane remains intact even after Bax-induced release of cytochrome c (6, 10, 14 -16).How cytochrome c leaves mitochondria during apoptosis after relocation of Bax to the mitochondrial outer membrane still remains an unanswered puzzle. Potential mechanisms involve mitochondrial swelling caused by opening the permeability transition pore in the inner membrane (17) or by mitochondrial hyperpolarization followed by swelling and membrane rupture (18). However, it has been reported that the pro-apoptotic proteins Bid and Bax can release cytochrome c from isolated mitochondria in the absence of detectable mitochondrial swelling (19). Although it was believed earlier that Bax induces the release of cytochrome c by inhibiting Bcl-2 function through binding of the Bcl-2 homology domains BH 1 , BH 2 , and BH 3 , there is evidence to suggest that Bax and Bcl-2 function independently in regulating apoptosis (20,21). Formation of ion channels in synthetic lipid bilayer by members of the Bcl-2 family (22) has suggested that pro-apoptotic members may rearrange in the outer mitochondrial membranes to allow the efflux of cytochrome c by forming large channels. Even though both Bcl-2 and Bax are capable of forming ion channels in artificial membranes, it is unclear how these proteins can form similar channels and still exert opposing actions. The data would suggest that Bax function can be inhibited by Bcl-2/ Bcl-x L , but does not require direct Bax/Bcl-2 or Bax/Bcl-x L interaction for regulating Bax function (23, 24). For example, enforced dimerization of Bax, as a chimeric protein with FK506 binding protein, resulted in its translocation to the mitochondria and induced cell death even in the presence of Bcl-x L (25). Likewise, Bax mutant proteins that fail to bind to Bcl-2 are capable of inducing apoptosis (20). In ...

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A forward problem for the Dirac system is to find obeying for ; for , and for , with the real . An input–output map is of the convolution form , where is a response function. By hyperbolicity of the system, for any , function is determined by . An inverse problem is the following: for an (arbitrary) fixed , given to recover . The procedure that determines is proposed, and the characteristic solvability conditions on r are provided. Our approach is purely time domain and is based on studying the controllability properties of the Dirac system. In itself the system is not controllable: the local completeness of states does not hold, but its relevant extension gains controllability. This is the fact that enables one to apply the boundary control method for solving the inverse problem.

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