The cell-toxic bile salt glycochenodeoxycholic acid (GCDCA) and taurochenodeoxycholic acid (TCDCA) are responsible for hepatocyte demise in cholestatic liver diseases, while tauroursodeoxycholic acid (TUDCA) is regarded hepatoprotective. We demonstrate the direct mitochondrio-toxicity of bile salts which deplete the mitochondrial membrane potential and induce the mitochondrial permeability transition (MPT). The bile salt mediated mechanistic mode of destruction significantly differs from that of calcium, the prototype MPT inducer. Cell-toxic bile salts initially bind to the mitochondrial outer membrane. Subsequently, the structure of the inner boundary membrane disintegrates. And it is only thereafter that the MPT is induced. This progressive destruction occurs in a dose- and time-dependent way. We demonstrate that GCDCA and TCDCA, but not TUDCA, preferentially permeabilize liposomes containing the mitochondrial membrane protein ANT, a process resembling the MPT induction in whole mitochondria. This suggests that ANT is one decisive target for toxic bile salts. To our knowledge this is the first report unraveling the consecutive steps leading to mitochondrial destruction by cell-toxic bile salts.

The family of general Jacobi polynomials P (α,β) n where α, β ∈ C can be characterised by complex (nonhermitian) orthogonality relations (cf. [15]). The special subclass of Jacobi polynomials P (α,β) n where α, β ∈ R are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the n real zeros, have been well studied. There is another special subclass of Jacobi polynomials P (α,β) n with α, β ∈ C, β = α which are known as Pseudo-Jacobi polynomials. The sequence of Pseudo-Jacobi polynomials {P α,α n } ∞ n=0 is the only other subclass in the general Jacobi family (beside the classical Jacobi polynomials) that has n real zeros for every n = 0, 1, 2, . . . for certain values of α ∈ C. For some parameter ranges Pseudo-Jacobi polynomials are fully orthogonal, for others there is only complex (non-Hermitian) orthogonality. We summarise the orthogonality and quasi-orthogonality properties and study the zeros of Pseudo-Jacobi polynomials, providing asymptotics, bounds and results on the monotonicity and convexity of the zeros.

BackgroundThe permeabilization of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the calcium-induced mitochondrial permeability transition. Upon Ca2+-uptake into mitochondria an increase in inner membrane permeability occurs by a yet unclear mechanism. This leads to a net water influx in the mitochondrial matrix, mitochondrial swelling, and finally the rupture of the outer membrane. Although already described more than thirty years ago, many unsolved questions surround this important biological phenomenon. Importantly, theoretical modeling of the mitochondrial permeability transition has only started recently and the existing mathematical models fail to characterize the swelling process throughout the whole time range.ResultsWe propose here a new mathematical approach to the mitochondrial permeability transition introducing a specific delay equation and resulting in an optimized representation of mitochondrial swelling. Our new model is in accordance with the experimentally determined course of volume increase throughout the whole swelling process, including its initial lag phase as well as its termination. From this new model biological consequences can be deduced, such as the confirmation of a positive feedback of mitochondrial swelling which linearly depends on the Ca2+-concentration, or a negative exponential dependence of the average swelling time on the Ca2+-concentration. Finally, our model can show an initial shrinking phase of mitochondria, which is often observed experimentally before the actual swelling starts.ConclusionsWe present a model of the mitochondrial swelling kinetics. This model may be adapted and extended to diverse other inducing/inhibiting conditions or to mitochondria from other biological sources and thus may benefit a better understanding of the mitochondrial permeability transition.

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