In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na+/K+ pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. The model can replicate these recordings. We propose that Na+/K+ pump activity controls the intrinsic firing mode of cerbellar Purkinje cells.

Cancer cells have a more hyperpolarised mitochondrial membrane potential (Ψ IM ) than normal cells. Ψ IM = ~-220 mV in cancer cells as compared to ~-140 mV in normal cells. Until now it has not been known why. This paper explains this disparity, in a mathematical framework, and identifies molecular targets and operations unique to cancer cells. These are thence prospective cancer drug targets. BMS-199264 is proposed as an anti-cancer drug. It inhibits the reverse, proton-pumping mode of ATP synthase, which this paper identifies as crucial to cancer cells but not to healthy, normal adult cells. In the cancer cell model, the adenine nucleotide exchanger (ANT) is inversely orientated in the mitochondrial inner membrane as compared to normal cells. This predicts it to have a different drug interaction profile, which can be leveraged for cancer therapy. Uncouplers, which dissipate the proton motive force, are proposed as anti-cancer medicines e.g. 2,4-dinitrophenol.

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