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.

The sodium-potassium pump is an information processing element in brain computation

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.

Without synaptic input, Purkinje neurons can spontaneously fire in a repeating trimodal pattern that consists of tonic spiking, bursting and quiescence. Climbing fiber input (CF) switches Purkinje neurons out of the trimodal firing pattern and toggles them between a tonic firing and a quiescent state, while setting the gain of their response to Parallel Fiber (PF) input. The basis to this transition is unclear. We investigate it using a biophysical Purkinje cell model under conditions of CF and PF input. The model can replicate these toggle and gain functions, dependent upon a novel account of intracellular calcium dynamics that we hypothesise to be applicable in real Purkinje cells.

An approach to investigate brain function/dysfunction is to simulate neuron circuits on a computer. A problem, however, is that detailed neuron descriptions are computationally expensive and this handicaps the pursuit of realistic network investigations, where many neurons need to be simulated. We confront this issue; we employ a novel reduction algorithm to produce a 2 compartment model of the cerebellar Purkinje neuron from a previously published, 1089 compartment model. It runs more than 400 times faster and retains the electrical behavior of the full model. So, it is more suitable for inclusion in large network models, where computational power is a limiting issue. We show the utility of this reduced model by demonstrating that it can replicate the full model’s response to alcohol, which can in turn reproduce experimental recordings from Purkinje neurons following alcohol application. We show that alcohol may modulate Purkinje neuron firing by an inhibition of their sodium-potassium pumps. We suggest that this action, upon cerebellar Purkinje neurons, is how alcohol ingestion can corrupt motor co-ordination. In this way, we relate events on the molecular scale to the level of behavior.

Hodgkin and Huxley (H-H) fitted their model of voltage-dependent conductances to experimental data using empirical functions of voltage. The thermodynamic H-H model of voltage dependent conductances is more physically plausible, as it constrains and parameterises its empirical fit by assuming that ion channel transition rates depend exponentially on a free energy barrier that in turn, linearly or non-linearly, depends on voltage. The original H-H model contains no explicit temperature terms and requires Q₁₀ factors to describe data at different temperatures. The thermodynamic H-H model does have explicit terms for temperature. Do these endow the model with extrapolation for temperature? We utilised voltage clamp data for a voltage-gated K⁺ current, recorded at three different temperatures. The thermodynamic H-H model’s free parameters were fitted (Marquardt-Levenberg algorithm) to a data set recorded at one (or more) temperature(s). Then we assessed whether it could describe another data set, recorded at a different temperature, with these same free parameter values and its temperature terms set to the new temperature. We found that it could not.