CellMLPhysiome: F - J

A Biophysically-Based Mathematical Representation of Interstitial Cells of Cajal Pacemaker Potentials produced from a Unitary Potential Basis

A simple model of pacemaking using ion transport at the neuronal membrane that would help to analyse the implied energy usage is presented. The model has been used to study the association between repetitive firing pattern of Substantia nigra neurons and cytosolic calcium. With the help of detailed mechanism to describe the functioning of pumps and exchangers at the membrane, this model is capable of describing energy expenditure of these neurons due to the activity at its membrane. The model can also be used to simulate the response of these neurons to channel blockers such as TTX and dihydropyridines.

The original reference is cited below:

Francis F, Garcia MR, Middleton RH (2012) Energetics of ion transport in dopaminergic substantia nigra neurons. In: Wellstead P, Cloutier M, editors, Systems Biology of Parkinson's Disease, Springer New York. pp. 81-109

A model is developed to study the membrane oscillations of a dissociated substantia nigra neuron, by describing its geometry based on a hyperbolic tetrahedron. The model demonstrates the dependance of these neurons on the L-type calcium channel for its autonomous pacemaking activity. Existence of stable limit cycles for important state variables establishes the robustness of the system.

Cytosolic calcium plays a crucial role as a second messenger in cellular signalling. Various cell types, including hepatocytes, display Ca2+ oscillations when stimulated by an extracellular signal. However, the biological relevance of this temporal organization remains unclear. In this paper, we investigate theoretically the e!ect of Ca2+ oscillations on a particular example of cell regulation: the phosphorylation/dephosphorylation cycle controlling the activation of glycogen phosphorylase in hepatocytes. By modelling periodic sinusoidal variations in the intracellular Ca2+ concentration, we show that Ca2+ oscillations reduce the threshold for the activation of the enzyme. Furthermore, as the activation of a given enzyme depends on the kinetics of its phosphorylation/dephosphorylation cycle, speciality can be encoded by the oscillation frequency. Finally, using a model for signal-induced Ca2+ oscillations based on Ca2+-induced Ca2+ release, we show that realistic Ca2+ oscillations can potentiate the response to a hormonal stimulation. These results indicate that Ca2+ oscillations in hepatocytes could contribute to increase the efficiency and speciality of cellular signalling, as shown experimentally for gene expression in lymphocytes (Dolmetsch et al., 1998).

Circadian rhythms, which occur spontaneously with a period of about 24 h in a variety of organisms, allow their adaptation to the periodic variations of the environment. These rhythms are generated by a genetic regulatory network involving a negative feedback loop on transcription. Mathematical models based on the negative autoregulation of gene expression by the protein product of a clock gene account for the occurrence of self-sustained circadian oscillations. These models differ by their degree of complexity and, hence, by the number of variables considered. Some of these models can be considered as minimal because they contain a reduced number of biochemical processes and variables capable of producing sustained oscillations. In three of these minimal models, the period of the oscillations significantly changes with the rate of degradation of the clock protein. However, depending on the model considered, the period increases, decreases or passes through a maximum as a function of the protein degradation rate. We clarify the bases for these markedly different results by bringing to light the roles of (i) protein phosphorylation, which is required for protein degradation, and (ii) the velocity and degree of saturation of mRNA and protein degradation. Changes in the parameter values of the more complex of the minimal models can produce the period profiles observed in the other two models. The analysis allows us to reconcile the contradictory predictions for the dependence of the period on the clock protein degradation rate in three minimal models used to describe circadian rhythms.

We consider a minimal cascade model previously proposed for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a bicyclic phosphorylation-dephosphorylation cascade involving cyclin and cdc2 kinase. By constructing stability diagrams showing domains of periodic behavior as a function of the maximum rates of the kinases and phosphatases involved in the two cycles of the cascade, we investigate the role of these converter enzymes in the oscillatory mechanism. Oscillations occur when the balance of kinase and phosphatase rates in each cycle is in a range bounded by two critical values. The results suggest ways to arrest the mitotic oscillator by altering the maximum rates of the converter enzymes. These results bear on the control of cell proliferation.