The fundamental process underlying all brain function is the ability of the neurons to adapt to external inputs in the context of the neuronal state. The adaptive processes span multiple spatial and temporal scales ranging from millisecond dynamics of the ion channels, seconds to minutes time scale of the signaling pathways, and tens of minutes to hours time scale of the gene regulation and its feedback onto the signaling pathways and electrophysiology. Mathematical modeling and analysis provides appropriate tools to decipher how the signals are integrated in this complex multi-scale system. The present study focuses on integrating two levels of the neuronal adaptation: signaling dynamics elicited by neuropeptide receptors and the consequences on the electrophysiology. The particular system considered is the angiotensin II receptor signaling and electrical activity in the cardiorespiratory neurons in the Nucleus Tractus Solitarius (NTS) in the brainstem. The octapeptide angiotensin II (AngII) is a multifunctional hormone and is involved in stimulation of water and sodium uptake, vasopressin secretion, increased blood pressure and modulation of baroreflexes. Most of the effects are mediated by the activation of the receptor type I (AT1R) in the NTS neurons. Stimulation of the NTS neurons by AngII has been shown to result in a transient increase in the electrical activity leading to neuronal adaptation. Pharmacological studies have implicated the signaling kinases, PKC and CaMKII, in modulation of the different ion channels.

To understand the dynamics of the AT1R mediated neuromodulation and the relative contribution of different kinases, we have developed an integrated model of AngII induced neuronal firing behavior. This multi-scale model integrates a Hodgkin-Huxley like model of the electrophysiology describing the millisecond dynamics of the ion channels and a detailed kinetic reaction model of the AT1R mediated intracellular signaling pathway. The membrane electrical model includes descriptions of different ion channels in the NTS neurons: sodium, delayed rectifier potassium, calcium activated potassium, high threshold L-type calcium, and leak channel. The signaling model was adapted from Mishra and Bhalla (Biophys J, 2002) by adding kinetic descriptions of receptor desensitization and the sodium-calcium exchanger. The modified model includes the dynamics of PLC, PKC, CaMKII, DAG, IP3 and intracellular calcium. The key aspect of integrating the signaling and electrical models is the change in the conductance of different ion channels upon phosphorylation by the kinases PKC and CamKII. The exact kinetics of this phosphorylation is not clear and hence different formulations of kinetic behavior were explored in the simulations. Analysis of the model dynamics revealed distinct regulatory properties corresponding to different ion channels and a novel role for the delayed rectifier potassium channel as a dual regulator. In addition, the simulations indicate that the non-voltage-activated transport dynamics lead to transient inhibition in response to AT1R stimulation. However, phosphorylation of the delayed rectifier potassium channel by PKC counteracts this transient inhibition to result in a net increase in the electrical activity, in concordance with the electrophysiological experimental observations.

The current model forms the basis for developing a multi-scale neuronal adaptation model that integrates electrophysiology, signaling and gene regulation.