Modeling recovery of rhythmic activity: Hypothesis for the role of a calcium pump
Introduction
Networks that produce rhythmic patterns of activity are commonly involved in behaviors serving basic biological functions (e.g. breathing, mastication, etc.). The existence of mechanisms of recovery of function may therefore be essential for survival. One example of such a system is the pyloric network of crustaceans. The pyloric network generates a rhythmic activity pattern that normally depends obligatorily on the actions of neuromodulatory substances released by axon terminals from adjacent ganglia onto the neurons of the network: after action potential transmission along these axons is blocked or destroyed (decentralization), rhythmic activity ceases [11]. However, activity recovers spontaneously within several hours [3], [4], [9], [13] following a very complex temporal dynamical process that involves the alternating turning on and off of the rhythm (‘bouting’) [9]. This bouting activity can last several hours, after which a stable pyloric rhythm emerges that is characterized by a lower frequency than control but otherwise similar properties (Fig. 1, [3], [4], [9]). Experimental evidence indicates that STG neurons [3], [4], [14], crayfish leg axons [6] and other neuronal types [15] possess feedback mechanisms that sense neuronal activity and can regulate specific ionic currents and pumps. Intracellular Ca2+, [Ca]in, is a likely second messenger that can act as a feedback element for conductance regulation because [Ca]in changes appear correlated with neuronal activity changes [15] and are involved in many intracellular signaling pathways. The recovery process of rhythmic pyloric activity has previously been accounted for theoretically in a simplified pyloric network model in terms of activity-dependent regulation of ionic currents [3], [4]. However, the transition between the quiescent and the stable recovery states in this model was monotonic and it failed to explain the complex bouting dynamics that precedes full recovery.
Here we reevaluate the mechanism of long-term activity-dependent regulation of conductances by introducing an intracellular molecular network of [Ca]in regulation that involves pumping of Ca2+ into intracellular Ca2+ stores (e.g. endoplasmic reticulum, ER) and inositol 1,4,5-trisphosphate (IP3) receptor-dependent (IP3RCa) Ca2+ release from the ER. Our model suggests that slow activity-dependent regulation of an intracellular Ca2+ pump is key to generating the complex temporal dynamics of recovery observed during the bouting period.
Section snippets
Methods
For simplicity we build a single isolated neuron using XPP [1], based on experiments showing that rhythmic activity recovery takes place in isolated neurons of the STG [9]. The model neuron consists of two compartments with a soma/neurite (S/N) compartment generating slow-wave oscillations and an axonal compartment generating Hodgkin & Huxley (H&H)-type action potentials (e.g. Fig. 2C). Ionic currents are modeled closely following those described by [3], [4], with only two modifications: V1/2
Results
The single-cell model, with all ionic currents activated, including the neuromodulator-activated current IP, generates stable bursting activity (Fig. 2B, bottom left and 2C, top trace).
There are several signature features of the process of pyloric activity recovery after decentralization [9]: (1) The time required to produce the first bout after decentralization on average takes >3 h; (2) The average period of bouting activity before stable recovery takes >52 h, (3) The average bout duration is
Discussion
We have developed a model to explain the complex temporal dynamics of the pyloric network activity following the removal of central input to the STG. We assume that STG neurons recover rhythmic activity as they sense changes in their activity [3], [4], [14], [15]. [Ca]in changes regulate three Ca2+ sensors acting as activity transducers (representing Ca-dependent metabolic pathways) to regulate the maximal conductances of Ca2+ and K+ currents, and the intracellular Ca2+ pump activity. Parameter
Yili Zhang is a graduate student in Biological Sciences (Computational Biology) Department at Rutgers University. She obtained a Master of Science in Pathology from National University of Singapore in 2000 and a Master of Science in Computer Science from Virginia Polytechnic Institute in 2002.
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Yili Zhang is a graduate student in Biological Sciences (Computational Biology) Department at Rutgers University. She obtained a Master of Science in Pathology from National University of Singapore in 2000 and a Master of Science in Computer Science from Virginia Polytechnic Institute in 2002.
Jorge Golowasch received his PhD in Biophysics from Brandeis University. He is currently an associate professor in Mathematical Sciences at New Jersey Institute of Technology and Biological Sciences at Rutgers University.