A Dynamic Model of Interactions of Ca2+, Calmodulin, and Catalytic Subunits of Ca2+/Calmodulin-Dependent Protein Kinase II

Abstract

During the acquisition of memories, influx of Ca2+ into the postsynaptic spine through the pores of activated N-methyl-d-aspartate-type glutamate receptors triggers processes that change the strength of excitatory synapses. The pattern of Ca2+ influx during the first few seconds of activity is interpreted within the Ca2+-dependent signaling network such that synaptic strength is eventually either potentiated or depressed. Many of the critical signaling enzymes that control synaptic plasticity, including Ca2+/calmodulin-dependent protein kinase II (CaMKII), are regulated by calmodulin, a small protein that can bind up to 4 Ca2+ ions. As a first step toward clarifying how the Ca2+-signaling network decides between potentiation or depression, we have created a kinetic model of the interactions of Ca2+, calmodulin, and CaMKII that represents our best understanding of the dynamics of these interactions under conditions that resemble those in a postsynaptic spine. We constrained parameters of the model from data in the literature, or from our own measurements, and then predicted time courses of activation and autophosphorylation of CaMKII under a variety of conditions. Simulations showed that species of calmodulin with fewer than four bound Ca2+ play a significant role in activation of CaMKII in the physiological regime, supporting the notion that processing of Ca2+ signals in a spine involves competition among target enzymes for binding to unsaturated species of CaM in an environment in which the concentration of Ca2+ is fluctuating rapidly. Indeed, we showed that dependence of activation on the frequency of Ca2+ transients arises from the kinetics of interaction of fluctuating Ca2+ with calmodulin/CaMKII complexes. We used parameter sensitivity analysis to identify which parameters will be most beneficial to measure more carefully to improve the accuracy of predictions. This model provides a quantitative base from which to build more complex dynamic models of postsynaptic signal transduction during learning.

Mechanisms of CaMKII action in long-term potentiation

“…The ability to optically measure LTP-induced calcium elevation and CaMKII activation in single spines raises the prospect of understanding the initial processes of LTP at a quantitative level. Models of increasing sophistication 121, 122 have been developed for how CaMKII is activated by calcium and calmodulin in vitro. Using these models to understand how CaMKII is activated in the living cell requires knowledge of the state of calmodulin, about which less is known.…”

Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics

“…We applied GCCD to this system as modeled by [1] and as simulated by the Plenum implementation of dynamical grammars [2, 4] and also in a much larger spatial simulation using MCell [3]. …”

“…The pathway as studied and modeled in [1] is structurally a bit involved. It begins with an externally imposed influx of calcium ion Ca 2+ .…”

“…Dimers may phosphorylate one of their constituent subunits and promptly dissociate; autophosphorylated monomer CaMKII is taken to be the pathway output. Our goal is to produce a reduced stochastic model simplifying the structure of this fine-scale model as formulated in the MCell and Plenum models (model files in supplementary information) that aim to implement stochastic versions of the reaction network of [1]. …”

A Novel Explanation for Observed CaMKII Dynamics in Dendritic Spines with Added EGTA or BAPTA

“…(For a summary of some of the work conducted between 1998 and 2004, see Sundstrom (9).) Theoretical work on CaMKII models has, among other things, explored the possibility of bistable (10) and tristable (11) biochemical switches formed from the pairing of CaMKII to a suitable phosphatase, as well as the effect of manipulating the frequency of calcium stimulation (12,13). Other work (6)(7)(8) has focused on measuring the kinetic constants of some of the reactions involved in activating CaMKII in vitro, or finding a simplified way to model autophosphorylation (14).…”