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

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.Author Summary: Networks of neurons in the brain are connected together by specialized signaling devices called synapses. One way an active neuron relays its activity to other neurons is by releasing small amounts of chemical transmitters from its presynaptic terminals which induce electrical activity in postsynaptic neurons connected to it. Memories are formed when synapses in the network encoding the memory change their strength in order to stabilize the network. The decision whether or not a synapse becomes potentiated is controlled by delicate variations in the amount of Ca2+ ions that flow across the membrane at the postsynaptic site, and by the pattern of influx over time. The mechanisms of activation of regulatory enzymes that decode this Ca2+ signal have been extensively studied under laboratory conditions which are different from the conditions encountered inside a neuron. Therefore, we created a dynamic model of activation of one enzyme that is critical for learning by Ca2+. The model allows us to simulate activation of the enzyme within a biochemical milieu similar to what it will encounter at the postsynaptic site. It predicts unexpected behaviors of the enzyme in vivo and provides a framework for quantitative exploration of complex mechanisms of synaptic plasticity.