Decoding time-varying calcium signals by the postsynaptic biochemical network: Computer simulations of molecular kinetics

Computer simulations and mathematical analyses were applied to a study of the molecular signaling mechanisms that underlie post-synaptic responses to synaptic activation. In this report three models are described: a new detailed kinetic model examining possible relationships between spike frequency modulation and calmodulin-dependent kinase II (CaMKII) activity; a second post-synaptic biochemical network model involving CaMKII, calmodulin, calcineurin, adenylate cyclase, phosphodiesterase, cAMP-dependent protein kinase, protein phosphatase 1, inhibitor 1, Ras protein, synaptic Ras-GTPase activating protein (p135 Syn-GAP), mitogen-activated protein kinase and other regulatory factors; and a biophysical model which combines the post-synaptic biochemical network with known ionic mechanisms in dendritic spines. The kinetic model of CaMKII was first shown to replicate experimental evidence by Koninck and Schulman (Science 279 (1998) 227-230.) that CaMKII can decode the frequency of post-synaptic Ca²⁺ spikes induced by pre-synaptic activity into distinct amounts of kinase activity. The model was then used to suggest that the functional role of CaMKII may extend beyond simple frequency decoding to allow differential responses to different temporal patterns of pre-synaptic activation. Perturbation analyses of model suggests how CaMKII activity reflects time-varying Ca²⁺ signals and also suggests that the behavior of this entire biophysical pathway depends on the total amount of CaMKII and other postsynaptic proteins. Our mathematical model provides a tool to quantitatively estimate the role of protein synthesis at the spine head in modulating synaptic function.