Competitive Tuning Among Ca 2+ /Calmodulin-Dependent Proteins: Analysis of In Silico Model Robustness and Parameter Variability

Calcium/calmodulin-dependent (Ca2+/CaM-dependent) regulation of protein signaling has long been recognized for its importance in a number of physiological contexts. Found in almost all eukaryotic cells, Ca2+/CaM-dependent signaling participates in muscle development, immune responses, cardiac myocyte function and regulation of neuronal connectivity. In excitatory neurons, dynamic changes in the strength of synaptic connections, known as synaptic plasticity, occur when calcium ions (Ca2+) flux through NMDA receptors and bind the Ca2+-sensor calmodulin (CaM). Ca2+/CaM, in turn, regulates downstream protein signaling in actin polymerization, receptor trafficking, and transcription factor activation. The activation of downstream Ca2+/CaM-dependent binding proteins (CBPs) is a function of the frequency of Ca2+ flux, such that each CBP is preferentially “tuned” to different Ca2+ input signals. We have recently reported that competition among CBPs for CaM binding is alone sufficient to recreate in silico the observed in vivo frequency-dependence of several CBPs. However, CBP activation may strongly depend on the identity and concentration of proteins that constitute the competitive pool; with important implications in the regulation of CBPs in both normal and disease states. Here, we extend our previous deterministic model of competition among CBPs to include phosphodiesterases, AMPAR receptors that are important in synaptic plasticity, and enzymatic function of CBPs: cAMP regulation, kinase activity, and phosphatase activity. After rigorous parameterization and validation by global sensitivity analysis using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC), we explore how perturbing the competitive pool of CBPs influences downstream signaling events. In particular, we hypothesize that although perturbations may decrease activation of one CBP, increased activation of a separate, but enzymatically-related CBP could compensate for this loss, providing a homeostatic effect. First we compare dynamic model output of two models: a two-state model of Ca2+/CaM binding and a four-state model of Ca2+/CaM binding. We find that a four-state model of Ca2+/CaM binding best captures the dynamic nature of the rapid response of CaM and CBPs to Ca2+ flux in the system. Using global sensitivity analysis, we find that model output is robust to parameter variability. Indeed, although variations in the expression of the CaM buffer neurogranin (Ng) may cause a decrease in Ca2+/CaM-dependent kinase II (CaMKII) activation, overall AMPA receptor phosphorylation is preserved; ostensibly by a concomitant increase in adenylyl cyclase 8 (AC8)-mediated activation of protein kinase A (PKA). Indeed phosphorylation of AMPAR receptors by CaMKII and PKA is robust across a wide range of Ng concentrations, though increases in AMPAR phosphorylation is seen at low Ng levels approaching zero. Our results may explain recent counter-intuitive results in neurogranin knockout mice and provide further evidence that competitive tuning is an important mechanism in synaptic plasticity. These results may be readily translated to other Ca2+/CaM-dependent signaling systems in other cell types and can be used to suggest targeted experimental investigation to explain counter-intuitive or unexpected downstream signaling outcomes.