Competitive Tuning Among Ca²⁺/Calmodulin-Dependent Proteins: Analysis of in silico Model Robustness and Parameter...

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.Tamara Kinzer-Ursem is an Assistant Professor in the Weldon School of Biomedical Engineering. She received her B.S. in Bioengineering from the University of Toledo and her M.S. and Ph.D. degrees in Chemical Engineering from the University of Michigan, and her post-doctoral training in Molecular Neuroscience at the California Institute of Technology. Prior to joining Purdue she was the Head of R&D in Biochemistry at Maven Biotechnologies and Visiting Associate in Chemical Engineering at the California Institute of Technology.Research in the Kinzer-Ursem lab focuses on developing tools to advance quantitative descriptions of cellular processes and disease within three areas of expertise: 1) Using particle diffusivity measurements to quantify biomolecular processes. Particle diffusometry is being used as a sensitive biosensor to detect the presence of pathogens in environmental and patient samples. 2) Development of novel protein tagging technologies that are used to label proteins in vivo to enable quantitative description of protein function and elucidate disease mechanisms. 3) Computational modeling of signal transduction mechanisms to understand cellular processes. Using computational techniques, we have recently described "competitive tuning" as a mechanism that might be used to regulate information transfer through protein networks, with implications in cell behavior and drug target analysis.