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Competitive Tuning Among Ca2+/Calmodulin-Dependent Proteins: Analysis of In Silico Model Robustness and Parameter Variability

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Abstract

Introduction

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.

Methods

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.

Results and Conclusions

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.

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Abbreviations

AC1:

Adenylyl cyclase 1

AC8nt, AC8ct:

Adenylyl cyclase 8N/C-terminus

AMPAR:

α-Amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor

Ca2+ :

Calcium ion

CaM:

Calmodulin

CBP:

Calmodulin binding protein

CaMKII:

Calcium/calmodulin-dependent protein kinase II

CaN:

Calcineurin

Inh-1:

Inhibitor 1

LTP:

Long-term potentiation

MLCK:

Myosin light chain kinase

NOS:

Nitric oxide synthetase

Ng:

Neurogranin

NMDAR:

N-methyl-d-aspartic acid receptor

PDE1, PDE4:

Phosphodiesterase 1/4

PKA:

Protein kinase A

PP1:

Protein phosphatase 1

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Acknowledgments

The authors thank members of the Kinzer-Ursem Lab for helpful discussion and comment on the manuscript. We gratefully acknowledge support from the National Institute of Neurological Disorders And Stroke (NINDS) of The National Institutes of Health (NIH) under Award Number R21NS095218. The content is solely the responsibility of the authors and does not necessarily represent the official view of the NIH. Also, this material is based on upon work supported by the National Science Foundation CAREER Award Grant No. 1752366. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Conflict of interest

Authors Matthew Pharris, Neal Patel, and Tamara Kinzer-Ursem declare that they have no conflicts of interest.

Ethical Standards

No animal studies were carried out by the authors for this article. Additionally, no human subjects research was conducted in this study.

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Authors and Affiliations

  1. Weldon School of Biomedical Engineering, Purdue University, 260 South Martin Jischke Drive, West Lafayette, IN, 47907, USA

    Matthew C. Pharris, Neal M. Patel & Tamara L. Kinzer-Ursem

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  1. Matthew C. Pharris
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  2. Neal M. Patel
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Correspondence to Tamara L. Kinzer-Ursem.

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Tamara L. 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, 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) 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; (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; and (3) 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.

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Pharris, M.C., Patel, N.M. & Kinzer-Ursem, T.L. Competitive Tuning Among Ca2+/Calmodulin-Dependent Proteins: Analysis of In Silico Model Robustness and Parameter Variability. Cel. Mol. Bioeng. 11, 353–365 (2018). https://doi.org/10.1007/s12195-018-0549-4

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