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.

中文翻译：

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Ca2+/钙调蛋白依赖蛋白之间的竞争性调整：计算机模型稳健性和参数变异性分析。

介绍

长期以来，蛋白质信号传导的钙/钙调蛋白依赖性（Ca ^{2+ /CaM 依赖性）调节因其在许多生理环境中的重要性而得到认可。}在几乎所有真核细胞中发现，Ca ²⁺ /CaM 依赖性信号传导参与肌肉发育、免疫反应、心肌细胞功能和神经元连接的调节。^{在兴奋性神经元中，当钙离子 (Ca 2+} ) 流过 NMDA 受体并结合 Ca ²⁺传感器钙调蛋白 (CaM)时，会发生突触连接强度的动态变化，称为突触可塑性。钙²⁺/CaM 反过来调节肌动蛋白聚合、受体运输和转录因子激活中的下游蛋白质信号传导。下游 Ca ²⁺ /CaM 依赖性结合蛋白 (CBP) 的激活是 Ca ²⁺通量频率的函数，因此每个 CBP 优先“调谐”到不同的 Ca ²⁺输入信号。我们最近报道了 CBPs 之间对 CaM 结合的竞争足以在计算机上重建观察到的体内几个 CBP 的频率依赖性。然而，CBP 的激活可能在很大程度上取决于构成竞争池的蛋白质的特性和浓度。对正常和疾病状态下 CBP 的调节具有重要意义。

方法

在这里，我们扩展了我们之前的 CBP 之间竞争的确定性模型，包括磷酸二酯酶、在突触可塑性中很重要的 AMPAR 受体和 CBP 的酶功能：cAMP 调节、激酶活性和磷酸酶活性。在使用拉丁超立方抽样 (LHS) 和偏秩相关系数 (PRCC) 通过全局敏感性分析进行严格参数化和验证后，我们探讨了扰乱 CBP 竞争池如何影响下游信号事件。特别是，我们假设虽然扰动可能会减少一个 CBP 的激活，但增加一个单独的但与酶相关的 CBP 的激活可以补偿这种损失，提供稳态效应。

结果和结论

首先，我们比较两个模型的动态模型输出：Ca 2+ /CaM 结合的二态模型和 Ca ^{2+ /} CaM 结合的四态模型。我们发现 Ca ^{2+ /CaM 结合的四态模型最好地捕捉到 CaM 和 CBPs 对系统中 Ca 2+}通量的快速响应的动态特性。使用全局敏感性分析，我们发现模型输出对参数可变性具有鲁棒性。事实上，尽管 CaM 缓冲神经颗粒蛋白 (Ng) 表达的变化可能导致 Ca ²⁺/CaM 依赖性激酶 II (CaMKII) 激活，AMPA 受体整体磷酸化被保留；表面上是通过腺苷酸环化酶 8 (AC8) 介导的蛋白激酶 A (PKA) 活化的伴随增加。事实上，CaMKII 和 PKA 对 AMPAR 受体的磷酸化在很宽的 Ng 浓度范围内都是稳健的，尽管在接近零的低 Ng 水平下观察到 AMPAR 磷酸化的增加。我们的结果可以解释最近在神经颗粒蛋白敲除小鼠中的反直觉结果，并进一步证明竞争性调节是突触可塑性的重要机制。这些结果可以很容易地转化为其他 Ca ²⁺/CaM 依赖的信号系统在其他细胞类型中，可用于建议有针对性的实验研究，以解释反直觉或意外的下游信号结果。