Competitive tuning: Competition's role in setting the frequency-dependence of Ca2+-dependent proteins

Mechanistic Computational Modeling of Implantable, Bioresorbable Drug Release Systems

Implantable, bioresorbable drug delivery systems offer an alternative to current drug administration techniques; allowing for patient-tailored drug dosage, while also increasing patient compliance. Mechanistic mathematical modeling allows for the acceleration of the design of the release systems, and for prediction of physical anomalies that are not intuitive and may otherwise elude discovery. This study investigates short-term drug release as a function of water-mediated polymer phase inversion into a solid depot within hours to days, as well as long-term hydrolysis-mediated degradation and erosion of the implant over the next few weeks. Finite difference methods are used to model spatial and temporal changes in polymer phase inversion, solidification, and hydrolysis. Modeling reveals the impact of non-uniform drug distribution, production and transport of H+ ions, and localized polymer degradation on the diffusion of water, drug, and hydrolyzed polymer byproducts. Compared to experimental data, the computational model accurately predicts the drug release during the solidification of implants over days and drug release profiles over weeks from microspheres and implants. This work offers new insight into the impact of various parameters on drug release profiles, and is a new tool to accelerate the design process for release systems to meet a patient specific clinical need.

Physiology of intracellular calcium buffering

Calcium signaling underlies much of physiology. Almost all the Ca2+ in the cytoplasm is bound to buffers, with typically only ∼1% being freely ionized at resting levels in most cells. Physiological Ca2+ buffers include small molecules and proteins, and experimentally Ca2+ indicators will also buffer calcium. The chemistry of interactions between Ca2+ and buffers determines the extent and speed of Ca2+ binding. The physiological effects of Ca2+ buffers are determined by the kinetics with which they bind Ca2+ and their mobility within the cell. The degree of buffering depends on factors such as the affinity for Ca2+, the Ca2+ concentration, and whether Ca2+ ions bind cooperatively. Buffering affects both the amplitude and time course of cytoplasmic Ca2+ signals as well as changes of Ca2+ concentration in organelles. It can also facilitate Ca2+ diffusion inside the cell. Ca2+ buffering affects synaptic transmission, muscle contraction, Ca2+ transport across epithelia, and the killing of bacteria. Saturation of buffers leads to synaptic facilitation and tetanic contraction in skeletal muscle and may play a role in inotropy in the heart. This review focuses on the link between buffer chemistry and function and how Ca2+ buffering affects normal physiology and the consequences of changes in disease. As well as summarizing what is known, we point out the many areas where further work is required.

An Integrative Biology Approach to Quantify the Biodistribution of Azidohomoalanine In Vivo

Background

Identification and quantitation of newly synthesized proteins (NSPs) are critical to understanding protein dynamics in development and disease. Probing the nascent proteome can be achieved using non-canonical amino acids (ncAAs) to selectively label the NSPs utilizing endogenous translation machinery, which can then be quantitated with mass spectrometry. We have previously demonstrated that labeling the in vivo murine proteome is feasible via injection of azidohomoalanine (Aha), an ncAA and methionine (Met) analog, without the need for Met depletion. Aha labeling can address biological questions wherein temporal protein dynamics are significant. However, accessing this temporal resolution requires a more complete understanding of Aha distribution kinetics in tissues.

Results

To address these gaps, we created a deterministic, compartmental model of the kinetic transport and incorporation of Aha in mice. Model results demonstrate the ability to predict Aha distribution and protein labeling in a variety of tissues and dosing paradigms. To establish the suitability of the method for in vivo studies, we investigated the impact of Aha administration on normal physiology by analyzing plasma and liver metabolomes following various Aha dosing regimens. We show that Aha administration induces minimal metabolic alterations in mice.

Conclusions

Our results demonstrate that we can reproducibly predict protein labeling and that the administration of this analog does not significantly alter in vivo physiology over the course of our experimental study. We expect this model to be a useful tool to guide future experiments utilizing this technique to study proteomic responses to stimuli.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-023-00760-4.

Investigation the global effect of rare earth gadolinium on the budding Saccharomyces cerevisiae by genome-scale screening

Introduction

The rare earth gadolinium (Gd) is widely used in industry and medicine, which has been treated as an emerging pollutant in environment. The increasing pollution of Gd has potential hazards to living organisms. Thus it is essential to investigate the toxicity and action mechanism of Gd in biological system.

Methods

In this study, the global effect and activation mechanism of Gd on yeast were investigated by genome-scale screening.

Results and discussion

Our results show that 45 gene deletion strains are sensitive to Gd and 10 gene deletion strains are Gd resistant from the diploid gene deletion strain library of Saccharomyces cerevisiae. The result of localization analysis shows that most of these genes are involved in cell metabolism, cell cycle, transcription, translation, protein synthesis, protein folding, and cell transport. The result of functional analysis shows that four genes (CNB1, CRZ1, VCX1, and GDT1) are involved in the calcium signaling pathway, and four genes (PHO84, PHO86, PHO2, and PHO4) are involved in phosphorus metabolism. For Gd3+ has the similar ion radius with Ca2+ and easily binds to the phosphate radical, it affects Ca2+ signaling pathway and phosphorus metabolism. The genes ARF1, ARL1, ARL3, SYS1, COG5, COG6, YPT6, VPS9, SSO2, MRL1, AKL1, and TRS85 participate in vesicle transport and protein sorting. Thus, Gd accumulation affects the function of proteins related to vesicle transport, which may result in the failure of Gd transport out of cells. In addition, the intracellular Gd content in the 45 sensitive deletion strains is higher than that in the wild type yeast under Gd stress. It suggests that the sensitivity of yeast deletion strains is related to the excessive intracellular Gd accumulation.

A Modeling and Analysis Study Reveals That CaMKII in Synaptic Plasticity Is a Dominant Affecter in CaM Systems in a T286 Phosphorylation-Dependent Manner

NMDAR-dependent synaptic plasticity in the hippocampus consists of two opposing forces: long-term potentiation (LTP), which strengthens synapses and long-term depression (LTD), which weakens synapses. LTP and LTD are associated with memory formation and loss, respectively. Synaptic plasticity is controlled at a molecular level by Ca2+-mediated protein signaling. Here, Ca2+ binds the protein, calmodulin (CaM), which modulates synaptic plasticity in both directions. This is because Ca2+-bound CaM activates both LTD-and LTP-inducing proteins. Understanding how CaM responds to Ca2+ signaling and how this translates into synaptic plasticity is therefore important to understanding synaptic plasticity induction. In this paper, CaM activation by Ca2+ and calmodulin binding to downstream proteins was mathematically modeled using differential equations. Simulations were monitored with and without theoretical knockouts and, global sensitivity analyses were performed to determine how Ca2+/CaM signaling occurred at various Ca2+ signals when CaM levels were limiting. At elevated stimulations, the total CaM pool rapidly bound to its protein binding targets which regulate both LTP and LTD. This was followed by CaM becoming redistributed from low-affinity to high-affinity binding targets. Specifically, CaM was redistributed away from LTD-inducing proteins to bind the high-affinity LTP-inducing protein, calmodulin-dependent kinase II (CaMKII). In this way, CaMKII acted as a dominant affecter and repressed activation of opposing CaM-binding protein targets. The model thereby showed a novel form of CaM signaling by which the two opposing pathways crosstalk indirectly. The model also found that CaMKII can repress cAMP production by repressing CaM-regulated proteins, which catalyze cAMP production. The model also found that at low Ca2+ stimulation levels, typical of LTD induction, CaM signaling was unstable and is therefore unlikely to alone be enough to induce synaptic depression. Overall, this paper demonstrates how limiting levels of CaM may be a fundamental aspect of Ca2+ regulated signaling which allows crosstalk among proteins without requiring directly interaction.

Conformational spread drives the evolution of the calcium-calmodulin protein kinase II

The calcium calmodulin (Ca²⁺/CaM) dependent protein kinase II (CaMKII) decodes Ca²⁺ frequency oscillations. The CaMKIIα isoform is predominantly expressed in the brain and has a central role in learning. I matched residue and organismal evolution with collective motions deduced from the atomic structure of the human CaMKIIα holoenzyme to learn how its ring architecture abets function. Protein dynamic simulations showed its peripheral kinase domains (KDs) are conformationally coupled via lateral spread along the central hub. The underlying β-sheet motions in the hub or association domain (AD) were deconvolved into dynamic couplings based on mutual information. They mapped onto a coevolved residue network to partition the AD into two distinct sectors. A second, energetically stressed sector was added to ancient bacterial enzyme dimers for assembly of the ringed hub. The continued evolution of the holoenzyme after AD–KD fusion targeted the sector’s ring contacts coupled to the KD. Among isoforms, the α isoform emerged last and, it alone, mutated rapidly after the poikilotherm–homeotherm jump to match the evolution of memory. The correlation between dynamics and evolution of the CaMKII AD argues single residue substitutions fine-tune hub conformational spread. The fine-tuning could increase CaMKIIα Ca²⁺ frequency response range for complex learning functions.

Calcineurin in the heart: New horizons for an old friend

Calcineurin, also known as PP2B or PPP3, is a member of the PPP family of protein phosphatases that also includes PP1 and PP2A. Together these three phosphatases carryout the majority of dephosphorylation events in the heart. Calcineurin is distinct in that it is activated by the binding of calcium/calmodulin (Ca2+/CaM) and therefore acts as a node for integrating Ca2+ signals with changes in phosphorylation, two fundamental intracellular signaling cascades. In the heart, calcineurin is primarily thought of in the context of pathological cardiac remodeling, acting through the Nuclear Factor of Activated T-cell (NFAT) family of transcription factors. However, calcineurin activity is also essential for normal heart development and homeostasis in the adult heart. Furthermore, it is clear that NFAT-driven changes in transcription are not the only relevant processes initiated by calcineurin in the setting of pathological remodeling. There is a growing appreciation for the diversity of calcineurin substrates that can impact cardiac function as well as the diversity of mechanisms for targeting calcineurin to specific sub-cellular domains in cardiomyocytes and other cardiac cell types. Here, we will review the basics of calcineurin structure, regulation, and function in the context of cardiac biology. Particular attention will be given to: the development of improved tools to identify and validate new calcineurin substrates; recent studies identifying new calcineurin isoforms with unique properties and targeting mechanisms; and the role of calcineurin in cardiac development and regeneration.

Mathematical Model Predicts Effective Strategies to Inhibit VEGF-eNOS Signaling

The endothelial nitric oxide synthase (eNOS) signaling pathway in endothelial cells has multiple physiological significances. It produces nitric oxide (NO), an important vasodilator, and enables a long-term proliferative response, contributing to angiogenesis. This signaling pathway is mediated by vascular endothelial growth factor (VEGF), a pro-angiogenic species that is often targeted to inhibit tumor angiogenesis. However, inhibiting VEGF-mediated eNOS signaling can lead to complications such as hypertension. Therefore, it is important to understand the dynamics of eNOS signaling in the context of angiogenesis inhibitors. Thrombospondin-1 (TSP1) is an important angiogenic inhibitor that, through interaction with its receptor CD47, has been shown to redundantly inhibit eNOS signaling. However, the exact mechanisms of TSP1's inhibitory effects on this pathway remain unclear. To address this knowledge gap, we established a molecular-detailed mechanistic model to describe VEGF-mediated eNOS signaling, and we used the model to identify the potential intracellular targets of TSP1. In addition, we applied the predictive model to investigate the effects of several approaches to selectively target eNOS signaling in cells experiencing high VEGF levels present in the tumor microenvironment. This work generates insights for pharmacologic targets and therapeutic strategies to inhibit tumor angiogenesis signaling while avoiding potential side effects in normal vasoregulation.

Design Principle for Decoding Calcium Signals to Generate Specific Gene Expression Via Transcription

The second messenger calcium plays a key role in conveying specificity of signaling pathways in plant cells. Specific calcium signatures are decoded to generate correct gene expression responses and amplification of calcium signatures is vital to this process. (1) It is not known if this amplification is an intrinsic property of all calcium-regulated gene expression responses and whether all calcium signatures have the potential to be amplified, or (2) how a given calcium signature maintains specificity in cells containing a great number of transcription factors (TFs) and other proteins with the potential to be calcium-regulated. The work presented here uncovers the design principle by which it is possible to decode calcium signals into specific changes in gene transcription in plant cells. Regarding the first question, we found that the binding mechanism between protein components possesses an intrinsic property that will nonlinearly amplify any calcium signal. This nonlinear amplification allows plant cells to effectively distinguish the kinetics of different calcium signatures to produce specific and appropriate changes in gene expression. Regarding the second question, we found that the large number of calmodulin (CaM)-binding TFs or proteins in plant cells form a buffering system such that the concentration of an active CaM-binding TF is insensitive to the concentration of any other CaM-binding protein, thus maintaining specificity. The design principle revealed by this work can be used to explain how any CaM-binding TF decodes calcium signals to generate specific gene expression responses in plant cells via transcription.

Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm

Intracellular calcium ([Ca²⁺]_i) is a basic and ubiquitous cellular signal controlling a wide variety of biological processes. A remarkable example is the steering of sea urchin spermatozoa towards the conspecific egg by a spatially and temporally orchestrated series of [Ca²⁺]_i spikes. Although this process has been an experimental paradigm for reproduction and sperm chemotaxis studies, the composition and regulation of the signalling network underlying the cytosolic calcium fluctuations are hitherto not fully understood. Here, we used a differential equations model of the signalling network to assess which set of channels can explain the characteristic envelope and temporal organisation of the [Ca²⁺]_i-spike trains. The signalling network comprises an initial membrane hyperpolarisation produced by an Upstream module triggered by the egg-released chemoattractant peptide, via receptor activation, cGMP synthesis and decay. Followed by downstream modules leading to intraflagellar pH (pH_i), voltage and [Ca²⁺]_i fluctuations. The Upstream module outputs were fitted to kinetic data on cGMP activity and early membrane potential changes measured in bulk cell populations. Two candidate modules featuring voltage-dependent Ca²⁺-channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelope and the progressive spacing of the spikes. In the first module, [Ca²⁺]_i-spike trains require the concerted action of a classical Ca_V-like channel and a potassium channel, BK (Slo1), whereas the second module relies on pH_i-dependent CatSper dynamics articulated with voltage-dependent neutral sodium-proton exchanger (NHE). We analysed the dynamics of these two modules alone and in mixed scenarios. We show that the [Ca²⁺]_i dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper and NHE module but not by those including the pH-independent Ca_V and BK module or proportionate mixed scenarios. We conclude in favour of the module containing CatSper and NHE and highlight experimentally testable predictions that would corroborate this conclusion.

Fertilisation in marine invertebrates, such as the sea urchin, occurs during broadcast spawning events in which males and females of co-localised species ejaculate sperm and spawn eggs synchronously. During these events, spermatozoa have to find and fertilise conspecific eggs in the midst of all the other ones, which is a remarkable navigation and mating choice achievement. Sperm cells do this by navigating towards the source of species-specific peptides released by the egg, steered by spatial and temporally orchestrated peaks in intracellular calcium concentration that trigger sudden reorientations. How these calcium spikes are regulated and timed remains elusive. Different calcium channels have been implicated by indirect experimental evidence giving rise to a complex network of putative interacting components. We gained insight into the structure and function of this network by modelling it as a set of candidate modules that could be studied separately. By using this ‘divide and conquer’ approach to the complexity of the network, we could characterise the potential dynamics of each module and confront these dynamics with specific quantitative data. Our results indicate that the channel mediating calcium signals in sea urchin sperm is likely CatSper, a calcium channel necessary for human male fertility.

Neurogranin stimulates Ca2+/calmodulin-dependent kinase II by suppressing calcineurin activity at specific calcium spike frequencies

Calmodulin sits at the center of molecular mechanisms underlying learning and memory. Its complex and sometimes opposite influences, mediated via the binding to various proteins, are yet to be fully understood. Calcium/calmodulin-dependent protein kinase II (CaMKII) and calcineurin (CaN) both bind open calmodulin, favoring Long-Term Potentiation (LTP) or Depression (LTD) respectively. Neurogranin binds to the closed conformation of calmodulin and its impact on synaptic plasticity is less clear. We set up a mechanistic computational model based on allosteric principles to simulate calmodulin state transitions and its interactions with calcium ions and the three binding partners mentioned above. We simulated calcium spikes at various frequencies and show that neurogranin regulates synaptic plasticity along three modalities. At low spike frequencies, neurogranin inhibits the onset of LTD by limiting CaN activation. At intermediate frequencies, neurogranin facilitates LTD, but limits LTP by precluding binding of CaMKII with calmodulin. Finally, at high spike frequencies, neurogranin promotes LTP by enhancing CaMKII autophosphorylation. While neurogranin might act as a calmodulin buffer, it does not significantly preclude the calmodulin opening by calcium. On the contrary, neurogranin synchronizes the opening of calmodulin's two lobes and promotes their activation at specific frequencies. Neurogranin suppresses basal CaN activity, thus increasing the chance of CaMKII trans-autophosphorylation at high-frequency calcium spikes. Taken together, our study reveals dynamic regulatory roles played by neurogranin on synaptic plasticity, which provide mechanistic explanations for opposing experimental findings.

Understanding Calcium-Dependent Conformational Changes in S100A1 Protein: A Combination of Molecular Dynamics and Gene Expression Study in Skeletal Muscle

The S100A1 protein, involved in various physiological activities through the binding of calcium ions (Ca²⁺), participates in several protein-protein interaction (PPI) events after Ca²⁺-dependent activation. The present work investigates Ca²⁺-dependent conformational changes in the helix-EF hand-helix using the molecular dynamics (MD) simulation approach that facilitates the understanding of Ca²⁺-dependent structural and dynamic distinctions between the apo and holo forms of the protein. Furthermore, the process of ion binding by inserting Ca²⁺ into the bulk of the apo structure was simulated by molecular dynamics. Expectations of the simulation were demonstrated using cluster analysis and a variety of structural metrics, such as interhelical angle estimation, solvent accessible surface area, hydrogen bond analysis, and contact analysis. Ca²⁺ triggered a rise in the interhelical angles of S100A1 on the binding site and solvent accessible surface area. Significant configurational regulations were observed in the holo protein. The findings would contribute to understanding the molecular basis of the association of Ca²⁺ with the S100A1 protein, which may be an appropriate study to understand the Ca²⁺-mediated conformational changes in the protein target. In addition, we investigated the expression profile of S100A1 in myoblast differentiation and muscle regeneration. These data showed that S100A1 is expressed in skeletal muscles. However, the expression decreases with time during the process of myoblast differentiation.

A multi-state model of the CaMKII dodecamer suggests a role for calmodulin in maintenance of autophosphorylation

Ca2+/calmodulin-dependent protein kinase II (CaMKII) accounts for up to 2 percent of all brain protein and is essential to memory function. CaMKII activity is known to regulate dynamic shifts in the size and signaling strength of neuronal connections, a process known as synaptic plasticity. Increasingly, computational models are used to explore synaptic plasticity and the mechanisms regulating CaMKII activity. Conventional modeling approaches may exclude biophysical detail due to the impractical number of state combinations that arise when explicitly monitoring the conformational changes, ligand binding, and phosphorylation events that occur on each of the CaMKII holoenzyme's subunits. To manage the combinatorial explosion without necessitating bias or loss in biological accuracy, we use a specialized syntax in the software MCell to create a rule-based model of a twelve-subunit CaMKII holoenzyme. Here we validate the rule-based model against previous experimental measures of CaMKII activity and investigate molecular mechanisms of CaMKII regulation. Specifically, we explore how Ca2+/CaM-binding may both stabilize CaMKII subunit activation and regulate maintenance of CaMKII autophosphorylation. Noting that Ca2+/CaM and protein phosphatases bind CaMKII at nearby or overlapping sites, we compare model scenarios in which Ca2+/CaM and protein phosphatase do or do not structurally exclude each other's binding to CaMKII. Our results suggest a functional mechanism for the so-called "CaM trapping" phenomenon, wherein Ca2+/CaM may structurally exclude phosphatase binding and thereby prolong CaMKII autophosphorylation. We conclude that structural protection of autophosphorylated CaMKII by Ca2+/CaM may be an important mechanism for regulation of synaptic plasticity.

From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity

Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.

Constructing network topologies for multiple signal-encoding functions

Background

Cells use signaling protein networks to sense their environment and mediate specific responses. Information about environmental stress is usually encoded in the dynamics of the signaling molecules, and qualitatively distinct dynamics of the same signaling molecule can lead to dramatically different cell fates. Exploring the design principles of networks with multiple signal-encoding functions is important for understanding how distinct dynamic patterns are shaped and integrated by real cellular networks, and for building cells with targeted sensing–response functions via synthetic biology.

Results

In this paper, we investigate multi-node enzymatic regulatory networks with three signal-encoding functions, i.e., dynamic responses of oscillation, transient activation, and sustained activation upon step stimulation by three different inducers, respectively. Taking into account competition effects of the substrates for the same enzyme in the enzymatic reactions, we searched for robust subnetworks for each signal-encoding function by three-node-network enumeration and then integrated the three subnetworks together via node-merging. The obtained tri-functional networks consisted of four to six nodes, and the core structures of these networks were hybrids of the motifs for the subfunctions.

Conclusions

The simplest but relatively robust tri-functional networks demonstrated that the three functions were compatible within a simple negative feedback loop. Depending on the network structure, the competition effects of the substrates for the same enzyme within the networks could promote or hamper the target functions, and can create implicit functional motifs. Overall, the networks we obtained could in principle be synthesized to construct dynamic control circuits with multiple target functions.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0676-5) contains supplementary material, which is available to authorized users.

Mechanistic insight into activation of MAPK signaling by pro-angiogenic factors

Background

Angiogenesis is important in physiological and pathological conditions, as blood vessels provide nutrients and oxygen needed for tissue growth and survival. Therefore, targeting angiogenesis is a prominent strategy in both tissue engineering and cancer treatment. However, not all of the approaches to promote or inhibit angiogenesis lead to successful outcomes. Angiogenesis-based therapies primarily target pro-angiogenic factors such as vascular endothelial growth factor-A (VEGF) or fibroblast growth factor (FGF) in isolation. However, pre-clinical and clinical evidence shows these therapies often have limited effects. To improve therapeutic strategies, including targeting FGF and VEGF in combination, we need a quantitative understanding of the how the promoters combine to stimulate angiogenesis.

Results

In this study, we trained and validated a detailed mathematical model to quantitatively characterize the crosstalk of FGF and VEGF intracellular signaling. This signaling is initiated by FGF binding to the FGF receptor 1 (FGFR1) and heparan sulfate glycosaminoglycans (HSGAGs) or VEGF binding to VEGF receptor 2 (VEGFR2) to promote downstream signaling. The model focuses on FGF- and VEGF-induced mitogen-activated protein kinase (MAPK) signaling and phosphorylation of extracellular regulated kinase (ERK), which promotes cell proliferation. We apply the model to predict the dynamics of phosphorylated ERK (pERK) in response to the stimulation by FGF and VEGF individually and in combination. The model predicts that FGF and VEGF have differential effects on pERK. Additionally, since VEGFR2 upregulation has been observed in pathological conditions, we apply the model to investigate the effects of VEGFR2 density and trafficking parameters. The model predictions show that these parameters significantly influence the response to VEGF stimulation.

Conclusions

The model agrees with experimental data and is a framework to synthesize and quantitatively explain experimental studies. Ultimately, the model provides mechanistic insight into FGF and VEGF interactions needed to identify potential targets for pro- or anti-angiogenic therapies.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0668-5) contains supplementary material, which is available to authorized users.

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

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.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.