A simulation study on the activation of cardiac CaMKII delta-isoform and its regulation by phosphatases

Nitric oxide modulates NMDA receptor through a negative feedback mechanism and regulates the dynamical behavior of neuronal postsynaptic components

Nitric oxide (NO) is known to be an important regulator of neurological processes in the central nervous system which acts directly on the presynaptic neuron and enhances the release of neurotransmitters like glutamate into the synaptic cleft. Calcium influx activates a cascade of biochemical reactions to influence the production of nitric oxide in the postsynaptic neuron. This has been modeled in the present work as a system of ordinary differential equations, to explore the dynamics of the interacting components and predict the dynamical behavior of the postsynaptic neuron. It has been hypothesized that nitric oxide modulates the NMDA receptor via a feedback mechanism and regulates the dynamic behavior of postsynaptic components. Results obtained by numerical analyses indicate that the biochemical system is stimulus-dependent and shows oscillations of calcium and other components within a limited range of concentration. Some of the parameters such as stimulus strength, extracellular calcium concentration, and rate of nitric oxide feedback are crucial for the dynamics of the components in the postsynaptic neuron.

Role of Oxidation-Dependent CaMKII Activation in the Genesis of Abnormal Action Potentials in Atrial Cardiomyocytes: A Simulation Study

Atrial fibrillation is a common cardiac arrhythmia with an increasing incidence rate. Particularly for the aging population, understanding the underlying mechanisms of atrial arrhythmia is important in designing clinical treatment. Recently, experiments have shown that atrial arrhythmia is associated with oxidative stress. In this study, an atrial cell model including oxidative-dependent Ca²⁺/calmodulin- (CaM-) dependent protein kinase II (CaMKII) activation was developed to explore the intrinsic mechanisms of atrial arrhythmia induced by oxidative stress. The simulation results showed that oxidative stress caused early afterdepolarizations (EADs) of action potentials by altering the dynamics of transmembrane currents and intracellular calcium cycling. Oxidative stress gradually elevated the concentration of calcium ions in the cytoplasm by enhancing the L-type Ca²⁺ current and sarcoplasmic reticulum (SR) calcium release. Owing to increased intracellular calcium concentration, the inward Na⁺/Ca²⁺ exchange current was elevated which slowed down the repolarization of the action potential. Thus, the action potential was prolonged and the L-type Ca²⁺ current was reactivated, resulting in the genesis of EAD. Furthermore, based on the atrial single-cell model, a two-dimensional (2D) ideal tissue model was developed to explore the effect of oxidative stress on the electrical excitation wave conduction in 2D tissue. Simulation results demonstrated that, under oxidative stress conditions, EAD hindered the conduction of electrical excitation and caused an unstable spiral wave, which could disrupt normal cardiac rhythm and cause atrial arrhythmia. This study showed the effects of excess reactive oxygen species on calcium cycling and action potential in atrial myocytes and provided insights regarding atrial arrhythmia induced by oxidative stress.

A Spatiotemporal Ventricular Myocyte Model Incorporating Mitochondrial Calcium Cycling

Intracellular calcium (Ca2+) cycling dynamics in cardiac myocytes are spatiotemporally generated by stochastic events arising from a spatially distributed network of coupled Ca2+ release units that interact with an intertwined mitochondrial network. In this study, we developed a spatiotemporal ventricular myocyte model that integrates mitochondria-related Ca2+ cycling components into our previously developed ventricular myocyte model consisting of a three-dimensional Ca2+ release unit network. Mathematical formulations of mitochondrial membrane potential, mitochondrial Ca2+ cycling, mitochondrial permeability transition pore stochastic opening and closing, intracellular reactive oxygen species signaling, and oxidized Ca2+/calmodulin-dependent protein kinase II signaling were incorporated into the model. We then used the model to simulate the effects of mitochondrial depolarization on mitochondrial Ca2+ cycling, Ca2+ spark frequency, and Ca2+ amplitude, which agree well with experimental data. We also simulated the effects of the strength of mitochondrial Ca2+ uniporters and their spatial localization on intracellular Ca2+ cycling properties, which substantially affected diastolic and systolic Ca2+ levels in the mitochondria but exhibited only a small effect on sarcoplasmic reticulum and cytosolic Ca2+ levels under normal conditions. We show that mitochondrial depolarization can cause Ca2+ waves and Ca2+ alternans, which agrees with previous experimental observations. We propose that this new, to our knowledge, spatiotemporal ventricular myocyte model, incorporating properties of mitochondrial Ca2+ cycling and reactive-oxygen-species-dependent signaling, will be useful for investigating the effects of mitochondria on intracellular Ca2+ cycling and action potential dynamics in ventricular myocytes.

Conformational coupling by trans-phosphorylation in calcium calmodulin dependent kinase II

The calcium calmodulin-dependent protein kinase II (CaMKII) is a dodecameric holoenzyme important for encoding memory. Its activation, triggered by binding of calcium-calmodulin, persists autonomously after calmodulin dissociation. One (receiver) kinase captures and subsequently phosphorylates the regulatory domain peptide of a donor kinase forming a chained dimer as the first stage of autonomous activation. Protein dynamics simulations examined the conformational changes triggered by dimer formation and phosphorylation, aimed to provide a molecular rationale for human mutations that result in learning disabilities. Ensembles generated from X-ray crystal structures were characterized by network centrality and community analysis. Mutual information related collective motions to local fragment dynamics encoded with a structural alphabet. Implicit solvent tCONCOORD conformational ensembles revealed the dynamic architecture of inactive kinase domains was co-opted in the activated dimer but the network hub shifted from the nucleotide binding cleft to the captured peptide. Explicit solvent molecular dynamics (MD) showed nucleotide and substrate binding determinants formed coupled nodes in long-range signal relays between regulatory peptides in the dimer. Strain in the extended captured peptide was balanced by reduced flexibility of the receiver kinase C-lobe core. The relays were organized around a hydrophobic patch between the captured peptide and a key binding helix. The human mutations aligned along the relays. Thus, these mutations could disrupt the allosteric network alternatively, or in addition, to altered binding affinities. Non-binding protein sectors distant from the binding sites mediated the allosteric signalling; providing possible targets for inhibitor design. Phosphorylation of the peptide modulated the dielectric of its binding pocket to strengthen the patch, non-binding sectors, domain interface and temporal correlations between parallel relays. These results provide the molecular details underlying the reported positive kinase cooperativity to enrich the discussion on how autonomous activation by phosphorylation leads to long-term behavioural effects.

Protein kinases play central roles in intracellular signalling. Auto-phosphorylation by bound nucleotide typically precedes phosphate transfer to multiple substrates. Protein conformational changes are central to kinase function, altering binding affinities to change cellular location and shunt from one signal pathway to another. In the brain, the multi-subunit kinase, CaMKII is activated by calcium-calmodulin upon calcium jumps produced by synaptic stimulation. Auto-transphosphorylation of a regulatory peptide enables the kinase to remain activated and mediate long-term behavioural effects after return to basal calcium levels. A database of mutated residues responsible for these effects is difficult to reconcile solely with impaired nucleotide or substrate binding. Therefore, we have computationally generated interaction networks to map the conformational plasticity of the kinase domains where most mutations localize. The network generated from the atomic structure of a phosphorylated dimer resolves protein sectors based on their collective motions. The sectors link nucleotide and substrate binding sites in self-reinforcing relays between regulatory peptides. The self-reinforcement is strengthened by phosphorylation consistent with the reported positive cooperativity of kinase activity with calcium-calmodulin concentration. The network gives a better match with the mutations and, in addition, reveals target sites for drug development.

Global sensitivity analysis of a model related to memory formation in synapses: Model reduction based on epistemic parameter uncertainties and related issues

We investigate the epistemic uncertainties of parameters of a mathematical model that describes the dynamics of CaMKII-NMDAR complex related to memory formation in synapses using global sensitivity analysis (GSA). The model, which was published in this journal, is nonlinear and complex with Ca²⁺ patterns with different level of frequencies as inputs. We explore the effects of parameter on the key outputs of the model to discover the most sensitive ones using GSA and partial ranking correlation coefficient (PRCC) and to understand why they are sensitive and others are not based on the biology of the problem. We also extend the model to add presynaptic neurotransmitter vesicles release to have action potentials as inputs of different frequencies. We perform GSA on this extended model to show that the parameter sensitivities are different for the extended model as shown by PRCC landscapes. Based on the results of GSA and PRCC, we reduce the original model to a less complex model taking the most important biological processes into account. We validate the reduced model against the outputs of the original model. We show that the parameter sensitivities are dependent on the inputs and GSA would make us understand the sensitivities and the importance of the parameters. A thorough phenomenological understanding of the relationships involved is essential to interpret the results of GSA and hence for the possible model reduction.

Modelling bidirectional modulations in synaptic plasticity: A biochemical pathway model to understand the emergence of long term potentiation (LTP) and long term depression (LTD)

Synaptic plasticity induces bidirectional modulations of the postsynaptic response following a synaptic transmission. The long term forms of synaptic plasticity, named long term potentiation (LTP) and long term depression (LTD), are critical for the antithetic functions of the memory system, memory formation and removal, respectively. A common Ca(2+) signalling upstream triggers both LTP and LTD, and the critical proteins and factors coordinating the LTP/LTD inductions are not well understood. We develop an integrated model based on the sub-models of the indispensable synaptic proteins in the emergence of synaptic plasticity to validate and understand their potential roles in the expression of synaptic plasticity. The model explains Ca(2+)/calmodulin (CaM) complex dependent coordination of LTP/LTD expressions by the interactions among the indispensable proteins using the experimentally estimated kinetic parameters. Analysis of the integrated model provides us with insights into the effective timescales of the key proteins and we conclude that the CaM pool size is critical for the coordination between LTP/LTD expressions.

Mechanistic Investigation of the Arrhythmogenic Role of Oxidized CaMKII in the Heart

Oxidative stress and calcium (Ca(2+))/calmodulin (CaM)-dependent protein kinase II (CaMKII) both play important roles in the pathogenesis of cardiac disease. Although the pathophysiological relevance of reactive oxygen species (ROS) and CaMKII has been appreciated for some time, recent work has shown that ROS can directly oxidize CaMKII, leading to its persistent activity and an increase of the likelihood of cellular arrhythmias such as early afterdepolarizations (EADs). Because CaMKII modulates the function of many proteins involved in excitation-contraction coupling, elucidation of its role in cardiac function, in both healthy and oxidative stress conditions, is challenging. To investigate this role, we have developed a model of CaMKII activation that includes both the phosphorylation-dependent and the newly identified oxidation-dependent activation pathways. This model is incorporated into our previous local-control model of the cardiac myocyte that describes excitation-contraction coupling via stochastic simulation of individual Ca(2+) release units and CaMKII-mediated phosphorylation of L-type Ca(2+) channels (LCCs), ryanodine receptors and sodium (Na(+)) channels. The model predicts the experimentally measured slow-rate dependence of H2O2-induced EADs. Upon increased H2O2, simulations suggest that selective activation of late Na(+) current (INaL), although it prolongs action potential duration, is not by itself sufficient to produce EADs. Similar results are obtained if CaMKII effects on LCCs and ryanodine receptors are considered separately. However, EADs emerge upon simultaneous activation of both LCCs and Na(+) channels. Further modeling results implicate activation of the Na(+)-Ca(2+) exchanger (NCX) as an important player in the generation of EADs. During bradycardia, the emergence of H2O2-induced EADs was correlated with a shift in the timing of NCX current reversal toward the plateau phase earlier in the action potential. Using the timing of NCX current reversal as an indicator event for EADs, the model identified counterintuitive ionic changes-difficult to experimentally dissect-that have the greatest influence on ROS-related arrhythmia propensity.

Computational analysis of the regulation of Ca(2+) dynamics in rat ventricular myocytes

Force-frequency relationships of isolated cardiac myocytes show complex behaviors that are thought to be specific to both the species and the conditions associated with the experimental preparation. Ca(2+) signaling plays an important role in shaping the force-frequency relationship, and understanding the properties of the force-frequency relationship in vivo requires an understanding of Ca(2+) dynamics under physiologically relevant conditions. Ca(2+) signaling is itself a complicated process that is best understood on a quantitative level via biophysically based computational simulation. Although a large number of models are available in the literature, the models are often a conglomeration of components parameterized to data of incompatible species and/or experimental conditions. In addition, few models account for modulation of Ca(2+) dynamics via β-adrenergic and calmodulin-dependent protein kinase II (CaMKII) signaling pathways even though they are hypothesized to play an important regulatory role in vivo. Both protein-kinase-A and CaMKII are known to phosphorylate a variety of targets known to be involved in Ca(2+) signaling, but the effects of these pathways on the frequency- and inotrope-dependence of Ca(2+) dynamics are not currently well understood. In order to better understand Ca(2+) dynamics under physiological conditions relevant to rat, a previous computational model is adapted and re-parameterized to a self-consistent dataset obtained under physiological temperature and pacing frequency and updated to include β-adrenergic and CaMKII regulatory pathways. The necessity of specific effector mechanisms of these pathways in capturing inotrope- and frequency-dependence of the data is tested by attempting to fit the data while including and/or excluding those effector components. We find that: (1) β-adrenergic-mediated phosphorylation of the L-type calcium channel (LCC) (and not of phospholamban (PLB)) is sufficient to explain the inotrope-dependence; and (2) that CaMKII-mediated regulation of neither the LCC nor of PLB is required to explain the frequency-dependence of the data.

Modelling the dynamics of CaMKII-NMDAR complex related to memory formation in synapses: the possible roles of threonine 286 autophosphorylation of CaMKII in long term potentiation

A synaptic protein, Ca(2+)/Calmodulin dependent protein kinase II (CaMKII), has complex state transitions and facilitates the emergence of long term potentiation (LTP), which is highly correlated to memory formation. Two of the state transitions are critical for LTP: (1) threonine 286 autophosphorylation of CaMKII; and (2) binding to N-methyl-d-aspartate receptor (NMDAR) in the postsynaptic density (PSD) to form CaMKII-NMDAR complex. Both of these state transitions retain the activity of CaMKII when the induction signal disappears which is very important for the long-lasting characteristics of LTP. However, the possible relationships between the state transitions in the emergence of LTP are not well understood. We develop a mathematical model of the formation of CaMKII-NMDAR complex with the full state transitions of CaMKII, including the autophosphorylation, based on ordinary differential equations. In addition, we formulate a probabilistic framework for the binding between CaMKII and NMDAR. The model gives accurate predictions of the behaviours of CaMKII in comparisons to the experimental observations. Using the model, we show that: (1) the formation of CaMKII-NMDAR complex is dependent not only on the binding affinity between CaMKII and NMDAR, but also on the translocation of CaMKII into PSD; and (2) the autophosphorylation is not a requirement for the formation of CaMKII-NMDAR complex, but is important for the rapid formation of CaMKII-NMDAR complex during LTP.

Calcium signaling recruits substrate transporters GLUT4 and CD36 to the sarcolemma without increasing cardiac substrate uptake

Activation of AMP-activated protein kinase (AMPK) in cardiomyocytes induces translocation of glucose transporter GLUT4 and long-chain fatty acid (LCFA) transporter CD36 from endosomal stores to the sarcolemma to enhance glucose and LCFA uptake, respectively. Ca(2+)/calmodulin-activated kinase kinase-β (CaMKKβ) has been positioned directly upstream of AMPK. However, it is unknown whether acute increases in [Ca(2+)]i stimulate translocation of GLUT4 and CD36 and uptake of glucose and LCFA or whether Ca(2+) signaling converges with AMPK signaling to exert these actions. Therefore, we studied the interplay between Ca(2+) and AMPK signaling in regulation of cardiomyocyte substrate uptake. Exposure of primary cardiomyocytes to inhibitors or activators of Ca(2+) signaling affected neither AMPK-Thr(172) phosphorylation nor basal and AMPK-mediated glucose and LCFA uptake. Despite their lack of an effect on substrate uptake, Ca(2+) signaling activators induced GLUT4 and CD36 translocation. In contrast, AMPK activators stimulated GLUT4/CD36 translocation as well as glucose/LCFA uptake. When cardiomyocytes were cotreated with Ca(2+) signaling and AMPK activators, Ca(2+) signaling activators further enhanced AMPK-induced glucose/LCFA uptake. In conclusion, Ca(2+) signaling shows no involvement in AMPK-induced GLUT4/CD36 translocation and substrate uptake but elicits transporter translocation via a separate pathway requiring CaMKKβ/CaMKs. Ca(2+)-induced transporter translocation by itself appears to be ineffective to increase substrate uptake but requires additional AMPK activation to effectuate transporter translocation into increased substrate uptake. Ca(2+)-induced transporter translocation might be crucial under excessive cardiac stress conditions that require supraphysiological energy demands. Alternatively, Ca(2+) signaling might prepare the heart for substrate uptake during physiological contraction by inducing transporter translocation.

Systems biology of synaptic plasticity: a review on N-methyl-D-aspartate receptor mediated biochemical pathways and related mathematical models

Synaptic plasticity, an emergent property of synaptic networks, has shown strong correlation to one of the essential functions of the brain, memory formation. Through understanding synaptic plasticity, we hope to discover the modulators and mechanisms that trigger memory formation. In this paper, we first review the well understood modulators and mechanisms underlying N-methyl-D-aspartate receptor dependent synaptic plasticity, a major form of synaptic plasticity in hippocampus, and then comment on the key mathematical modelling approaches available in the literature to understand synaptic plasticity as the integration of the established functionalities of synaptic components.

Modeling CaMKII-mediated regulation of L-type Ca(2+) channels and ryanodine receptors in the heart

Excitation-contraction coupling (ECC) in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca²⁺ transport. Voltage- and Ca²⁺-dependent L-type Ca²⁺ channels (LCCs) allow for Ca²⁺ entry into the myocyte, which then binds to nearby ryanodine receptors (RyRs) and triggers Ca²⁺ release from the sarcoplasmic reticulum in a process known as Ca²⁺-induced Ca²⁺ release. The highly coordinated Ca²⁺-mediated interaction between LCCs and RyRs is further regulated by the cardiac isoform of the Ca²⁺/calmodulin-dependent protein kinase (CaMKII). Because CaMKII targets and modulates the function of many ECC proteins, elucidation of its role in ECC and integrative cellular function is challenging and much insight has been gained through the use of detailed computational models. Multiscale models that can both reconstruct the detailed nature of local signaling events within the cardiac dyad and predict their functional consequences at the level of the whole cell have played an important role in advancing our understanding of CaMKII function in ECC. Here, we review experimentally based models of CaMKII function with a focus on LCC and RyR regulation, and the mechanistic insights that have been gained through their application.

The delicate bistability of CaMKII

Calcium/calmodulin-dependent protein kinase II (CaMKII) is a synaptic, autophosphorylating kinase that is essential for learning and memory. Previous models have suggested that CaMKII functions as a bistable switch that could be the molecular correlate of long-term memory, but experiments have failed to validate these predictions. These models involved significant approximations to overcome the combinatorial complexity inherent in a multisubunit, multistate system. Here, we develop a stochastic particle-based model of CaMKII activation and dynamics that overcomes combinatorial complexity without significant approximations. We report four major findings. First, the CaMKII model system is never bistable at resting calcium concentrations, which suggests that CaMKII activity does not function as the biochemical switch underlying long-term memory. Second, the steady-state activation curves are either laserlike or steplike. Both are characterized by a well-defined threshold for activation, which suggests that thresholding is a robust feature of this system. Third, transiently activated CaMKII can maintain its activity over the time course of many experiments, and such slow deactivation may account for the few reports of bistability in the literature. And fourth, under in vivo conditions, increases in phosphatase activity can increase CaMKII activity. This is a surprising and counterintuitive effect, as dephosphorylation is generally associated with CaMKII deactivation.

Modeling CaMKII in cardiac physiology: from molecule to tissue

Post-translational modification of membrane proteins (e.g., ion channels, receptors) by protein kinases is an essential mechanism for control of excitable cell function. Importantly, loss of temporal and/or spatial control of ion channel post-translational modification is common in congenital and acquired forms of cardiac disease and arrhythmia. The multifunctional Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) regulates a number of diverse cellular functions in heart, including excitation-contraction coupling, gene transcription, and apoptosis. Dysregulation of CaMKII signaling has been implicated in human and animal models of disease. Understanding of CaMKII function has been advanced by mathematical modeling approaches well-suited to the study of complex biological systems. Early kinetic models of CaMKII function in the brain characterized this holoenzyme as a bistable molecular switch capable of storing information over a long period of time. Models of CaMKII activity have been incorporated into models of the cell and tissue (particularly in the heart) to predict the role of CaMKII in regulating organ function. Disease models that incorporate CaMKII overexpression clearly demonstrate a link between its excessive activity and arrhythmias associated with congenital and acquired heart disease. This review aims at discussing systems biology approaches that have been applied to analyze CaMKII signaling from the single molecule to intact cardiac tissue. In particular, efforts to use computational biology to provide new insight into cardiac disease mechanisms are emphasized.

Apo states of calmodulin and CaBP1 control CaV1 voltage-gated calcium channel function through direct competition for the IQ domain

In neurons, binding of calmodulin (CaM) or calcium-binding protein 1 (CaBP1) to the CaV1 (L-type) voltage-gated calcium channel IQ domain endows the channel with diametrically opposed properties. CaM causes calcium-dependent inactivation and limits calcium entry, whereas CaBP1 blocks calcium-dependent inactivation (CDI) and allows sustained calcium influx. Here, we combine isothermal titration calorimetry with cell-based functional measurements and mathematical modeling to show that these calcium sensors behave in a competitive manner that is explained quantitatively by their apo-state binding affinities for the IQ domain. This competition can be completely blocked by covalent tethering of CaM to the channel. Further, we show that Ca(2+)/CaM has a sub-picomolar affinity for the IQ domain that is achieved without drastic alteration of calcium-binding properties. The observation that the apo forms of CaM and CaBP1 compete with each other demonstrates a simple mechanism for direct modulation of CaV1 function and suggests a means by which excitable cells may dynamically tune CaV activity.

Structural studies on the regulation of Ca2+/calmodulin dependent protein kinase II

Ca(2+)/calmodulin dependent protein kinase II (CaMKII) is a broadly distributed metazoan Ser/Thr protein kinase that is important in neuronal and cardiac signaling. CaMKII forms oligomeric assemblies, typically dodecameric, in which the calcium-responsive kinase domains are organized around a central hub. We review the results of crystallographic analyses of CaMKII, including the recently determined structure of a full-length and autoinhibited form of the holoenzyme. These structures, when combined with other data, allow informed speculation about how CaMKII escapes calcium-dependence when calcium spikes exceed threshold frequencies.

Role of CaMKII in post acidosis arrhythmias: a simulation study using a human myocyte model

Postacidotic arrhythmias have been associated to increased sarcoplasmic reticulum (SR) Ca(2+) load and Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activation. However, the molecular mechanisms underlying these arrhythmias are still unclear. To better understand this process, acidosis produced by CO2 increase from 5% to 30%, resulting in intracellular pH (pHi) change from 7.15 to 6.7, was incorporated into a myocyte model of excitation-contraction coupling and contractility, including acidotic inhibition of L-type Ca(2+) channel (I(CaL)), Na(+)-Ca(2+) exchanger, Ca(2+) release through the SR ryanodine receptor (RyR2) (I(rel)), Ca(2+) reuptake by the SR Ca(2+) ATPase2a (I(up)), Na(+)-K(+) pump, K(+) efflux through the inward rectifier K(+) channel and the transient outward K(+) flow (I(to)) together with increased activity of the Na(+)-H(+) exchanger (I(NHE)). Simulated CaMKII regulation affecting I(rel), I(up), I(CaL), I(NHE) and I(to) was introduced in the model to partially compensate the acidosis outcome. Late Na(+) current increase by CaMKII was also incorporated. Using this scheme and assuming that diastolic Ca(2+) leak through the RyR2 was modulated by the resting state of this channel and the difference between SR and dyadic cleft [Ca(2+)], postacidotic delayed after depolarizations (DADs) were triggered upon returning to normal pHi after 6 min acidosis. The model showed that DADs depend on SR Ca(2+) load and on increased Ca(2+) leak through RyR2. This postacidotic arrhythmogenic pattern relies mainly on CaMKII effect on I(CaL) and I(up), since its individual elimination produced the highest DAD reduction. The model further revealed that during the return to normal pHi, DADs are fully determined by SR Ca(2+) load at the end of acidosis. Thereafter, DADs are maintained by SR Ca(2+) reloading by Ca(2+) influx through the reverse NCX mode during the time period in which [Na(+)]i is elevated.

CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation

The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKII holoenzyme dynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzyme structure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinite subunit holoenzyme approximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity.

A mechanism for tunable autoinhibition in the structure of a human Ca2+/calmodulin- dependent kinase II holoenzyme

Calcium/calmodulin-dependent kinase II (CaMKII) forms a highly conserved dodecameric assembly that is sensitive to the frequency of calcium pulse trains. Neither the structure of the dodecameric assembly nor how it regulates CaMKII are known. We present the crystal structure of an autoinhibited full-length human CaMKII holoenzyme, revealing an unexpected compact arrangement of kinase domains docked against a central hub, with the calmodulin-binding sites completely inaccessible. We show that this compact docking is important for the autoinhibition of the kinase domains and for setting the calcium response of the holoenzyme. Comparison of CaMKII isoforms, which differ in the length of the linker between the kinase domain and the hub, demonstrates that these interactions can be strengthened or weakened by changes in linker length. This equilibrium between autoinhibited states provides a simple mechanism for tuning the calcium response without changes in either the hub or the kinase domains.

Computational models reduce complexity and accelerate insight into cardiac signaling networks

Cardiac signaling networks exhibit considerable complexity in size and connectivity. The intrinsic complexity of these networks complicates the interpretation of experimental findings. This motivates new methods for investigating the mechanisms regulating cardiac signaling networks and the consequences these networks have on cardiac physiology and disease. Next-generation experimental techniques are also generating a wealth of genomic and proteomic data that can be difficult to analyze or interpret. Computational models are poised to play a key role in addressing these challenges. Computational models have a long history in contributing to the understanding of cardiac physiology and are useful for identifying biological mechanisms, inferring multiscale consequences to cell signaling activities and reducing the complexity of large data sets. Models also integrate well with experimental studies to explain experimental observations and generate new hypotheses. Here, we review the contributions computational modeling approaches have made to the analysis of cardiac signaling networks and forecast opportunities for computational models to accelerate cardiac signaling research.

Minor contribution of cytosolic Ca2+ transients to the pacemaker rhythm in guinea pig sinoatrial node cells

The question of the extent to which cytosolic Ca(2+) affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the "Ca(2+) clock" (C) and "membrane clock" (M) hypotheses, together with patch-clamp experiments in isolated guinea pig sinoatrial node cells. By applying lead potential analysis to the models, the C mechanism, which is dependent on potentiation of Na(+)/Ca(2+) exchange current via spontaneous Ca(2+) release from the sarcoplasmic reticulum (SR) during diastole, was found to overlap M mechanisms in the C model. Rapid suppression of pacemaker rhythm was observed in the C model by chelating intracellular Ca(2+), whereas the M model was unaffected. Experimental rupturing of the perforated-patch membrane to allow rapid equilibration of the cytosol with 10 mM BAPTA pipette solution, however, failed to decrease the rate of spontaneous action potential within ∼30 s, whereas contraction ceased within ∼3 s. The spontaneous rhythm also remained intact within a few minutes when SR Ca(2+) dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca(2+) dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca(2+)-mediated inactivation of the L-type Ca(2+) currents induced by BAPTA, were well explained by assuming Ca(2+) chelation, even in the proximity of the channel pore in addition to the bulk cytosol in the M model. Taken together, the experimental and model findings strongly suggest that the C mechanism explicitly described by the C model can hardly be applied to guinea pig sinoatrial node cells. The possible involvement of L-type Ca(2+) current rundown induced secondarily through inhibition of Ca(2+)/calmodulin kinase II and/or Ca(2+)-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca(2+) concentration reduction for >5 min.

Regulation of excitation-contraction coupling in mouse cardiac myocytes: integrative analysis with mathematical modelling

Background

The cardiomyocyte is a prime example of inherently complex biological system with inter- and cross-connected feedback loops in signalling, forming the basic properties of intracellular homeostasis. Functional properties of cells and tissues have been studied e.g. with powerful tools of genetic engineering, combined with extensive experimentation. While this approach provides accurate information about the physiology at the endpoint, complementary methods, such as mathematical modelling, can provide more detailed information about the processes that have lead to the endpoint phenotype.

Results

In order to gain novel mechanistic information of the excitation-contraction coupling in normal myocytes and to analyze sophisticated genetically engineered heart models, we have built a mathematical model of a mouse ventricular myocyte. In addition to the fundamental components of membrane excitation, calcium signalling and contraction, our integrated model includes the calcium-calmodulin-dependent enzyme cascade and the regulation it imposes on the proteins involved in excitation-contraction coupling. With the model, we investigate the effects of three genetic modifications that interfere with calcium signalling: 1) ablation of phospholamban, 2) disruption of the regulation of L-type calcium channels by calcium-calmodulin-dependent kinase II (CaMK) and 3) overexpression of CaMK. We show that the key features of the experimental phenotypes involve physiological compensatory and autoregulatory mechanisms that bring the system to a state closer to the original wild-type phenotype in all transgenic models. A drastic phenotype was found when the genetic modification disrupts the regulatory signalling system itself, i.e. the CaMK overexpression model.

Conclusion

The novel features of the presented cardiomyocyte model enable accurate description of excitation-contraction coupling. The model is thus an applicable tool for further studies of both normal and defective cellular physiology. We propose that integrative modelling as in the present work is a valuable complement to experiments in understanding the causality within complex biological systems such as cardiac myocytes.

Expression of active p21-activated kinase-1 induces Ca2+ flux modification with altered regulatory protein phosphorylation in cardiac myocytes

p21-Activated kinase-1 (Pak1) is a serine-threonine kinase that associates with and activates protein phosphatase 2A in adult ventricular myocytes and, thereby, induces increased Ca2+ sensitivity of skinned-fiber tension development mediated by dephosphorylation of myofilament proteins (Ke Y, Wang L, Pyle WG, de Tombe PP, Solaro RJ. Circ Res 94: 194-200, 2004). We test the hypothesis that activation of Pak1 also moderates cardiac contractility through regulation of intracellular Ca2+ fluxes. We found no difference in field-stimulated intracellular Ca2+ concentration ([Ca2+]i) transient amplitude and extent of cell shortening between myocytes expressing constitutively active Pak1 (CA-Pak1) and controls expressing LacZ; however, time to peak shortening was significantly faster and rate of [Ca2+]i decay and time of relengthening were slower. Neither caffeine-releasable sarcoplasmic reticulum (SR) Ca2+ content nor fractional release was different in CA-Pak1 myocytes compared with controls. Isoproterenol application revealed a significantly blunted increase in [Ca2+]i transient amplitude, as well as a slowed rate of [Ca2+]i decay, increased SR Ca2+ content, and increased cell shortening, in CA-Pak1 myocytes. We found no significant change in phospholamban phosphorylation at Ser16 or Thr17 in CA-Pak1 myocytes. Analysis of cardiac troponin I revealed a significant reduction in phosphorylated species that are primarily attributable to Ser(23/24) in CA-Pak1 myocytes. Nonstimulated, spontaneous SR Ca2+ release sparks were significantly smaller in amplitude in CA-Pak1 than LacZ myocytes. Propagation of spontaneous Ca2+ waves resulting from SR Ca2+ overload was significantly slower in CA-Pak1 myocytes. Our data indicate that CA-Pak1 expression has significant effects on ventricular myocyte contractility through altered myofilament Ca2+ sensitivity and modification of the [Ca2+]i transient.