Graphical Approach to Model Reduction for Nonlinear Biochemical Networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a “concentration-clamp” procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β1-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal “kinetic biomarkers” of the overall β1-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of 'source' species, which receive input signals. Signals are transmitted to all other species in the system (the 'target' species) with a specific delay and transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and recalled to build discrete dynamical models. By separating reaction time and concentration we can greatly simplify the model, circumventing typical problems of complex dynamical systems. The transfer function transformation can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant insight, while remaining an executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modules that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. We also found that overall interconnectedness depends on the magnitude of input, with high connectivity at low input and less connectivity at moderate to high input. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.Comment: 13 pages, 5 tables, 15 figure

Subcellular heterogeneity of ryanodine receptor properties in ventricular myocytes with low T-tubule density

Rationale: In ventricular myocytes of large mammals, not all ryanodine receptor (RyR) clusters are associated with T-tubules (TTs); this fraction increases with cellular remodeling after myocardial infarction (MI). Objective: To characterize RyR functional properties in relation to TT proximity, at baseline and after MI. Methods: Myocytes were isolated from left ventricle of healthy pigs (CTRL) or from the area adjacent to a myocardial infarction (MI). Ca2+ transients were measured under whole-cell voltage clamp during confocal linescan imaging (fluo-3) and segmented according to proximity of TTs (sites of early Ca2+ release, F>F50 within 20 ms) or their absence (delayed areas). Spontaneous Ca2+ release events during diastole, Ca2+ sparks, reflecting RyR activity and properties, were subsequently assigned to either category. Results: In CTRL, spark frequency was higher in proximity of TTs, but spark duration was significantly shorter. Block of Na+/Ca2+ exchanger (NCX) prolonged spark duration selectively near TTs, while block of Ca2+ influx via Ca2+ channels did not affect sparks properties. In MI, total spark mass was increased in line with higher SR Ca2+ content. Extremely long sparks (>47.6 ms) occurred more frequently. The fraction of near-TT sparks was reduced; frequency increased mainly in delayed sites. Increased duration was seen in near-TT sparks only; Ca2+ removal by NCX at the membrane was significantly lower in MI. Conclusion: TT proximity modulates RyR cluster properties resulting in intracellular heterogeneity of diastolic spark activity. Remodeling in the area adjacent to MI differentially affects these RyR subpopulations. Reduction of the number of sparks near TTs and reduced local NCX removal limit cellular Ca2+ loss and raise SR Ca2+ content, but may promote Ca2+ waves

Development of FRET Assay into Quantitative and High-throughput Screening Technology Platforms for Protein–Protein Interactions

Förster resonance energy transfer (FRET) technology has been widely used in biological and biomedical research and is a very powerful tool in elucidating protein interactions in many cellular processes. Ubiquitination and SUMOylation are multi-step cascade reactions, involving multiple enzymes and protein–protein interactions. Here we report the development of dissociation constant (Kd) determination for protein–protein interaction and cell-based high-throughput screening (HTS) assay in SUMOylation cascade using FRET technology. These developments are based on steady state and high efficiency of fluorescent energy transfer between CyPet and YPet fused with SUMO1 and Ubc9, respectively. The developments in theoretical and experimental procedures for protein interaction Kd determination and cell-based HTS provide novel tools in affinity measurement and protein interaction inhibitor screening. The Kd determined by FRET between SUMO1 and Ubc9 is compatible with those determined with other traditional approaches, such as isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR). The FRET-based HTS is pioneer in cell-based HTS. Both Kd determination and cell-based HTS, carried out in 384-well plate format, provide powerful tools for large-scale and high-throughput applications

Cross-Talk between Signaling Pathways Can Generate Robust Oscillations in Calcium and cAMP

BACKGROUND:To control and manipulate cellular signaling, we need to understand cellular strategies for information transfer, integration, and decision-making. A key feature of signal transduction is the generation of only a few intracellular messengers by many extracellular stimuli. METHODOLOGY/PRINCIPAL FINDINGS:Here we model molecular cross-talk between two classic second messengers, cyclic AMP (cAMP) and calcium, and show that the dynamical complexity of the response of both messengers increases substantially through their interaction. In our model of a non-excitable cell, both cAMP and calcium concentrations can oscillate. If mutually inhibitory, cross-talk between the two second messengers can increase the range of agonist concentrations for which oscillations occur. If mutually activating, cross-talk decreases the oscillation range, but can generate 'bursting' oscillations of calcium and may enable better filtering of noise. CONCLUSION:We postulate that this increased dynamical complexity allows the cell to encode more information, particularly if both second messengers encode signals. In their native environments, it is unlikely that cells are exposed to one stimulus at a time, and cross-talk may help generate sufficiently complex responses to allow the cell to discriminate between different combinations and concentrations of extracellular agonists

Calcium-Dependent Increases in Protein Kinase-A Activity in Mouse Retinal Ganglion Cells Are Mediated by Multiple Adenylate Cyclases

Neurons undergo long term, activity dependent changes that are mediated by activation of second messenger cascades. In particular, calcium-dependent activation of the cyclic-AMP/Protein kinase A signaling cascade has been implicated in several developmental processes including cell survival, axonal outgrowth, and axonal refinement. The biochemical link between calcium influx and the activation of the cAMP/PKA pathway is primarily mediated through adenylate cyclases. Here, dual imaging of intracellular calcium concentration and PKA activity was used to assay the role of different classes of calcium-dependent adenylate cyclases (ACs) in the activation of the cAMP/PKA pathway in retinal ganglion cells (RGCs). Surprisingly, depolarization-induced calcium-dependent PKA transients persist in barrelless mice lacking AC1, the predominant calcium-dependent adenylate cyclase in RGCs, as well as in double knockout mice lacking both AC1 and AC8. Furthermore, in a subset of RGCs, depolarization-induced PKA transients persist during the inhibition of all transmembrane adenylate cyclases. These results are consistent with the existence of a soluble adenylate cyclase that plays a role in calcium-dependent activation of the cAMP/PKA cascade in neurons

Cyclic Nucleotide Phosphodiesterases and Compartmentation in Normal and Diseased Heart

International audienceCyclic nucleotide phosphodiesterases (PDEs) degrade the second messengers cAMP and cGMP, thereby regulating multiple aspects of cardiac function. This highly diverse class of enzymes encoded by 21 genes encompasses 11 families which are not only responsible for the termination of cyclic nucleotide signalling, but are also involved in the generation of dynamic microdomains of cAMP and cGMP controlling specific cell functions in response to various neurohormonal stimuli. In myocardium, the PDE3 and PDE4 families are predominant to degrade cAMP and thereby regulate cardiac excitation-contraction coupling. PDE3 inhibitors are positive inotropes and vasodilators in human, but their use is limited to acute heart failure and intermittent claudication. PDE5 is particularly important to degrade cGMP in vascular smooth muscle, and PDE5 inhibitors are used to treat erectile dysfunction and pulmonary hypertension. However, these drugs do not seem efficient in heart failure with preserved ejection fraction. There is experimental evidence that these PDEs as well as other PDE families including PDE1, PDE2 and PDE9 may play important roles in cardiac diseases such as hypertrophy and heart failure. After a brief presentation of the cyclic nucleotide pathways in cardiac cells and the major characteristics of the PDE superfamily, this chapter will present their role in cyclic nucleotide compartmentation and the current use of PDE inhibitors in cardiac diseases together with the recent research progresses that could lead to a better exploitation of the therapeutic potential of these enzymes in the future

Phosphodiesterase 10A Upregulation Contributes to Pulmonary Vascular Remodeling

Phosphodiesterases (PDEs) modulate the cellular proliferation involved in the pathophysiology of pulmonary hypertension (PH) by hydrolyzing cAMP and cGMP. The present study was designed to determine whether any of the recently identified PDEs (PDE7-PDE11) contribute to progressive pulmonary vascular remodeling in PH. All in vitro experiments were performed with lung tissue or pulmonary arterial smooth muscle cells (PASMCs) obtained from control rats or monocrotaline (MCT)-induced pulmonary hypertensive (MCT-PH) rats, and we examined the effects of the PDE10 inhibitor papaverine (Pap) and specific small interfering RNA (siRNA). In addition, papaverine was administrated to MCT-induced PH rats from day 21 to day 35 by continuous intravenous infusion to examine the in vivo effects of PDE10A inhibition. We found that PDE10A was predominantly present in the lung vasculature, and the mRNA, protein, and activity levels of PDE10A were all significantly increased in MCT PASMCs compared with control PASMCs. Papaverine and PDE10A siRNA induced an accumulation of intracellular cAMP, activated cAMP response element binding protein and attenuated PASMC proliferation. Intravenous infusion of papaverine in MCT-PH rats resulted in a 40%–50% attenuation of the effects on pulmonary hypertensive hemodynamic parameters and pulmonary vascular remodeling. The present study is the first to demonstrate a central role of PDE10A in progressive pulmonary vascular remodeling, and the results suggest a novel therapeutic approach for the treatment of PH

Rate-dependent Ca2+ signalling underlying the force-frequency response in rat ventricular myocytes: A coupled electromechanical modeling study

Rate-dependent effects on the Ca2+ sub-system in a rat ventricular myocyte are investigated. Here, we employ a deterministic mathematical model describing various Ca2+ signalling pathways under voltage clamp (VC) conditions, to better understand the important role of calmodulin (CaM) in modulating the key control variables Ca2+/calmodulin-dependent protein kinase-II (CaMKII), calcineurin (CaN), and cyclic adenosine monophosphate (cAMP) as they affect various intracellular targets. In particular, we study the frequency dependence of the peak force generated by the myofilaments, the force-frequency response (FFR). Our cell model incorporates frequency-dependent CaM-mediated spatially heterogenous interaction of CaMKII and CaN with their principal targets (dihydropyridine (DHPR) and ryanodine (RyR) receptors and the SERCA pump). It also accounts for the rate-dependent effects of phospholamban (PLB) on the SERCA pump; the rate-dependent role of cAMP in up-regulation of the L-type Ca2+ channel (ICa;L); and the enhancement in SERCA pump activity via phosphorylation of PLB.Our model reproduces positive peak FFR observed in rat ventricular myocytes during voltage-clamp studies both in the presence/absence of cAMP mediated -adrenergic stimulation. This study provides quantitative insight into the rate-dependence of Ca2+-induced Ca2+-release (CICR) by investigating the frequency-dependence of the trigger current (ICa;L) and RyR-release. It also highlights the relative role of the sodium-calcium exchanger (NCX) and the SERCA pump at higher frequencies, as well as the rate-dependence of sarcoplasmic reticulum (SR) Ca2+ content. A rigorous Ca2+ balance imposed on our investigation of these Ca2+ signalling pathways clarifies their individual roles. Here, we present a coupled electromechanical study emphasizing the rate-dependence of isometric force developed and also investigate the temperature-dependence of FFR. Our model provides mechanistic biophysically based explanations for the rate-dependence of CICR, generating useful and testable hypotheses. Although rat ventricular myocytes exhibit a positive peak FFR in the presence/absence of beta-adrenergic stimulation, they show a characteristic increase in the positive slope in FFR due to the presence of Norepinephrine or Isoproterenol. Our study identifies cAMP-mediated stimulation, and rate-dependent CaMKII-mediated up-regulation of ICa;L as the key mechanisms underlying the aforementioned positive FFR