Glucagon-like peptide-1 (GLP-1) elevates intracellular concentration of cAMP ([cAMP]) and facilitates glucose-dependent insulin secretion in pancreatic β-cells. There has been much evidence to suggest that multiple key players such as the GLP-1 receptor, G_sprotein, adenylate cyclase (AC), phosphodiesterase (PDE), and intracellular Ca²⁺concentration ([Ca²⁺]) are involved in the regulation of [cAMP]. However, because of complex interactions among these signaling factors, the kinetics of the reaction cascade as well as the activities of ACs and PDEs have not been determined in pancreatic β-cells. We have constructed a minimal mathematical model of GLP-1 receptor signal transduction based on experimental findings obtained mostly in β-cells and insulinoma cell lines. By fitting this theoretical reaction scheme to key experimental records of the GLP-1 response, the parameters determining individual reaction steps were estimated. The model reconstructed satisfactorily the dynamic changes in [cAMP] and predicted the activities of cAMP effectors, protein kinase A (PKA), and cAMP-regulated guanine nucleotide exchange factor [cAMP-GEF or exchange protein directly activated by cAMP (Epac)] during GLP-1 stimulation. The simulations also predicted the presence of two sequential desensitization steps of the GLP1 receptor that occur with fast and very slow reaction rates. The cross talk between glucose- and GLP-1-dependent signal cascades for cAMP synthesis was well reconstructed by integrating the direct regulation of AC and PDE by [Ca²⁺]. To examine robustness of the signaling system in controlling [cAMP], magnitudes of AC and PDE activities were compared in the presence or absence of GLP-1 and/or the PDE inhibitor IBMX.¹

Control of the extracellular fluid volume is one of the most indispensable issues for homeostasis of the internal milieu. However, complex interdependence of the pressures involved in determination of fluid exchange makes it difficult to predict a steady-state tissue volume under various physiological conditions without mathematical approaches. Here, we developed a capillary model based on the Starling's principle, which allowed us to clarify the mechanisms of the interstitial-fluid volume regulation. Three well known safety factors against edema: (1) low tissue compliance in negative pressure ranges; (2) lymphatic flow driven by the tissue pressure; and (3) protein washout by the lymph, were incorporated into the model in sequence. An increase in blood pressure at the venous end of the capillary induced an interstitial-fluid volume increase, which, in turn, reduced negative tissue pressure to prevent edema. The lymphatic flow alleviated the edema by both carrying fluid away from the tissue and decreasing the colloidal osmotic pressure. From the model incorporating all three factors, we found that the interstitial-fluid volume changed quickly after the blood pressure change, and that the protein movement towards a certain equilibrium point followed the volume change. Mathematical analyses revealed that the system of the capillary is stable near the equilibrium point at steady state and normal physiological capillary pressure. The time course of the tissue-volume change was determined by two kinetic mechanisms: rapid fluid exchange and slow protein fluxes.

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (G_x) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of G_x estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of G_xs of the baseline model. G_xs of 4–6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5–15% and used as an initial parameter set for the gradient-based automatic G_xs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE–G_x relationship during optimization revealed progressive convergence of the randomized population of G_xs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing G_xs over a range of 0.1–10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

A new contraction model of cardiac muscle was developed by combining previously described biochemical and biophysical models. The biochemical component of the new contraction model represents events in the presence of Ca²⁺–crossbridge attachment and power stroke following inorganic phosphate release, detachment evoked by the replacement of ADP by ATP, ATP hydrolysis, and recovery stroke. The biophysical component focuses on Ca²⁺ activation and force (F_b) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F_b activation by transient Ca²⁺ ([Ca²⁺]–F_b), [Ca²⁺]–ATP hydrolysis relations, sarcomere length–F_b, and F_b recovery after jumps in length under the isometric mode and upon sarcomere shortening after a rapid release of mechanical load under the isotonic mode together with the load–velocity relationship. ATP consumption was obtained for all responses. When incorporated in a ventricular cell model, the contraction model was found to share approximately 60% of the total ATP usage in the cell model.

Cardiomyocytes and myocardial sleeves dissociated from pulmonary veins (PVs) potentially generate ectopic automaticity in response to noradrenaline (NA), and thereby trigger atrial fibrillation. We developed a mathematical model of rat PV cardiomyocytes (PVC) based on experimental data that incorporates the microscopic framework of the local control theory of Ca²⁺ release from the sarcoplasmic reticulum (SR), which can generate rhythmic Ca²⁺ release (limit cycle revealed by the bifurcation analysis) when total Ca²⁺ within the cell increased. Ca²⁺ overload in SR increased resting Ca²⁺ efflux through the type II inositol 1,4,5-trisphosphate (IP₃) receptors (InsP₃R) as well as ryanodine receptors (RyRs), which finally triggered massive Ca²⁺ release through activation of RyRs via local Ca²⁺ accumulation in the vicinity of RyRs. The new PVC model exhibited a resting potential of −68 mV. Under NA effects, repetitive Ca²⁺ release from SR triggered spontaneous action potentials (APs) by evoking transient depolarizations (TDs) through Na⁺/Ca²⁺ exchanger (AP_TDs). Marked and variable latencies initiating AP_TDs could be explained by the time courses of the α1- and β1-adrenergic influence on the regulation of intracellular Ca²⁺ content and random occurrences of spontaneous TD activating the first AP_TD. Positive and negative feedback relations were clarified under AP_TD generation.

Retinal photoreceptor cells, rods and cones, convert photons of light into chemical and electrical signals as the first step of the visual transduction cascade. Although the chemical processes in the phototransduction system are very similar to each other in these photoreceptors, the light sensitivity and time resolution of the photoresponse in rods are functionally different than those in the photoresponses of cones. To systematically investigate how photoresponses are divergently regulated in rods and cones, we have developed a detailed mathematical model on the basis of the Hamer model. The current model successfully reconstructed light intensity-, ATP- and GTP-dependent changes in concentrations of phosphorylated visual pigments (VPs), activated transducins (Tr*s) and phosphodiesterases (PDEs) in rods and cones. In comparison to rods, the lower light sensitivity of cones was attributed not only to the lower affinity of activated VPs for Trs but also to the faster desensitization of the VPs. The assumption of an intermediate inactive state, MIIⁱ, in the thermal decay of activated VPs was essential for inducing faster inactivation of VPs in rods, and possibly also in cones.