Abstract Parameter optimization (PO) methods to determine the ionic current composition of experimental cardiac action potential (AP) waveform have been developed using a computer model of cardiac ...membrane excitation. However, it was suggested that fitting a single AP record in the PO method was not always successful in providing a unique answer because of a shortage of information. We found that the PO method worked perfectly if the PO method was applied to a pair of a control AP and a model output AP in which a single ionic current out of six current species, such as I Kr , I CaL , I Na , I Ks , I Kur or I bNSC was partially blocked in silico. When the target was replaced by a pair of experimental control and I Kr -blocked records of APs generated spontaneously in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), the simultaneous fitting of the two waveforms by the PO method was hampered to some extent by the irregular slow fluctuations in the V m recording and/or sporadic alteration in AP configurations in the hiPSC-CMs. This technical problem was largely removed by selecting stable segments of the records for the PO method. Moreover, the PO method was made fail-proof by running iteratively in identifying the optimized parameter set to reconstruct both the control and the I Kr -blocked AP waveforms. In the lead potential analysis, the quantitative ionic mechanisms deduced from the optimized parameter set were totally consistent with the qualitative view of ionic mechanisms of AP so far described in physiological literature.
Although repolarization has been suggested to propagate in cardiac tissue both theoretically and experimentally, it has been challenging to estimate how and to what extent the propagation of ...repolarization contributes to relaxation because repolarization only occurs in the course of membrane excitation in normal hearts. We established a mathematical model of a 1D strand of 600 myocytes stabilized at an equilibrium potential near the plateau potential level by introducing a sustained component of the late sodium current (INaL). By applying a hyperpolarizing stimulus to a small part of the strand, we succeeded in inducing repolarization which propagated along the strand at a velocity of 1~2 cm/s. The ionic mechanisms responsible for repolarization at the myocyte level, i.e., the deactivation of both the INaL and the L-type calcium current (ICaL), and the activation of the rapid component of delayed rectifier potassium current (IKr) and the inward rectifier potassium channel (IK1), were found to be important for the propagation of repolarization in the myocyte strand. Using an analogy with progressive activation of the sodium current (INa) in the propagation of excitation, regenerative activation of the predominant magnitude of IK1 makes the myocytes at the wave front start repolarization in succession through the electrical coupling via gap junction channels.
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 Ca
-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 Ca
activation and force (F
) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F
activation by transient Ca
(Ca
-F
), Ca
-ATP hydrolysis relations, sarcomere length-F
, and F
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.
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
) 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
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
s of the baseline model. G
s 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
s recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-G
relationship during optimization revealed progressive convergence of the randomized population of G
s 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
s 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.
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 Ca
release from the sarcoplasmic reticulum (SR), which can generate rhythmic Ca
release (limit cycle revealed by the bifurcation analysis) when total Ca
within the cell increased. Ca
overload in SR increased resting Ca
efflux through the type II inositol 1,4,5-trisphosphate (IP
) receptors (InsP
R) as well as ryanodine receptors (RyRs), which finally triggered massive Ca
release through activation of RyRs via local Ca
accumulation in the vicinity of RyRs. The new PVC model exhibited a resting potential of -68 mV. Under NA effects, repetitive Ca
release from SR triggered spontaneous action potentials (APs) by evoking transient depolarizations (TDs) through Na
/Ca
exchanger (AP
s). Marked and variable latencies initiating AP
s could be explained by the time courses of the α1- and β1-adrenergic influence on the regulation of intracellular Ca
content and random occurrences of spontaneous TD activating the first AP
. Positive and negative feedback relations were clarified under AP
generation.
The cell volume continuously changes in response to varying physiological conditions, and mechanisms underlying volume regulation have been investigated in both experimental and theoretical studies. ...Here, general formulations concerning cell volume change are presented in the context of developing a comprehensive cell model which takes Ca2+ dynamics into account. Explicit formulas for charge conservation and steady-state volumes of the cytosol and endoplasmic reticulum (ER) are derived in terms of membrane potential, amount of ions, Ca2+-bound buffer molecules, and initial cellular conditions. The formulations were applied to a ventricular myocyte model which has plasma-membrane Ca2+ currents with dynamic gating mechanisms, Ca2+-buffering reactions with diffusive and non-diffusive buffer proteins, and Ca2+ uptake into or release from the sarcoplasmic reticulum (SR) accompanied by compensatory cationic or anionic currents through the SR membrane. Time-dependent volume changes in cardiac myocytes induced by varying extracellular osmolarity or by action potential generation were successfully simulated by the novel formulations. Through application of bifurcation analysis, the existence and uniqueness of steady-state solutions of the cell volume were validated, and contributions of individual ion channels and transporters to the steady-state volume were systematically analyzed. The new formulas are consistent with previous fundamental theory derived from simple models of minimum compositions. The new formulations may be useful for examination of the relationship between cell function and volume change in other cell types.
► Cell volume change was described by general formulations with Ca2+ dynamics in modeling study. ► Explicit formulas of charge conservation and steady-state volume in cytosol and ER are derived. ► Volume changes in cardiac myocytes were simulated with release or uptake of Ca2+ across SR membrane. ► Influences of ionic currents on the steady-state volume were examined with bifurcation analysis.
A new glucose transport model relying upon diffusion and convection across the capillary membrane was developed, and supplemented with tissue space and lymph flow. The rate of glucose utilization (J
...) in the tissue space was described as a saturation function of glucose concentration in the interstitial fluid (C
), and was varied by applying a scaling factor f to J
. With f = 0, the glucose diffusion ceased within ~20 min. While, with increasing f, the diffusion was accelerated through a decrease in C
, but the convective flux remained close to resting level. When the glucose supplying capacity of the capillary was measured with a criterion of J
/J
= 0.5, the capacity increased in proportion to the number of perfused capillaries. A consistent profile of declining C
along the capillary axis was observed at the criterion of 0.5 irrespective of the capillary number. Increasing blood flow scarcely improved the supplying capacity.
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.
The matrix metalloproteinase (MMP) family (approximately 25 members in mammals) has been implicated in extracellular matrix remodeling associated with embryonic development, cancer formation and ...progression, and various other physiological and pathological events. Inactivating mutations in individual matrix metalloproteinase genes in mice described so far, however, are nonlethal at least up to the first few weeks after birth, suggesting functional redundancy among MMP family members. Here, we report that mice lacking two MMPs, MMP-2 (nonmembrane type) and MT1-MMP (membrane type), die immediately after birth with respiratory failure, abnormal blood vessels, and immature muscle fibers reminiscent of central core disease. In the absence of MMP-2 and MT1-MMP, myoblast fusion in vitro is also significantly retarded. These findings suggest functional overlap in mice between the two MMPs with distinct molecular natures.
Intense exercise leads to muscle fatigue, a contractile and metabolic failure of contracting muscle to sustain desired work. It is widely accepted that the close relationship between intense exercise ...and the accumulation of metabolic by-products is the major cause of skeletal muscle fatigue. High-intensity exercise activates ATPase activity and strongly promotes ATP production, leading to an alteration of metabolic by-products. However, the complex mechanisms underlying the development of muscle fatigue are not fully understood. In this study, we developed a novel mathematical model for whole-body mechanisms that can reproduce the key biological processes of metabolic fatigue during high-intensity exercise. Five vital compartments are represented: skeletal muscle, liver, lungs, blood vessels and other organs. These compartments capture the key mechanisms involved, including the buffering role of creatine kinase, the bicarbonate buffer system in the regulation of blood pH, and the accumulation of metabolic by-products. The simulation results provide the essential evidence for a better understanding of muscle fatigue such as increases in blood lactate and muscle inorganic phosphate, and drop in blood pH level. Moreover, we revised our previous contraction model by introducing the inhibitory effect of metabolic by-products based on structural and experimental data. The accumulation of metabolic by-products reduces the number of strongly bound cross-bridges, leading to a reduction in maximal contraction. In conclusion, our simplified model reliably reflects metabolic fluxes and concentrations that are in good agreement with experimental findings, yielding a better understanding of metabolic fatigue during high-intensity exercise.
•Whole-body mathematical model quantitatively estimates the key metabolic fluxes and concentrations during intense exercise.•The constant workload expressed as percentage of maximum oxygen uptake is used as an input parameter for this novel model.•The model has several parameters that can be modified to analyze the effect of individual differences.
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