Since the left ventricle (LV) has pressure (Plv) and volume (Vlv), we can define LV elastance from the ratio between Plv and Vlv, termed as "instantaneous elastance." On the other hand, end-systolic ...elastance (Emax) is known to be a good index of LV contractility, which is measured by the slope of several end-systolic Plv-Vlv points obtained by using different loads. The word Emax originates from the assumption that LV elastance increases during the ejection phase and attains its maximum at the end-systole. From this concept, we can define another elastance determined by the slope of isochronous Plv-Vlv points, that is Plv-Vlv points at a certain time after the ejection onset time by using different loads. We refer to this elastance as "load-dependent elastance." To reveal the relation between these two elastances, we used a hemodynamic model that included a detailed ventricular myocyte contraction model. From the simulation results, we found that the isochronous Plv-Vlv points lay in one line and that the line slope corresponding to the load-dependent elastance slightly decreased during the ejection phase, which is quite different from the instantaneous elastance. Subsequently, we analyzed the mechanism determining these elastances from the model equations. We found that instantaneous elastance is directly related to contraction force generated by the ventricular myocyte, but the load-dependent elastance is determined by two factors: one is the transient characteristics of the cardiac cell, i.e., the velocity-dependent force drops characteristics in instantaneous shortening. The other is the force-velocity relation of the cardiac cell. We also found that the linear isochronous pressure-volume relation is based on the approximately linear relation between the time derivative of the cellular contraction force and the cellular shortening velocity that results from the combined characteristics of LV and aortic compliances.
Abstract
To date, no effective treatment has been established for photoreceptor loss due to energy imbalances, but numerous therapeutic approaches have reported some success in slowing photoreceptor ...degeneration by downregulating energy demand. However, the detailed mechanisms remain unclear. This study aimed to clarify the composition of ATP consumption factors in photoreceptors in darkness and in light. We introduced mathematical formulas for ionic current activities combined with a phototransduction model to form a new mathematical model for estimating the energy expenditure of each ionic current. The proposed model included various ionic currents identified in mouse rods using a gene expression database incorporating an available electrophysiological recording of each specific gene. ATP was mainly consumed by Na
+
/K
+
-ATPase and plasma membrane Ca
2+
-ATPase pumps to remove excess Na
+
and Ca
2+
. The rod consumed 7
$$\times$$
×
10
7
molecules of ATP s
−1
, where 65% was used to remove ions from the cyclic nucleotide-gated channel and 20% from the hyperpolarization-activated current in darkness. Increased light intensity raised the energy requirements of the complex phototransduction cascade mechanisms. Nevertheless, the overall energy consumption was less than that in darkness due to the significant reduction in ATPase activities, where the hyperpolarization-activated current proportion increased to 83%. A better understanding of energy demand/supply may provide an effective tool for investigating retinal pathophysiological changes and analyzing novel therapeutic treatments related to the energy consumption of photoreceptors.
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.
Key points
The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant during physiological cardiac workload transition.
How this is accomplished is not yet ...clarified, though Ca2+ has been suggested to be one of the possible mechanisms.
We constructed a detailed mathematical model of cardiac mitochondria based on experimental data and studied whether known Ca2+‐dependent regulation mechanisms play roles in the metabolite constancy.
Model simulations revealed that the Ca2+‐dependent regulation mechanisms have important roles under the in vitro condition of isolated mitochondria where malate and glutamate were mitochondrial substrates, while they have only a minor role and the composition of substrates has marked influence on the metabolite constancy during workload transition under the simulated in vivo condition where many substrates exist.
These results help us understand the regulation mechanisms of cardiac energy metabolism during physiological cardiac workload transition.
The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant over a wide range of cardiac workload, though the mechanisms are not yet clarified. One possible regulator of mitochondrial metabolism is Ca2+, because it activates several mitochondrial enzymes and transporters. Here we constructed a mathematical model of cardiac mitochondria, including oxidative phosphorylation, substrate metabolism and ion/substrate transporters, based on experimental data, and studied whether the Ca2+‐dependent activation mechanisms play roles in metabolite constancy. Under the in vitro condition of isolated mitochondria, where malate and glutamate were used as mitochondrial substrates, the model well reproduced the Ca2+ and inorganic phosphate (Pi) dependences of oxygen consumption, NADH level and mitochondrial membrane potential. The Ca2+‐dependent activations of the aspartate/glutamate carrier and the F1Fo‐ATPase, and the Pi‐dependent activation of Complex III were key factors in reproducing the experimental data. When the mitochondrial model was implemented in a simple cardiac cell model, simulation of workload transition revealed that cytoplasmic Ca2+ concentration (Ca2+cyt) within the physiological range markedly increased NADH level. However, the addition of pyruvate or citrate attenuated the Ca2+ dependence of NADH during the workload transition. Under the simulated in vivo condition where malate, glutamate, pyruvate, citrate and 2‐oxoglutarate were used as mitochondrial substrates, the energy metabolites were more stable during the workload transition and NADH level was almost insensitive to Ca2+cyt. It was revealed that mitochondrial substrates have a significant influence on metabolite constancy during cardiac workload transition, and Ca2+ has only a minor role under physiological conditions.
Key points
The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant during physiological cardiac workload transition.
How this is accomplished is not yet clarified, though Ca2+ has been suggested to be one of the possible mechanisms.
We constructed a detailed mathematical model of cardiac mitochondria based on experimental data and studied whether known Ca2+‐dependent regulation mechanisms play roles in the metabolite constancy.
Model simulations revealed that the Ca2+‐dependent regulation mechanisms have important roles under the in vitro condition of isolated mitochondria where malate and glutamate were mitochondrial substrates, while they have only a minor role and the composition of substrates has marked influence on the metabolite constancy during workload transition under the simulated in vivo condition where many substrates exist.
These results help us understand the regulation mechanisms of cardiac energy metabolism during physiological cardiac workload transition.
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.
Mathematical models have been used to describe the complex physiological processes of light response in photoreceptors for decades. However, the detailed model has not yet been invented. In this ...study, we aimed to construct a new photoreceptor model for estimating the chemical and electrical responses to a light stimulus. The proposed model was developed from our previous works (Takeda et at. 2021; Ito et al. 2017; Sato et al. 2017) based on the ionic current model of vertebrate photoreceptor incorporating the classical Goldman-Hodgkin-Katz constant field equation. The novel model successfully describes the biophysical processes of ionic current dynamics during the light responses. Furthermore, the changes in intracellular ion concentrations are in good agreement with theoretical works and experimental data. This study provides an effective framework for future experimental studies and serves as a powerful guideline for better understanding of the pathophysiology of the retina and improving the new treatment studies.
Mathematical models have been used to describe the complex physiological processes of light response in photoreceptors for decades. However, the detailed model has not yet been invented. In this ...study, we aimed to construct a new photoreceptor model for estimating the chemical and electrical responses to a light stimulus. The proposed model was developed from our previous works (Takeda et at. 2021; Ito et al. 2017; Sato et al. 2017) based on the ionic current model of vertebrate photoreceptor incorporating the classical Goldman-Hodgkin-Katz constant field equation. The novel model successfully describes the biophysical processes of ionic current dynamics during the light responses. Furthermore, the changes in intracellular ion concentrations are in good agreement with theoretical works and experimental data. This study provides an effective framework for future experimental studies and serves as a powerful guideline for better understanding of the pathophysiology of the retina and improving the new treatment studies.
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.
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