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.
Reduced cardiac sodium (Na
) channel current (I
) resulting from the loss-of-function of Na
channel is a major cause of lethal arrhythmias in Brugada syndrome (BrS). Inspired by previous experimental ...studies which showed that in heart diseases I
was reduced along with expression changes in Na
channel within myocytes, we hypothesized that the local decrease in I
caused by the alteration in Na
channel expression in myocytes leads to the occurrence of phase-2 reentry, the major triggering mechanism of lethal arrhythmias in BrS. We constructed in silico human ventricular myocardial strand and ring models, and examined whether the Na
channel expression changes in each myocyte cause the phase-2 reentry in BrS. Reducing Na
channel expression in the lateral membrane of each myocyte caused not only the notch-and-dome but also loss-of-dome type action potentials and slowed conduction, both of which are typically observed in BrS patients. Furthermore, the selective reduction in Na
channels on the lateral membrane of each myocyte together with spatial tissue heterogeneity of Na
channel expression caused the phase-2 reentry and phase-2 reentry-mediated reentrant arrhythmias. Our data suggest that the BrS phenotype is strongly influenced by expression abnormalities as well as genetic abnormalities of Na
channels.
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, MII
, in the thermal decay of activated VPs was essential for inducing faster inactivation of VPs in rods, and possibly also in cones.
•Mouse critical flicker fusion frequency (CFF) was estimated by behavioral performance using an operant system.•Two different types of psychological methods were employed, the ascending method of ...limit and method of constant stimuli.•We estimated the mouse CFF to be about 14 Hz.•Our results highlight the usefulness of the operant conditioning method for measuring mouse visual temporal resolution.
The critical flicker-fusion frequency (CFF), defined as the frequency at which a flickering light is indistinguishable from a continuous light, is a useful measure of visual temporal resolution. The mouse CFF has been studied by electrophysiological approaches such as recordings of the electroretinogram (ERG) and the visually evoked potential (VEP), but it has not been measured behaviorally. Here we estimated the mouse CFF by using a touchscreen based operant system. The test with ascending series of frequencies and that with randomized frequencies resulted in about 17 and 14 Hz, respectively, as the frequency which could not be distinguished from steady lights. Since the ascending method of limits tend to overestimate the threshold than the descending method, we estimated the mouse CFF to be about 14 Hz. Our results highlight usefulness of the operant conditioning method in measurement of the mouse visual temporal resolution.
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.
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