Regularity of beating of small clusters of embryonic chick ventricular heart-cells: experiment vs. stochastic single-channel population model

Abstract

The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of ∼20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincaré plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (I), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noise-current into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of time-scales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channel-noise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.

Sinoatrial Beat to Beat Variability Assessed by Contraction Strength in Addition to the Interbeat Interval

“…The spontaneous activity of pacemaker cells in the SAN tissue is based on two tightly linked clocks referred to as calcium and membrane clock (Lakatta and DiFrancesco, 2009 ). Both clocks exhibit inherent random components which arise from stochastic opening and closing of transmembrane ion channels (Krogh-Madsen et al, 2017 ) in the case of the membrane clock and from spontaneous stochastic calcium release via sarcoplasmic ryanodine receptors (Yaniv et al, 2014b ) in the case of the calcium clock. The spontaneous calcium release in turn activates the sodium-calcium exchanger thereby triggering the action potential upstroke and subsequently a massive calcium release from sarcoplasmic reticulum, thus coupling excitation with contraction.…”

Biological noise is a key determinant of the reproducibility and adaptability of cardiac pacemaking and EC coupling

“…In Fig. 1 a , a record of the time course of interburst intervals and their power spectral distribution from a chick cardiomyocyte are shown ( Krogh-Madsen et al, 2017 ). Note that the power spectral distribution in this example has equal intensities at all frequencies, producing a constant power spectral density that is typical of white noise ( Fig.…”

“…(a) Example of white noise. Data in this panel were reproduced from Krogh-Madsen et al (2017) and show the time course of interburst intervals (left column) recorded from a chick ventricular cardiomyocyte and corresponding power spectral density (right column). (b) Example of pink noise.…”

“…The spectral power in Gaussian white noise is uniformly distributed across all frequencies and is normally distributed in the time domain. Gaussian noise is one of the most common descriptors of fluctuations in biological systems and is therefore implemented in simulations of ionic currents and EC coupling (e.g., Aghasafari et al, 2021 ; Sato et al, 2009 ; Krogh-Madsen et al, 2017 ; Guevara and Lewis, 1995 ). However, as discussed in further detail below, there is a paucity of analyses of [Ca 2+ ] i and electrical noise during EC coupling and therefore of computational models that incorporate experimentally determined noise; without inclusion of these data, the predictions of these models are altered.…”

Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers

“…respectively. Bifractals were already addressed in other research fields [54][55][56] including fluid mechanics. [57][58][59][60] For instance, Sreenivasan et al 61 discussed turbulent mixing in the case of a large Sc and argued that the fractal dimensions should be different for scales larger and smaller than the Kolmogorov length scale, see Fig.…”