Search

The intracellular Na+ concentration ([Na+]) regulates cardiac contractility. Previous studies have suggested that subsarcolemmal [Na+] is higher than cytosolic [Na+] in cardiac myocytes, but this concept remains controversial. Here, we used electrophysiological experiments and mathematical modeling to test whether there are subsarcolemmal pools with different [Na+] and dynamics compared with the bulk cytosol in rat ventricular myocytes. A Na+ dependency curve for Na+-K+-ATPase (NKA) current was recorded with symmetrical Na+ solutions, i.e., the same [Na+] in the superfusate and internal solution. This curve was used to estimate [Na+] sensed by NKA in other experiments. Three experimental observations suggested that [Na+] is higher near NKA than in the bulk cytosol: 1) when extracellular [Na+] was high, [Na+] sensed by NKA was ~6 mM higher than the internal solution in quiescent cells; 2) long trains of Na+ channel activation almost doubled this gradient; compared with an even intracellular distribution of Na+, the increase of [Na+] sensed by NKA was 10 times higher than expected, suggesting a local Na+ domain; and 3) accumulation of Na+ near NKA after trains of Na+ channel activation dissipated very slowly. Finally, mathematical models assuming heterogeneity of [Na+] between NKA and the Na+ channel better reproduced experimental data than the homogeneous model. In conclusion, our data suggest that NKAsensed [Na+] is higher than [Na+] in the bulk cytosol and that there are differential Na+ pools in the subsarcolemmal space, which could be important for cardiac contractility and arrhythmogenesis. [ABSTRACT FROM AUTHOR]

Single channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.