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Capturing intracellular pH dynamics by coupling its molecular mechanisms within a fully tractable mathematical model.

ABSTRACT: We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on coupling the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady-state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady-state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. Finally, instead of including a limited set of experimental results to fit our model, we show examples of numerical calculations that are extremely consistent with the wide body of intracellular pH experimental measurements gathered by different groups in many different cellular systems.

SUBMITTER: Bouret Y

PROVIDER: S-EPMC3894979 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:ROMK channels are regulated by internal pH (pH(i)) and extracellular K(+) (K(+)(o)). The mechanisms underlying this regulation were studied in these channels after expression in Xenopus oocytes. Replacement of the COOH-terminal portion of ROMK2 (Kir1.1b) with the corresponding region of the pH-insensitive channel IRK1 (Kir 2.1) produced a chimeric channel (termed C13) with enhanced sensitivity to inhibition by intracellular H(+), increasing the apparent pKa for inhibition by approximately 0.9 pH units. Three amino acid substitutions at the COOH-terminal end of the second transmembrane helix (I159V, L160M, and I163M) accounted for these effects. These substitutions also made the channels more sensitive to reduction in K(+)(o), consistent with coupling between the responses to pH(i) and K(+)(o). The ion selectivity sequence of the activation of the channel by cations was K(+) congruent with Rb(+) > NH(4)(+) >> Na(+), similar to that for ion permeability, suggesting an interaction with the selectivity filter. We tested a model of coupling in which a pH-sensitive gate can close the pore from the inside, preventing access of K(+) from the cytoplasm and increasing sensitivity of the selectivity filter to removal of K(+)(o). We mimicked closure of this gate using positive membrane potentials to elicit block by intracellular cations. With K(+)(o) between 10 and 110 mM, this resulted in a slow, reversible decrease in conductance. However, additional channel constructs, in which inward rectification was maintained but the pH sensor was abolished, failed to respond to voltage under the same conditions. This indicates that blocking access of intracellular K(+) to the selectivity filter cannot account for coupling. The C13 chimera was 10 times more sensitive to extracellular Ba(2+) block than was ROMK2, indicating that changes in the COOH terminus affect ion binding to the outer part of the pore. This effect correlated with the sensitivity to inactivation by H(+). We conclude that decreasing pH(I) increases the sensitivity of ROMK2 channels to K(+)(o) by altering the properties of the selectivity filter.

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Capturing intracellular pH dynamics by coupling its molecular mechanisms within a fully tractable mathematical model.

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