Kinetics of Extracellular ATP from Goldfish Hepatocytes: A Lesson from Mathematical Modeling

CHARA OSVALDO; PAFUNDO DIEGO; SCHWARZBAUM PABLO JULIO

BULLETIN OF MATHEMATICAL BIOLOGY

Springer

Lugar: New York; Año: 2009 vol. 71 p. 1025 - 1047

0092-8240

In goldfish hepatocytes, hypotonic exposure leads to cell swelling, followedby a compensatory shrinkage termed RVD. It has been previously shown that ATP isaccumulated in the extracellular medium of swollen cells in a non-linear fashion, and thatextracellular ATP (ATPe) is an essential intermediate to trigger RVD.Thus, to understand how RVD proceeds in goldfish hepatocytes, we developed twomathematical models accounting for the experimental ATPe kinetics reported recently byPafundo et al. in Am. J. Physiol. 294, R220–R233, 2008. Four different equations forATPe fluxes were built to account for the release of ATP by lytic (JL) and nonlytic mechanisms(JNL), ATPe diffusion (JD), and ATPe consumption by ectonucleotidases (JV ).Particular focus was given to JNL, defined as the product of a time function (JR) and apositive feedback mechanism whereby ATPe amplifies JNL. Several JR functions (Constant,Step, Impulse, Gaussian, and Lognormal) were studied.Models were tested without(model 1) or with (model 2) diffusion of ATPe.Mathematical analysis allowed us to get a general expression for each of the models.Subsequently, by using model dependent fit (simulations) as well as model analysis atinfinite time, we observed that:– useof JD does not lead to improvements of the models.– Constant and Step time functions are only applicable when JR = 0 (and thus, JNL = 0),so that the only source of ATPe would be JL, a result incompatible with experimentaldata.– use of impulse, Gaussian, and lognormal JRs in the models led to reasonable good fitsto experimental data, with the lognormal function in model 1 providing the best option.Finally, the predictive nature of model 1 loaded with a lognormal JR was tested by simulatingdifferent putative in vivo scenarios where JV and JNL were varied over ampleranges.