How relevant are in vivo and in vitro studies for clinical sepsis? A mathematical model of LPS signaling based on endotoxin tolerance.

The goal of this paper is to explain: (1) the low-level TNF-alpha concentration in some septic patients and (2) the relevance of the in vivo and in vitro models of endotoxin tolerance for the clinical sepsis. We hypothesized that the low level of TNF-alpha concentration in septic patients can be understood, at least in part, by two particularities of these patients: the kinetics of LPS plasma levels and the existence of a "endotoxin tolerance-like phenomenon" (a particular type of down regulation of LPS signaling). The kinetics of TNF-alpha, as expression of the cytokine releasing capacity, was modeled considering LPS as a command (function of time) and the existence of a brake system (a summation of the down regulating factors of LPS signaling). The mathematical model, based on Michaelis-Menten (Hill) equations, is a non-autonomous first-order differential system of two equations with two unknowns describing the dynamics of TNF-alpha concentration and of the brake system, LPS being considered as an input. To test the above model four scenarios concerning the LPS signaling were considered TNF-alpha dynamics 1) following a single LPS stimulus 2) in in vivo experiments 3) in in vitro experiments and 4) in clinical sepsis. Our hypothesis, that in LPS signaling the kinetics of LPS as well as the existence of an endotoxin-like phenomenon are crucial features, may explain the contradictory data obtained in in vitro, in vivo experimental studies and in sepsis patients.