Fractal-like kinetics of intracellular enzymatic reactions: a chemical framework of endotoxin tolerance and a possible non-specific contribution of macromolecular crowding to cross-tolerance

Abstract

BackgroundThe response to endotoxin (LPS), and subsequent signal transduction lead to the production of cytokines such as tumor necrosis factor-α (TNF-α) by innate immune cells. Cells or organisms pretreated with endotoxin enter into a transient state of hyporesponsiveness, referred to as endotoxin tolerance (ET) which represents a particular case of negative preconditioning. Despite recent progress in understanding the molecular basis of ET, there is no consensus yet on the primary mechanism responsible for ET and for the more complex cases of cross tolerance. In this study, we examined the consequences of the macromolecular crowding (MMC) and of fractal-like kinetics (FLK) of intracellular enzymatic reactions on the LPS signaling machinery. We hypothesized that this particular type of enzyme kinetics may explain the development of ET phenomenon.MethodOur aim in the present study was to characterize the chemical kinetics framework in ET and determine whether fractal-like kinetics explains, at least in part, ET. We developed an ordinary differential equations (ODE) mathematical model that took into account the links between the MMC and the LPS signaling machinery leading to ET. We proposed that the intracellular fractal environment (MMC) contributes to ET and developed two mathematical models of enzyme kinetics: one based on Kopelman’s fractal-like kinetics framework and the other based on Savageau’s power law model.ResultsKopelman’s model provides a good image of the potential influence of a fractal intracellular environment (MMC) on ET. The Savageau power law model also partially explains ET. The computer simulations supported the hypothesis that MMC and FLK may play a role in ET.ConclusionThe model highlights the links between the organization of the intracellular environment, MMC and the LPS signaling machinery leading to ET. Our FLK-based model does not minimize the role of the numerous negative regulatory factors. It simply draws attention to the fact that macromolecular crowding can contribute significantly to the induction of ET by imposing geometric constrains and a particular chemical kinetic for the intracellular reactions.

Function of metabolic and organelle networks in crowded and organized media

“…Modeling and experimental work (Kim and Yethiraj, 2009 ; Pastor et al, 2014 ) also supports the idea that macromolecular crowding can contribute significantly to changes in enzymatic reactions (Vasilescu et al, 2013 ). To simulate rapid metabolite transfer between the enzymatic components of the phosphotransferase system (PTS), macromolecular crowding had to be assumed both to increase the association rate constants and to decrease the dissociation rate constants of the PTS complexes (Rohwer et al, 1998 ).…”

Down-Regulated Receptor Interacting Protein 140 Is Involved in Lipopolysaccharide-Preconditioning-Induced Inactivation of Kupffer Cells and Attenuation of Hepatic Ischemia Reperfusion Injury

“…Moreover, endotoxin tolerance induction seems to be effective not only in alleviating the toxic effects of LPS but also in protecting against noninfectious challenge such as I/RI. This cross-tolerant effect is recognized as LPS preconditioning [ 6 , 10 ]. It has been reported that endotoxin tolerance can attenuate I/RI in various organs including liver [ 11 – 13 ], while the precise molecular mechanism remains unclear.…”

Demystifying the spreading of pandemics I: The fractal kinetics SI model quantifies the dynamics of COVID-19

“…This approach has found numerous applications for the study of the rate of processes in a plethora of disciplines e.g. pharmacokinetics (8,12), oral drug absorption (13), drug dissolution, drug release (14)(15)(16)(17), drug metabolism (18,19), enzymatic reactions (20,21), anaerobic digestion (22), surface reactions (23). However, this type of kinetics is also very appropriate in studying the "reaction" of susceptible-infected individuals under "real life" conditions.…”

“…Thus, instead of a constant infection rate, the fractal SI model considers a rate which is a decreasing function of time (7). The choice of a power law for the functional form is of course arbitrary, however, it has proven to be quite simple and effective in the description of physicochemical reaction processes (8,(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23). In this work, we divide time with a scaling constant τ=1 day which is not an adjustable parameter and allow us to express the parameter α in (time) -1 units regardless of the value of h (29).…”