Effect of palytoxin on the sodium–potassium pump: model and simulation

Abstract

We propose a reaction model for the palytoxin-sodium-potassium (PTX-Na(+)/K(+)) pump complex. The model, which is similar to the Albers-Post model for Na(+)/K(+)-ATPase, is used to elucidate the effect of PTX on Na(+)/K(+)-ATPase during the enzyme interactions with Na(+) and/or K(+) ions. Conformational substates and reactions for the pump are incorporated into the Albers-Post model to represent enzymes with or without bound PTX. A mathematical model based on the reaction scheme is used in simulations modeling experimental studies of PTX-induced ionic currents. Our simulations suggest that (i) extracellular Na(+) as well as K(+) promotes PTX-induced channel blockage; (ii) extracellular K(+) accelerates PTX unbinding; and (iii) K(+) occlusion in the PTX-pump complex is essential for describing the PTX-induced current dynamics.

Hypothesized diprotomeric enzyme complex supported by stochastic modelling of palytoxin-induced Na/K pump channels

“…These are the same concentrations used in the reported experimental procedures and were also used in the computational simulations [5,6,9]. The initial conditions used were as follows: $n_{\mathrm{normalE}1}=n_{\mathrm{normaltotal}},n_{\mathrm{normalE}2}=\hspace{0.17em}{n}_{\mathrm{normalNa}3\mathrm{normalE}1}=n_{\mathrm{normalE}2}=n_{\mathrm{normalNa}2\mathrm{normalE}2}=n_{\mathrm{normalPTXEc}}=n_{\mathrm{normalPTXEo}}=n_{\mathrm{normalPTX}(\mathrm{Na})2\mathrm{normalEc}}=0$.…”

“…The reaction constants of p1–p6 were extracted from Rodrigues et al . [9]. The reaction rates of p7, p9 and p10 (table 3) were assumed to be equal to the rates of reactions p1, p4 and p3, respectively (table 2).…”

“…Using this model, experimental procedures were simulated [6,7] to investigate reactions and substates responsible for increasing the enzyme affinity for PTX and its effects on enzyme phosphorylation [8]. A reaction model was also proposed to investigate the interference of PTX with the pump when the enzyme interacts with Na + and/or K + in the absence of ATP [9]. These models resulted in the proposal of a set of reactions that lead to substates of the PTX–Na + /K + pump complex, following reported descriptions [2,4–6].…”

“…The substates and reaction rates extracted from the literature [9] were represented mathematically. Using probabilistic analyses and simulating populations of single channels based on stochastic semantics, the model was validated and the single-channel dynamic was compared with experimental data.…”

Biophysical Aspects of the Nonsynaptic Epileptiform Activity

“…The permeability parameters for the glial cells, P Na glia (1.00 × 10 -8 cm/s), P K glia (1.08 × 10 -7 cm/s) and P Cl glia (2.50 × 10 -8 cm/s), were adjusted aiming at reproducing the resting potential typical for these cells (Pan & Stringer, 1996). The Na/K pump parameter, P A glia (2.04 × The sodium potassium ATPase function was modeled considering the main reactions involved, always following the Albers-Post model (Heyse et al, 1994;Rodrigues et al, 2008). From the reactions describing the Albers-Post cycles, two reactions were derived, one for the forward cycle, 3NaiEi + 2KoEo + ATPEi ↔ Ai, and other for the reverse cycle, 3NaoEo + 2KiEi + ADPEi + PEi ↔ Ao.…”