Lebeda2008 - BoTN Paralysis (4 step model)

Lebeda2008 - BoTN Paralysis (4 step
model)

The
onset of paralysis of skeletal muscles induced by BoNT/A at the
isolated rat neuromuscular junction is described in this model.
This model is the extended model of 
BIOMD0000000267
,
which itself is the reduced form of the model developed by
Simpson 1980; PMID 
6243359

This model is described in the article:

Onset dynamics of type A
botulinum neurotoxin-induced paralysis.

Lebeda FJ, Adler M, Erickson K,
Chushak Y.
J Pharmacokinet Pharmacodyn 2008 Jun;
35(3): 251-267
Abstract:

Experimental studies have demonstrated that botulinum
neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a
multi-step mechanism. Following its binding to specific
receptors at peripheral cholinergic nerve endings, BoNT/A is
internalized by receptor-mediated endocytosis. Subsequently its
zinc-dependent catalytic domain translocates into the
neuroplasm where it cleaves a vesicle-docking protein, SNAP-25,
to block neurally evoked cholinergic neurotransmission. We
tested the hypothesis that mathematical models having a minimal
number of reactions and reactants can simulate published data
concerning the onset of paralysis of skeletal muscles induced
by BoNT/A at the isolated rat neuromuscular junction (NMJ) and
in other systems. Experimental data from several laboratories
were simulated with two different models that were represented
by sets of coupled, first-order differential equations. In this
study, the 3-step sequential model developed by Simpson (J
Pharmacol Exp Ther 212:16-21,1980) was used to estimate upper
limits of the times during which anti-toxins and other
impermeable inhibitors of BoNT/A can exert an effect. The
experimentally determined binding reaction rate was verified to
be consistent with published estimates for the rate constants
for BoNT/A binding to and dissociating from its receptors.
Because this 3-step model was not designed to reproduce
temporal changes in paralysis with different toxin
concentrations, a new BoNT/A species and rate (k(S)) were added
at the beginning of the reaction sequence to create a 4-step
scheme. This unbound initial species is transformed at a rate
determined by k(S) to a free species that is capable of
binding. By systematically adjusting the values of k(S), the
4-step model simulated the rapid decline in NMJ function (k(S)
>or= 0.01), the less rapid onset of paralysis in mice
following i.m. injections (k (S) = 0.001), and the slow onset
of the therapeutic effects of BoNT/A (k(S) < 0.001) in man.
This minimal modeling approach was not only verified by
simulating experimental results, it helped to quantitatively
define the time available for an inhibitor to have some effect
(t(inhib)) and the relation between this time and the rate of
paralysis onset. The 4-step model predicted that as the rate of
paralysis becomes slower, the estimated upper limits of
(t(inhib)) for impermeable inhibitors become longer. More
generally, this modeling approach may be useful in studying the
kinetics of other toxins or viruses that invade host cells by
similar mechanisms, e.g., receptor-mediated endocytosis.

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and identified by:
BIOMD0000000178.
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