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Lebeda2008 - BoTN Paralysis (4 step model)

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This is the 4 step model from

Onset dynamics of type A botulinum neurotoxin-induced paralysis.
Lebeda FJ, Adler M, Erickson K, Chushak Y.; J Pharmacokinet Pharmacodyn. 2008 Jun;35(3):251-67. Epub 2008 Jun 13.
pubmedID: 18551355

Related Publication
  • Onset dynamics of type A botulinum neurotoxin-induced paralysis.
  • Lebeda FJ, Adler M, Erickson K, Chushak Y
  • Journal of pharmacokinetics and pharmacodynamics , 6/ 2008 , Volume 35 , pages: 251-267
  • Integrated Toxicology Division, US Army Medical Research Institute of Infectious Diseases, Fort Detrick, MD 21702-5011, USA.
  • 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.
Lukas Endler

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BIOMD0000000178.xml.origin SBML L2V3 representation of Lebeda2008 - BoTN Paralysis (4 step model) 8.08 KB Preview | Download

  • Model originally submitted by : Lukas Endler
  • Submitted: Aug 11, 2008 5:44:46 PM
  • Last Modified: May 18, 2017 12:01:40 PM
  • Version: 2 public model Download this version
    • Submitted on: May 18, 2017 12:01:40 PM
    • Submitted by: Lukas Endler
    • With comment: Current version of Lebeda2008 - BoTN Paralysis (4 step model)
  • Version: 1 public model Download this version
    • Submitted on: Aug 11, 2008 5:44:46 PM
    • Submitted by: Lukas Endler
    • With comment: Original import of Lebeda2008_bot_tox_paralysis
Curator's comment:
(added: 07 Sep 2010, 15:24:42, updated: 07 Sep 2010, 15:24:42)
Figure 3 and Figure 4 of the reference publication has been reproduced. The model was integrated and simulated using Copasi v4.5.31.