A reaction-diffusion model of the receptor-toxin-antibody interaction
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RESEARCH
Open Access
A reaction-diffusion model of the receptor-toxinantibody interaction Vladas Skakauskas1, Pranas Katauskis1 and Alex Skvortsov2* * Correspondence: alex. [email protected] 2 HPP Division, Defence Science and Technology Organisation, 506 Lorimer st., VIC 3207, Melbourne, Australia Full list of author information is available at the end of the article
Abstract Background: It was recently shown that the treatment effect of an antibody can be described by a consolidated parameter which includes the reaction rates of the receptor-toxin-antibody kinetics and the relative concentration of reacting species. As a result, any given value of this parameter determines an associated range of antibody kinetic properties and its relative concentration in order to achieve a desirable therapeutic effect. In the current study we generalize the existing kinetic model by explicitly taking into account the diffusion fluxes of the species. Results: A refined model of receptor-toxin-antibody (RTA) interaction is studied numerically. The protective properties of an antibody against a given toxin are evaluated for a spherical cell placed into a toxin-antibody solution. The selection of parameters for numerical simulation approximately corresponds to the practically relevant values reported in the literature with the significant ranges in variation to allow demonstration of different regimes of intracellular transport. Conclusions: The proposed refinement of the RTA model may become important for the consistent evaluation of protective potential of an antibody and for the estimation of the time period during which the application of this antibody becomes the most effective. It can be a useful tool for in vitro selection of potential protective antibodies for progression to in vivo evaluation.
1. Background The successful bio-medical application of antibodies is well-documented (see [1,2] and references therein) and there is an ever-increasing interest in the application of antibodies for a mitigation of the effect of toxins associated with various biological threats (epidemic outbreaks or malicious releases) [3-5]. With the recent progress in bioengineering, many antibodies with different affinity parameters have been generated. For a long time the main target of antibody design has been the antibody affinity. However, according to recent results [6], affinity, on its own, is a poor predictor of protective or therapeutic potential of an antibody. In fact, the treatment effect of an antibody can be described by a consolidated parameter which includes the reaction rates of the receptortoxin-antibody kinetics and the relative concentration of reacting species [6]. As a result, any given value of this parameter determines an associated range of antibody kinetic properties and its relative concentration in order to achieve a desirable therapeutic effect. Analytical models, similar to those reported in [6], can be a useful tool for in vitro selection of potentially protective antibodies for progression to in viv
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