Temporal characteristics of botulinum neurotoxin therapy

Abstract

Botulinum neurotoxin is a pharmaceutical treatment used for an increasing number of neurological and non-neurological indications, symptoms and diseases. Despite the wealth of clinical reports that involve the timing of the therapeutic effects of this toxin, few studies have attempted to integrate these data into unified models. Secondary reactions have also been examined including the development of adverse events, resistance to repeated applications, and nerve terminal sprouting. Our primary intent for conducting this review was to gather relevant pharmacodynamic data from suitable biomedical literature regarding botulinum neurotoxins via the use of automated data-mining techniques. We envision that mathematical models will ultimately be of value to those who are healthcare decision makers and providers, as well as clinical and basic researchers. Furthermore, we hypothesize that the combination of this computer-intensive approach with mathematical modeling will predict the percentage of patients who will favorably or adversely respond to this treatment and thus will eventually assist in developing the increasingly important area of personalized medicine.

Figure 1. A minimal model for the actions of botulinum neurotoxin A (BoNT/A)

Each compartment represents a species of BoNT/A molecule, for example, the bulk amount in solution distal to its receptors, free in solution proximal to its receptors, bound to receptor, undergoing internalization and translocation, and, ultimately, exerting its proteolytic effect. The rate constants shown determine the unidirectional interconversions among these species. Based on previously published experimental data and kinetic models [6,7].

Figure 2. Framework for a physiologically based model

Based on the minimal model in Figure 1, more details have been included to account for the amount of BoNT in the blood, and its distribution to organs where it is eliminated. BoNT/A is distributed to its targets such as the cholinergic terminals at the NMJ. The traditional ADME model has been expanded to include the multistep molecular processes involved in the toxin mechanism of reaction. At these sites, BoNT/A binds to its receptors, becomes internalized, and undergoes low-pH dependent translocation from an intracellular vesicular compartment into the neuroplasm. Inside the neuron, BoNT/A enzymatically cleaves its substrate SNAP-25. The amount of uncleaved substrate remaining is a function of tension that can be developed by the muscles (not shown). The substrate itself is synthesized and degraded. The toxin is eliminated by as yet unknown mechanisms. ADME: Absorption, distribution, metabolism and excretion; BoNT/A: Botulinum neurotoxin A; im: Intramuscular; ip.: Intraperitoneal; NMJ: Neuromuscular junction; sc.: Subcutaneous; SNAP-25: Synaptosomal-associated protein of 25 kDa.

Figure 3. Variability in compound muscle action potential responses from healthy volunteers injected with BOTOX in the extensor digitorum brevis muscle

(A) Superimposed responses from 14 subjects following injection of 4 U on day 0. (B) Calculated average values with a measure of variability (bars represent standard error). Data from [26].

Figure 4. Relationship between the administered doses of type B toxin (MYOBLOC^®) and the resulting duration of effect in patients with glabellar rhytids

Data were least-squares fit to a hyperbolic function: percentage duration: [(max duration) (U)]/(ED₅₀ + U). SE: Standard error; U: Units of MYOBLOC. Data from [35,74,75].