Lebeda et. al. (2008), Onset dynamics of type A botulinum neurotoxin-induced paralysis.
The deadly naturally occurring neurotoxin, Botulinum neurotoxin (BoNT) producedby an anaerobic and spore forming bacterium Clostridium botulinum (and rarely by other Clostridium species such as C. butyricum, C. baratii and C. argentinense), induces apotentially fatal paralysis known as botulism. Botulism is characterized by symmetric, descending, flaccid paralysis of motorand autonomic nerves, usually beginning with the cranial nerves. Blurredvision, dysphagia, and dysarthria are common initial complaints.C. botulinum produces seven antigenitically and serologically distint butstructurally similar toxins (A to G) that are found in soil and ocean sediment.Human botulism is mainly caused by types A, B, E and F. Types C, D and G causetoxicity in birds, horses, cattle and primates.
BoNT enters through 1) Ingestion of preformed toxin, 2) Inhalation of preformed toxin,3) Local production of toxin by C botulinum organisms in the gastrointestinaltract 4) Local production of toxin by C botulinum organisms in devitalizedtissue at the site of a wound.
Figure 1: Botulinum toxin structure A) schematic representation of BoNT, B) Crystal structure of BoNT/A - PDBcode:3BTA. Figure B - taken from . The Light chain catalytic domain is coloured in blue. The heavy chain translocation domain is coloured in green, N-terminal and the C-terminal receptor binding domains are coloured in yellow and red respectively. The catalytic zinc is represented as a ball in gray. The colour code is same for Figures 1A and 1B.
Figure 2:Mechanism of action of BoNTs (right) compared to the normal cell (left). Shown are the individual stages of BoNT intoxication, including cell surface recognition, vesicle internalization, translocation of the catalytic domain (light chain) into the cytosol, and proteolytic cleavage of one of the proteins of the SNARE complex. These steps lead to inhibition of neurotransmitter-containing vesicle release. BoNT/B, D, F, and G cleave proteins of the VAMP family (blue), and BoNT/A, C, and E cleave SNAP-25 (yellow). BoNT/C can also cleave syntaxin (purple).Figure taken from .
The underlying mechanism of BoNT that causes diseases also provides clinicalbenefits. BoNT/A and B are used as medication to treat patients with nerve and muscle disorders.The toxin has been tested and adopted for therapeutic use in four clinical areas1) ophthalmology (for treating blepharospasm and strabismus), 2) neurology (for treating dystonias (focal and some segmental)), 3) otolaryngology (for treating spasmodic dysphonia) and gastroenterolgy that focus on smooth muscle and sphincter control (for treating achalasia).For details [click here].Apart from its medical use, it is also used as cosmetic agents for thetreatment of facial wrinkles. For details [click here].In spite of all these beneficial effect, BoNTs is considered among the most dangerous biological weapon due to their extreme toxicity and easy production. For details [click here]
BoNT is expressed as a single polypeptide chain (~150kDa) which is activatedby proteolytic cleavage to form two chains (a heavy chain (100kDa) and a lightchain (50kDa)) that are connected by a single disulphide bond. The heavychain comprises of translocation domain andreceptor-binding domain. The light chain (catalytic domain) is a zinc-containing metalloproteinase. Schematic representation and crystal structure of BoNT/A is shown in Figure 1.
BoNT enters the blood stream andis transported to the neuromuscular junction. The receptor-binding domainprovides cholinergic specificity and binds the toxin to the presynapticreceptors. The toxin then enters the neuronal cell via receptor-mediatedendocytosis. The translocation domain of the heavy chain promotes the entry oflight chain (toxic moiety) to neuroplasm, thatcleaves one ore more of the proteins thatform SNARE protein complex (complex formed by SNAP-25,Syntaxin and VAMP) depending on the BoTN serotype. SNARE protein complex normally allow neurotransmitter, Acetylcholine toleave the cell and transmits anerve impulse to a muscle, signalling the muscle to contract. As BoNT prevents the formation of the SNARE protein complex by cleaving the proteins that form SNARE protein complex, the Acetylcholine release is blocked. As the result, signal transmission between the nerve andmuscle is stopped causing botulism (paralysis). The mechanism of neurotransmitter release in normal cell and cells that are affected by BoNT/A is shown in (Figure 2).
In this paper, Lebeda et al. , have used the model developed by Simpson 1980 ,to estimate upper limits of the time during which antitoxin and other impermeable inhibitors of BoNT/A can exert an effect.Experimental data of several laboratories were tested on two differentmathematical models, the 3-step model [BIOMD0000000267]and the 4-step model [BIOMD0000000178]. The 3-step model is the reduced form of the model developedby Simpson , i.e., it omits three unknown parameters that represents the binding sites for each species of the toxin .The models were designed to predict the time available for an inhibitor tohave some effect (tinhib) on the free BoNT/A and the relation between this time andthe rate of paralysis onset.
The 3-step model consisted of a sequence of reactions based on the mechanism ofBoNT/A action, namely, 1) diffusion of free BoNT/A to its binding sites at synaptictermini, 2) translocation of the bound toxin into the neuroplasm, and 3) exertionof the toxic effect by the toxic moiety.
Each species of BoNT/A is associated with a different environment: 1) extracellular in solution (free), 2) on the surface - bound to a receptor (bound), 3) intracellular endocytotic vesicle (trans) and 4) intracellular neuroplasm (lytic).
Figure 3: 3-step model: Simulation result (using data obtained from isolated NMJ (NeuroMuscular Junction), for details refer , ) of the different species of BoNT/A species and normalized amount of tension remaining after the formation of the lytic species. The time-to-10% tension, t10, was 204 mins. The upper limit for the amount of time available foran inhibitor of BoNT/A to exert some effect, tinhib, was ≤ 40mins.Figuretaken from [BIOMD0000000267] which reproduces Figure 1 of 
Figure 4: 4-step model: Different values of kS in the 4-step model simulated the onset of BoNT/A-induced effect (tension). The maximum BoNT/A-induced effect, achieved by day 11, was simulated with kS=0.00015min-1 which was used as the estimated value for the 4-step model. Figure taken from [BIOMD0000000178] which reproduces Figure 3 of 
The paralysis that occurs postsynaptically isembedded in the species, lytic. Rates of the reaction were taken from ,where kB=0.058min-1, kT=0.141min-1and kL=0.013min-1.This model predicted that, to exert some degree of inhibition, impermeableneutralizing antibodies or BoNT/A inhibitors need to be applied within 40mins ofthe addition of 0.1nM BoNT/A to the bathing chamber, i.e., before a ~20%reduction of nerve-evoked twitch tension occurs (
As the 3-step model did not reproduce (changing the rate constant kB, kT andkL failed to produce the slower onset of BoNT/A induced paralysis observed invivo, refer ) the temporal changes in paralysis with different toxin concentrations, a new, initial rate (kS) was added that represents the movement ofBoNT/A (bulk species) from distal location from its receptors to the proximalvolume where the BoNT/A free species is available for binding.
Figure 4 shows the different values of kS in the 4-step model,simulated the onset of BoNT/A-induced effects in a variety of in vitro and invivo data sets (refer to ). It is predicted that as kS decreased, the abosolute values for t10 and tinhib is increased. Starting as approximately day 11, the maximum relief fromsymptoms was noted by the patient (t10=10.6 days). The rate constant kS wassystematically varied and was estimated to 0.00015min-1 for this model.From the plots Figure 3 and Figure 5 it is inferred that in the3-step model the time-to-10% tension (t10) was 5 times slower than tinhib butin the 4-step model they are almost identical. i.e. in the 4-step model(clinical data), the time course of the unbound BoNT/A species was predictedto develop at essentially the same rate as the time course of paralysis.
Although, the binding, translocation and lytic processes of BoNT involve multiple reaction steps, these three processes are simplified as single-step reaction in these models. Also, for computational convenience, it is assumed that the models were independent of compartments and that uniform distribution existed for all the BoNT/A species and binding sites. Nevertheless, these models provide initial, quantitative framework for making extrapolationsfrom animal model to human data and also could be extended once the rates associated with many intermediate reactions are determined. This type of modeling approach may also beuseful to study the kinetics of other toxins or viruses that invade host cellsby similar mechanisms, e.g. receptor-mediated endocytosis.
Figure 5: Simulation result (obtained using clinical data in vivo data) of the different species of BoNT/A species and normalized amount of tension remaining after the formation of the lytic species. The time courses of the different species can be compared with the relatively slow loss of tension (t10=15,450mins or 106 days) of BoNT/A-induced paralysis. In contrast to the results of the 3-step model (figure 3), the time courses of the unbound BoNT/A and the lytic species overlapped (yellow and red plot in the figure), making the estimated upper limit value of tinhib longer in vivo than at the isolated NMJ (NeuroMuscular Junction). Simulation result taken from [BIOMD0000000178] which reproduces Figure 4 of 
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