Kinetic and Reaction Pathway Analysis in the Application of Botulinum Toxin A for Wound Healing

Table 1

Summary of processes involved in wound healing as described in text. Recurrence of symptoms results from long-term observations [55] was analyzed in the present paper and is highlighted in bold.

Parameter	Relative rates	Rate constant symbol	Units	Value
Onset of initial wounding	Very fast	𝑘1	msec^−1 or sec^−1	N.A.^a
Development of chronic wound	Moderate	𝑘2	days^−1 or weeks^−1	N.A.
Healing of acute wound	Slow	𝑘3	weeks^−1 or months^−1	N.A.
Healing of chronic wound	Very slow	𝑘4	years^−1	N.A.
Recurrence of symptoms [55], [Figure 3]	Very slow	𝐤𝐝𝐞𝐜𝐚𝐲	years^−1	0.85
4-step reaction [19]
Diffusion toxin to receptors	Moderate	𝑘5	min^−1	0.001
Binding of toxin	Fast	𝑘𝐵	min^−1	0.058
Translocation of toxin	Fast	𝑘𝑇	min^−1	0.141
Toxic reaction (lysis)	Fast	𝑘𝐿	min^−1	0.013

^a N.A., because data are not presently available, order of magnitude estimates are given.