TABLE 3.

The summary of nomenclature

Symbols	Units	Definitions
A0	mM	Initial insulin concentration.
A1	mM	Insulin monomer or insulin monomer concentration.
Ahex	mM	Original insulin hexamer or its concentration.
Ai	mM	Insulin cluster consisting of i monomers or its concentration.
b	mM−1	Proportional constant relating fibril concentration to experimental signal.
dAF	m	The mean free path between monomer and fibril.
DAi	m2 s−1	Diffusivity of oligomer Ai.
DF	m2 s−1	Diffusivity of fibril.
ΔG°	Kcal/mol	Gibbs free energy of the reaction of monomers becoming (n–1)-mers.
f	—	Our fibrillation model expressed as a function.
F	mM	Fibrils or fibril concentration.
i	Number	Our fibrillation model expressed as a function.
Jhex	h−1 mM	The reaction flux of original insulin decomposition.
Jnu,i	h−1 mM	The flux of ith nucleation reaction.
Jfb,i	h−1 mM	The flux of ith fibrillation reaction.
kapp	h−1	The apparent growth rate of fibril, which is equal to 1/τ.
Kc	mM−(n−2)	Equilibrium constant between monomers and (n−1)-mers.
khex	h−1	Reaction rate constant of original insulin decomposition.
kfb−	h−1	General reverse rate constant of fibrillation reaction.
kfb,1	h−1 mM−1	Forward rate constant of the first fibrillation reaction.
kfb,i	h−1 mM−1	Forward rate constant of ith fibrillation reaction.
kfb,−1	h−1	Reverse rate constant of ith fibrillation reaction.
knu,1	h−1 mM−1	Forward rate constant of the first nucleation reaction.
knu−	h−1	General reverse rate constant of nucleation reaction.
knu,i	h−1 mM−1	Forward rate constant of ith nucleation reaction.
knu,−i	h−1	Reverse rate constant of ith nucleation reaction.
mi, mf	h−1	The slope of initial and final fibrillation response curve, respectively.
n	Number	Critical number of monomers in a nucleus.
nexp	Number	The number of experimental data points.
N	Number	The average size of fibrils in terms of number of monomer.
	mol−1	Avogadro constant.
Φ(θ)	—	The objective function to be optimized with respect to θ.
R	J/mol K	Ideal gas constant, 8.314.
R2	—	Coefficient of determination.
RAi	m	Characteristic length of oligomer Ai.
r1, r2	mM	The first and second roots of the fibril quadratic equation.
t0	h	The time to 50% of maximal signal or the time of inflection point.
ti	h	The time of ith experimental data point.
tν,α/2	—	Student's t-distribution with degree of freedom ν, significance level α.
τ	h	The time constant of fibril growth; it is equal to 1/kapp.
θ	—	The vector of parameters to be estimated.
V1	m3	The mean volume of a monomer.
X	—	Linearized design matrix (Jacobian matrix).
Y	—	UV-vis absorbance of ThT fluorescence intensity.