Solving the kinetic model and fit algorithm

This protocol is extracted from research article:

Allosteric pathway selection in templated assembly

**
Sci Adv**,
Oct 11, 2019;
DOI:
10.1126/sciadv.aaw3353

Allosteric pathway selection in templated assembly

Procedure

We solved the kinetic model numerically using the Runge-Kutta method, with step size d*t* = 0.01 τ_{B} for the initial 10 τ_{B} of the simulation and d*t* = 0.25 τ_{B} for the remainder. Parameters for the kinetic model were found by minimizing the sum of squared residuals (*R*) between the kinetic diagrams and the kinetic model for each binned data point$$R={\displaystyle \sum _{i=1}^{n}}[{({[\mathrm{F}]}_{i}-{f}_{\mathrm{F},i})}^{2}+{({[\text{FA}]}_{i}-{f}_{\text{FA},i})}^{2}+{({[\mathrm{D}]}_{i}-{f}_{\mathrm{D},i})}^{2}+{({[\text{DA}]}_{i}-{f}_{\text{DA},i})}^{2}]$$(11)where *n* = 2000 equals the number of logarithmic spaced binned data points, [FA]* _{i}* is the number density of assemblers in the FA state at data point

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