In vitro rate constant optimization

This protocol is extracted from research article:

Animal simulations facilitate smart drug design through prediction of nanomaterial transport to individual tissue cells

**
Sci Adv**,
Jan 22, 2020;
DOI:
10.1126/sciadv.aax2642

Animal simulations facilitate smart drug design through prediction of nanomaterial transport to individual tissue cells

Procedure

In vitro rate constants (*k*_{a}, *k*_{des}, *k*_{i}, and *k*_{deg}) were optimized using the GA, originally developed by Holland in the early 1970s. This was typically used as an artificial intelligence algorithm [e.g., it is used for training artificial neural networks (*65*)] for a more robust optimization of parameters based on evolutionary ideas of natural selection where it does not rely heavily on initial input and often leads to a global minimum (*66*). For optimization, rate constants were supplied by the GA to produce simulation outputs at particular time points. When fed to the model equations (described above), membrane ([*Mem*](*t*)) and cell space ([*Cell*](*t*)) simulated outputs were summed at each time point and compared to in vitro measured values using the residual sum of squares described below. To supply model equations (Eqs. 11 and 12) with rate constants, initial vectors (“chromosomes”) composed of rate constants (“genes”) were randomly populated by the GA, fed to the cell kinetic model, calculated for fitness, and underwent selection, crossover, and mutations to maximize diversity and produce better fitness at each iteration (“generation”). Specifically, Eqs. 11 and 12 were first optimized to the calibrated datasets where no degradation was present, holding *k*_{deg} at 0. Once optimized, we reconsidered QD raw concentration values containing degradation effects to determine the rate of degradation (*k*_{deg}), holding the previously optimized adsorption, desorption, and internalization rates (*k*_{ads}, *k*_{des}, and *k*_{int}) as constant. All simulations were performed in MATLAB v2015b. Parameter optimization was implemented with the GA optimization function from the Optimization Toolbox. Parameters for estimation included the following: initial population, 300; population size, 50; generations, 100; mutation rate, mutation Gaussian; crossover rate, 0.80; selection function, stochastic uniform.

The GA was evaluated using the residual sum squares as the fitness function (Eq. 19)$$\text{RSS}={\displaystyle {\sum}_{i}^{n}}{({y}_{i}-{m}_{i})}^{2}$$(19)where RSS represented the residual sum of squares from model output (*m _{i}*) at time (

Model output upper and lower bounds were evaluated at the 95% confidence interval through$$\text{CL}(95\%)={m}_{i}\pm 2*S$$(21)where CL(95%) represented 95% confidence limit. The GA was run for 100 generations, enough to allow convergence at a fitness value representative of measured data.

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