Development of a MATLAB® model for estimating the amount of protein adsorption on nanoparticles covered with poly (ethylene glycol)
Authors:   , Mehta Asavari , Wheatley Margaret A. , Sarver Joseph J. , Allen Fred D. 
Published: July 2021

Targeted drug delivery to cancerous tumors is a promising strategy for the treatment of cancer that mitigates the comprehensive, deleterious effects of current chemotherapy methods. The ability to selectively deliver cancer drugs to solid tumors can be achieved with constructs like micro-bubbles, micro-particles, nanoparticles and micelles that can carry and elute a conjugated drug. Moreover, poly (ethylene glycol) (PEG) can be incorporated into these delivery vehicles to provide a "stealth" coating that prevents the immune system from recognizing and prematurely eliminating them before the drug delivery is complete. The mechanism of immune system avoidance is accomplished when the incorporated PEG chains create a steric hindrance on the surface of the carrier particle that blocks the adsorption of blood plasma proteins onto the particle surface which consequently marks the particle as an antigen that must be removed by the immune system. Mathematically modeling the amount of plasma protein that can adsorb on a carrier particle with a PEG coating offers the benefit of expediting the selection of optimal values for three key parameters of particle fabrication: 1) PEG molecular weight, 2) PEG mass fraction and 3) carrier particle diameter which are essential to the creation of a PEG-coated, carrier particle that will minimize plasma protein adsorption. The basis for this mathematical model is a characteristic formula obtained from the research paper, Gref et al. [11], which describes the surface density threshold (SDT) representing the smallest area between PEG chains on the surface of a nanoparticle that creates the maximal blockage of protein adsorption. This SDT formulation, which contains all three key parameters mentioned above, was used to represent the amount of PEG in terms of molecular weight and mass fraction which was necessary for minimizing protein adsorption on nanoparticles that were also fabricated by the Gref study. In this current study, we use MATLAB® programming to combine the SDT formula and its corresponding experimental data from the Gref study to produced two curve-fit equations (effectively two separate models) that can be used to predict the protein adsorption values that occur for either changing molecular weight of PEG or changing mass fraction of PEG. The simulated values of protein adsorption resultant from variation of the given parameter was then directly compared to the experimental values obtained from Gref et al. in order to evaluate the model accuracy in estimating protein adsorption. The evaluation indicated that the success of the models in estimating protein adsorption was restricted to the parameter it was derived from, either PEG molecular weight or PEG mass fraction. In other words, the model to estimate protein adsorption due to variation of PEG molecular weight was not valid for estimating protein adsorption due to variation of PEG mass fraction and vice versa. Therefore examining changes in a parameter of interest must be done with the appropriate model. The correlation coefficients for the correlations tests showed R² = 0.997 for PEG molecular weight and R² = 0.988 for PEG mass fraction. Additionally, the models were not successful in estimating the protein adsorption values that corresponded to the average diameter of the nanoparticles because there was no experimental nanoparticle diameter data from Gref et al. [11] on which to base a curve-fitted estimation model. So, the two models in this study cannot account for a changing particle diameter. The two models developed in this study still require further refinement and validation with more experimental data other than that found in the study by Gref et al. [11]. In that sense, experiments with the parameter of particle diameter can be included to broaden the modeling perspective. Attempts were made to combine the two separate models of PEG molecular weight and PEG mass fraction to find a more universal metric that could establish the optimal parameters of nanoparticle fabrication that would minimize protein adsorption. One metric was to create a ratio of the two parameters and another was to create the product (multiplication) of the two parameters, and then develop a curve fit model for each metric. The results did not show promise because the variation of each metric did not produce a matched correlation to the data. In conclusion, researchers can inexpensively use this modeling tool as a starting point for designing PEG-coated, drug-carrier nanoparticles as it pertains to variation of PEG molecular weight or PEG mass fraction. The modeling presented in this study has extended the framework for simulating plasma protein adsorption on nanoparticles that would significantly inform the fabrication of effective, immuno-evasive, drug-eluting nanoparticles for cancer treatments.