Accompanying data for the paper "Accounting for the mechanical response of the cell membrane during the uptake of random nanoparticles"

Contributions

Iaquinta Sarah did contribute to the first draft edition, the development of the theoretical background of the algorithms and their implementation

Khazaie Sharam did contribute to the revision and edition of the draft, and to the development of the theoretical background of the algorithms

Jacquemin Frédéric did contribute to the project management and to the revision of the article.

Fréour Sylvain did contribute to the project management and to the revision of the article.

Funding sources

i-Site NExT : Grant/Award Number: ANR-16-IDEX-0007, Région Pays de la Loire and CNRS (French National Centre for Scientific Research).

Data structure and information

code - np_uptake source and data directory

workflow - scripts to reproduce figures

np_uptake - source code producing results and figures

figures - utility module to produce figures

model - see detailed description below

metamodel_implementation - see detailed description below

sensitivity_analysis - see detailed description below

Detailed description

Abstract

In order to improve the efficiency of the delivery of cancer treatments to cancer cells, the cellular uptake of nanoparticles (NPs), used as drug delivery systems, is numerically investigated through a mechanical approach. The objective is to optimize the NP's mechanical and geometrical properties to enhance their entry into cancer cells while avoiding benign ones. In previous studies, these properties are modeled as constant during the process of cellular uptake. However, recent observations of the displacement of the membrane's constituents towards the region in the cell membrane where the uptake of the NPs takes place show that the mechanical properties of the membrane vary during this process. Reason for writing The important contribution of adhesion to the wrapping process is already well documented in literature. It is therefore crucial to model this parameter properly as the conclusions made with a constant adhesion model may not be accurate compared to reality. Methodology Based on the existing knowledge on the reaction of membrane constituents to interaction with NPs, a 3-parameter sigmoidal function, accounting for the delay, amplitude, and speed of the reaction, has been used to model the evolution of adhesion. A variance-based sensitivity analysis has then been performed in order to quantify the influence of these parameters on the outputs of the model. Results It was found that the introduction of a variable adhesion tends to alter the predictions of endocytosis of NPs. The contribution of the amplitude and delay is respectively 0.32 and 0.43 times as important as that of the NP's aspect ratio, which is the prominent parameter. The influence of the slope of the transition is the least important parameter and does not appear to contribute to endocytosis. Implications Hence, models of the cellular uptake of NPs should use a variable, instead of constant, adhesion in order a representative as possible of the behavior of the cell membrane. The predictions are different from those obtained using a model with constant adhesion.

Code

This repository is divided into 4 folders:

model: contains the code used to compute the total variation of energy of the interface between a circular NP and a membrane by accounting for the mechanical accommodation of the latter. This folder also contains the routine to determine the final wrapping phase of the system.

metamodel_implementation: contains a script to check for the representativeness of the dataset used to create a metamodel, a script to create Kriging and PCE metamodels using the Openturns opensource library, and a routine to validate the metamodel that has just been created;

sensitivity_analysis: contains a script that allows to create samples based on the Kriging metamodels that have been created and exported as .pkl files in the metamodel folder. These samples are then used to the apply sensitivity algorithms. The user can choose among the various sensitivity algorithms provided by Openturns. For PCE metamodels, a routine is implemented to directly get the Sobol indices from the coefficients of the PCE metamodel. The indices can be plotted through plot routines;

figures: contains a utils script to display the graphs and save them as PNG files with consistency.