An in vitro assay and artificial intelligence approach to determine rate constants of nanomaterial-cell interactions

In vitro assays and simulation technologies are powerful methodologies that can inform scientists of nanomaterial (NM) distribution and fate in humans or pre-clinical species. For small molecules, less animal data is often needed because there are a multitude of in vitro screening tools and simulation-based approaches to quantify uptake and deliver data that makes extrapolation to in vivo studies feasible. Small molecule simulations work because these materials often diffuse quickly and partition after reaching equilibrium shortly after dosing, but this cannot be applied to NMs. NMs interact with cells through energy dependent pathways, often taking hours or days to become fully internalized within the cellular environment. In vitro screening tools must capture these phenomena so that cell simulations built on mechanism-based models can deliver relationships between exposure dose and mechanistic biology, that is biology representative of fundamental processes involved in NM transport by cells (e.g. membrane adsorption and subsequent internalization). Here, we developed, validated, and applied the FORECAST method, a combination of a calibrated fluorescence assay (CF) with an artificial intelligence-based cell simulation to quantify rates descriptive of the time-dependent mechanistic biological interactions between NMs and individual cells. This work is expected to provide a means of extrapolation to pre-clinical or human biodistribution with cellular level resolution for NMs starting only from in vitro data.

. Schematic representative of FORECAST and its potential application in predictive animal simulations. NMs or fluorophores must be chosen in order to run a fluorescent study on a variety of cell lines with different dosing scenarios on the cell-based assay. The cell based assay captures biological serum and cellular-induced degradative effects. Data obtained from the cell based assay provides a quantitative cellular dose that feeds to an in silico model. This model then optimizes rate constants, which serve as inputs towards in vivo PBPK models to capture accurate animal biodistribtuion.
b Supplementary Figure 2. MTS assay data for all NMs included in cell kinetic analysis. (a) QSH (negatively charged) and (b) PS. Negatively charged QSH experienced minimal toxicity for all doses, and PS exhibited minimal toxicity at 10nM or below. Positive control contained cells exposed to water and negative control contained cells exposed to complete growth media.  In one case, a triplicate of wells exposed to 10nM QD from the MPE compartment was dissolved in 1/3% v/v aqua regia, while in the other, 10nM QSH was dissolved a vial with 1/3% v/v aqua regia. Both scenarios were then transferred to vials for AAS analysis.and measured for cadmium content. The ratio of MPEt to vials were taken, as the plots indicate [Unwashed No Cells] / [QD in vial].. No significant trends in data were noted, and values ratios remained approximately equal to 1, which indicates diluted vials and collected wells were similar in cadmium content.
Supplementary Figure 16. Extraction efficiency for washed well cadmium content. 2X washed cells from CKDt exposed to trypsin or no trypsin with the 10nM QSH dose were all exposed to 1/3 v/v% aqua regia for 10 minutes and transferred to vials for AAS analysis. The ratio of CKD Cd content of non-trypsinized to trypsinized was close to 1, indicative of full cadmium extraction from cell interior.
Supplementary Figure 17. Harvest efficiency above describes the potential to harvest QSH from the total well when there are cells present. Wells exposed to equal doses of QSH with and without cells (unwashed) were given equal doses of 1/3 v/v% aqua regia for 10 minutes. AAS was performed and the ratio of unwashed cells to no cells is approximately 1, indicative of full cadmium extraction, as well as minimal cellular matrix interference on the AAS instrument.

Mathematical Degradation and Uptake Proof
All parameter labels (MPE, CSI, and CKD) are in reference to the diagram in Figure 1b. Any NM located in the CSI compartment at time t is exposed to both media and cells, which by default, cause the NM located in the CSI compartment to undergo total degradation (media and cell), decreasing its total intensity from its starting intensity at time 0, shown in the equation (4) below.
Equation (4) can be rearranged to solve for .
NM located within cells in the CKD compartment have undergone both media and cell induced degradation.
Here, the raw NM intensity obtained from washed cells at time t for the CKD compartment ( ) should be equal to the theoretical NM intensity of the washed cells under non-degradative conditions at time t for CKD ( ′ ) minus the fraction of degradation, which is the intensity of degradation at time t with respect to total intensity at time 0, specifically Equation (6) The calibrated fraction of NM uptake by cells under degradative (assuming time in intracellular environment induces degradation) conditions is equal to the raw intensity of washed cells in CKD compartment taken relative to raw intensity of unwashed cells in CSI compartment at time t. Here, we assume NM located within CKD and CSI compartments have undergone media and cell-induced degradation, giving it a calibration for this effect. = Assuming that the internal standard ( ) and washed cells in CKD ( ) undergo degradation under the same conditions, the fraction here, , should be equal to the fraction of uptake under non-degradative conditions ( ′), ′ = Equation (7) can be rearranged by substituting their respective intensities according to equations (5) and (6), where can be substituted by equation (3) above. This is shown by equation (9) Equation (12) states that the total unwashed NM intensity after a period of time t is equal to the unwashed initial NM intensity (where we assume 0 hours of cell exposure to have no degradation) minus the intensity value of degradation for that period of time t. Substituting ( 0 − ) by the definition of equation (2), yields = Calculation for raw fraction of uptake of for cells is similar to the calibrated, but instead, we take it relative to 0 for comparison, Here, we are taking the raw CKD washed cell NM intensity (which undergoes cell and media degradation) relative to unwashed CSI compartment (which does not undergo cell and media degradation) to understand the degradative effect cells and media can have on a NM.
Calibrated ( ) and raw ( ) fraction of uptake for cells were then used to obtain [Uptake]t concentrations in nM at time t, according to Where is or depending on if cell-induced degradation is present or not, and [Dose] is the exposure dose to cells in nM.