Predicting in situ nanoparticle behavior using multiple particle tracking and artificial neural networks

Abstract

Predictive models of nanoparticle transport can drive design of nanotherapeutic platforms to overcome biological barriers and achieve localized delivery. In this paper, we demonstrate the ability of artificial neural networks to predict both nanoparticle properties, such as size and protein adsorption, and aspects of the brain microenvironment, such as cell internalization, viscosity, and brain region by using large (>100 000) trajectory datasets collected via multiple particle tracking in in vitro gel models of the brain and cultured organotypic brain slices. Our neural network achieved a 0.75 recall score when predicting gel viscosity based on trajectory datasets, compared to 0.49 using an obstruction scaling model. When predicting in situ nanoparticle size based on trajectory datasets, neural networks achieved a 0.90 recall score compared to 0.83 using an optimized Stokes-Einstein predictor. To distinguish between nanoparticles of different sizes in more complex nanoparticle mixtures, our neural network achieved up to a recall score of 0.85. Even in cases of more nuanced output variables where mathematical models are not available, such as protein adhesion, neural networks retained the ability to distinguish between particle populations (recall score of 0.89). These findings demonstrate how trajectory datasets in combination with machine learning techniques can be used to characterize the particle-microenvironment interaction space.

Fig. 1

Size-dependent nanoparticle diffusion analysis. (a) 100-, 200-, and 500 nm carboxyl-modified polystyrene particles. (b) Hydrodynamic diameter (intensity mean) distributions (purple: 100 nm, teal: 200 nm, yellow-green: 500 nm) measured in 10 mM NaCl (n = 3 measurements). (c) 〈MSD〉 profiles of PS-COOH nanoparticles of varying size (n = 2 wells per particle size, n = 5 videos per well). (d) log D_eff distributions stratified by particle size and binned by predicted particle size using the Stokes–Einstein based predictor with anomalous diffusion exponent. (e) Average component profile of PCA analysis stratified by particle size. (f) Principle component distributions of PCA analysis stratified by particle size. (g) The first three primary components of 400 randomly selected trajectories per size plotted against each other.

Fig. 2

Particle surface property-dependent nanoparticle diffusion analysis. (a) Carboxyl- and PEG-modified polystyrene nanoparticles incubated with and without horse serum. (b) Hydrodynamic diameter (intensity mean) distributions (purple: PS-COOH, teal: PS-PEG, blue: PS-COOH in serum, yellow-green: PS-PEG in serum) measured in 10 mM NaCl (n = 3 measurements). (c) Concentration of surface-adhered proteins from horse serum-incubated PS-COOH (orange) and PS-PEG (purple) nanoparticles determined using BCA assay. UV-Vis adsorption calibration curve generated from BSA standards is shown in blue. (d) log D_eff distributions stratified by particle type and binned by predicted particle type using log median predictor.

Fig. 3

Particle surface property-dependent nanoparticle diffusion analysis in an organotypic brain slice model. (a) Carboxyl- and PEG-modified polystyrene nanoparticles incubated with and without horse serum were allowed to diffuse in rat brain slices. (b) (top left) 2D computational diffusion model varying the “stickiness” of cellular surfaces (purple squares: cells). (top right) Example nanoparticle trajectories. (bottom left) 〈MSD〉 profiles as a function of cell “stickiness”. Stickiness was quantified as the probability a particle remains adhered to a cell’s surface when in contact with the cell boundary (distance between cells: 20 pixels), (bottom right) 〈MSD〉 profiles as a function of cell “stickiness” (distance between cells: 10 pixels) (c) FACS results quantifying cell uptake of nanoparticles in microglia stratified by particle type (n = 3 slices per condition, purple: PS-PEG in serum, blue: PS-PEG, teal: PS-COOH in serum, yellow-green: PS-COOH) (d) log D_eff distributions stratified by particle type and binned by predicted particle size using log median predictor.

Fig. 4

Diffusion analysis for the prediction of agarose gel concentration. (a) Schematic representation of the relationship between agarose concentration and gel stiffness. (b) Computational model of diffusion in agarose gel of increasing agarose concentration. Agarose is modeled as 2D squares with “sticky” surfaces. (c) Computational model generated 〈MSD〉 profiles for increasing agarose concentrations. Concentrations represent multiples of the base agarose concentration (256 squares/512 × 512 μm²) (d) oscillatory rheological analysis of agarose gels of varying weight % (purple: 0.4%, blue: 0.6%, light-blue: 0.8%, teal: 1.0%) (e) log D_eff distributions stratified by agarose gel concentration binned by predicted agarose gel concentration using log median predictor (purple: 0.4%, blue: 0.6%, light-blue: 0.8%, teal: 1.0%, yellow-green: 1.2%).

Fig. 5

(a) Particle type- and cellular internalization-dependent diffusion analysis. (b) (left) Example frame of PS-PEG nanoparticle diffusion in BV-2 microglial cell culture. (right) Example frame of PS-COOH nanoparticle diffusion in BV-2 microglial cell culture. (c) Demonstration of cell image analysis. (top left) Raw image. (top middle) Binarized image. (top right) Euclidean distance transform of binarized image (bottom left). Binarized image with area 10 pixels from cell surfaces highlighted in red. (bottom middle) Binarized image with area 20 pixels from cell surfaces highlighted in red. (d) log D_eff distributions stratified by agarose gel concentration binned by predicted agarose gel concentration using log median predictor (purple: PS-PEG out of cells, blue: PS-COOH out of cells, teal: PS-PEG in cells, yellow-green: PS-COOH in cells).