Optimization and Multimachine Learning Algorithms to Predict Nanometal Surface Area Transfer Parameters for Gold and Silver Nanoparticles

Abstract

Interactions between gold metallic nanoparticles and molecular dyes have been well described by the nanometal surface energy transfer (NSET) mechanism. However, the expansion and testing of this model for nanoparticles of different metal composition is needed to develop a greater variety of nanosensors for medical and commercial applications. In this study, the NSET formula was slightly modified in the size-dependent dampening constant and skin depth terms to allow for modeling of different metals as well as testing the quenching effects created by variously sized gold, silver, copper, and platinum nanoparticles. Overall, the metal nanoparticles followed more closely the NSET prediction than for Förster resonance energy transfer, though scattering effects began to occur at 20 nm in the nanoparticle diameter. To further improve the NSET theoretical equation, an attempt was made to set a best-fit line of the NSET theoretical equation curve onto the Au and Ag data points. An exhaustive grid search optimizer was applied in the ranges for two variables, 0.1≤C≤2.0 and 0≤α≤4, representing the metal dampening constant and the orientation of donor to the metal surface, respectively. Three different grid searches, starting from coarse (entire range) to finer (narrower range), resulted in more than one million total calculations with values C=2.0 and α=0.0736. The results improved the calculation, but further analysis needed to be conducted in order to find any additional missing physics. With that motivation, two artificial intelligence/machine learning (AI/ML) algorithms, multilayer perception and least absolute shrinkage and selection operator regression, gave a correlation coefficient, R2, greater than 0.97, indicating that the small dataset was not overfitting and was method-independent. This analysis indicates that an investigation is warranted to focus on deeper physics informed machine learning for the NSET equations.

Keywords: FRET; Lasso method; NSET; exhaustive grid search; machine learning; multilayer perceptron; nanoparticles; optimization; quenching.

Figure 1

(a) Schematic model (not to scale) of a AuNP–DNA–TET dye molecule construct. (b) Spectral overlap between the experimentally found acceptor’s (20 nm AuNPs) adsorption spectrum and the donor’s emission. Overlap area is highlighted between the two spectra.

Figure 2

Calculated absorbance spectrums for (a) gold, (c) silver, (e) copper, and (g) platinum NPs of varying commercially available or easily synthesized sizes compared to the emission spectrum of the TET dye. The resulting calculated FRET and NSET fluorescence quenching efficiencies for those same-sized (b) gold, (d) silver, (f) copper, and (h) platinum NPs.

Figure 3

Calculated NSET and FRET values for AuNPs of size (a) d = 10 nm and (b) d = 20 nm, compared to experimentally found values. Each DNA length was measured four times with the mean and standard error displayed. The distance error bars are partially covered by the symbols.

Figure 4

(a) Absorbance spectrum of the 10 nm AgNPs at varying steps of the conjugation process for the 60 bp DNA strands. Notice the small red shifting of the main plasmon peak, possibly coming from AgNP aggregation. (b) Comparison of experimental 10 nm AgNP–TET to FRET and NSET models. Averages and standard errors from 3 measurements are plotted.

Figure 5

EGS for $0.04\le \alpha \le 0.1$ and $0.1\le C\le 2.0$ for (a) MRE and (b) RMSE.

Figure 6

Experimental values compared to calculated FRET (red dots), initial NSET value (black dashes), and final fitted NSET values (dashes are the best optimization results from the exhaustive grid searches) for (a) 10 nm AuNPs, (b) 20 nm AuNPs, and (c) 10 nm AgNPs.

Figure 7

Blind test of the MLP and Lasso models with $10\%$ validation data extracted from the total data.