Physics-informed deep learning for plasmonic sensing of nanoscale protein dynamics in solution

Quantifying nanoscale protein secondary structure in aqueous solutions is crucial for understanding protein interactions and dynamics. Deep learning models are adept at predicting protein secondary structures, but their ability to model them in aqueous solutions is hindered by data constraints. Here, we present a mid-infrared plasmonic sensor integrated with a synthesized complex-frequency wave (s-CFW)-informed convolutional neural network (CNN) to address these limitations. The sensor enables direct probing of the amide I band in sub-10-nanometer proteins. By using s-CFW to amplify target spectral features, the developed physics-informed CNN achieves a mean relative error of less than 0.1 in predicting secondary structure percentages, more than twice as accurate as a pristine CNN. This method enables in situ and real-time quantification of subtle conformational changes during protein assembly, thereby addressing the issue of data scarcity that now hinders the development of advanced deep learning models for predicting protein dynamics and interactions in physiological environments.