Optical Theory Group

Abstract : Amyloid-β42 assemblies form a dynamic network of oligomers and fibrils, with fibrillar species acting as reservoirs that maintain equilibrium among intermediates. Perturbing a single species shifts the oligomer-fibril balance, highlighting the challenge of selectively targeting toxic species while maintaining the dynamic equilibrium of the amyloid network. Here, we show that the small molecule EPPS (4-(2-hydroxyethyl)-1-piperazine-propanesulfonic acid) fine tunes this network through cooperative, concentration-dependent disaggregation. At optimal concentrations, EPPS efficiently shifts the equilibrium away from the fibrillar structures via multisite, allosteric interactions. At higher concentrations, EPPS self-assembles into supramolecular clusters, depleting free molecules and allowing partially disaggregated amyloid intermediates to reassemble. Notably, at elevated concentrations, interactions transition from molecule-to-molecule to higher-order ensemble-to-ensemble engagement, where EPPS clusters and amyloid fibrils mutually reshape each other's dynamics. Molecular crowding, modeled with polyethylene glycol, further restricts EPPS access to fibrillar surfaces, modulating activity. These findings reveal that small molecule dynamics, including cooperative binding, self-assembly, and environment-dependent accessibility, critically govern amyloid network control, providing a mechanistic blueprint for rational design of next-generation amyloid-targeting therapeutics.

Abstract : Modeling the propagation of light through disordered media is central to understanding and controlling wave transport in diverse optical and mesoscopic applications. Here, we present a random matrix simulation framework for modeling the transport of polarized light through random media composed of arbitrary particulate scatterers. Our approach employs extended scattering channels applied to angular spectral decompositions of the underlying fields, enabling flexible representations of arbitrary illumination and detection profiles. In contrast to previous work, this framework provides a rigorous treatment of scattering matrix correlations and offers novel geometric insights into the optical memory effect. We provide a detailed exposition of the underlying theory and illustrate several key features through numerical simulations. Our work is supported by a free accompanying codebase.

Abstract : Digital assays represent a shift from traditional diagnostics and enable the precise detection of low-abundance analytes, critical for early disease diagnosis and personalized medicine, through discrete counting of biomolecular reporters. Within this paradigm, we present a particle counting algorithm for nanoparticle based imaging assays, formulated as a multiple-hypothesis statistical test under an explicit image-formation model and evaluated using a penalized likelihood rule. In contrast to thresholding or machine learning methods, this approach requires no training data or empirical parameter tuning, and its outputs remain interpretable through direct links to imaging physics and statistical decision theory. Through numerical simulations we demonstrate robust count accuracy across weak signals, variable backgrounds, magnification changes and moderate PSF mismatch. Particle resolvability tests further reveal characteristic error modes, including under-counting at very small separations and localized over-counting near the resolution limit. Practically, we also confirm the algorithm’s utility, through application to experimental dark-field images comprising a nanoparticle-based assay for detection of DNA biomarkers derived from SARS-CoV-2. Statistically significant differences in particle count distributions are observed between control and positive samples. Full count statistics obtained further exhibit consistent over-dispersion, and provide insight into non-specific and target-induced particle aggregation. These results establish our method as a reliable framework for nanoparticle-based detection assays in digital molecular diagnostics.