Modelling of the dynamic polarizability of macromolecules for single-molecule optical biosensing

Shadow Molecular Dynamics for a Charge-Potential Equilibration Model

We introduce a shadow molecular dynamics (MD) approach based on the Atom-Condensed Kohn-Sham second-order (ACKS2) charge-potential equilibration model. In contrast to regular flexible charge models, the ACKS2 model includes both flexible atomic charges and potential fluctuation parameters that allow for physically correct charge fragmentation and improved scaling of the polarizability. Our shadow MD scheme is based on an approximation of the ACKS2's flexible charge-potential energy function, in combination with extended Lagrangian Born-Oppenheimer MD. Utilizing this shadow charge-potential equilibration approach mitigates the costly overhead and stability problems associated with finding well-converged iterative solutions to the charges and potential fluctuations of the ACKS2 model in an MD simulation. Our work provides a robust and versatile framework for efficient, high-fidelity MD simulations of diverse physical phenomena and applications.

Theoretical Basis for Refractive Index Changes Resulting from Solution Phase Molecular Interaction

Refractive index (RI) is a fundamental optical property widely used to investigate the physical and chemical characteristics of materials. Here, we build on our previous work to refine the framework for RI sensing in solution-phase chemical and biochemical interactions. Starting from the Clausius-Mossotti relation, we present a first-principles derivation of a relationship for the RI signal resulting from chemical binding. We then demonstrate how the binding-induced conformational and hydration changes of interacting species relate to their estimated change in dielectric and thus the solution-phase change in refractive index (ΔRI). By varying the model parameters, such as solvation shell size and polarizability, we investigate the RI changes for two interactions: Ca2+ with the protein Recoverin and benzenesulfonamide with carbonic anhydrase 2 (CAII). These examples show that our theory predicts that even for small changes in binding-induced polarizability (relative to previous literature values), a quantifiable RI change is produced within the detectable range of RI detectors operating at ca. 10-6 RIU. Empirical observations confirm our theoretical predictions. Surprisingly, theory and experiment yield a decrease in ΔRI for the benzenesulfonamide-CAII interaction. We attribute this observation to shielding of charged residues and water molecule displacement during the binding event. Our approach is generalized, enabling it to be extended to other binding systems, as well as those undergoing nonbinding conformational changes, and facilitates the exploration of diverse biological and chemical processes by solution-phase RI sensing.

The Origin of Single-Molecule Sensitivity in Label-Free Solution-Phase Optical Microcavity Detection

Fiber Fabry-Perot microcavities (FFPCs) enhance light-matter interactions by localizing light in time and space. Such FFPCs are at the heart of this powerful detection scheme exploiting photothermal nonlinearities and Pound-Drever-Hall frequency locking that enabled label-free profiling of single solution-phase biomolecules with unprecedented sensitivity. Here, we deploy a combination of experiment and simulation to provide a quantitative mechanism for the observed single-molecule sensitivity and achieve quantitative agreement with experiment. A key element of the mechanism is maintaining the FFPC in an unstable regime and allowing it to rapidly shift between hot and cold photothermal equilibria upon perturbation. We show how Brownian molecular trajectories, introducing resonance fluctuations less than 1000th of the already narrow microcavity line width, can produce selective and highly amplified responses. Such perturbations are found to exist in a specific and tunable frequency window termed the molecular velocity filter window. The model's predictive capacity suggests it will be an important tool to identify additional modes of sensitivity to single-molecule hydrodynamic behavior.

Direct observation of small molecule activator binding to single PR65 protein

The reactivation of heterotrimeric protein phosphatase 2A (PP2A) through small molecule activators is of interest to therapeutic intervention due to its dysregulation, which is linked to chronic conditions. This study focuses on the PP2A scaffold subunit PR65 and a small molecule activator, ATUX-8385, designed to bind directly to this subunit. Using a label-free single-molecule approach with nanoaperture optical tweezers (NOT), we quantify its binding, obtaining a dissociation constant of 13.6 ± 2.5 μM, consistent with ensemble fluorescence anisotropy results but challenging to achieve with other methods due to low affinity. Single-molecule NOT measurements reveal that binding increases optical scattering, indicating PR65 elongation. This interpretation is supported by all-atom molecular dynamics simulations showing PR65 adopts more extended conformations upon binding. This work highlights NOT's utility in quantifying binding kinetics and structural impact, offering insights valuable for drug discovery.

Energy landscape of conformational changes for a single unmodified protein

Resolving the free energy landscapes that govern protein biophysics has been obscured by ensemble averaging. While the folding dynamics of single proteins have been observed using fluorescent labels and/or tethers, a simpler and more direct measurement of the conformational changes would not require modifications to the protein. We use nanoaperture optical tweezers to resolve the energy landscape of a single unmodified protein, Bovine Serum Albumin (BSA), and quantify changes in the three-state conformation dynamics with temperature. A Markov model with Kramers' theory transition rates is used to model the dynamics, showing good agreement with the observed state transitions. This first look at the intrinsic energy landscape of proteins provides a transformative tool for protein biophysics and may be applied broadly, including mapping out the energy landscape of particularly challenging intrinsically disordered proteins.

Dielectric Signatures of Late Carcinoma Immune Cells Using MMTV-PyMT Mammary Carcinoma Models

Peripheral blood mononuclear cells (PBMCs) are specialized immune cells produced from hematopoietic stem cells (HSC). They actively surveil for any signs of infection, foreign invaders, and abnormal or aberrant cells associated with diseases. Numerous inherent interactions between PBMCs and proliferating cancer cells facilitate cellular communication, inducing alterations in the composition of the PBMCs. These subtle alterations can be detected by using dielectrophoresis (DEP). The ultimate objective is to apply this knowledge in a clinical setting to achieve noninvasive early detection of breast cancer while minimizing the occurrence of false positives and negatives commonly associated with standard screening methods like mammography. To realize our long-term goal, we are probing the dielectric properties of the PBMCs from FVB/N MMTV-PyMT+ (late carcinoma, PyMT+ PBMC) and FVB/N (wild-type, WT-PBMC) age-matched mice at 14+ weeks using dielectrophoresis on a microfluidic platform. The central hypothesis of this research is that the changes triggered in the subcellular components, such as the cytoskeleton, lipid bilayer membrane, cytoplasm, focal adhesion proteins, and extracellular matrix (ECM) at the onset of carcinoma, regulate dielectric properties (conductivity, σ; and permittivity, ε), thus affecting the bioelectric signals that aid in the detection of breast cancer. The ANOVA results suggest a significant difference in PyMT+ PBMCs crossover frequencies at 0.01 and 0.05 S/m medium conductivity levels. Post hoc pairwise analysis of WT-PBMCs showed that the crossover frequencies are distinct across the medium conductivity ranges from 0.01 to 0.05 S/m. This study revealed that on average, PyMT+ PBMCs have increased crossover frequency, polarizability, higher membrane capacitance, and a folding factor compared with the age-matched wild-type PBMCs.

Exploring the role of macromolecular crowding and TNFR1 in cell volume control

The excessive cosolute densities in the intracellular fluid create a physicochemical condition called macromolecular crowding (MMC). Intracellular MMC entropically maintains the biochemical thermodynamic equilibria by favoring associative reactions while hindering transport processes. Rapid cell volume shrinkage during extracellular hypertonicity elevates the MMC and disrupts the equilibria, potentially ushering cell death. Consequently, cells actively counter the hypertonic stress through regulatory volume increase (RVI) and restore the MMC homeostasis. Here, we establish fluorescence anisotropy of EGFP as a reliable tool for studying cellular MMC and explore the spatiotemporal dynamics of MMC during cell volume instabilities under multiple conditions. Our studies reveal that the actin cytoskeleton enforces spatially varying MMC levels inside adhered cells. Within cell populations, MMC is uncorrelated with nuclear DNA content but anti-correlated with the cell spread area. Although different cell lines have statistically similar MMC distributions, their responses to extracellular hypertonicity vary. The intensity of the extracellular hypertonicity determines a cell's ability for RVI, which correlates with nuclear factor kappa beta (NFkB) activation. Pharmacological inhibition and knockdown experiments reveal that tumor necrosis factor receptor 1 (TNFR1) initiates the hypertonicity-induced NFkB signaling and RVI. At severe hypertonicities, the elevated MMC amplifies cytoplasmic microviscosity and hinders receptor interacting protein kinase 1 (RIPK1) recruitment at the TNFR1 complex, incapacitating the TNFR1-NFkB signaling and consequently, RVI. Together, our studies unveil the involvement of TNFR1-NFkB signaling in modulating RVI and demonstrate the pivotal role of MMC in determining cellular osmoadaptability.

Single Molecule Thermodynamic Penalties Applied to Enzymes by Whispering Gallery Mode Biosensors

Optical microcavities, particularly whispering gallery mode (WGM) microcavities enhanced by plasmonic nanorods, are emerging as powerful platforms for single-molecule sensing. However, the impact of optical forces from the plasmonic near field on analyte molecules is inadequately understood. Using a standard optoplasmonic WGM single-molecule sensor to monitor two enzymes, both of which undergo an open-to-closed-to-open conformational transition, the work done on an enzyme by the WGM sensor as atoms of the enzyme move through the electric field gradient of the plasmonic hotspot during conformational change has been quantified. As the work done by the sensor on analyte enzymes can be modulated by varying WGM intensity, the WGM microcavity system can be used to apply free energy penalties to regulate enzyme activity at the single-molecule level. The findings advance the understanding of optical forces in WGM single-molecule sensing, potentially leading to the capability to precisely manipulate enzyme activity at the single-molecule level through tailored optical modulation.

Influence of point mutations on PR65 conformational adaptability: Insights from molecular simulations and nanoaperture optical tweezers

PR65 is the HEAT repeat scaffold subunit of the heterotrimeric protein phosphatase 2A (PP2A) and an archetypal tandem repeat protein. Its conformational mechanics plays a crucial role in PP2A function by opening/closing substrate binding/catalysis interface. Using in silico saturation mutagenesis, we identified PR65 "hinge" residues whose substitutions could alter its conformational adaptability and thereby PP2A function, and selected six mutations that were verified to be expressed and soluble. Molecular simulations and nanoaperture optical tweezers revealed consistent results on the specific effects of the mutations on the structure and dynamics of PR65. Two mutants observed in simulations to stabilize extended/open conformations exhibited higher corner frequencies and lower translational scattering in experiments, indicating a shift toward extended conformations, whereas another displayed the opposite features, confirmed by both simulations and experiments. The study highlights the power of single-molecule nanoaperture-based tweezers integrated with in silico approaches for exploring the effect of mutations on protein structure and dynamics.

Whispering-Gallery Mode Optoplasmonic Microcavities: From Advanced Single-Molecule Sensors and Microlasers to Applications in Synthetic Biology

Optical microcavities, specifically, whispering-gallery mode (WGM) microcavities, with their remarkable sensitivity to environmental changes, have been extensively employed as biosensors, enabling the detection of a wide range of biomolecules and nanoparticles. To push the limits of detection down to the most sensitive single-molecule level, plasmonic nanorods are strategically introduced to enhance the evanescent fields of WGM microcavities. This advancement of optoplasmonic WGM sensors allows for the detection of single molecules of a protein, conformational changes, and even atomic ions, marking significant contributions in single-molecule sensing. This Perspective discusses the exciting research prospects in optoplasmonic WGM sensing of single molecules, including the study of enzyme thermodynamics and kinetics, the emergence of thermo-optoplasmonic sensing, the ultrasensitive single-molecule sensing on WGM microlasers, and applications in synthetic biology.

Hybrid quantum-classical polarizability model for single molecule biosensing

Optical whispering gallery mode biosensors are able to detect single molecules through effects of their polarizability. We address the factors that affect the polarizability of amino acids, which are the building blocks of life, via electronic structure theory. Amino acids are detected in aqueous environments, where their polarizability is different compared to the gasphase due to solvent effects. Solvent effects include structural changes, protonation and the local field enhancement through the solvent (water). We analyse the impact of these effects and find that all contribute to an increased effective polarizability in the solvent. We also address the excess polarizability relative to the displaced water cavity and develop a hybrid quantum-classical model that is in good agreement with self-consistent calculations. We apply our model to calculate the excess polarizability of 20 proteinogenic amino acids and determine the minimum resolution required to distinguish the different molecules and their ionised conformers based on their polarizability.

Label-Free Tracking of Proteins through Plasmon-Enhanced Interference

Single unmodified biomolecules in solution can be observed and characterized by interferometric imaging approaches; however, Rayleigh scattering limits this to larger proteins (typically >30 kDa). We observe real-time image tracking of unmodified proteins down to 14 kDa using interference imaging enhanced by surface plasmons launched at an aperture in a metal film. The larger proteins show slower diffusion, quantified by tracking. When the diffusing protein is finally trapped by the nanoaperture, we perform complementary power spectral density and noise amplitude analysis, which gives information about the protein. This approach allows for rapid protein characterization with minimal sample preparation and opens the door to characterizing protein interactions in real time.

Influence of Point Mutations on PR65 Conformational Adaptability: Insights from Nanoaperture Optical Tweezer Experiments and Molecular Simulations

PR65 is the HEAT-repeat scaffold subunit of the heterotrimeric protein phosphatase 2A (PP2A) and an archetypal tandem-repeat protein, forming a spring-like architecture. PR65 conformational mechanics play a crucial role in PP2A function by opening/closing the substrate-binding/catalysis interface. Using in-silico saturation mutagenesis we identified "hinge" residues of PR65, whose substitutions are predicted to restrict its conformational adaptability and thereby disrupt PP2A function. Molecular simulations revealed that a subset of hinge mutations stabilized the extended/open conformation, whereas another had the opposite effect. By trapping in nanoaperture optical tweezer, we characterized PR65 motion and showed that the former mutants exhibited higher corner frequencies and lower translational scattering, indicating a shift towards extended conformations, whereas the latter showed the opposite behavior. Thus, experiments confirm the conformations predicted computationally. The study highlights the utility of nanoaperture-based tweezers for exploring structure and dynamics, and the power of integrating this single-molecule method with in silico approaches.

A Quantitative Description for Optical Mass Measurement of Single Biomolecules

Label-free detection of single biomolecules in solution has been achieved using a variety of experimental approaches over the past decade. Yet, our understanding of the magnitude of the optical contrast and its relationship with the underlying atomic structure as well as the achievable measurement sensitivity and precision remain poorly defined. Here, we use a Fourier optics approach combined with an atomic structure-based molecular polarizability model to simulate mass photometry experiments from first principles. We find excellent agreement between several key experimentally determined parameters such as optical contrast-to-mass conversion, achievable mass accuracy, and molecular shape and orientation dependence. This allows us to determine detection sensitivity and measurement precision mostly independent of the optical detection approach chosen, resulting in a general framework for light-based single-molecule detection and quantification.

Optical Monitoring of In Situ Iron Loading into Single, Native Ferritin Proteins

Ferritin is a protein that stores and releases iron to prevent diseases associated with iron dysregulation in plants, animals, and bacteria. The conversion between iron-loaded holo-ferritin and empty apo-ferritin is an important process for iron regulation. To date, studies of ferritin have used either ensemble measurements to quantify the characteristics of a large number of proteins or single-molecule approaches to interrogate labeled or modified proteins. Here we demonstrate the first real-time study of the dynamics of iron ion loading and biomineralization within a single, unlabeled ferritin protein. Using optical nanotweezers, we trapped single apo- and holo-ferritins indefinitely, distinguished one from the other, and monitored their structural dynamics in real time. The study presented here deepens the understanding of the iron uptake mechanism of ferritin proteins, which may lead to new therapeutics for iron-related diseases.

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Polarizabilities play significant roles in describing dispersive and inductive interactions of the atom and molecular systems. However, an accurate prediction of molecular polarizabilities from first principles is computationally prohibitive. Although physical models or statistical machine learning models have been proposed, either a lack of accurate description of local chemical environments or demanding a large number of samples for training has limited their practical applications. In this study, we combine a physically inspired dipole interaction model and an accurate neural network method for predicting the polarizability tensors of molecules. With the local chemical environment precisely described and the requirement of rotational covariance naturally fulfilled, this hybrid model is proven to give an accurate molecular polarizability prediction, essentially reducing the number of training samples. The atomic polarizabilities are physically interpretable and transferable to larger molecules unseen in the training set. This promising method may find its wide range of applications, such as spectroscopic simulations and the construction of polarizable force fields.

Modelling of the dynamic polarizability of macromolecules for single-molecule optical biosensing

The structural dynamics of macromolecules is important for most microbiological processes, from protein folding to the origins of neurodegenerative disorders. Noninvasive measurements of these dynamics are highly challenging. Recently, optical sensors have been shown to allow noninvasive time-resolved measurements of the dynamic polarizability of single-molecules. Here we introduce a method to efficiently predict the dynamic polarizability from the atomic configuration of a given macromolecule. This provides a means to connect the measured dynamic polarizability to the underlying structure of the molecule, and therefore to connect temporal measurements to structural dynamics. To illustrate the methodology we calculate the change in polarizability as a function of time based on conformations extracted from molecular dynamics simulations and using different conformations of motor proteins solved crystalographically. This allows us to quantify the magnitude of the changes in polarizablity due to thermal and functional motions.