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Molecular dynamics (MD) simulations are frequently carried out for proteins to investigate the role of electrostatics in their biological function. The choice of force field (FF) can significantly alter the MD results, as the simulated local electrostatic interactions lack benchmarking in the absence of appropriate experimental methods. We recently reported that the transition dipole moment (TDM) of the popular nitrile vibrational probe varies linearly with the environmental electric field, overcoming well-known hydrogen bonding (H-bonding) issues for the nitrile frequency and, thus, enabling the unambiguous measurement of electric fields in proteins ( J. Am. Chem. Soc. 2022 , 144 (17), 7562-7567). Herein, we utilize this new strategy to enable comparisons of experimental and simulated electric fields in protein environments. Specifically, previously determined TDM electric fields exerted onto nitrile-containing o -cyanophenylalanine residues in photoactive yellow protein are compared with MD electric fields from the fixed-charge AMBER FF and the polarizable AMOEBA FF. We observe that the electric field distributions for H-bonding nitriles are substantially affected by the choice of FF. As such, AMBER underestimates electric fields for nitriles experiencing moderate field strengths; in contrast, AMOEBA robustly recapitulates the TDM electric fields. The FF dependence of the electric fields can be partly explained by the presence of additional negative charge density along the nitrile bond axis in AMOEBA, which is due to the inclusion of higher-order multipole parameters; this, in turn, begets more head-on nitrile H-bonds. We conclude by discussing the implications of the FF dependence for the simulation of nitriles and proteins in general.

Magnetic particle spectroscopy (MPS) in the Brownian relaxation regime, also termed magnetic spectroscopy of Brownian motion (MSB), can detect and quantitate very low, sub-nanomolar concentrations of molecular biomarkers. MPS/MSB uses the harmonics of the magnetization induced by a small, low-frequency oscillating magnetic field to provide quantitative information about the magnetic nanoparticles' (mNPs') microenvironment. A key application uses antibody-coated mNPs to produce biomarker-mediated aggregation that can be detected using MPS/MSB. However, relaxation changes can also be caused by viscosity changes. To address this challenge, we propose a metric that can distinguish between aggregation and viscosity. Viscosity changes scale the MPS/MSB harmonic ratios with a constant multiplier across all applied field frequencies. The change in viscosity is exactly equal to the multiplier with generality, avoiding the need to understand the signal explicitly. This simple scaling relationship is violated when particles aggregate. Instead, a separate multiplier must be used for each frequency. The standard deviation of the multipliers over frequency defines a metric isolating viscosity (zero standard deviation) from aggregation (non-zero standard deviation). It increases monotonically with biomarker concentration. We modeled aggregation and simulated the MPS/MSB signal changes resulting from aggregation and viscosity changes. MPS/MSB signal changes were also measured experimentally using 100 nm iron-oxide mNPs in solutions with different viscosities (modulated by glycerol concentration) and with different levels of aggregation (modulated by concanavalin A linker concentrations). Experimental and simulation results confirmed that viscosity changes produced small changes in the standard deviation and aggregation produced larger values of standard deviation. This work overcomes a key barrier to using MPS/MSB to detect biomarkers in vivo with variable tissue viscosity.

Estimating statistical significance of the difference between two spectra or series is a fundamental statistical problem. Multivariate significance tests exist but the limitations preclude their use in many common cases; e.g., one-sided testing, unequal variance and when few repetitions are acquired all of which are required in magnetic spectroscopy of nanoparticle Brownian motion (MSB). We introduce a test, termed the T-S test, that is powerful and exact (exact type I error). It is flexible enough to be one- or two-sided and the one-sided version can specify arbitrary regions where each spectrum should be larger. The T-S test takes the-one or two-sided p-value at each frequency and combines them using Stouffer's method. We evaluated it using simulated spectra and measured MSB spectra. For the single-sided version, mean of the spectrum, A-T, was used as a reference; the T-S test is as powerful when the variance at each frequency is uniform and outperforms when the noise power is not uniform. For the two-sided version, the Hotelling T2 two-sided multivariate test was used as a reference; the two-sided T-S test is only slightly less powerful for large numbers of repetitions and outperforms rather dramatically for small numbers of repetitions. The T-S test was used to estimate the sensitivity of our current MSB spectrometer showing 1 nanogram sensitivity. Using eight repetitions the T-S test allowed 15 pM concentrations of mouse IL-6 to be identified while the mean of the spectra only identified 76 pM.

Nitriles are widely used vibrational probes; however, the interpretation of their IR frequencies is complicated by hydrogen bonding (H-bonding) in protic environments. We report a new vibrational Stark effect (VSE) that correlates the electric field projected on the -C≡N bond to the transition dipole moment and, by extension, the nitrile peak area or integrated intensity. This linear VSE applies to both H-bonding and non-H-bonding interactions. It can therefore be generally applied to determine electric fields in all environments. Additionally, it allows for semiempirical extraction of the H-bonding contribution to the blueshift of the nitrile frequency. Nitriles were incorporated at H-bonding and non-H-bonding protein sites using amber suppression, and each nitrile variant was structurally characterized at high resolution. We exploited the combined information available from variations in frequency and integrated intensity and demonstrate that nitriles are a generally useful probe for electric fields.