Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry.

We present an analytical method that yields the real and imaginary parts of the refractive index (RI) from low-coherence interferometry measurements, leading to the separation of the scattering and absorption coefficients of turbid samples. The imaginary RI is measured using time-frequency analysis, with the real part obtained by analyzing the nonlinear phase induced by a sample. A derivation relating the real part of the RI to the nonlinear phase term of the signal is presented, along with measurements from scattering and nonscattering samples that exhibit absorption due to hemoglobin.

Conformational kinetics reveals affinities of protein conformational states.

Most biological reactions rely on interplay between binding and changes in both macromolecular structure and dynamics. Practical understanding of this interplay requires detection of critical intermediates and determination of their binding and conformational characteristics. However, many of these species are only transiently present and they have often been overlooked in mechanistic studies of reactions that couple binding to conformational change. We monitored the kinetics of ligand-induced conformational changes in a small protein using six different ligands. We analyzed the kinetic data to simultaneously determine both binding affinities for the conformational states and the rate constants of conformational change. The approach we used is sufficiently robust to determine the affinities of three conformational states and detect even modest differences in the protein's affinities for relatively similar ligands. Ligand binding favors higher-affinity conformational states by increasing forward conformational rate constants and/or decreasing reverse conformational rate constants. The amounts by which forward rate constants increase and reverse rate constants decrease are proportional to the ratio of affinities of the conformational states. We also show that both the affinity ratio and another parameter, which quantifies the changes in conformational rate constants upon ligand binding, are strong determinants of the mechanism (conformational selection and/or induced fit) of molecular recognition. Our results highlight the utility of analyzing the kinetics of conformational changes to determine affinities that cannot be determined from equilibrium experiments. Most importantly, they demonstrate an inextricable link between conformational dynamics and the binding affinities of conformational states.

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators.

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.