Structure of a model salt bridge in solution investigated with 2D-IR spectroscopy

Salt bridges are known to be important for the stability of protein conformation, but up to now it has been difficult to study their geometry in solution. Here we characterize the spatial structure of a model salt bridge between guanidinium (Gdm+) and acetate (Ac-) using two-dimensional vibrational (2D-IR) spectroscopy. We find that as a result of salt bridging the infrared response of Gdm+ and Ac- change significantly, and in the 2D-IR spectrum, salt bridging of the molecules appears as cross peaks. From the 2D-IR spectrum we determine the relative orientation of the transition-dipole moments of the vibrational modes involved in the salt bridge, as well as the coupling between them. In this manner we reconstruct the geometry of the solvated salt bridge

Elucidating the structure of chiral molecules by using amplified vibrational circular dichroism: from theory to experimental realization

Recent experimental observations of enhanced vibrational circular dichroism (VCD) in molecular systems with low-lying electronically excited states suggest interesting new applications of VCD spectroscopy. The theory describing VCD enhancement through vibronic coupling schemes was derived by Nafie in 1983, but only recently experimental evidence of VCD amplification has demonstrated the extent to which this effect can be exploited as a structure elucidation tool to probe local structure. In this Concept paper, we give an overview of the physics behind vibrational circular dichroism, in particular the equations governing the VCD amplification effect, and review the latest experimental developments with a prospective view on the application of amplified VCD to locally probe biomolecular structure

Two-Dimensional Infrared Spectroscopy of Antiparallel β-Sheet Secondary Structure

We investigate the sensitivity of femtosecond Fourier transform two-dimensional infrared spectroscopy to protein secondary structure with a study of antiparallel β-sheets. The results show that 2D IR spectroscopy is more sensitive to structural differences between proteins than traditional infrared spectroscopy, providing an observable that allows comparison to quantitative models of protein vibrational spectroscopy. 2D IR correlation spectra of the amide I region of poly-L-lysine, concanavalin A, ribonuclease A, and lysozyme show cross-peaks between the IR-active transitions that are characteristic of amide I couplings for polypeptides in antiparallel hydrogen-bonding registry. For poly-L-lysine, the 2D IR spectrum contains the eight-peak structure expected for two dominant vibrations of an extended, ordered antiparallel β-sheet. In the proteins with antiparallel β-sheets, interference effects between the diagonal and cross-peaks arising from the sheets, combined with diagonally elongated resonances from additional amide transitions, lead to a characteristic “Z”-shaped pattern for the amide I region in the 2D IR spectrum. We discuss in detail how the number of strands in the sheet, the local configurational disorder in the sheet, the delocalization of the vibrational excitation, and the angle between transition dipole moments affect the position, splitting, amplitude, and line shape of the cross-peaks and diagonal peaks.

Combining Two Consistent Estimators

This chapter shows how a weighted average of a forward and reverse Jackknife IV estimator (JIVE) yields estimators that are robust against heteroscedasticity and many instruments. These estimators, called HFUL (Heteroscedasticity robust Fuller) and HLIM (Heteroskedasticity robust limited information maximum likelihood (LIML)) were introduced by Hausman, Newey, Woutersen, Chao, and Swanson (2012), but without derivation. Combining consistent estimators is a theme that is associated with Jerry Hausman and, therefore, we present this derivation in this volume. Additionally, and in order to further understand and interpret HFUL and HLIM in the context of jackknife type variance ratio estimators, we show that a new variant of HLIM, under specific grouped data settings with dummy instruments, simplifies to the Bekker and van der Ploeg (2005) MM (method of moments) estimator

An Expository Note on the Existence of Moments of Fuller and HFUL Estimators

In a recent paper, Hausman, Newey, Woutersen, Chao, and Swanson (2012) propose a new estimator, HFUL (Heteroscedasticity robust Fuller), for the linear model with endogeneity. This estimator is consistent and asymptotically normally distributed in the many instruments and many weak instruments asymptotics. Moreover, this estimator has moments, just like the estimator by Fuller (1977). The purpose of this note is to discuss at greater length the existence of moments result given in Hausman et al. (2012). In particular, we intend to answer the following questions: Why does LIML not have moments? Why does the Fuller modification lead to estimators with moments? Is normality required for the Fuller estimator to have moments? Why do we need a condition such as Hausman et al. (2012), Assumption 9? Why do we have the adjustment formula