Electronic circular dichroism (CD) spectroscopy is an important tool for the elucidation of biomolecular structure. This review describes the latest progress and developments in experimental and theoretical studies of proteins using CD spectroscopy, including time-resolved measurements, oriented CD, and stateof-the-art experiments using polarized UV light from high-energy synchrotron radiation. Statistical and machine learning methods for the analysis of experimental spectra are surveyed. Computational methods employed to predict CD spectra from structure include ab initio quantum chemistry techniques, time-dependent density functional theory, and exciton theory. We describe recent computations using exciton theory, where we outline the importance of electronic-vibrational coupling and the influence of electrostatics of the protein environment on the electronic transitions in the chromophores responsible for CD signals in the near UV. Improvements in the accuracy of the computational approaches should allow more quantitative studies, applying a combination of experimental data and modeling to a variety of interesting questions. Fundamentals of the Phenomenon of Electronic Circular DichroismCircular dichroism (CD) is the differential absorption of left-and right-handed circularly polarized light. An elliptically polarized light wave results when a linearly polarized light wave passes through an optically active chiral compound. The magnitude of the effect is given by

A fully quantitative theory connecting protein conformation and optical spectroscopy would facilitate deeper insights into biophysical and simulation studies of protein dynamics and folding. The web server DichroCalc (http://comp.chem.nottingham.ac.uk/dichrocalc) allows one to compute from first principles the electronic circular dichroism spectrum of a (modeled or experimental) protein structure or ensemble of structures. The regular, repeating, chiral nature of secondary structure elements leads to intense bands in the far-ultraviolet (UV). The near-UV bands are much weaker and have been challenging to compute theoretically. We report some advances in the accuracy of calculations in the near-UV, realized through the consideration of the vibrational structure of the electronic transitions of aromatic side chains. The improvements have been assessed over a set of diverse proteins. We illustrate them using bovine pancreatic trypsin inhibitor and present a new, detailed analysis of the interactions which are most important in determining the near-UV circular dichroism spectrum.