Visualizing sulfur with X-rays: From molecules to tissues

Exact Two-Component Relativistic Polarizable Density Embedding

We have implemented the fragment-based polarizable density embedding (PDE) model within a relativistic framework building on the eXact 2-Component (X2C) relativistic Hamiltonian, thereby taking the PDE method to a relativistic framework. The PDE model provides a robust solution to the electron-leakage problem, and we show that this newly implemented model offers an accurate way to model solvated systems possessing significant relativistic effects. To demonstrate the model's performance, we perform comparative calculations of the K- and L2,3-edge spectra of water-solvated cysteine (both protonated and deprotonated) with the X2C Hamiltonian. Particularly, with counterions such as Na+ in the solvent, electron leakage clearly shows in the older polarizable embedding model through spurious peaks in the spectra. However, when the PDE model is employed, these spurious peaks disappear.

Partial density of states representation for accurate deep neural network predictions of X-ray spectra

The performance of a machine learning (ML) algorithm for chemistry is highly contingent upon the architect's choice of input representation. This work introduces the partial density of states (p-DOS) descriptor: a novel, quantum-inspired structural representation which encodes relevant electronic information for machine learning models seeking to simulate X-ray spectroscopy. p-DOS uses a minimal basis set in conjunction with a guess (non-optimised) electronic configuration to extract and then discretise the density of states (DOS) of the absorbing atom to form the input vector. We demonstrate that while the electronically-focused p-DOS performs well in isolation, optimal performance is achieved when supplemented with nuclear structural information imparted via a geometric representation. p-DOS provides a description of the key electronic properties of a system which is not only concise and computationally efficient, but also independent of molecular size or choice of basis set. It can be rapidly generated, facilitating its application with large training sets. Its performance is demonstrated using a wide variety of examples at the sulphur K-edge, including the prediction of ultrafast X-ray spectroscopic signal associated with photoexcited 2(5H)-thiophenone. These results highlight the potential for ML models developed using p-DOS to contribute to the interpretation and prediction of experimental results e.g. in operando measurements of batteries and/or catalysts and femtosecond time-resolved studies, especially those made possible by emergent cutting-edge technologies, especially X-ray free electron lasers.

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations

Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837-847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C-F and third-period elements Si-Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT's limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT's limitations for Rydberg and charge-transfer excitations.

Understanding Cysteine Chemistry Using Conventional and Serial X-Ray Protein Crystallography

Proteins that use cysteine residues for catalysis or regulation are widely distributed and intensively studied, with many biomedically important examples. Enzymes where cysteine is a catalytic nucleophile typically generate covalent catalytic intermediates whose structures are important for understanding mechanism and for designing targeted inhibitors. The formation of catalytic intermediates can change enzyme conformational dynamics, sometimes activating protein motions that are important for catalytic turnover. However, these transiently populated intermediate species have been challenging to structurally characterize using traditional crystallographic approaches. This review describes the use and promise of new time-resolved serial crystallographic methods to study cysteine-dependent enzymes, with a focus on the main (M^pro) and papain-like (PL^pro) cysteine proteases of SARS-CoV-2 as well as other examples. We review features of cysteine chemistry that are relevant for the design and execution of time-resolved serial crystallography experiments. In addition, we discuss emerging X-ray techniques such as time-resolved sulfur X-ray spectroscopy that may be able to detect changes in sulfur charge state and covalency during catalysis or regulatory modification. In summary, cysteine-dependent enzymes have features that make them especially attractive targets for new time-resolved serial crystallography approaches, which can reveal both changes to enzyme structure and dynamics during catalysis in crystalline samples.