WaveTrain: A Python package for numerical quantum mechanics of chain-like systems based on tensor trains.

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.

Predicting Structural Motifs of Glycosaminoglycans using Cryogenic Infrared Spectroscopy and Random Forest.

In recent years, glycosaminoglycans (GAGs) have emerged into the focus of biochemical and biomedical research due to their importance in a variety of physiological processes. These molecules show great diversity, which makes their analysis highly challenging. A promising tool for identifying the structural motifs and conformation of shorter GAG chains is cryogenic gas-phase infrared (IR) spectroscopy. In this work, the cryogenic gas-phase IR spectra of mass-selected heparan sulfate (HS) di-, tetra-, and hexasaccharide ions were recorded to extract vibrational features that are characteristic to structural motifs. The data were augmented with chondroitin sulfate (CS) disaccharide spectra to assemble a training library for random forest (RF) classifiers. These were used to discriminate between GAG classes (CS or HS) and different sulfate positions (2-O-, 4-O-, 6-O-, and N-sulfation). With optimized data preprocessing and RF modeling, a prediction accuracy of >97% was achieved for HS tetra- and hexasaccharides based on a training set of only 21 spectra. These results exemplify the importance of combining gas-phase cryogenic IR ion spectroscopy with machine learning to improve the future analytical workflow for GAG sequencing and that of other biomolecules, such as metabolites.

Mussel-Inspired Polymerization of Peptides: The Chemical Activation Route as Key to Broaden the Sequential Space of Artificial Mussel-Glue Proteins.

A previously introduced tyrosinase-activated polymerization of Tyr- and Cys-bearing peptides yielding artificial mussel-glue proteins is realized without the need of the specific enzyme by a chemical activation route. This decouples the sequence of polymerizable peptides (unimers) from the constraints of tyrosinase substrates and enables the polymerization of minimal motifs such as Dopa-Lys-Cys (Umini *KC ) or Dopa-Gly-Cys (Umini *GC ). In the polymerization procedure, sodium periodate is used to oxidize Dopa residues of the unimers to Dopa-quinones to which the thiol of a Cys residue is added in a Michael-type reaction. The resulting polyUmini *KC and polyUmini *GC exhibit a thiol-catechol connectivity as a potent adhesive functionality at each repeat unit. QCM-D experiments show the excellent substrate adsorption properties of the products from the chemically activated polymerization. On aluminum oxide surfaces, polyUmini *KC rapidly forms a coating, even under seawater model conditions and the coating resists rinsing with hypersaline solution of 4.2 M salt mixtures. While the sodium periodate oxidation is less specific than the tyrosinase reaction and requires the implementation of Dopa instead of Tyr residues into the polymerizable unimers, the chemical route makes scale-up more easily accessible.