The biological functions of natural polyelectrolytes are strongly influenced by the presence of ions, which bind to the polymer chains and thereby modify their properties. Although the biological impact of such modifications is well recognized, a detailed molecular picture of the binding process and of the mechanisms that drive the subsequent structural changes in the polymer is lacking. Here, we study the molecular mechanism of the condensation of calcium, a divalent cation, on hyaluronan, a ubiquitous polymer in human tissues. By combining two-dimensional infrared spectroscopy experiments with molecular dynamics simulations, we find that calcium specifically binds to hyaluronan at millimolar concentrations. Because of its large size and charge, the calcium cation can bind simultaneously to the negatively charged carboxylate group and the amide group of adjacent saccharide units. Molecular dynamics simulations and single-chain force spectroscopy measurements provide evidence that the binding of the calcium ions weakens the intramolecular hydrogen-bond network of hyaluronan, increasing the flexibility of the polymer chain. We also observe that the binding of calcium to hyaluronan saturates at a maximum binding fraction of ∼10-15 mol %. This saturation indicates that the binding of Ca2+ strongly reduces the probability of subsequent binding of Ca2+ at neighboring binding sites, possibly as a result of enhanced conformational fluctuations and/or electrostatic repulsion effects. Our findings provide a detailed molecular picture of ion condensation and reveal the severe effect of a few, selective and localized electrostatic interactions on the rigidity of a polyelectrolyte chain.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.