The interactions between proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d and both binding and non-binding interactions are quantified by second osmotic virial coefficients B₂. As a measure of non-specific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid-liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvent, we can determine B₂ from insertion and removal energies by applying Bennett's acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvent, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. The high accuracy of our estimates for K_d and B₂ allows us to separate out the contributions of non-binding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities and overall stickiness. The accuracy and efficiency of K_d and B₂ calculations makes them well suited for high-throughput studies of large interactomes.

Protein folding is a fascinating, not fully understood phenomenon in biology. Molecular dynamics (MD) simulations are an invaluable tool to study conformational changes in atomistic detail, including folding and unfolding processes of proteins. However, the accuracy of the conformational ensembles derived from MD simulations inevitably relies on the quality of the underlying force field in combination with the respective water model. Here, we investigate protein folding, unfolding, and misfolding of fast-folding proteins by examining different force fields with their recommended water models, i.e., ff14SB with the TIP3P model and ff19SB with the OPC model. To this end, we generated long conventional MD simulations highlighting the perks and pitfalls of these setups. Using Markov state models, we defined kinetically independent conformational substates and emphasized their distinct characteristics, as well as their corresponding state probabilities. Surprisingly, we found substantial differences in thermodynamics and kinetics of protein folding, depending on the combination of the protein force field and water model, originating primarily from the different water models. These results emphasize the importance of carefully choosing the force field and the respective water model as they determine the accuracy of the observed dynamics of folding events. Thus, the findings support the hypothesis that the water model is at least equally important as the force field and hence needs to be considered in future studies investigating protein dynamics and folding in all areas of biophysics.

X-Entropy is a Python package used to calculate the entropy of a given distribution, in this case, based on the distribution of dihedral angles. The dihedral entropy facilitates an alignment-independent measure of local protein flexibility. The key feature of our approach is a Gaussian kernel density estimation (KDE) using a plug-in bandwidth selection, which is fully implemented in a C++ backend and parallelized with OpenMP. We further provide a Python frontend, with predefined wrapper functions for classical coordinate-based dihedral entropy calculations, using a 1D approximation. This makes the package very straightforward to include in any Python-based analysis workflow. Furthermore, the frontend allows full access to the C++ backend, so that the KDE can be used on any binnable one-dimensional input data. In this application note, we discuss implementation and usage details and illustrate potential applications. In particular, we benchmark the performance of our module in calculating the entropy of samples drawn from a Gaussian distribution and the analytical solution thereof. Further, we analyze the computational performance of this module compared to well-established python libraries that perform KDE analyses. X-Entropy is available free of charge on GitHub (https://github.com/liedllab/X-Entropy).

To characterize the thermosensitive coil–globule transition in atomistic detail, the conformational dynamics of linear polymer chains of acrylamide-based polymers have been investigated at multiple temperatures. Therefore, molecular dynamic simulations of 30mers of polyacrylamide (AAm), poly-N-methylacrylamide (NMAAm), poly-N-ethylacrylamide (NEAAm), and poly-N-isopropylacrylamide (NIPAAm) have been performed at temperatures ranging from 250 to 360 K for 2 μs. While two of the polymers are known to exhibit thermosensitivity (NEAAm, NIPAAm), no thermosensitivity is observed for AAm and NMAAm in aqueous solution. Our computer simulations consistently reproduce these properties. To understand the thermosensitivity of the respective polymers, the conformational ensembles at different temperatures have been separated according to the coil–globule transition. The coil and globule conformational ensembles were exhaustively analyzed in terms of hydrogen bonding with the solvent, the change of the solvent accessible surface, and enthalpic contributions. Surprisingly, independent of different thermosensitive properties of the four polymers, the surface affinity to water of coil conformations is higher than for globule conformations. Therefore, polymer–solvent interactions stabilize coil conformations at all temperatures. Nevertheless, the enthalpic contributions alone cannot explain the differences in thermosensitivity. This clearly implies that entropy is the distinctive factor for thermosensitivity. With increasing side chain length, the lifetime of the hydrogen bonds between the polymer surface and water is extended. Thus, we surmise that a longer side chain induces a larger entropic penalty due to immobilization of water molecules.