For deriving maximal advantage from information on biomacromolecular flexibility and rigidity, results from rigidity analyses must be linked to biologically relevant characteristics of a structure. Here, we describe the Python-based software package Constraint Network Analysis (CNA) developed for this task. CNA functions as a front- and backend to the graph-based rigidity analysis software FIRST. CNA goes beyond the mere identification of flexible and rigid regions in a biomacromolecule in that it (I) provides a refined modeling of thermal unfolding simulations that also considers the temperature-dependence of hydrophobic tethers, (II) allows performing rigidity analyses on ensembles of network topologies, either generated from structural ensembles or by using the concept of fuzzy noncovalent constraints, and (III) computes a set of global and local indices for quantifying biomacromolecular stability. This leads to more robust results from rigidity analyses and extends the application domain of rigidity analyses in that phase transition points ("melting points") and unfolding nuclei ("structural weak spots") are determined automatically. Furthermore, CNA robustly handles small-molecule ligands in general. Such advancements are important for applying rigidity analysis to data-driven protein engineering and for estimating the influence of ligand molecules on biomacromolecular stability. CNA maintains the efficiency of FIRST such that the analysis of a single protein structure takes a few seconds for systems of several hundred residues on a single core. These features make CNA an interesting tool for linking biomacromolecular structure, flexibility, (thermo-)stability, and function. CNA is available from http://cpclab.uni-duesseldorf.de/software for nonprofit organizations.

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Understanding the origin of thermostability is of fundamental importance in protein biochemistry. Opposing views on increased or decreased structural rigidity of the folded state have been put forward in this context. They have been related to differences in the temporal resolution of experiments and computations that probe atomic mobility. Here, we find a significant (p = 0.004) and fair (R 2 = 0.46) correlation between the structural rigidity of a well-characterized set of 16 mutants of lipase A from Bacillus subtilis (BsLipA) and their thermodynamic thermostability. We apply the rigidity theory-based Constraint Network Analysis (CNA) approach, analyzing directly and in a time-independent manner the statics of the BsLipA mutants. We carefully validate the CNA results on macroscopic and microscopic experimental observables and probe for their sensitivity with respect to input structures. Furthermore, we introduce a robust, local stability measure for predicting thermodynamic thermostability. Our results complement work that showed for pairs of homologous proteins that raising the structural stability is the most common way to obtain a higher thermostability. Furthermore, they demonstrate that related series of mutants with only a small number of mutations can be successfully analyzed by CNA, which suggests that CNA can be applied prospectively in rational protein design aimed at higher thermodynamic thermostability.

Inspecting protein and ligand electrostatic potential (ESP) surfaces in order to optimize electrostatic complementarity is a key activity in drug design. These ESP surfaces need to reflect the true electrostatic nature of the molecules, which typically means time-consuming high-level quantum mechanics (QM) calculations are required. For interactive design much faster alternative methods are required. Here, we present a graph convolutional deep neural network (DNN) model, trained on ESP surfaces derived from high quality QM calculations, that generates ESP surfaces for ligands in a fraction of a second. Additionally, we describe a method for constructing fast QM-trained ESP surfaces for proteins. We show that the DNN model generates ESP surfaces that are in good agreement with QM and that the ESP values correlate well with experimental properties relevant to medicinal chemistry. We believe that these high-quality, interactive ESP surfaces form a powerful tool for driving drug discovery programs forward. The trained model and associated code are available from https:// github.com/AstexUK/ESP_DNN.

The Constraint Network Analysis (CNA) web server provides a user-friendly interface to the CNA approach developed in our laboratory for linking results from rigidity analyses to biologically relevant characteristics of a biomolecular structure. The CNA web server provides a refined modeling of thermal unfolding simulations that considers the temperature dependence of hydrophobic tethers and computes a set of global and local indices for quantifying biomacromolecular stability. From the global indices, phase transition points are identified where the structure switches from a rigid to a floppy state; these phase transition points can be related to a protein’s (thermo-)stability. Structural weak spots (unfolding nuclei) are automatically identified, too; this knowledge can be exploited in data-driven protein engineering. The local indices are useful in linking flexibility and function and to understand the impact of ligand binding on protein flexibility. The CNA web server robustly handles small-molecule ligands in general. To overcome issues of sensitivity with respect to the input structure, the CNA web server allows performing two ensemble-based variants of thermal unfolding simulations. The web server output is provided as raw data, plots and/or Jmol representations. The CNA web server, accessible at http://cpclab.uni-duesseldorf.de/cna or http://www.cnanalysis.de, is free and open to all users with no login requirement.