How changes in enzyme structure and dynamics facilitate passage along the reaction coordinate is a fundamental unanswered question. Here, we use time-resolved mix-and-inject serial crystallography (MISC) at an X-ray free electron laser (XFEL), ambient-temperature X-ray crystallography, computer simulations, and enzyme kinetics to characterize how covalent catalysis modulates isocyanide hydratase (ICH) conformational dynamics throughout its catalytic cycle. We visualize this previously hypothetical reaction mechanism, directly observing formation of a thioimidate covalent intermediate in ICH microcrystals during catalysis. ICH exhibits a concerted helical displacement upon active-site cysteine modification that is gated by changes in hydrogen bond strength between the cysteine thiolate and the backbone amide of the highly strained Ile152 residue. These catalysis-activated motions permit water entry into the ICH active site for intermediate hydrolysis. Mutations at a Gly residue (Gly150) that modulate helical mobility reduce ICH catalytic turnover and alter its pre-steady-state kinetic behavior, establishing that helical mobility is important for ICH catalytic efficiency. These results demonstrate that MISC can capture otherwise elusive aspects of enzyme mechanism and dynamics in microcrystalline samples, resolving long-standing questions about the connection between nonequilibrium protein motions and enzyme catalysis.

Proteins operate and interact with partners by dynamically exchanging between functional substates of a conformational ensemble on a rugged free energy landscape. Understanding how these substates are linked by coordinated, collective motions requires exploring a high-dimensional space, which remains a tremendous challenge. While molecular dynamics simulations can provide atomically detailed insight into the dynamics, computational demands to adequately sample conformational ensembles of large biomolecules and their complexes often require tremendous resources. Kinematic models can provide high-level insights into conformational ensembles and molecular rigidity beyond the reach of molecular dynamics by reducing the dimensionality of the search space. Here, we model a protein as a kinematic linkage and present a new geometric method to characterize molecular rigidity from the constraint manifold Q and its tangent space Q at the current configuration q. In contrast to methods based on combinatorial constraint counting, our method is valid for both generic and non-generic, e.g., singular configurations. Importantly, our geometric approach provides an explicit basis for collective motions along floppy modes, resulting in an efficient procedure to probe conformational space. An atomically detailed structural characterization of coordinated, collective motions would allow us to engineer or allosterically modulate biomolecules by selectively stabilizing conformations that enhance or inhibit function with broad implications for human health.

Elastic network models (ENMs) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by noncovalent interactions, analogous to the eigenspectrum of normal modes. The zero modes decompose proteins into rigid clusters identical to those from topological rigidity, while nonzero modes rank protein motions by their hydrogen bond collective energy penalty. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, enabling a detailed analysis of motion modes obtained from both approaches. Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize experimental and simulated protein stiffness variations. Kinematic motion modes highly correlate with reported crystallographic B factors and molecular dynamics simulations of adenylate kinase. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy–entropy compensation. Taken together, our results suggest that hydrogen bond networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

The COVID-19 pandemic has kept the world in suspense for the past months. In most federal countries such as Germany, locally varying conditions demand for state- or county-level decisions. However, this requires a deep understanding of the meso-scale outbreak dynamics between micro-scale agent models and macro-scale global models. Here, we introduce a reparameterized SIQRD network model that accounts for local political decisions to predict the spatio-temporal evolution of the pandemic in Germany at county and city resolution. Our optimized model reproduces state-wise cumulative infections and deaths as reported by the Robert-Koch Institute, and predicts development for individual counties at convincing accuracy. We demonstrate the dominating effect of local infection seeds, and identify effective measures to attenuate the rapid spread. Our model has great potential to support decision makers on a state and community politics level to individually strategize their best way forward.

The COVID-19 pandemic has led to an unprecedented world-wide effort to gather data, model, and understand the viral spread. Entire societies and economies are desperate to recover and get back to normality. However, to this end accurate models are of essence that capture both the viral spread and the courses of disease in space and time at reasonable resolution. Here, we combine a spatially resolved county-level infection model for Germany with a memory-based integro-differential approach capable of directly including medical data on the course of disease, which is not possible when using traditional SIR-type models. We calibrate our model with data on cumulative detected infections and deaths from the Robert-Koch Institute and demonstrate how the model can be used to obtain county- or even city-level estimates on the number of new infections, hospitality rates and demands on intensive care units. We believe that the present work may help guide decision makers to locally fine-tune their expedient response to potential new outbreaks in the near future.