Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins. Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala₃-Nme peptide. For the Trp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap. Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at of 4.4 Å from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the and chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data. Understanding the mechanism by which proteins find their folded state is a holy grail of computational biology. Accurate all-atom simulations have the potential to describe such a process in great detail, but, unfortunately, folding of most proteins takes place on a time scale that is still not accessible to routine computer simulations. We introduce here an approach that allows for constructing an accurate kinetic and thermodynamic model of folding (or other complex biological processes) using trajectories in which the process under investigation is forced to happen in a short simulation time by an appropriate external bias. An important strength of this approach is the possibility of identifying and characterizing misfolded conformations that, in some proteins, are related to important diseases. We use this method to study the folding of Trp-cage, predicting the structure of the folded state and the presence of several intermediates. We find that, surprisingly, fully unstructured “unfolded” states relax towards the folded conformation rather quickly. The slowest relaxation time of the system is instead related to the equilibration between the folded state and another compact structure that acts as a kinetic trap. Thus, the experimental folding time would be determined primarily by this process.

International audienceComputer simulations play an important role in the study of transformation processes of condensed matter, including phase transitions, chemical reactions, and conformational changes of biomolecules. In principle, atomic trajectories, such as those generated using the molecular dynamics approach, contain detailed structural, thermodynamic, and kinetic information about activated processes. In practice, due to free energy barriers, there is often a wide gap between the time scale of the transformation and the time scale accessible with simulations. This review offers a practical guide to the ingenious methods aimed to accelerate the exploration and reconstruction of free energy landscapes of complex systems. The focus is on basic unifying concepts, successful strategies, and pitfalls, illustrated with examples of application to scientific problems from different disciplines. The current challenges in the field consist mainly in the cumbersome identification of optimal reaction coordinates and in the extensive recourse to expert human supervision and fine tuning of the algorithms. The full achievement of wide-spectrum formulations and easy reproducibility of results would constitute the breakthrough necessary to enter the era of routine use of enhanced sampling simulations

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, and bear a clear signature of an order-disorder transition. Once combined with ab~initio metadynamics, these coordinates are shown to be a powerful tool for the discovery of low-energy isomers of molecules and nanoclusters as well as for a blind exploration of isomerization, association, and dissociation reactions.

Significance: The study shows that Miller–Urey experiments produce RNA nucleobases in discharges and laser-driven plasma impact simulations carried out in a simple prototype of reducing atmosphere containing ammonia and carbon monoxide. We carried out a self-standing description of chemistry relevant to hypothesis of abiotic synthesis of RNA nucleobases related to early-Earth chemical evolution under reducing conditions. The research addresses the chemistry of simple-model reducing atmosphere (NH ₃ + CO + H ₂ O) and the role of formamide as an intermediate of nucleobase formation in Miller–Urey experiment. The explorations combine experiments performed using modern techniques of large, high-power shock wave plasma generation by hall terawatt lasers, electric discharges, and state-of-the-art ab initio free-energy calculations.