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The recent advances in accelerated polymerization ofN-carboxyanhydrides (NCAs) enriched the toolbox to prepare well-defined polypeptide materials. Herein we report the use of crown ether (CE) to catalyze the polymerization of NCA initiated by conventional primary amine initiators in solvents with low polarity and low hydrogen-bonding ability. The cyclic structure of the CE played a crucial role in the catalysis, with 18-crown-6 enabling the fastest polymerization kinetics. The fast polymerization kinetics outpaced common side reactions, enabling the preparation of well-defined polypeptides using an α-helical macroinitiator. Experimental results as well as the simulation methods suggested that CE changed the binding geometry between NCA and propagating amino chain-end, which promoted the molecular interactions and lowered the activation energy for ring-opening reactions of NCAs. This work not only provides an efficient strategy to prepare well-defined polypeptides with functionalized C-termini, but also guides the design of catalysts for NCA polymerization.

 

Single-molecule Förster resonance energy transfer (smFRET) is an experimental methodology to track the real-time dynamics of molecules using fluorescent probes to follow one or more intramolecular distances. These distances provide a low-dimensional representation of the full atomistic dynamics. Under mild technical conditions, Takens’ Delay Embedding Theorem guarantees that the full three-dimensional atomistic dynamics of a system are diffeomorphic (i.e., related by a smooth and invertible transformation) to a time-delayed embedding of one or more scalar observables. Appealing to these theoretical guarantees, we employ manifold learning, artificial neural networks, and statistical mechanics to learn from molecular simulation training data the a priori unknown transformation between the atomic coordinates and delay-embedded intramolecular distances accessible to smFRET. This learned transformation may then be used to reconstruct atomistic coordinates from smFRET time series data. We term this approach Single-molecule TAkens Reconstruction (STAR). We have previously applied STAR to reconstruct molecular configurations of a C24H50 polymer chain and the mini-protein Chignolin with accuracies better than 0.2 nm from simulated smFRET data under noise free and high time resolution conditions. In the present work, we investigate the role of signal-to-noise ratio, data volume, and time resolution in simulated smFRET data to assess the performance of STAR under conditions more representative of experimental realities. We show that STAR can reconstruct the Chignolin and Villin mini-proteins to accuracies of 0.12 and 0.42 nm, respectively, and place bounds on these conditions for accurate reconstructions. These results demonstrate that it is possible to reconstruct dynamical trajectories of protein folding from time series in noisy, time binned, experimentally measurable observables and lay the foundations for the application of STAR to real experimental data. 

Free energies as a function of a selected set of collective variables are commonly computed in molecular simulation and of significant value in understanding and engineering molecular behavior. These free energy surfaces are most commonly estimated using variants of histogramming techniques, but such approaches obscure two important facets of these functions. First, the empirical observations along the collective variable are defined by an ensemble of discrete observations, and the coarsening of these observations into a histogram bin incurs unnecessary loss of information. Second, the free energy surface is itself almost always a continuous function, and its representation by a histogram introduces inherent approximations due to the discretization. In this study, we relate the observed discrete observations from biased simulations to the inferred underlying continuous probability distribution over the collective variables and derive histogram-free techniques for estimating this free energy surface. We reformulate free energy surface estimation as minimization of a Kullback−Leibler divergence between a continuous trial function and the discrete empirical distribution and show that this is equivalent to likelihood maximization of a trial function given a set of sampled data. We then present a fully Bayesian treatment of this formalism, which enables the incorporation of powerful Bayesian tools such as the inclusion of regularizing priors, uncertainty quantification, and model selection techniques. We demonstrate this new formalism in the analysis of umbrella sampling simulations for the χ torsion of a valine side chain in the L99A mutant of T4 lysozyme with benzene bound in the cavity. 

Ribozymes synthesize proteins in a highly regulated local environment to minimize side reactions caused by various competing species. In contrast, it is challenging to prepare synthetic polypeptides from the polymerization of N -carboxyanhydrides (NCAs) in the presence of water and impurities, which induce monomer degradations and chain terminations, respectively. Inspired by natural protein synthesis, we herein report the preparation of well-defined polypeptides in the presence of competing species, by using a water/dichloromethane biphasic system with macroinitiators anchored at the interface. The impurities are extracted into the aqueous phase in situ, and the localized macroinitiators allow for NCA polymerization at a rate which outpaces water-induced side reactions. Our polymerization strategy streamlines the process from amino acids toward high molecular weight polypeptides with low dispersity by circumventing the tedious NCA purification and the demands for air-free conditions, enabling low-cost, large-scale production of polypeptides that has potential to change the paradigm of polypeptide-based biomaterials.