Kinetics of Phenol Escape from the Insulin R6 Hexamer

Temperature-Dependent Fold-Switching Mechanism of the Circadian Clock Protein KaiB

The oscillator of the cyanobacterial circadian clock relies on the ability of the KaiB protein to switch reversibly between a stable ground-state fold (gsKaiB) and an unstable fold-switched fold (fsKaiB). Rare fold-switching events by KaiB provide a critical delay in the negative feedback loop of this post-translational oscillator. In this study, we experimentally and computationally investigate the temperature dependence of fold switching and its mechanism. We demonstrate that the stability of gsKaiB increases with temperature compared to fsKaiB and that the Q10 value for the gsKaiB → fsKaiB transition is nearly three times smaller than that for the reverse transition. Simulations and native-state hydrogen-deuterium exchange NMR experiments suggest that fold switching can involve both subglobally and near-globally unfolded intermediates. The simulations predict that the transition state for fold switching coincides with isomerization of conserved prolines in the most rapidly exchanging region, and we confirm experimentally that proline isomerization is a rate-limiting step for fold switching. We explore the implications of our results for temperature compensation, a hallmark of circadian clocks, through a kinetic model.

Exploring the Higher Order Structure and Conformational Transitions in Insulin Microcrystalline Biopharmaceuticals by Proton-Detected Solid-State Nuclear Magnetic Resonance at Natural Abundance

The integrity of a higher order structure (HOS) is an essential requirement to ensure the efficacy, stability, and safety of protein therapeutics. Solution-state nuclear magnetic resonance (NMR) occupies a unique niche as one of the most promising methods to access atomic-level structural information on soluble biopharmaceutical formulations. Another major class of drugs is poorly soluble, such as microcrystalline suspensions, which poses significant challenges for the characterization of the active ingredient in its native state. Here, we have demonstrated a solid-state NMR method for HOS characterization of biopharmaceutical suspensions employing a selective excitation scheme under fast magic angle spinning (MAS). The applicability of the method is shown on commercial insulin suspensions at natural isotopic abundance. Selective excitation aided with proton detection and non-uniform sampling (NUS) provides improved sensitivity and resolution. The enhanced resolution enabled us to demonstrate the first experimental evidence of a phenol-escaping pathway in insulin, leading to conformational transitions to different hexameric states. This approach has the potential to serve as a valuable means for meticulously examining microcrystalline biopharmaceutical suspensions, which was previously not attainable in their native formulation states and can be seamlessly extended to other classes of biopharmaceuticals such as mAbs and other microcrystalline proteins.

Predicting rare events using neural networks and short-trajectory data

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. We illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction

Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition operator are useful for visualization, and they can provide an efficient basis for computing statistics, such as the likelihood and average time of events (predictions). Here, we develop inexact iterative linear algebra methods for computing these eigenfunctions (spectral estimation) and making predictions from a dataset of short trajectories sampled at finite intervals. We demonstrate the methods on a low-dimensional model that facilitates visualization and a high-dimensional model of a biomolecular system. Implications for the prediction problem in reinforcement learning are discussed.

Progress in Simulation Studies of Insulin Structure and Function

Insulin is a peptide hormone known for chiefly regulating glucose level in blood among several other metabolic processes. Insulin remains the most effective drug for treating diabetes mellitus. Insulin is synthesized in the pancreatic β-cells where it exists in a compact hexameric architecture although its biologically active form is monomeric. Insulin exhibits a sequence of conformational variations during the transition from the hexamer state to its biologically-active monomer state. The structural transitions and the mechanism of action of insulin have been investigated using several experimental and computational methods. This review primarily highlights the contributions of molecular dynamics (MD) simulations in elucidating the atomic-level details of conformational dynamics in insulin, where the structure of the hormone has been probed as a monomer, dimer, and hexamer. The effect of solvent, pH, temperature, and pressure have been probed at the microscopic scale. Given the focus of this review on the structure of the hormone, simulation studies involving interactions between the hormone and its receptor are only briefly highlighted, and studies on other related peptides (e.g., insulin-like growth factors) are not discussed. However, the review highlights conformational dynamics underlying the activities of reported insulin analogs and mimetics. The future prospects for computational methods in developing promising synthetic insulin analogs are also briefly highlighted.