Kinetics of Phenol Escape from the Insulin R6 Hexamer

Analysis of the Dynamics of a Complex, Multipathway Reaction: Insulin Dimer Dissociation

The protein hormone insulin forms a homodimer that must dissociate to bind to its receptor. Understanding the kinetics and mechanism of dissociation is essential for the rational design of therapeutic analogs. In addition to its physiological importance, this dissociation process serves as a paradigm for coupled (un)folding and (un)binding. Based on previous free energy simulations, insulin dissociation is thought to involve multiple pathways with comparable free energy barriers. Here, we analyze the mechanism of insulin dimer dissociation using a recently developed computational framework for estimating kinetic statistics from short-trajectory data. These statistics indicate that the likelihood of dissociation (the committor) closely tracks the decrease in the number of (native and nonnative) intermonomer contacts and the increase in the number of water contacts at the dimer interface; the transition state with equal likelihood of association and dissociation corresponds to an encounter complex with relatively few native contacts and many nonnative contacts. We identify four pathways out of the dimer state and quantify their contributions to the rate as well as their exchange by computing reactive fluxes. We show that both the pathways and their extents of exchange can be understood in terms of rotations around three axes of the dimer structure. Our results provide insights into the kinetics of insulin analogs and, more generally, how to characterize complex, multipathway processes.

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 posttranslational 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 in a construct optimized for NMR studies. Simulations and native-state hydrogen-deuterium exchange NMR experiments suggest that fold switching can involve both partially and completely 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.

Deciphering Pathways and Thermodynamics of Protein Assembly Using Native Mass Spectrometry

Protein oligomerization regulates many critical physiological processes, and its dysregulation can contribute to dysfunction and diseases. Elucidating the assembly pathways and quantifying their underlying thermodynamic and kinetic parameters are crucial for a comprehensive understanding of biological processes and for advancing therapeutics targeting abnormal protein oligomerization. Established binding assays, with limited mass precision, often rely on simplified models for data interpretation. In contrast, high-resolution native mass spectrometry (nMS) can directly determine the stoichiometry of biomolecular complexes in vitro. However, quantification is hindered by the fact that the relative abundances of gas-phase ions generally do not reflect solution concentrations due to nonuniform response factors. Recently, slow mixing mode (SLOMO)-nMS, which can quantify the relative response factors of interacting species, has been demonstrated to reliably measure the affinity (Kd) of binary biomolecular complexes. Here, we introduce an extended form of SLOMO-nMS that enables simultaneous quantification of the thermodynamics in multistep association reactions. Application of this method to homo-oligomerization of concanavalin A and insulin confirmed the reliability of the assay and uncovered details about the assembly processes that had previously resisted elucidation. Results acquired using SLOMO-nMS implemented with charge detection shed new light on the binding of recombinant human angiotensin-converting enzyme 2 and the SARS-CoV-2 spike protein. Importantly, new assembly pathways were uncovered, and the affinities of these interactions, which regulate host cell infection, were quantified. Together, these findings highlight the tremendous potential of SLOMO-nMS to accelerate the characterization of protein assembly pathways and thermodynamics and, in so doing, enhance fundamental biological understanding and facilitate therapeutic development. https://orcid.org/0000-0002-3389-7112.

Analysis of the dynamics of a complex, multipathway reaction: Insulin dimer dissociation

The protein hormone insulin forms a homodimer that must dissociate to bind to its receptor. Understanding the kinetics and mechanism of dissociation is essential for rational design of therapeutic analogs. In addition to its physiological importance, this dissociation process serves as a paradigm for coupled (un)folding and (un)binding. Based on previous free energy simulations, insulin dissociation is thought to involve multiple pathways with comparable free energy barriers. Here, we analyze the mechanism of insulin dimer dissociation using a recently developed computational framework for estimating kinetic statistics from short-trajectory data. These statistics indicate that the likelihood of dissociation (the committor) closely tracks the decrease in the number of (native and nonnative) intermonomer contacts and the increase in the number of water contacts at the dimer interface; the transition state with equal likelihood of association and dissociation corresponds to an encounter complex with relatively few native contacts and many nonnative contacts. We identify four pathways out of the dimer state and quantify their contributions to the rate, as well as their exchange, by computing reactive fluxes. We show that both the pathways and their extents of exchange can be understood in terms of rotations around three axes of the dimer structure. Our results provide insights into the kinetics of insulin analogues and, more generally, how to characterize complex, multipathway processes.

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.