Quantifying cooperative multisite binding in the hub protein LC8 through Bayesian inference.

Multistep protein-protein interactions underlie most biological processes, but their characterization through methods such as isothermal titration calorimetry (ITC) is largely confined to simple models that provide little information on the intermediate, individual steps. In this study, we primarily examine the essential hub protein LC8, a small dimer that binds disordered regions of 100+ client proteins in two symmetrical grooves at the dimer interface. Mechanistic details of LC8 binding have remained elusive, hampered in part by ITC data analyses employing simple models that treat bivalent binding as a single event with a single binding affinity. We build on existing Bayesian ITC approaches to quantify thermodynamic parameters for multi-site binding interactions impacted by significant uncertainty in protein concentration. Using a two-site binding model, we identify positive cooperativity with high confidence for LC8 binding to multiple client peptides. In contrast, application of an identical model to the two-site binding between the coiled-coil NudE dimer and the intermediate chain of dynein reveals little evidence of cooperativity. We propose that cooperativity in the LC8 system drives the formation of saturated induced-dimer structures, the functional units of most LC8 complexes. In addition to these system-specific findings, our work advances general ITC analysis in two ways. First, we describe a previously unrecognized mathematical ambiguity in concentrations in standard binding models and clarify how it impacts the precision with which binding parameters are determinable in cases of high uncertainty in analyte concentrations. Second, building on observations in the LC8 system, we develop a system-agnostic heat map of practical parameter identifiability calculated from synthetic data which demonstrates that the ability to determine microscopic binding parameters is strongly dependent on both the parameters themselves and experimental conditions. The work serves as a foundation for determination of multi-step binding interactions, and we outline best practices for Bayesian analysis of ITC experiments.

Structure of native lens connexin 46/50 intercellular channels by cryo-EM.

Gap junctions establish direct pathways for cell-to-cell communication through the assembly of twelve connexin subunits that form intercellular channels connecting neighbouring cells. Co-assembly of different connexin isoforms produces channels with unique properties and enables communication across cell types. Here we used single-particle cryo-electron microscopy to investigate the structural basis of connexin co-assembly in native lens gap junction channels composed of connexin 46 and connexin 50 (Cx46/50). We provide the first comparative analysis to connexin 26 (Cx26), which-together with computational studies-elucidates key energetic features governing gap junction permselectivity. Cx46/50 adopts an open-state conformation that is distinct from the Cx26 crystal structure, yet it appears to be stabilized by a conserved set of hydrophobic anchoring residues. 'Hot spots' of genetic mutations linked to hereditary cataract formation map to the core structural-functional elements identified in Cx46/50, suggesting explanations for many of the disease-causing effects.

Vascular KATP channel structural dynamics reveal regulatory mechanism by Mg-nucleotides.

Vascular tone is dependent on smooth muscle KATP channels comprising pore-forming Kir6.1 and regulatory SUR2B subunits, in which mutations cause Cantú syndrome. Unique among KATP isoforms, they lack spontaneous activity and require Mg-nucleotides for activation. Structural mechanisms underlying these properties are unknown. Here, we determined cryogenic electron microscopy structures of vascular KATP channels bound to inhibitory ATP and glibenclamide, which differ informatively from similarly determined pancreatic KATP channel isoform (Kir6.2/SUR1). Unlike SUR1, SUR2B subunits adopt distinct rotational "propeller" and "quatrefoil" geometries surrounding their Kir6.1 core. The glutamate/aspartate-rich linker connecting the two halves of the SUR-ABC core is observed in a quatrefoil-like conformation. Molecular dynamics simulations reveal MgADP-dependent dynamic tripartite interactions between this linker, SUR2B, and Kir6.1. The structures captured implicate a progression of intermediate states between MgADP-free inactivated, and MgADP-bound activated conformations wherein the glutamate/aspartate-rich linker participates as mobile autoinhibitory domain, suggesting a conformational pathway toward KATP channel activation.

#COVIDisAirborne: AI-enabled multiscale computational microscopy of delta SARS-CoV-2 in a respiratory aerosol.

We seek to completely revise current models of airborne transmission of respiratory viruses by providing never-before-seen atomic-level views of the SARS-CoV-2 virus within a respiratory aerosol. Our work dramatically extends the capabilities of multiscale computational microscopy to address the significant gaps that exist in current experimental methods, which are limited in their ability to interrogate aerosols at the atomic/molecular level and thus obscure our understanding of airborne transmission. We demonstrate how our integrated data-driven platform provides a new way of exploring the composition, structure, and dynamics of aerosols and aerosolized viruses, while driving simulation method development along several important axes. We present a series of initial scientific discoveries for the SARS-CoV-2 Delta variant, noting that the full scientific impact of this work has yet to be realized.

Connexin 46 and connexin 50 gap junction channel properties are shaped by structural and dynamic features of their N-terminal domains.

KEY POINTS: Gap junctions formed by different connexins are expressed throughout the body and harbour unique channel properties that have not been fully defined mechanistically. Recent structural studies by cryo-electron microscopy have produced high-resolution models of the related but functionally distinct lens connexins (Cx50 and Cx46) captured in a stable open state, opening the door for structure-function comparison. Here, we conducted comparative molecular dynamics simulation and electrophysiology studies to dissect the isoform-specific differences in Cx46 and Cx50 intercellular channel function. We show that key determinants Cx46 and Cx50 gap junction channel open stability and unitary conductance are shaped by structural and dynamic features of their N-terminal domains, in particular the residue at the 9th position and differences in hydrophobic anchoring sites. The results of this study establish the open state Cx46/50 structural models as archetypes for structure-function studies targeted at elucidating the mechanism of gap junction channels and the molecular basis of disease-causing variants. ABSTRACT: Connexins form intercellular communication channels, known as gap junctions (GJs), that facilitate diverse physiological roles, from long-range electrical and chemical coupling to coordinating development and nutrient exchange. GJs formed by different connexin isoforms harbour unique channel properties that have not been fully defined mechanistically. Recent structural studies on Cx46 and Cx50 defined a novel and stable open state and implicated the amino-terminal (NT) domain as a major contributor for isoform-specific functional differences between these closely related lens connexins. To better understand these differences, we constructed models corresponding to wildtype Cx50 and Cx46 GJs, NT domain swapped chimeras, and point variants at the 9th residue for comparative molecular dynamics (MD) simulation and electrophysiology studies. All constructs formed functional GJ channels, except the chimeric Cx46-50NT variant, which correlated with an introduced steric clash and increased dynamical behaviour (instability) of the NT domain observed by MD simulation. Single channel conductance correlated well with free-energy landscapes predicted by MD, but resulted in a surprisingly greater degree of effect. Additionally, we observed significant effects on transjunctional voltage-dependent gating (Vj gating) and/or open state dwell times induced by the designed NT domain variants. Together, these studies indicate intra- and inter-subunit interactions involving both hydrophobic and charged residues within the NT domains of Cx46 and Cx50 play important roles in defining GJ open state stability and single channel conductance, and establish the open state Cx46/50 structural models as archetypes for structure-function studies targeted at elucidating GJ channel mechanisms and the molecular basis of cataract-linked connexin variants.

A systems-biology approach to molecular machines: Exploration of alternative transporter mechanisms.

Motivated by growing evidence for pathway heterogeneity and alternative functions of molecular machines, we demonstrate a computational approach for investigating two questions: (1) Are there multiple mechanisms (state-space pathways) by which a machine can perform a given function, such as cotransport across a membrane? (2) How can additional functionality, such as proofreading/error-correction, be built into machine function using standard biochemical processes? Answers to these questions will aid both the understanding of molecular-scale cell biology and the design of synthetic machines. Focusing on transport in this initial study, we sample a variety of mechanisms by employing Metropolis Markov chain Monte Carlo. Trial moves adjust transition rates among an automatically generated set of conformational and binding states while maintaining fidelity to thermodynamic principles and a user-supplied fitness/functionality goal. Each accepted move generates a new model. The simulations yield both single and mixed reaction pathways for cotransport in a simple environment with a single substrate along with a driving ion. In a "competitive" environment including an additional decoy substrate, several qualitatively distinct reaction pathways are found which are capable of extremely high discrimination coupled to a leak of the driving ion, akin to proofreading. The array of functional models would be difficult to find by intuition alone in the complex state-spaces of interest.

A kinetic mechanism for enhanced selectivity of membrane transport.

Membrane transport is generally thought to occur via an alternating access mechanism in which the transporter adopts at least two states, accessible from two different sides of the membrane to exchange substrates from the extracellular environment and the cytoplasm or from the cytoplasm and the intracellular matrix of the organelles (only in eukaryotes). In recent years, a number of high resolution structures have supported this general framework for a wide class of transport molecules, although additional states along the transport pathway are emerging as critically important. Given that substrate binding is often weak in order to enhance overall transport rates, there exists the distinct possibility that transporters may transport the incorrect substrate. This is certainly the case for many pharmaceutical compounds that are absorbed in the gut or cross the blood brain barrier through endogenous transporters. Docking studies on the bacterial sugar transporter vSGLT reveal that many highly toxic compounds are compatible with binding to the orthosteric site, further motivating the selective pressure for additional modes of selectivity. Motivated by recent work in which we observed failed substrate delivery in a molecular dynamics simulation where the energized ion still goes down its concentration gradient, we hypothesize that some transporters evolved to harness this 'slip' mechanism to increase substrate selectivity and reduce the uptake of toxic molecules. Here, we test this idea by constructing and exploring a kinetic transport model that includes a slip pathway. While slip reduces the overall productive flux, when coupled with a second toxic molecule that is more prone to slippage, the overall substrate selectivity dramatically increases, suppressing the accumulation of the incorrect compound. We show that the mathematical framework for increased substrate selectivity in our model is analogous to the classic proofreading mechanism originally proposed for tRNA synthase; however, because the transport cycle is reversible we identified conditions in which the selectivity is essentially infinite and incorrect substrates are exported from the cell in a 'detoxification' mode. The cellular consequences of proofreading and membrane slippage are discussed as well as the impact on future drug development.

A gentle introduction to the non-equilibrium physics of trajectories: Theory, algorithms, and biomolecular applications.

Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be understood with a minimum of formalism based on a rigorous trajectory picture. The fundamental object is the ensemble of trajectories, a set of independent time-evolving systems, which easily can be visualized or simulated (e.g., for protein folding) and which can be analyzed rigorously in analogy to an ensemble of static system configurations. The trajectory picture provides a straightforward basis for understanding first-passage times, "mechanisms" in complex systems, and fundamental constraints on the apparent reversibility of complex processes. Trajectories make concrete the physics underlying the diffusion and Fokker-Planck partial differential equations. Last but not least, trajectory ensembles underpin some of the most important algorithms that have provided significant advances in biomolecular studies of protein conformational and binding processes.

Should Virus Capsids Assemble Perfectly? Theory and Observation of Defects.

Although published structural models of viral capsids generally exhibit a high degree of regularity or symmetry, structural defects might be expected because of the fluctuating environment in which capsids assemble and the requirement of some capsids for disassembly before genome delivery. Defective structures are observed in computer simulations, and are evident in single-particle cryoelectron microscopy studies. Here, we quantify the conditions under which defects might be expected, using a statistical mechanics model allowing for ideal, defective, and vacant sites. The model displays a threshold in affinity parameters below which there is an appreciable population of defective capsids. Even when defective sites are not allowed, there is generally some population of vacancies. Analysis of single particles in cryoelectron microscopy micrographs yields a confirmatory ≳15% of defective particles. Our findings suggest structural heterogeneity in virus capsids may be under-appreciated, and also points to a nontraditional strategy for assembly inhibition.

OPTIMIZING WEIGHTED ENSEMBLE SAMPLING OF STEADY STATES.

We propose parameter optimization techniques for weighted ensemble sampling of Markov chains in the steady-state regime. Weighted ensemble consists of replicas of a Markov chain, each carrying a weight, that are periodically resampled according to their weights inside of each of a number of bins that partition state space. We derive, from first principles, strategies for optimizing the choices of weighted ensemble parameters, in particular the choice of bins and the number of replicas to maintain in each bin. In a simple numerical example, we compare our new strategies with more traditional ones and with direct Monte Carlo.

Computational Estimation of Microsecond to Second Atomistic Folding Times.

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 µs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τf = 0.8-9 µs), NTL9 at water-like viscosity (τf = 0.2-2 ms), and Protein G at low viscosity (τf = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture.

Probability currents are fundamental in characterizing the kinetics of nonequilibrium processes. Notably, the steady-state current Jss for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition from the source to sink. Because transient nonequilibrium behavior is quantified in some modern path sampling approaches, such as the "weighted ensemble" strategy, there is strong motivation to determine bounds on Jss-and hence on the MFPT-as the system evolves in time. Here, we show that Jss is bounded from above and below by the maximum and minimum, respectively, of the current as a function of the spatial coordinate at any time t for one-dimensional systems undergoing overdamped Langevin (i.e., Smoluchowski) dynamics and for higher-dimensional Smoluchowski systems satisfying certain assumptions when projected onto a single dimension. These bounds become tighter with time, making them of potential practical utility in a scheme for estimating Jss and the long time scale kinetics of complex systems. Conceptually, the bounds result from the fact that extrema of the transient currents relax toward the steady-state current.

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process.

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated "kinetic equivalence" of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Escape of a Small Molecule from Inside T4 Lysozyme by Multiple Pathways.

The T4 lysozyme L99A mutant is often used as a model system to study small-molecule binding to proteins, but pathways for ligand entry and exit from the buried binding site and the associated protein conformational changes have not been fully resolved. Here, molecular dynamics simulations were employed to model benzene exit from its binding cavity using the weighted ensemble (WE) approach to enhance sampling of low-probability unbinding trajectories. Independent WE simulations revealed four pathways for benzene exit, which correspond to transient tunnels spontaneously formed in previous simulations of apo T4 lysozyme. Thus, benzene unbinding occurs through multiple pathways partially created by intrinsic protein structural fluctuations. Motions of several α-helices and side chains were involved in ligand escape from metastable microstates. WE simulations also provided preliminary estimates of rate constants for each exit pathway. These results complement previous works and provide a semiquantitative characterization of pathway heterogeneity for binding of small molecules to proteins.

Clinically Observed Estrogen Receptor Alpha Mutations within the Ligand-Binding Domain Confer Distinguishable Phenotypes.

OBJECTIVE: Twenty to fifty percent of estrogen receptor-positive (ER+) metastatic breast cancers express mutations within the ER ligand-binding domain. While most studies focused on the constitutive ER signaling activity commonly engendered by these mutations selected during estrogen deprivation therapy, our study was aimed at investigating distinctive phenotypes conferred by different mutations within this class. METHODS: We examined the two most prevalent mutations, D538G and Y537S, employing corroborative genome-edited and lentiviral-transduced ER+ T47D cell models. We used a luciferase-based reporter and endogenous phospho-ER immunoblot analysis to characterize the estrogen response of ER mutants and determined their resistance to known ER antagonists. RESULTS: Consistent with their selection during estrogen deprivation therapy, these mutants conferred constitutive ER activity. While Y537S mutants showed no estrogen dependence, D538G mutants demonstrated an enhanced estrogen-dependent response. Both mutations conferred resistance to ER antagonists that was overcome at higher doses acting specifically through their ER target. CONCLUSIONS: These observations provide a tenable hypothesis for how D538G ESR1-expressing clones can contribute to shorter progression-free survival observed in the exemestane arm of the BOLERO-2 study. Thus, in those patients with dominant D538G-expressing clones, longitudinal analysis for this mutation in circulating free DNA may prove beneficial for informing more optimal therapeutic regimens.

Preface: Special Topic on Enhanced Sampling for Molecular Systems.

This special topic highlights recent developments in enhanced sampling methods for molecular-level simulations of chemical and biological systems. These methods are designed to enable more efficient exploration of phase space and extend the time scales that can be explored by simulations.

Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories.

The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation--by orders of magnitude for some observables.

Structural integrity of the ribonuclease H domain in HIV-1 reverse transcriptase.

The mature form of reverse transcriptase (RT) is a heterodimer comprising the intact 66-kDa subunit (p66) and a smaller 51-kDa subunit (p51) that is generated by removal of most of the RNase H (RNH) domain from a p66 subunit by proteolytic cleavage between residues 440 and 441. Viral infectivity is eliminated by mutations such as F440A and E438N in the proteolytic cleavage sequence, while normal processing and virus infectivity are restored by a compensatory mutation, T477A, that is located more than 10 Å away from the processing site. The molecular basis for this compensatory effect has remained unclear. We therefore investigated structural characteristics of RNH mutants using computational and experimental approaches. Our Nuclear Magnetic Resonance and Differential Scanning Fluorimetry results show that both F440A and E438N mutations disrupt RNH folding. Addition of the T477A mutation restores correct folding of the RNH domain despite the presence of the F440A or E438N mutations. Molecular dynamics simulations suggest that the T477A mutation affects the processing site by altering relative orientations of secondary structure elements. Predictions of sequence tolerance suggest that phenylalanine and tyrosine are structurally preferred at residues 440 and 441, respectively, which are the P1 and P1' substrate residues known to require bulky side chains for substrate specificity. Interestingly, our study demonstrates that the processing site residues, which are critical for protease substrate specificity and must be exposed to the solvent for efficient processing, also function to maintain proper RNH folding in the p66/p51 heterodimer.

Tabulation as a high-resolution alternative to coarse-graining protein interactions: Initial application to virus capsid subunits.

Traditional coarse-graining based on a reduced number of interaction sites often entails a significant sacrifice of chemical accuracy. As an alternative, we present a method for simulating large systems composed of interacting macromolecules using an energy tabulation strategy previously devised for small rigid molecules or molecular fragments [S. Lettieri and D. M. Zuckerman, J. Comput. Chem. 33, 268-275 (2012); J. Spiriti and D. M. Zuckerman, J. Chem. Theory Comput. 10, 5161-5177 (2014)]. We treat proteins as rigid and construct distance and orientation-dependent tables of the interaction energy between them. Arbitrarily detailed interactions may be incorporated into the tables, but as a proof-of-principle, we tabulate a simple α-carbon Go-like model for interactions between dimeric subunits of the hepatitis B viral capsid. This model is significantly more structurally realistic than previous models used in capsid assembly studies. We are able to increase the speed of Monte Carlo simulations by a factor of up to 6700 compared to simulations without tables, with only minimal further loss in accuracy. To obtain further enhancement of sampling, we combine tabulation with the weighted ensemble (WE) method, in which multiple parallel simulations are occasionally replicated or pruned in order to sample targeted regions of a reaction coordinate space. In the initial study reported here, WE is able to yield pathways of the final ∼25% of the assembly process.