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.

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.

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.

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. We examine the hub protein LC8, which binds to disordered regions of 100+ client proteins in a wide range of stoichiometries. Despite evidence that LC8 binds clients cooperatively, prior ITC thermodynamic analyses have relied on models that do not accommodate allostery, and furthermore do not account for critical uncertainties in analyte concentrations. To characterize allostery in a more rigorous fashion, we build on existing Bayesian approaches to ITC to quantify thermodynamic parameters for multi-step binding interactions impacted by significant uncertainty in protein concentration. Notably, we account for a previously unrecognized intrinsic ambiguity in concentrations in standard binding models and clarify how this ambiguity impacts the extent to which binding parameters can be determined in cases of highly uncertain analyte concentrations. Our approach is applicable to a host of multi-step binding interactions, and we use it to investigate two systems. First, we deeply examine 2:2 LC8 binding and find it to be significantly positively cooperative with high confidence for multiple clients. Building on observations in the LC8 system, we develop a system-agnostic "phase diagram" calculated from synthetic data demonstrating that certain binding parameters intrinsically inflate parameter uncertainty in ITC analysis, independent of experimental uncertainties. Second, we study 2:2 binding between the dynein intermediate chain and binding protein NudE, where in contrast, we find little evidence of allostery.

In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three-dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo-multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single-domain protein native topologies as well as distinct single-domain proteins from multimeric complexes within noisy volumes.