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.Author summary: Multi-site protein-protein interactions govern many protein functions throughout the cell. Precise determination of thermodynamic constants of multi-site binding is a significant challenge, however. The application of complex models to multi-step interactions is difficult and hampered further by complications arising from uncertainty in analyte concentrations. To extract binding parameter estimates from minimal and hard-to-obtain data on these large complicated systems, we utilize Bayesian statistical techniques which calculate the ‘likelihood’ of parameters giving rise to experimental observations. Bayesian computations yield probability density distributions for thermodynamic parameters of binding. To demonstrate the validity of the method and improve our understanding how the hub protein LC8 promotes dimerization of its 100+ binding partners, we test the pipeline on several of these partners and demonstrate that LC8 can bind clients cooperatively, driving interactions towards a ‘fully bound’ functional state. We additionally examine an interaction between the dimer NudE and the intermediate chain of dynein, which does not appear to bind with cooperativity. Our work provides a solid foundation for future analysis of more complicated binding interactions, including oligomeric complexes formed between LC8 and clients with multiple LC8-binding sites.