Quantifying cooperative multisite binding through Bayesian inference

Abstract

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 model LC8 binding and identify positive cooperativity with high confidence for multiple client peptides. Application of an identical model to two-site binding between the coiled-coil dimer NudE and the intermediate chain of dynein reveals little evidence of cooperativity, in contrast to LC8. We propose that cooperativity in the LC8 system drives the formation of saturated 2:2 bound states, which play a functional role in many 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 can be determined 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 certain binding parameters intrinsically inflate parameter uncertainty in ITC analysis, independent of experimental uncertainties. Author SummaryMulti-site protein-protein interactions govern many protein functions throughout the cell. Precise determination of thermodynamic constants of multi-site binding is a significant biophysical 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 address these issues, we utilize Bayesian statistical techniques which calculate the likelihood of parameters giving rise to experimental observations to build probability density distributions for thermodynamic parameters of binding. To demonstrate 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.