Fig 1.
LC8 binds clients through a two-site mechanism.
(a) Diagram of LC8-client binding, showing a structure of apo LC8 on the left, and a fully bound structure (PDB 3E2B) on the right. Intermediates are boxed to indicate they are symmetric and indistinguishable species. (b) Example isotherms for binding between dimeric LC8 and client peptide taken from GLCCI (left) and between the coiled-coil protein NudE and its client, the intermediate chain (IC) of dynein (right).
Fig 2.
Exact degeneracy in binding isotherms.
Based on the scaling relations of Eq (3), for any set of ligand and total macromolecule concentrations (Xt, Mt), there are infinitely many alternative concentrations (e.g., filled circles) on a diagonal line in the ([Xt], [Mt]) plane which yield exactly equivalent isotherms (inset, isotherms for points 1, 2, and 3 are drawn in distinct colors but overlay exactly) for a fixed set of thermodynamic parameters. For any given point in parameter space, equivalent degenerate lines can be drawn in a radial manner (e.g. the two additional black lines), passing through the point and the origin. The plotted synthetic isotherms are for 1:1 binding, but analogous degeneracy also holds for multivalent binding—see text. Note that no fixed relationship among concentrations is assumed during Bayesian inference.
Fig 3.
Analysis of two-site model using synthetic isotherms.
(a) A set of synthetic isotherms for two-site binding with varied ΔΔG parameters demonstrating how cooperativity changes isotherm shape. Thermodynamic parameters are ΔG = -7, ΔH = -10, and ΔΔH = 0. Concentrations are set at 17 and 500 μM for cell and syringe respectively, and injection volumes are 6 μL. (b) A synthetic isotherm (ΔG = -7, ΔH = -10, ΔΔG = -1, ΔΔH = -1.5 kcal/mol) with added gaussian noise (points) with 50 fitted isotherms (lines) generated through the Bayesian pipeline, i.e., sampled from the posterior. (c) One and two-dimensional marginal distributions for thermodynamic parameters, with contours in the two-dimensional plots set at 95 (yellow), 75 (orange), 50(purple) and 25%(black) confidence. Red lines and dots indicate true values for the synthetic isotherm. Marginal distributions and MCMC chains for all eight model parameters, including nuisance parameters can be found in S1 Fig. (d) Marginal distributions for concentration parameters, exhibiting characteristic diagonal shape (Fig 2) with contours as in (c). Plots at the top of each column in panels c and d are one-dimensional probability density distributions. (e,f) One-dimensional distributions for ΔG (e) and ΔH (f) plotted for models with prior ranges for concentrations of 1, 5, 10, 30 and 50% of the stated concentration. (g) Width of the 95% Bayesian credibility region, akin to a confidence interval, for thermodynamic parameters as a function of the width of the concentration prior used in modeling, plotted from models with prior ranges for concentrations of ± 1, 5, 10, 30 and 50% of the stated concentration.
Table 1.
Ranges for thermodynamic parameters for LC8-client binding.
Values delineate 95% Bayesian credibility regions from sampled posterior distributions in kcal/mol, which are akin to 95% confidence intervals. Previously published binding parameters from an identical-sites model for these isotherms are available in S3 Table.
Fig 4.
LC8 binding to a peptide from the protein SPAG5.
(a) Experimental titration isotherm of SPAG5 into LC8 (points) with 50 example traces (lines) drawn from the posterior distribution of thermodynamic parameters and concentrations. (b) One and two-dimensional marginal distributions for thermodynamic parameters, with contours in the two-dimensional plots set at 95 (yellow), 75 (orange), 50(purple) and 25%(black) credibility. (c) Marginal distributions for concentrations of LC8 and peptide, showing a line of degenerate solutions, which may be compared to Fig 2. (d) Marginal distributions for entropy (-TΔS) and change of entropy (-TΔΔS). Plots at the top of each column in panels b,c,d are one-dimensional probability density distributions.
Fig 5.
Thermodynamic parameter distributions from 3 LC8-peptide isotherms.
Binding between LC8 and peptides from Ebola VP35 (a), SLC9A2 (b) and motif 1 from BSN (c). Isotherms are shown at the top, and distributions for thermodynamic parameters are shown below. Horizontal axes represent the full width of the uniform prior range for each parameter to allow for direct comparison between each isotherm.
Fig 6.
binding between the intermediate chain (IC) and NudE.
(a) A model of NudE-IC binding, which forms a 2:2 complex. A cartoon diagram of NudE is shown in purple and IC in orange. (b) Sampled distributions modeled from a ‘global’ model based on two isotherms for binding between IC and NudE from yeast. Marginal distributions for thermodynamic parameters are shown on the left, and the top right corner contains the experimental isotherms (points) with model values (lines) drawn from the posterior.
Fig 7.
Strong dependence of posterior distributions on model parameters.
(a,b) Graphical depiction of enthalpy uncertainty on a grid of ΔΔG and ΔG values, generated from the Bayesian posterior for each grid point based on synthetic data (with fixed ΔH = -10, ΔΔH = -1.5 kcal/mol). Boxes are colored by the width of the 95% credibility region for ΔH (a) and ΔΔH (b), with lighter colors corresponding to wider credibility regions (color bars). Red polygons demonstrate where each Kd (Kd1 for left, Kd2 for right) is greater than 17 μM, which is the cell concentration set for these synthetic isotherms. Black symbols indicate mean values for experimental isotherms for binding for BSN motif I (star) and SLC9A2 (octagon), for comparison. (c) Isotherms for binding between LC8 and SLC9A2 (top) and BSN I (bottom). C values for each step of binding, based on mean values taken from the posterior distribution are shown. (d) Synthetic isotherms designed to mimic BSN 1 (ΔG = -5.1, ΔΔG = -1.7, ΔH = -11, ΔΔH = -2), simulated at cell concentrations of 17 (orange) and 70 (purple) μM (syringe concentrations at 900 and 2000 μM respectively). (e,f) One-dimensional probability distributions for binding enthalpy (e) and change in enthalpy (f) for the isotherms in panel (d). (g,h) Two-dimensional marginal distributions (plotting ΔH against ΔΔH for isotherms in panel (d)). Isotherms at 17 μM in (g) and 70 μM in (h). Dimension widths are fixed for both plots for better comparison.