PMC

Parameterizing α in terms of ν. We plot the relation between α and ν for implict solvent simulations with the ABSINTH model[] for a variety of sequences (see legend). Note that each data point corresponds to a single temperature from the replica exchange simulations of each protein.

Correlations between correction coefficient α and structural descriptors. Descriptors include mean squared radius of gyration (a), mean asphericity 〈δ*〉 (b), variance of squared radius of gyration (c) or variance of asphericity σ(δ*) (d) for a series of ensembles selected by fixing the other three valuables. Legends show the corresponding fixed and 〈δ*〉 for the ensembles used.

Fit of different models to low-q experimental data. The fit of SAXS data for R17 (black) obtained in 0.58M GdmCl using different approximations, including Guinier analysis (blue, with q_maxR_g = 1.1), Debye's equation (red, with q_maxR_g = 2.0), and extended Guinier analysis (cyan, with q_maxR_g = 2.0). Vertical black lines indicate different values of qR_g, using the R_g determined by ensemble fitting, as labelled on top axis.

Testing using all-atom MD simulations with explicit solvent. The R_g-s determined from Guinier analysis (blue), Debye's equation (red), and extended Guinier analysis (cyan) are compared with reference values obtained directly from the simulation trajectories. The three columns show the results for fitting ranges q_maxR_g = 1.1, 1.3 and 2.0, respectively. In (a) we compare R_g from analysis to the true simulation R_g, and in (b) the scaling exponent ν from analysis with that calculated from the internal distance scaling in the simulations. In (c), we summarize the deviation of inferred R_g from the true value using χ², RMSE and MSRE.

Investigation of fourth order correction term to the Guinier approximation. a) Magnitude of the correction term to Guinier analysis, as a function of . The blue lines show the curve for individual configurations in the ensemble whereas red lines show the ensemble averaged values. Dashed lines show the best fit linear curve with slope α (fitting between 0 ≤ < 4). Legends show the polymer scaling exponent ν determined from internal distance scaling with sequence separation for each ensemble. b) The fitted slope α of curves in (a) plotted as a function of ν. Left column shows R17, middle column ACTR and right column poly-Val.

Testing on experimental data for different proteins and denaturation conditions. We show a comparison between the R_g extracted from (a) Guinier analysis, (b), Debye's equation and (c) extended Guinier analysis on different experimental data sets including R17 and ACTR in different denaturant conditions. The corresponding scaling exponent, ν, from extended Guinier analysis is shown in (d). The reference values (grey shaded regions) are from ensembles fitted to both FRET and SAXS experimental data from Ref. []. e) Errors estimated using χ², RMSE and MSRE for using Guinier analysis with q_maxR_g = 1.3 (blue), Debye's equation with q_maxR_g = 2.0 (red) and extended Guinier analysis with q_maxR_g = 2.0 (cyan). Color code is shown in the legend: q_maxR_g used for fitting in (a), (b), (c) and (d); or the method used for interpreting data in (e).