A collection of programs for one-dimensional Ising analysis of linear repeat proteins with point substitutions

Abstract

A collection of programs is presented to analyze the thermodynamics of folding of linear repeat proteins using a 1D Ising model to determine intrinsic folding and interfacial coupling free energies. Expressions for folding transitions are generated for a series of constructs with different repeat numbers and are globally fitted to transitions for these constructs. These programs are designed to analyze Ising parameters for capped homopolymeric consensus repeat constructs as well as heteropolymeric constructs that contain point substitutions, providing a rigorous framework for analysis of the effects of mutation on intrinsic and directional (i.e., N-versus C-terminal) interfacial coupling freeenergies. A bootstrap analysis is provided to estimate parameter uncertainty as well as correlations among fitted parameters. Rigorous statistical analysis is essential for interpreting fits using the complex models required for Ising analysis of repeat proteins, especially heteropolymeric repeat proteins. Programs described here are available at https://github.com/barricklab-at-jhu/Ising_programs. 3

Analysis of Tandem Repeat Protein Folding Using Nearest-Neighbor Models

“…We present fits of these equations to folding transitions for a series of NARPs and SARPs and a FARP. Fitting is performed with a nonlinear least squares package that we have developed in Python (25), which is freely available at https://github.com/barricklab-atjhu/Ising_programs.…”

“…Y c is the spectroscopic signal from conformation c, and p c is its population; p c depends on the intrinsic and interfacial free energies, which in turn depend on the solution variable x. When x represents denaturant concentration, the free energy terms are linearly dependent on denaturant concentration (see 15,25).…”

“…However, homopolymeric consensus NARP arrays are often insoluble and must be capped with N-and C-terminal repeats containing polar substitutions. This sequence heterogeneity increases the number of thermodynamic parameters that must be determined and, as a result, the number and types of constructs that need to be included in analysis (see 25). Because individual repeats from NARPs are unstable, there are limits to the amount of heterogeneity that can be accommodated using nearest-neighbor analysis.…”

“…An example of a global fit of folding transitions of consensus ankyrin repeat proteins with a 1D-Ising model is shown in Figure 4a (for fitted parameters for all data sets, see Table 4). The data set includes 18 melts for 9 constructs that differ in repeat number and capping structure (see 2,25). The model contains four free energies (the intrinsic folding energies of the N-and C-terminal caps and the internal R repeats, G N , G R , and G C , respectively, and an interfacial coupling energy, G i−1,i ) along with a shared denaturant dependence (m) for the three intrinsic free energy terms.…”

Surface residues and non-additive interactions stabilize a consensus homeodomain protein

“…To minimize these uncertainties (21), we fit all unfolding curves for all variants to a global model (see Supplementary Materials, Fig S1 for a comparison of the global fits to local fits). In the global model, each unfolding curve was fit with local folded and unfolded baselines and a local DG°H2O parameter, a single m-value parameter was shared among all curves and all variants.…”