Estimation of Peptide Helicity from Circular Dichroism Using the Ensemble Model

Abstract

An established method for the quantitation of the helix content in peptides using circular dichroism (CD) relies on the linear spectroscopic model. This model assumes an average value of the helix-length correction for all peptide conformers, irrespective of the length of the helical segment. Here we assess the validity of this approximation and introduce a more physically realistic ensemble-based analysis of the CD signal in which the length correction is assigned specifically to each ensemble conformer. We demonstrate that the linear model underestimates peptide helicity, with the difference depending on the ensemble composition. We developed a computer program that implements the ensemble model to estimate the peptide helicity. Using this model and the CD data set covering a broad range of helicities, we recalibrate CD baseline parameters and redetermine helix-coil parameters for the alanine-rich peptide. We show that the ensemble model leverages small differences in signal between conformers to extract more information from the experimental data, enabling the determination of several poorly defined quantities, such as the nucleation constant and heat capacity change associated with helix folding. Overall, the presented ensemble-based treatment of the CD signal, together with the recalibrated values of the spectroscopic baseline parameters, provides a coherent framework for the analysis of the peptide helix content.

Figure 1

Comparison of the helix-length corrections used by different spectroscopic models. The upper panel shows a peptide conformer with a helix segment of n_H = 15 helical units out of a total of N_pep = 33 units. Coil units are shaded gray, single-hydrogen-bonded helical units are in blue, while double-bonded units are shown in red. Only a few units neighboring the helix segment are shown for the sake of clarity. Backbone hydrogen bonds are shown as black dashed lines. The table below shows the corresponding residue definitions (coil or helix conformation) and the helical ellipticity contributions assigned by the linear, dichroic, and empirical length correction. The final helical ellipticity values for this conformer as calculated using different models are listed on the right assuming parameters [θ]_H∞ = −40,000 deg cm² dmol^–1, k = 4, and N_pep = 33 and eqs 2 and 3.

Figure 2

Ellipticity of peptide conformers with increasing length of the helical segment. A) Helix ellipticity ([θ]_H in units per peptide bond) as a function of the number of helical units (n_H) calculated with different models. Due to the constant length correction approximation, the linear model fails to predict the nonlinear dependence on helix length (red line) given by the two ensemble models, which evaluate the length correction for each conformer individually (black and blue for dichroic and empirical, respectively). The inset shows the ellipticity of short helix segments where dichroic and empirical models diverge. B) The relative difference in the helix ellipticities is calculated in the upper panel. The parameters used in the calculation are the same as in Figure 1.

Figure 3

Ellipticity of the peptide ensemble as a function of the propagation constant. A) Changing the propagation constant w tunes the overall ensemble helicity. The top panel shows the overall ensemble signal calculated with different models as a function of w (v = 0.048, other parameters are the same as in Figure 1). The lower panel shows the corresponding signal difference (linear model minus dichroic or empirical). The largest overestimation of the CD signal by the linear model is observed at the intermediate ensemble helicities. B) Ensemble composition (eq 6) for the selected w values. The population of peptide conformers with different numbers of helical units (n_H) is shown as bars. Gray bars correspond to conformers with a single helical segment, and darker bars correspond to conformers with two helix segments. Conformers that contribute to the coil (n_H < 4) are not shown.

Figure 4

Ensemble ellipticity as a function of the nucleation constant. A) Changing the nucleation constant v changes the ratio between single- and double-helix conformers. Top panel shows the total ensemble signal calculated with different models as a function of v (w = 1.2, other parameters are the same as in Figure 1). Lower panel shows the corresponding signal difference (linear model minus dichroic or empirical). Increasing fraction of double-helix conformers leads to larger overestimate of CD signal by the linear models (red line). B) Ensemble composition (eq 6 in Methods) for the selected v values. Population of peptide conformers with different number of helical units (n_H) is shown as bars. Gray bars correspond to conformers with a single helical segment, and darker bars correspond to conformers with two helix segments. Conformers that contribute to coil (n_H < 4) are not shown.

Figure 5

Estimation of helix and coil spectroscopic baselines. A) Symbols show the experimental ellipticity [θ]₂₂₂ for peptides where all units are in the helix state at 0 °C. (Further details of these systems are reported in Table S3.) The solid line shows the helix baseline length dependence based on the best-fit values [θ]_H∞ and k obtained from the global fit using the dichroic model (eq 2). B) Symbols show the pretransition (T ≪ T_m) slopes of measured ellipticities obtained from the thermal melts of helical peptides (Table S3). The solid line shows the helix baseline temperature dependence based on the best-fit values of ∂[θ]_H∞/∂T and temperature-independent k (eq 8). C) Symbols show the measured ellipticity for the AAKAA peptide as a function of temperature. The solid line shows the fit to the data using the helix–coil model, which accounts for the minor fraction of helix conformers, while the dashed line shows the “true” coil baseline (where all peptide units populate only the coil conformation) with best-fit values of [θ]_C and ∂[θ]_C/∂T (eq 9).

Figure 6

Estimation of spectroscopic and helix–coil parameters by global fitting of CD datasets. A) CD thermal denaturation spectra of the (AAKAA)₆-GY peptide. Spectra of other peptides in the series are shown in the Supporting Information (Figure S5). B) Global fit to (AAKAA)_n-GY thermal melts with data shown as symbols. The black and red lines represent the global fit using the dichroic and linear models, respectively. The inset shows a close view of the AAKAA data and the model fits. C) Distributions of model parameters and their pairwise correlations for the ensemble dichroic model (black) and linear model (red) obtained using the Markov Chain Monte Carlo method. The parameter’s posterior distributions are shown along the matrix diagonal, with numerical values reported in Table 1.