The origin of the various cross peaks in coherent multidimensional vibrational spectroscopies in the amide I region of a TGF-b -binding protein-like domain is treated by differential sensitivity analysis based on a local basis Hamiltonian. Regions in 2D correlation plots of four-wave mixing signals associated with specific secondary structure motifs and their couplings are identified. The double quantum coherence of the signal generated in the directions k_III = k₁ + k₂ – k₃ shows higher sensitivity to the couplings and a better resolution compared with the k_I = –k₁ + k₂ + k₃ signal.

MD simulations were used to compute the averages of the fluctuating frequencies e _m. For each of the 74 modes in the TB6, the fundamental frequency is e _m = e – D e _m, where e = 1,707 cm^–1 (1) is the frequency of isolated N-methyl acetamide (NMA) in the gas phase, and D e _m is the frequency shift caused by the environment. This shift was assumed to be purely an electrostatic effect and was calculated by using the linear correlation formula of the electric potential and the amide I frequency (2) . The point charges of the peptide unit atoms (O=C–N–H) were obtained from ref. 2, and the charges of the bath atoms were obtained from the CHARMM27 force field (3). For each amide I mode, this frequency shift was calculated for 100 snapshots and used the average values were used in our Hamiltonian. The distribution of the local amide I modes for all of the three structure types are presented in Fig. 5.

Tasumi’s (4) ab initio map was used for the couplings of nearest covalently bound modes. All other couplings were calculated using the electrostatic transition dipole coupling model (4). The normalized distribution of the various couplings is presented in Fig. 6.

1. Torii, H. & Tasumi, M. (1992) J. Chem. Phys. 96, 3379–3387.

2. Cha, S. Y., Ham, S. H. & Cho, M. H. (2002) J. Chem. Phys. 117, 740–750.

3. Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. & Karplus, M. (1983) J. Comput. Chem. 4, 187–217.

4. Torii, H. & Tasumi, M. (1998) J. Raman Spectrosc. 29, 81–86.