Electronic circular dichroism of proteins computed using a diabatisation scheme

Figures & data

Figure 1. Molecular orbitals for diamide 2a [φ = 180°, ψ = 180°] with an isosurface cut-off of 0.05. Orbitals from a state-averaged CASSCF calculation as described in reference 32. (a) π* for amide 1, (b) n for amide 1, (c) π_nb for amide 1, (d) π* for amide 2, (e) n for amide 2 and (f) π_nb for amide 2.

Table 1. The 13 diamides and their secondary structure and associated DichroCalc parameter set.

φ angle (°)	ψ angle (°)	Secondary structure	Diamide in Oakley et al. [32]	DichroCalc parameter set [22]
180	180	Fully extended	2a	CT01009A
−120	180		2b	CT02009B
−60	180		2c	CT03009A
−135	135	β strand	2d	CTBE009A
−120	120		2e	CT05009A
−120	60		2f	CT08009A
−120	0		2g	CT11009A
−60	0		2h	CT12009A
−74	−4	310 helix	2i	CT31009A*
−48	−57	α helix	2j	CTAL009A
−60	−60	α helix	2k	CT15009A
−62	−41	α helix	2l^#	CTBT009B*
−75	145	Polyproline II	2m^#	CTP2007A

^# Notation following Oakley et al. [32] * Set exclusive to Oakley and Hirst [31].

Figure 2. Ramachandran plot of the φ and ψ dihedral angles for the 13 diamide and 13 20 L-Ala peptide structures. The scatter points are labelled by the alphabetical (second) character naming each structure (see Table 1). Inset is the structure of peptide 2k [φ = −60°, ψ = −60°].

Figure 3. CD spectra for the model peptides comprising 20 L-Ala residues and named as the diamides. CD spectra with band shapes from convolution with Gaussian functions of FWHM of 9.0 nm. Spectra from DichroCalc ab initio Hamiltonian (black line) and diabatic Hamiltonian (blue line). (a) 2d [−135°, 135°], (b) 2i [−74°, −4°], (c) 2j [−48°, −57°], (d) 2k [−60°, −60°], (e) 2l [−62°, −41°] and (f) 2m [−75°, 145°].

Table 2. Inter-amide interactions. Off-diagonal elements of the Hamiltonian (cm⁻¹). DichroCalc ab initio matrix elements in the first row and diabatic matrix elements in the second row for each diamide geometry. The ab initio parameters have nπ* and π_nbπ*transition energies at 220 nm (45455 cm⁻¹) and 193 nm (51813 cm⁻¹), respectively.

Matrix element index	H13	H14	H23	H24
Diamide (φ, ψ)	n1π1*:n2π2*	n1π1*:πnb2π2*	πnb1π1*:n2π2*	πnb1π1*:πnb2π2*
2d (−135°, 135°)	72	−20	292	−907
	109	−279	−244	−89
2i (−74°, −4°)	15	−36	161	−662
	289	−148	230	284
2j (−48°, −57°)	−18	−17	−131	−272
	97	−808	0	−191
2k (−60°, −60°)	−42	−29	−180	−83
	−21	−1707	267	173
2l (−62°, −41°)	−17	−37	−52	−292
	−359	−660	−131	−363
2m (−75°, 145°)	31	−7	16	−971
	81	356	145	29

Table 3. Dot products of the un-normalised transition dipole moments (D²) for six of the 13 diamide structures (Table S1). Upper triangle of Hamiltonian H_ij. Intra-amide interactions are 1–2 and 3–4. Inter-amide interactions are 1–3, 1–4, 2–3 and 2–4. Transition dipole moments are not normalised.

Transitions	1–2	1–3	1–4	2–3	2–4	3–4
Diamide (φ, ψ)	Monomer
2d (−135°, 135°)	0.0	−0.032	−0.350	−0.342	−2.037	0.0
2i (−74°, −4°)	0.0	−0.013	−0.454	0.615	−2.985	0.0
2j (−48°, −57°)	0.0	−0.002	−0.595	0.593	1.312	0.0
2k (−60°, −60°)	0.0	0.009	−0.563	0.578	3.020	0.0
2l (−62°, −41°)	0.0	−0.003	−0.547	0.629	0.984	0.0
2m (−75°, 145°)	0.0	−0.002	0.005	−0.619	−2.865	0.0
Diamide (φ, ψ)	Dimer
2d (−135°, 135°)	0.284	−0.036	0.407	−0.399	2.842	−0.052
2i (−74°, −4°)	0.065	0.011	−0.280	−0.730	3.175	−0.512
2j (−48°, −57°)	−0.445	−0.040	−0.020	0.759	1.140	−0.127
2k (−60°, −60°)	−0.155	−0.040	−0.296	0.390	−5.282	0.529
2l (−62°, −41°)	−0.389	−0.035	−0.116	0.618	−3.997	0.434
2m (−75°, 145°)	−0.953	0.048	0.543	−0.610	−4.660	0.637

Figure 4. Rotational strength line spectra (upper panel) and CD spectra with band shapes from convolution with Gaussian functions of FWHM of 9.0 nm (lower panel) for peptide 2d [φ = −135°, ψ = 135°]. Spectra computed using the ab initio (black line), diabatic (blue), diabatic with H₁₄ modified (red), diabatic with H₂₃ modified (green), diabatic with H₂₄ modified (magenta), diabatic with H₁₄ and H₂₃ modified (yellow) and diabatic with H₁₄, H₂₃ and H₂₄ modified (cyan) Hamiltonians.

Table 4. Inter-amide interactions (cm⁻¹ rounded to integer values) for diamide 2d [φ = −135°, ψ = 135°] and used to compute the spectra in Figure 2.

Matrix element index	H13	H14	H23	H24
Hamiltonian	n1π1*:n2π2*	n1π1*:πnb2π2*	πnb1π1*:n2π2*	πnb1π1*:πnb2π2*
Ab initio	72	−20	292	−907
Diabatic	109	−279	−244	−89
Modified diabatic	109	−3	244	−894

M.T. Oakley, B.M. Bulheller and J.D. Hirst, Chirality. 18, 340–347 (2006). doi:10.1002/chir.20264.

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B.M. Bulheller and J.D. Hirst, Bioinformatics. 25, 539–540 (2009). doi:10.1093/bioinformatics/btp016.

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M.T. Oakley and J.D. Hirst, J. Am. Chem. Soc. 128, 12414–12415 (2006). doi:10.1021/ja0644125.

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Data availability statement

The DichroCalc code is available at https://github.com/dmrogers75/DichroCalc. Data, example files and other code used in this study are available in a folder named ‘diabatisation’.