Quantitative first principles calculations of protein circular dichroism in the near-ultraviolet

Abstract

Vibrational structure in the near-UV circular dichroism (CD) spectra of proteins is an important source of information on protein conformation and can be exploited to study structure and folding. A fully quantitative theory of the relationship between protein conformation and optical spectroscopy would facilitate deeper interpretation of and insight into biophysical and simulation studies of protein dynamics and folding. We have developed new models of the aromatic side chain chromophores toluene, p-cresol and 3-methylindole, which incorporate ab initio calculations of the Franck-Condon effect into first principles calculations of CD using an exciton approach. The near-UV CD spectra of 40 proteins are calculated with the new parameter set and the correlation between the computed and the experimental intensity from 270 to 290 nm is much improved. The contribution of individual chromophores to the CD spectra has been calculated for several mutants and in many cases helps rationalize changes in their experimental spectra. Considering conformational flexibility by using families of NMR structures leads to further improvements for some proteins and illustrates an informative level of sensitivity to side chain conformation. In several cases, the near-UV CD calculations can distinguish the native protein structure from a set of computer-generated misfolded decoy structures.

Fig. 1. The vibrational modes which are Franck–Condon active in the excitation process of toluene. The direction and the magnitude are illustrated by the arrows located on the atoms.

Fig. 2. The vibrational modes which are Franck–Condon active in the excitation process of p-cresol. The direction and the magnitude are illustrated by the arrows located on the atoms.

Fig. 3. C–C stretch mode (left panel) and benzene C–H bend mode (right panel) of 3-methylindole which are Franck–Condon active in the excitation process. The direction and the magnitude of each normal mode are illustrated by the arrows located on the atoms.

Fig. 4. Experimental near-UV CD spectrum (bold solid line) and calculated spectra of adenylate kinase (PDB code: ; 2ECK) with ‘non-vib’ (dotted line) or ‘vib’ (thin solid line) parameter sets. The RMSE of the spectrum calculated with the ‘vib’ parameters is 11 deg cm² dmol^–1 and with the ‘non-vib’ parameters is 34 deg cm² dmol^–1.

Fig. 5. Root mean square error (RMSE) of the intensities between the experimental and calculated near-UV CD spectra, computed with ‘non-vib’ (open bar) and ‘vib’ (solid bar) parameters for the 40 proteins.

Fig. 6. Spearman rank correlation coefficients between the calculated and experimental intensity for the ‘vib’ (solid line) and the ‘non-vib’ (dotted line) parameter sets, based on 40 proteins.

Fig. 7. Experimental near-UV CD spectra (bold solid line) and calculated spectra with ‘non-vib’ (dotted line) or ‘vib’ (thin solid line) parameter sets: (a) calmodulin (PDB code: ; 4CLN), (b) subtilisin BPN′ (PDB code: ; 1ST2), (c) insulin (PDB code: ; 5ENA), and (d) odorant binding protein (PDB code: ; 1A3Y).

Fig. 8. Difference spectra (wild-type minus the mutants) of barnase (experimental: (a) and (c); calculated: (b) and (d)). (a) and (b) ΔY78F (solid line), ΔY90F (dotted line), ΔY97F (dashed line); (c) and (d) ΔW35F (solid line), ΔW71F (dotted line), and ΔW94F (dashed line). The dotted-dash line in (b) is the difference spectrum calculated with the X-ray structure of Y78F barnase (PDB: 1BAO).

Fig. 9. (a) Experimental CD spectra of wild-type bovine pancreatic trypsin inhibitor (solid line) and mutants F22L (dashed line), F45L (dot-dashed line) and Y23L (dotted line), and (b) calculated CD spectra from X-ray structures: wild-type (PDB: 5PTI, solid line), F22A (PDB: ; 1BTI, dashed line), F45A (PDB: ; 1FAN, dot-dashed line) and Y23A (PDB: ; 1BPT, dotted line).

Fig. 10. Difference spectra (wild-type minus the mutants) of RNase A ((a) experiment, (b) calculation). ΔY25F (solid line), ΔY73F (dashed line), ΔY76F (dotted line), ΔY92F (triangle), ΔY97F (dot-dashed line) and ΔY115F (square).

Fig. 11. Difference spectra (wild-type minus the mutants) of human carbonic anhydrase II ((a) experiment, (b) calculation); ΔW5F (solid line), ΔW16F (square), ΔW97C (circle), ΔW123C (triangle), ΔW209F (dotted line) and ΔW245C (dot-dashed line).

Fig. 12. Comparison between the experimental spectrum (solid line) and calculated spectrum with ‘vib’ parameters from the X-ray structure (dotted line) and the NMR structures (dashed line) of (a) apolipophorin III and (b) staphylococcal nuclease.