Experimental Results

The two lowest energy absorption bands of the peptide chromophore are the p-p* and n-p* transitions. The p-p* transition is generally observed in the range of 175 through 196 nm and is dependent on the degree of substitution of the nitrogen atom. The energy of the transition is not significantly affected by solvent interactions. The CD bands of Figures 2-6 are due to n-p* transitions.

The two CD bands of the 300 K spectrum in TEP would appear to have their maxima at 224 and 242 nm, however it is certain that the n-p* transitions giving rise to these bands do not correspond to these energies. Interpretation of CD spectra with overlapping bands is complicated by several factors. The bandwidths of two overlapping bands may vary, as will the degree to which the bands overlap, the intensity of each band may vary and most importantly, the sign of the bands may differ. The resultant spectrum may therefore be misleading. For example, a CD spectrum composed of an intense, positive band with a narrow bandwidth and a weaker, negative band with a large bandwidth would result in two weak negative bands separated by a positive band. These three bands would result from two transitions. As parameters such as solvent are altered, each transition is affected independently, however, the resulting CD bands of the spectrum are not independent from one another.

The two bands of the 300 K spectrum in Figure 2 are likely the result of the n-p* transitions of two conformational isomers of L-AADKP. The n-p* transitions of the conformers must therefore produce CD bands with opposite sign and have different energies. If the energies of the n-p* transitions are equal, the result is total cancellation of the bands, assuming the intensity of each band is also equal. In this case, the transition energy of each conformer is not the same. As the temperature decreases, the conformer giving rise to the positive CD band to the red becomes more populated as indicated by the increasing intensity of the band. The intensity of the negative band to the blue is decreasing. If the temperature were lowered further, it would be possible to determine the actual energy of the n-p* transition of this conformer producing the positive band, as this conformer would approach 100% population. This would facilitate more accurate calculation of the theoretical CD spectrum, as this requires accurate energies for the n-p* transitions.

In acetonitrile, there is only one CD band indicating a single conformer which is more stable in this solvent. Another more likely explanation however, is that two conformers are present in acetonitrile with opposing n-p* CD bands of the same wavelength. A good comparison can be made between Figures 3 and 4 where the two solvents are acetonitrile and methanol respectively. Methanol is a good hydrogen-bond donor and acceptor while acetonitrile is a hydrogen-bond acceptor. Methanol would be expected to form hydrogen bonds to both the carbonyl oxygen and the amide hydrogen, while acetonitrile can only hydrogen bond with the amide hydrogen. Thus in acetonitrile, there would be no perturbation of the energies of the n-p* transitions while in methanol, a variable blue-shift would be expected which is dependent on conformation. The result in acetonitrile is cancellation of the opposing CD bands. The decreased intensity of the n-p* CD band in acetonitrile is further evidence for this.

In Figure 4 where the solvent is methanol, the CD spectra show both positive and negative bands at 300, 202 and 143 K, indicating two conformers are present. Decreasing temperature appears to favor the conformer producing the positive band to the red, as is the case in TEP. So it would seem that there are two possible conformations for L-AADKP, with that conformer producing the negative n-p* CD band being more stable in TEP and methanol. Between acetonitrile and methanol, the stability of the conformer producing the negative n-p* CD band in methanol would seem to result from favorable hydrogen-bonding to the carbonyl oxygen in this conformation.

Further evidence for this can be found in Figure 5 and Figure 6. Here, water is being added to the acetonitrile and methanol respectively, further increasing the hydrogen bonding capacity of the solvents. Increasing the water content of the solvents in all cases increases the intensity of the negative n-p* CD band, indicating a shift in population to that conformer producing the negative band as well as a blue-shift of tis CD band.

When comparing the CD spectrum of a molecule in several solvents, the effect of the solvent on the energy of the transitions giving rise to the CD bands must be considered. This is especially true of the n-p* transition of the peptide chromophore, where a blue-shift of the band is to be expected in polar solvent.

In the ground state, solvation energy is primarily due to dipole-dipole forces and the solvent cage surrounding the solute molecule is oriented. For the n-p* transition, the solute dipole moment decreases during the excited state and thus the solvation energy in the excited state is lower, causing a blue-shift relative to a less polar solvent. In addition, the solvent molecules in the pre-equilibrium "Franck-Condon" state are oriented in a manner appropriate to the ground state and this too will cause a blue-shift. The extent of the blue-shift depends on among other factors, the degree to which the solute and solvent molecules are "exposed" to each other. In L-AADKP, the exposure of the carbonyl lone-pair electrons is not equivalent in each of the two conformations. (see Figure 21) It can be seen from the calculation of the Connolly (25) surfaces that in the (+) conformation there is greater exposure of the carbonyl lone-pair electrons to the solvent than in the (-) conformation, where the methyl groups are eclipsing the carbonyl groups. Molecular mechanics calculations reinforce this point. So the magnitude of the blue-shift should be greater for the (+) conformer relative to the (-) conformer.

So in determining the populations of the two conformers as the solvent polarity changes, the relative magnitude of the two bands is not necessarily an accurate measure. This is due to the difference in the blue-shift as solvent polarity increases and the difference in the degree of band overlap in each solvent. however, a trend toward a shift in population toward the conformer producing the negative n-p* CD band is evident as solvent polarity increases.

It can be noted that Hooker (12) found no concentration dependence on the CD spectra of L-AADKP in the concentration range used for these experiments. So it is unlikely that the effects seen in the spectra are due to association.

Theoretical Results

The conformational energy calculations using AMBER and CHARMM in a vacuum each indicate two potential energy minima corresponding to two conformers. This would agree qualitatively with the experimental results in TEP, acetonitrile/water and methanol if this experimental data is indeed the result of two conformers producing n-p* transitions with opposing signs. The theoretical spectra generated from these molecular mechanics results provides for comparison with the experminetal data.

Of the parameters used for these theoretical CD calculations, the choice of lmax is most critical where the n-p* transition is concerned. This is due to the dependence on both solvent and conformation of the transition energy in cases where the solvent is a hydrogen-bond donor. This point has been addressed in the discussion of experimental results.

For the vacuum calculations, the basis for setting the n-p* transition energy at 235 nm is the experimental CD spectrum in acetonitrile at 143 K. As acetonitrile will not hydrogen-bond to the carbonyl oxygen, no significant perturbation to the transition energy is expected due to this solvent. As there is no significant interaction of the solvent with the carbonyl oxygen, there is no basis for a variation in the transition energy due to differences in solvent accessibility in various conformations. The experimental CD spectra in acetonitrile, with only a single positive band, confirm this.

For CD calculations based on solvated conformers, the effects of solvent and conformation on the n-p* transition energy are approximated as follows. First, the minimizations on both AMBER and CHARMM predict a single conformer in contrast to experimental data which indicate two conformers. For this reason, theoretical calculations approximating the difference in solvation between the two conformers were based on the vacuum minimizations which predict two conformers. For structures with a positive torsion b which produce a negative n-p* CD band, 220 nm was used as the transition energy. This value was based on the experimental CD of L-AADKP in 70/30 methanol/water, where the n-p* CD band is almost entirely negative and has a lmax at 220 nm. The effects of band overlap and cancellation where opposing CD bands are present limit this value to being a reasonable approximation.

For conformers with a negative torsion b which produce a positive n-p* CD band, a value of 225 nm was used. This value was chosen somewhat arbitrarily to reflect the fact that the positive n-p* CD band is to the red of the negative band assigned at 220 nm. Further, it is to the blue of the n-p* tranistion in acetonitrile at 235 nm due to the expected blue-shift of the transition in polar solvents. As mentioned in the discussion of the experimental results, the determination of lmax where opposing CD bands are present is difficult. Despite the approximations, a good comparison between experimental and theoretical results can be made.

As no siginificant solvent or conformational effects are expected on the energy of the p-p* transition, the same value was used throughout. The choice of bandwidth for these calculations may influence the appearance of the spectrum. This is especially true of the n-p* CD bands which result from two relatively weak and oppposing bands. The values used in these calculations are those found to characterize the bandwidths of L-AADKP in water. (12) Other reasonable values have been used and generally produce results which are consistent with respect to the pattern of the band sign.

The p-p* couplet centered at 188 nm is not in agreement with the experimental results of Hooker (12) with respect to sign (positive, negative) for neither CHARMM nor AMBER vacuum calculations. However, as each AMBER structure having a negative torsion angle b along the potential energy surface produces a p-p* couplet with the correct sign pattern, only a slight relative decrease in the potential energy of these structures would produce an average CD spectrum with the correct sign pattern. The same applies to CHARMM, however the required decrease in potential energy of structures with a negative torsion b is greater than for AMBER.

For the n-p* transitions, both AMBER and CHARMM predict negative ellipticity in contrast to experimental spectra which show a positive component to the spectrum above 210 nm in all solvents. Again, for AMBER structures with a negative torsion angle b, the rotatory strength of the n-p* transition was positive. Thus a slight decrease in the potential energy of these structures would produce a positive n-p* band for the average spectrum.

The results of the solvated molecular mechanics calculations are similar for both AMBER and CHARMM with the major exception being the greater depth of the AMBER potential energy minimum. The resulting theoretical CD spectra based on these conformers are also in close agreement with each other. The p-p* couplet centered at 188 nm which has a positive lobe to the blue and a negative lobe to the red, is in agreement with experimental results. (12)

The CD band associated with the n-p* transition is predicted to be positive for these structures however, and experimental data indicate increasingly negative ellipticity in this region of the spectrum when water is added to the solvent.

From the optical parameters in Tables 4 and 5, it can be seen that no low energy conformers generate negative rotatory strength for the n-p* transition. To have agreement with the experimental spectra, the torsion angle b must be positive, which produces negative rotatory strength for this transition. This is most easily seen by comparing the n-p* rotatory strength in the molecular dynamics simulation (Figure 14) with the corresponding values of the torsion angle b (Figure 12).

The increasing energy as b assumes positive values (Figure 8) is due primarly to the non-bonding terms in both force fields. This term is consistently higher in CHARMM relative to AMBER (Table 1), however at 20 degrees in water, the difference is only 0.52 kcals/mol. The non-bonding terms in CHARMM include an electrostatic and van der Waals term. It is the electrostatic term which increases as b assumes positive values, while the van der Waals term remains constant. The non-bonding terms in AMBER include a 1,4 electrostatic, 1.4 van der Waals and hydrogen bonding term, however these remain relatively constant as the torsion angle b changes. Again, the electrostatic term is responsible for the increasing non-bonding energy as b increases, while the van der Waals term decreases.

The theoretical CD spectra which approximate the difference in solvation between the two conformer in a hydrogen-bond donor solvent show reasonable agreement with the experimental spectra with respect to the pattern of band sign. For the CHARMM spectrum in Figure 11, there is a negative band with lmax near 223 nm and a positive band above 235 nm. For the AMBER spectrum in this same figure, the general pattern is the same. In these theoretical spectra however, the intensity and lmax of the n-p* CD bands should not be taken too seriously. In this case, the choice of bandwidth would be significant. For example, there is considerable overlap between the more intense p-p* band and the negative n-p* band near 220 nm. The higher wavelength lobe of the p-p* couplet was assigned a bandwidth of 19.0 nm, however other reasonable values could be used. This would alter the intensity and apparent lmax of the negative n-p* CD band. And of course, these spectra were based on the results of the vacuum minimizations where solvent was not explicitly included. These spectra do however support the interpretation of the experimental CD spectra of L-AADKP in hydrogen-bond donor solvents as resulting from two conformers. These two conformers have n-p* transitions with opposing bands and different energies. The difference in energy results from a difference in solvation of the carbonyl oxygen in each conformation.

The dynamics simulations are based on the AMBER force field and this has not produced theoretical results which are entirely in agreement with experimental data. However, by calculating the rotatory strength of structures at regular intervals and calculating geometric parameters of these same structures, the relationship between conformation and rotatory strength can be determined. It can be seen that the sign of the n-p* transition is dependent on the sign of the torsion angle b. The rotation of the methyl groups are as expected, represented by a three-fold potential barrier. At 143 K, there is no rotation. There is no apparent correlation between the rotation of the methyl group and the sign of the n-p* transition. This is not unexpected as the three conformations of the methyl group are electronically identical.

The MD trajectories do provide an indication of the rate of flipping between conformations with negative and positive b. As expected, the rate at 300 K is considerably faster than at 143 K. At 300 K, the rate is 55 interconversions per 700 ps. At 143 K, this rate is only 1 per 700 ps. A simple calculation using the Arrhenius equation gives a value of 2.2 kcals/mol for an energy barrier between the two conformations. This value is consistent with the molecular mechanics plot of energy vs. b using the AMBER force field, which predicts an energy barrier of 1.7 kcals/mol for the transition from positive to negative b. An energy barrier of 1.4 kcals/mol is predicted for the transition from negative to positive b when starting from the minimum.

The solvated MD simulation indicates no flipping between the two conformations. This result is consistent with the molecular mechanics data which indicates a single conformer with a negative torsion angle b. The rotation of the methyl group does appear to be slowed relative to the vacuum simulation at 300 K. These results however, along with the molecular mechanics minimization in water, are in sharp contrast to the experimental data, which indicates that a conformer with a positive torsion b is favored in aqueous solvent.

A comparison of this MD data with the experimental CD data is beset by various problems. First, the timescales of the MD and CD data are not similar. Thus, the MD simulations of 800 ps do not necessarily indicate the relative populations of the two conformers on the timescale of the CD experiments. Further, determining the relative populations of the two conformers from the CD data is complicated by the presence of two opposing and overlapping bands. This has been discussed previously. Also, the rotatory strength of the n-p* transitions in each conformation are not equivalent. (Figure 14) So comparing the intensities of the positive and negative bands at various temperatures provides only a general indication of the relative populations.

And finally, a Conclusion