Experimental Results

To investigate the possiblity of conformational isomerism in the diketopiperazines, CD spectra were obtained at low temperature. If there is a difference in energy between two or more conformers and the temperature is sufficiently lowered, the higher energy conformer will be less populated than the lower. Figure 2 presents the CD spectra of 6.70 mM L-AADKP in triethylphosphate (TEP) at 300, 203 and 143 K. At 300 K, two bands of approximately equal intensity and opposite sign are present. With decreasing temperature, the positive band increases in intensity and appears to blue shift while the intensity of the negative band diminishes.

Figure 3 and Figure 4 show the CD spectra of L-AADKP at 300, 203 and 143 K, however the solvents are acetonitrile and methanol respectively. In acetonitrile (1.03 mM) at 300 K, there is a single positive band which is blue shifted and increases in intensity as the temperature decreases. The CD spectra in the hydrogen-bond donor solvent methanol (2.22 mM) indicates two bands as in TEP, however the negative band at 220 nm is considerably more intense than the positive band to the red. As the temperature decreases, the positive band increases in intensity and appears to blue shift while the negative band loses intensity and also appears to blue shift. The negative band remains in this solvent at 143 K with the intensity of the positive and negative bands being approximately equal.

Figure 5 shows the CD spectra of 1.03 mM L-AADKP at 300 K in acetonitrile with increasing concentrations of water. The polarity and hydrogen-bond donor capacity of the solvent is increasing. As before, at 100% acetonitrile, only a single positive band is present. At 95% acetonitrile/water, the intensity of the positive band decreases by nearly half its intensity at 100% acetonitrile and a weak negative band begins to appear. At 50% acetonitrile/water, two bands of opposite sign and approximately equal intensity are present. Figure 6 shows the CD spectra of 2.22 mM L-AADKP at 300 K in 100% methanol and 70% methanol/water. As the concentration of water increases from 0 to 30%, the positive band decreases in intensity and becomes extremely weak, while the negative band becomes more intense.

Theoretical Results

Figure 7 shows a plot of potential energy vs. torsion angle (N1C'CaN2) for L-AADKP calculated in a vacuum using both AMBER and CHARMM. The reported energies are all relative to 0 kcal/mol at 0 degrees, which is an arbitrary value. For both AMBER and CHARMM calculations, there is a potential energy minimum on either side of 0 degrees and a potential barrier at 0 degrees. For AMBER calculations, the potential energy minima are -1.7 kcal/mol at +34 degrees and -1.4 kcal/mol at -23 degrees. For CHARMM calculations, the potential minima are -1.1 kcal/mol at +22 degrees and -0.3 kcal/mol at -17 degrees.

Figure 8 presents a plot of potential energy vs. torsion angle (N1C'CaN2) for L-AADKP calculated using AMBER and CHARMM with the explicit inclusion of 40 water molecules. In both cases there is a single potential energy minimum. For AMBER, the minimum occurs at -20 degrees and -1.9 kcal/mol and for CHARMM, -19 degrees and -0.9 kcal/mol. In both cases, the energy rises sharply when (N1C'CaN2) assumes positive values.

Table 1 presents the energy difference of CHARMM relative to AMBER (ECHARMM - EAMBER) for L-AADKP. The energy is divided into its component terms. Results are calculated at -30 and 30 degrees for the vacuum data and -25 and 20 degrees for the solvated case.

Figure 9shows the calcualted CD spectra of L-AADKP in a vacuum based on the AMBER and CHARMM minimizations. In both cases there is a couplet centered at 188 nm which is associated with the peptide p-p* transition. The sign of the couplet is negative to the blue then positive to the red in both cases. The sign of the n-p* band furthest to the red is negative in both cases.

Figure 10 presents the calculated CD spectra of L-AADKP based on the AMBER and CHARMM minimizations in a solvent water bath. In both cases the sign of the p-p* couplet centered at 188 nm is positive to the blue then negative to the red. The sign of the n-p* band to the red is positive for both AMBER and CHARMM.

Figure 11 presents the calculated CD spectra of L-AADKP with the n-p* transition energy assigned values of 220 nm and 225 nm. These spectra were based on the AMBER and CHARMM vacuum conformations. In both cases there is a positive band to the red and a negative band with a maximum between 200 and 225 nm.

Tables 2-7 show the optical parameters used to generate the average CD spectra. (not available)

Figure 12 shows the results of a molecular dynamics simulation of L-AADKP in a vacuum using the AMBER force field. The plot is B (N1C'CaN2) vs. time, which shows the fold of the diketopiperazine ring as a function of time at 300 K. Over the 750 ps. simulation, the torsion angle assumes both positive and negative values for periods of time lasting more than 100 ps. and at times interconverts rapidly between positive and negative values of B.

Figure 13 shows the rotation of one of the two methyl groups of L-AADKP as a function of time. This is calculated by measuring the trosion angle formed by the HBCBCAC' atoms. The torsion angle assumes a value near 60, 180 or 300 degrees and fluctuates about these values by up to 40 degrees.

Figure 14 shows the rotatory strengths of the n-p* transition of L-AADKP as a function of time. These rotatory strengths may be compared directly to the geometric parameters of Figure 12 and Figure 13.

Figure 15 presents a plot of the torsion angle B of L-AADKP vs time for an AMBER molecular dynamics simulation at 143 K lasting 900 ps. The torsion angle B is negative at the beginning of the simulation and remains negative until 350 ps. where it assumes positive values for the next 500 ps. Just before the simulation reaches 900 ps. the torsion angle B again assumes negative values.

Figure 16 shows the position of a methyl group of L-AADKP during the simulation at 143 K. The torsion angle (HBCBCAC' ) assumes values near 300 degrees throughout the 900 ps. simulation, with a fluctuation of no more than 30 degrees.

Figure 17 presents the rotatory strength of the n-p* transitions of L-AADKP for the AMBER simulation at 143 K. The rotatory strength is positive before 350 ps. where it becomes negative through 900 ps. The magnitude of the rotatory strength fluctuates during the simulation and assumes greater absolute values from 350 through 900 ps.

Figure 18 presents a plot of torsion angle B of L-AADKP vs time for an AMBER water solvated MD simulation at 300 K. The torsion angle remains negative throughout the 500 ps. simulation.

Figure 19 shows the rotation of a methyl group of L-AADKP during the solvated simulation. This is presented as the torsion angle formed by the (HBCBCAC' ) atoms. The torsion angle assumes values near 360 degrees for most of the simulation with brief rotation by 120 degrees to values near 240 degrees.

Figure 20 presents the rotatory strength of the n-p* transitions of L-AADKP for the solvated MD simulation. The rotatory strength is positive throughout the 500 ps. simulation.

Next, a Discussion of the results.