Theoretical Methods

Optical calculations were performed using a variant of the matrix formalism of Bayley (21) which includes all interaction mechanisms known to be of importance in the generation of optical rotatory power in an intrinsically symmetric chromophore. The theory is developed and the details are presented for the case of a dipeptide as a function of conformational angles. Inherent in the formalism is the one-electron mechanism of Condon, Altar and Eyring (16), the dipole-coupling mechanism of Kuhn, Kirkwood and Moffitt (16-19) and the m-m mechanism of Schellman. (20,21) In this variation of the formalism however, rather than calculate rotatory strengths from the electric and mangetic transition moments using the equation:

the chiral strength was calculated from the following equation:

where pok is the linear momentum moment of the electronic transition and Lok is the angular momentum moment of the electronic transition. a is the fine structure contstant. The chiral strength is analogous to the oscillator strength in absorbance spectroscopy. This modification avoids problems associated with the origin dependence of the original matrix method. Theoretical spectra can then be generated by calculating the molar ellipticities from the following equation:

where lok is the characteristic wavelength of the electronic transition in cm having a bandwidth Dok. The other symbols have their usual meanings. Chiral strengths may be converted to rotatory strengths using the equation:

The optical data needed for these calculations include energies and polarizations for the electronic transitions of the amide chromophore. Absorption data for the electronic transitions are from the paper by Nielsen and Schellman. (13) Transition energies for the n-p* transition in a vacuum are set to 235 nm based on the experimental CD spectrum of L-AADKP in acetonitrile at 143K. n-p* transition energies for the solvated calculations are 220 nm for conformers producing a negative CD band. This is based on experimental CD spectra in 70/30 methanol/water. For conformers producing a positive n-p* CD band, 225 nm was used. Polarizations of the electronic transitions are from Bailey. (21) Electronic charges on peptide atoms are as given by Poland and Scheraga. (22) Average CD spectra are calculated by averaging the rotatory strength of each individual conformer according to a Boltzmann distribution of the conformational energy. An average CD spectrum is then obtained from this Boltzmann averaged rotatory strength.

Experimental Methods

L-AADKP was obtained from Bachem Fine Chemicals. All samples were Ninhydrin negative and showed a single spot when subjected to thin layer chromatography.

CD spectra were recorded using an extensively modified Cary 60 recording spectrophotometer. Fused silica cells with path lengths of 0.1 and 1.0 cm were used for recording CD spectra from 250 to 210 nm. For spectra recorded in TEP, the concentration of L-AADKP was 6.70 mM. In acetonitrile or acetonitrile/water, all samples were 1.03 mM. In methanol or methanol/water, samples were 2.22 mM. A liquid nitrogen temperature controller was used to maintain sample temperature for low temperature scans.

Molecular Mechanics Calculations

Molecular mechanics calculations were performed using version 3.0 of the AMBER (4,5) force field and version 22 of CHARMM. (8) Potential energy parameters for the AMBER calculations were from the set PARMALLHB supplied with the program. For the CHARMM calculations, the Developmental Parameter File for Proteins Using All Hydrogens of May 1992 was used. These parameters were supplied with the program which was obtained from M. Karplus of Harvard University. Starting structures for the minimizations were generated using the model building facilities of the Chem-X (23) molecular modelling software. A large number of high-energy, randomly built starting structures were first minimized on AMBER using an initial 50 cycles of the steepest descents algorithm followed by the conjugate gradient algorithm. The Adopted Basis Newton Rhaphson (ABNR) algorithm was used for CHARMM calculations. Minimizations were carried out initially with no constraints to obtain low energy structures. Constraints were then placed on the torsion angle defined by the N1CaC'N2 atoms of the diketopiperazine ring. The torsion angle was assigned values in 5 degree intervals from -60 to +60 degrees or until the conformational energy became unrealistically high. Minimization was again performed on these constrained structures until the RMS energy gradient was no more than 0.01 kcal/molA. Variation of the torsion angle has the effect of varying the fold of the diketopiperazine ring away from planarity which defines the parameter B.

Electrostatic charges were as given by Poland and Schereaga (22) or calculated by the method of Gasteiger (25) using Chem-X. A constant dielectric of 1 was used where solvent was included explicitly. Solvent water molecules were added in AMBER calculations using the BOX option of the EDIT module. This model produces rigid water molecules characterized by three bonds rather than two bonds and an angle. Water molecules which were overlapping the dipeptide were excluded in the EDIT module of the program by specifying a minimum distance between solute and water molecule. Any waters within this distance are removed. For CHARMM calculations, the solute was placed in a cube of TIP3 (26) waters. Again, any water molecules overlapping the solute are discarded. In both cases, the charge on the oxygen was -0.834eu and 0.417eu on each hydrogen.

Molecular Dynamics Simulations

Molecular dynamics (MD) simulations were performed using version 3.0 of AMBER. An initial Maxwellian distribution of atomic velocities was used. The vacuum simulations were carried out for 800 ps using a timestep of 0.0005 ps. The SHAKE procedure was not applied. Vacuum simulations were performed using classical dynamics with constant energy at an average temperature of 300 and 143 K. Structures were saved every 5 ps and converted to PDB formatted files for analysis of their geometric parameters using Chem-X.

Solvated MD simulations were carried out for 500 ps using a timestep of 0.0015 ps at 300 K. The SHAKE procedure was applied. Water molecules were restrained in the solvated MD simulations using the CAP option of the MD module. A total of 60 water molecules were included in the simulation.

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