Local amide I mode frequencies And coupling constants in multiple-stranded antiparallel β-sheet polypeptides

Amide I local mode frequencies and vibrational coupling constants in various multiple-stranded antiparallel β-sheet polyalanines are calculated by using the semiempirical calculation method and Hessian matrix reconstruction methods. The amide I local mode frequency is strongly dependent on the nature and number of hydrogen bonds. Vibrational couplings among amide I local modes in the multiple-stranded β-sheets are shown to be fully characterized by eight different coupling constants. The intrastrand coupling constants are found to be much smaller than the interstrand ones. Introducing newly defined inverse participation ratios and phase-correlation factors, the extent of two-dimensional delocalization and the vibrational phase relationship of amide I normal modes are elucidated. The A-E₁ frequency splitting magnitude is shown to be strongly dependent on the number of strands but not on the length of each strand. A reduced one-dimensional Frenkel exciton model is used to describe the observed A-E₁ frequency splitting phenomenon.