Solitary waves for realistic parameter values

The lattice constant a for the H-bonded peptide chains in the a-helix is about 4.5 A [9]. As a representative value for the eigenfrequencies of a peptide group we choose f2o = 3.11 x 10 s from the amide-I vibration. The total mass M=Mi+ M2 corresponds to the mass of a peptide group plus an average residue in a muscle protein, which gives together about 100 proton masses [9,10]. The mass ratio q = M1/M2 is kept as a free parameter wdiich is varied between 1 and 10 (our results are invariant imder the transformation q - l//r). 

We model the hydrogen bonds between neighbouring peptide groups by a suitable non-linear interaction, e. g. a Toda potential with parameters fitted to an ab initio self-consistent-field molecular-orbital calculation for an H bond in a formamide dimer [9]. In our dimensionless units this corresponds to 

As a second example we take a Lennard-Jones potential with parameters fitted to the equilibrium distance a and the bond energy [11, 23], which gives 

For fixed mass ratio p, i.e. for fixed c , we choose a velocity c in the range of Eq. 32 calculating the corresponding solitary wave p z) and its Fourier transform (j iq). A first test shows that (p q l(p Qi) is indeed negligible for a large range of velocities (about 30% above Cs), as expected from the discussion of the radius of convergence q in Section 21.4. 

---