  We study local energy minima of twenty(L-alanine). The minima are generated
using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo
simulations, with subsequent minimization. We find that the lower-energy
configurations are $ \alpha $-helices for a wide range of dielectric constant
values $ (\epsilon = 1,10,80), $ and that there is no noticeable difference
between the distribution of energy minima in $ \phi \psi $ space for different
values of $ \epsilon . $ Ultrametricity tests show that lower-energy $ (\alpha
$ -helical) $ \epsilon =1 $ configurations form a set which is ultrametric to a
certain degree, providing evidence for the presence of fine structure among
those minima. We put forward a heuristic argument for this fine structure. We
also find evidence for ultrametricity of a different kind among $ \epsilon =10
$ and $ \epsilon =80 $ energy minima. We analyze the distribution of lengths of
$ \alpha $-helical portions among the minimized configurations and find a
persistence phenomenon for the $ \epsilon =1 $ ones, in qualitative agreement
with previous studies of critical lengths. Email contact:
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