We report a new, high-dimensional application of a
method for finding a transition state (TS)
between a reactant and a product on the potential energy surface:
the search of a growing string along a reaction path defined by any Newton
trajectory in combination with the Berny method
(W.Quapp, J.Chem.Phys. 122 (2005) 174106;
we have provided this algorithm on a web page).
Two given minima are connected by a one-dimensional, but usually
curvilinear reaction coordinate. It leads to the TS region.
The application of the method to alanine dipeptide
finds the TS of the isomerisation C_{7ax} --> C_5,
some TSs of the enantiomerisation of C_{7ax} from L-form to
quasi-D-form, and it finds the TS region of a transition of a partly 
unfolded, bent structure 
which turns back into a mainly alpha-helix in  the Ac(Ala)_{15}NHMe
polyalanine (all at the quantum mechanical level B3LYP/6-31G: the growing
string calculation is interfaced with the Gaussian03 package).
The formation or dissolvation of some
alpha- or 3_{10}-hydrogen bonds of the helix are discussed along the TS
pathway, as well as the case of an enantiomer at the central residue of the
helix.