  Intrachain contact formation rates, fundamental to the dynamics of biopolymer
self-organization such as protein folding, can be monitored in the laboratory
through fluorescence quenching measurements. The common approximations for the
intrachain contact rate given by the theory of Szabo, Schulten, and Schulten
(SSS) [J. Chem. Phys. {\bf 72}, 4350 (1980)] and Wilemski--Fixman (WF) [J.\
Chem. Phys. {\bf 60},878 (1973)] are shown to be complementary variational
bounds: the SSS and WF approximations are lower and upper bounds, respectively,
on the mean first contact times. As reported in the literature, the SSS
approximation requires an effective diffusion coefficient 10 to 100 times
smaller than expected to fit experimentally measured quenching rates. An all
atom molecular dynamics simulation of an eleven residue peptide sequence in
explicit water is analyzed to investigate the source of this surprising
parameter value. In analytical work, the polymer is typically modeled by a
Gaussian chain of effective monomers. Compared to Gaussian dynamics, the
simulated end-to-end distance autocorrelation has a much slower relaxation. The
long time behavior of the distance autocorrelation function can be approximated
by a Gaussian model in which the monomer diffusion coefficient D_0 is reduced
to D_0/6. This value of the diffusion coefficient brings the mean end-to-end
contact time from analytical approximations and simulation into agreement in
the sense that the SSS and WF approximations bracket the simulated mean first
contact time.
