A method for performing implicit-solvent molecular dynamics simulations at constant pH was applied to a pentapeptide acetyl-Ala-Asp-Ala-Lys-Ala-amide at pH 4. As a reference, molecular dynamics simulations were done for the same peptide with two variants of its fixed protonation patterns expected to dominate at pH 4, i.e., with a protonated and a deprotonated side chain of the Asp residue and the protonated Lys residue in both cases. The dynamic trajectories of the peptide were used to discuss the problem of the significance of the solute-solvent proton exchange phenomena for the dynamics and structural distributions of the polypeptide chain. The Asp-Lys distance was used as a probe of the overall molecular structure of the investigated pentapeptide. To characterize the dynamics, distributions of the "waiting" times for a transition from a "short" distance conformation to a "long" distance conformation were constructed, based on the generated molecular dynamics trajectories. We show that the relaxation time for the transitions, derived from the constant-pH simulations, is very close to the relaxation time characterizing a permanently protonated molecule, although the average protonation probability of the short-distance conformation is close to zero. However, the distribution of the Asp-Lys distances obtained from constant-pH simulations cannot be reproduced as a linear combination of the distributions resulting from the simulations with fixed protonation states.