  Equilibrating proteins and other biomacromolecules is cardinal for molecular
dynamics simulation of such biological systems in which they perform free
dynamics without any externally-applied mechanical constraint, until
thermodynamic equilibrium with the surrounding is attained. However, in some
important cases, we have to equilibrate the system of interest in the constant
presence of certain constraints, being referred to as constrained equilibration
in the present work. A clear illustration of this type is a single amyloid
\b{eta}-strand or RNA, when the reaction coordinate is defined as the distance
between the two ends of the strand and we are interested in carrying out
replica-exchange umbrella sampling to map the associated free energy profile as
the dependent quantity of interest. In such cases, each sample has to be
equilibrated with the two ends fixed. Here, we introduced a simulation trick to
perform this so-called constrained equilibration using steered molecular
dynamics. We then applied this method to equilibrate a single, stretched
\b{eta}-strand of an amyloid beta dodecamer fibril with fixed ends. Examining
the associated curves of the total energy and the force exerted on the
practically-fixed SMD atom over the total timespan broadly supported the
validity of this kind of equilibration.
