Metadynamics
(MTD) is one of the most effective methods for calculating
the free energy surface and finding rare events. Nevertheless, numerous
studies using MTD have been carried out using 3D or lower dimensional
collective variables (CVs), as higher dimensional CVs require costly
computational resources and the obtained results are too complex to
understand the important events. The latter issue can be conveniently
solved by utilizing the free energy reaction network (FERN), which
is a graph structure consisting of edges of minimum free energy paths
(MFEPs), nodes of equation (EQ) points, and transition state (TS)
points. In the present article, a new method for exploring FERNs on
high-dimensional CVs using MTD and the scaled hypersphere search (SHS)
method is described. A test calculation based on the MTD-SHS simulation
of met-enkephalin in explicit water with 7 CVs was conducted. As a
result, 889 EQ points and 1805 TS points were found. The MTD-SHS approach
can find MFEPs exhaustively; therefore, the FERNs can be estimated
without any a priori knowledge of the EQ and TS points.