  We introduce an extension to the Weighted Ensemble (WE) path sampling method
to restrict sampling to a one dimensional path through a high dimensional phase
space. Our method, which is based on the finite-temperature string method,
permits efficient sampling of both equilibrium and non-equilibrium systems.
Sampling obtained from the WE method guides the adaptive refinement of a
Voronoi tessellation of order parameter space, whose generating points, upon
convergence, coincide with the principle reaction pathway. We demonstrate the
application of this method to several simple, two-dimensional models of driven
Brownian motion and to the conformational change of the nitrogen regulatory
protein C receiver domain using an elastic network model. The simplicity of the
two-dimensional models allows us to directly compare the efficiency of the WE
method to conventional brute force simulations and other path sampling
algorithms, while the example of protein conformational change demonstrates how
the method can be used to efficiently study transitions in the space of many
collective variables.
