  We introduce a model for translational molecular motors to demonstrate that a
multivalent catalytic walker with flexible, uncoordinated legs can transform
the free energy of surface-bound substrate sites into mechanical work and
undergo biased, superdiffusive motion, even in opposition to an external load
force. The walker in the model lacks any inherent orientation of body or track,
and its legs have no chemomechanical coupling other than the passive constraint
imposed by their connection to a common body. Yet, under appropriate kinetic
conditions the walker's motion is biased in the direction of unvisited sites,
which allows the walker to move nearly ballistically away from the origin as
long as a local supply of unmodified substrate sites is available. The
multivalent random walker model is mathematically formulated as a
continuous-time Markov process and is studied numerically. We use Monte Carlo
simulations to generate ensemble estimates of the mean squared displacement and
mean work done for this non-ergodic system. Our results show that a residence
time bias between visited and unvisited sites leads to superdiffusive motion
over significant times and distances. This mechanism can be used to adapt any
enzyme--substrate system with appropriate kinetics for use as a functional
chemical implementation of a molecular motor, without the need for structural
anisotropy or conformationally mediated chemomechanical coordination.
