  Synthetic biology is a growing interdisciplinary field, with far-reaching
applications, which aims to design biochemical systems that behave in a desired
manner. With the advancement of strand-displacement DNA computing, a large
class of abstract biochemical networks may be physically realized using DNA
molecules. Methods for systematic design of the abstract systems with
prescribed behaviors have been predominantly developed at the (less-detailed)
deterministic level. However, stochastic effects, neglected at the
deterministic level, are increasingly found to play an important role in
biochemistry. In such circumstances, methods for controlling the intrinsic
noise in the system are necessary for a successful network design at the
(more-detailed) stochastic level. To bridge the gap, the noise-control
algorithm for designing biochemical networks is developed in this paper. The
algorithm structurally modifies any given reaction network under mass-action
kinetics, in such a way that (i) controllable state-dependent noise is
introduced into the stochastic dynamics, while (ii) the deterministic dynamics
are preserved. The capabilities of the algorithm are demonstrated on a
production-decay reaction system, and on an exotic system displaying
bistability. For the production-decay system, it is shown that the algorithm
may be used to redesign the network to achieve noise-induced multistability.
For the exotic system, the algorithm is used to redesign the network to control
the stochastic switching, and achieve noise-induced oscillations.
