  Synthetic biology is an interdisciplinary field aiming to design biochemical
systems with desired behaviors. To this end, molecular controllers have been
developed which, when embedded into a pre-existing ambient biochemical network,
control the dynamics of the underlying target molecular species. When
integrated into smaller compartments, such as biological cells in vivo, or
vesicles in vitro, controllers have to be calibrated to factor in the intrinsic
noise. In this context, molecular controllers put forward in the literature
have focused on manipulating the mean (first moment), and reducing the variance
(second moment), of the target species. However, many critical biochemical
processes are realized via higher-order moments, particularly the number and
configuration of the modes (maxima) of the probability distributions. To bridge
the gap, a controller called stochastic morpher is put forward in this paper,
inspired by gene-regulatory networks, which, under suitable time-scale
separations, morphs the probability distribution of the target species into a
desired predefined form. The morphing can be performed at the lower-resolution,
allowing one to achieve desired multi-modality/multi-stability, and at the
higher-resolution, allowing one to achieve arbitrary probability distributions.
Properties of the controller, such as robust perfect adaptation and
convergence, are rigorously established, and demonstrated on various examples.
Also proposed is a blueprint for an experimental implementation of stochastic
morpher.
