Abstract
One of the main objectives of synthetic biology is the development of molecular controllers that can manipulate the dynamics of a given biochemical network that is at most partially known. When integrated into smaller compartments, such as living or synthetic cells, controllers have to be calibrated to factor in the intrinsic noise. In this context, biochemical controllers put forward in the literature have focused on manipulating the mean (first moment) and reducing the variance (second moment) of the target molecular species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the probability distribution modes (maxima). To bridge the gap, we put forward the stochastic morpher controller that can, under suitable timescale separations, morph the probability distribution of the target molecular species into a predefined form. The morphing can be performed at a lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at a higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robustness and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.
Highlights
Synthetic biology is a growing interdisciplinary field of science and engineering whose aims include control of living cells [1,2,3,4,5,6,7,8] and design of synthetic cells with predefined behaviours [9,10,11,12,13]
We have introduced a molecular controller, called stochastic morpher, that can, under suitable conditions, gradually transform the probability-mass function (PMF) of a given black-box input network into a predefined shape
We have showcased the capabilities of 11 the stochastic morpher on particular biochemical networks in §§2–4
Summary
Synthetic biology is a growing interdisciplinary field of science and engineering whose aims include control of living cells [1,2,3,4,5,6,7,8] and design of synthetic cells with predefined behaviours [9,10,11,12,13]. The genetic bi-modality gives rise to a biphenotypic population of cells that can have a higher chance of surviving a changing environment [46]; for example, this phenomenon allows some bacteria to persistently survive antibiotic treatments [48] In this context, important is the number and configuration of the modes present in the probability distributions of the molecular species, and the timing and pattern of stochastic switching in the underlying sample paths. Stochastic morpher consists of a suitable faster interfacing sub-network de-signed to override the underlying black-box input network and, together with a suitable slower core sub-network, gradually transform (morph) the probability distribution of the desired species into a predened form This control architecture is based on the phenomenon called noise-induced mixing [25] that some gene-regulatory networks utilize in vivo [37].
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