Variance reduction for antithetic integral control of stochastic reaction networks

Abstract

The antithetic integral feedback motif recently introduced in [6] is known to ensure robust perfect adaptation for the mean dynamics of a given molecular species involved in a complex stochastic biomolecular reaction network. However, it was observed that it also leads to a higher variance in the controlled network than that obtained when using a constitutive (i.e. open-loop) control strategy. This was interpreted as the cost of the adaptation property and may be viewed as a performance deterioration for the overall controlled network. To decrease this variance and improve the performance, we propose to combine the antithetic integral feedback motif with a negative feedback strategy. Both theoretical and numerical results are obtained. The theoretical ones are based on a tailored moment closure method allowing one to obtain approximate expressions for the stationary variance for the controlled network and predict that the variance can indeed be decreased by increasing the strength of the negative feedback. Numerical results verify the accuracy of this approximation and show that the controlled species variance can indeed be decreased, sometimes below its constitutive level. Three molecular networks are considered in order to verify the wide applicability of two types of negative feedback strategies. The main conclusion is that there is a trade-off between the speed of the settling-time of the mean trajectories and the stationary variance of the controlled species; i.e. smaller variance is associated with larger settling-time. Author summaryHomeostasis, the ability of living organisms to regulate their internal state, is of fundamental importance for their adaptation to environmental changes and their survival. This is the reason why complex regulatory genetic networks evolved and allowed for the emergence of more and more complex organisms. Recently, the theoretical study of those regulatory networks using ideas and concepts from control theory and the design of novel ones have gained a lot of attention. Synthetic regulatory circuits are seen as elementary building blocks for the design of complex networks that need to incorporate some regulating elements to be fully functional. This is for instance the case in metabolic engineering where the production of biomolecules, such as drugs or biofuels, need to be optimized and tightly regulated. A particular circuit, the so-called antithetic integral controller, is now known to ensure homeostasis even when regulatory circuits are subject to randomness. However, it is also known that this circuit increases variability in the network. The effects of a correcting negative feedback loop on the variance are discussed here and it is shown that variability can be reduced this way. Notably, we show that there is a tradeoff between speed of the network and variability.

Extended Metabolic Biosensor Design for Dynamic Pathway Regulation of Cell Factories

“…Therefore, adjusting the biosensor parameters remains challenging and a strategy that relies on model-based design has been recently proposed by Mannan et al (2017). Here, we introduce an approach that combines the indirect measurement of the chemical target with an integral antithetic feedback controller, which has been demonstrated robust against environmental variability (Briat et al, 2016). A circuit called extended metabolic biosensor is introduced where a small amount of the chemical target is converted through several enzymatic steps into an effector for some given transcription factor.…”

“…To that end, integral feedback control appears as a promising solution for robust output regulation against perturbations. The antithetic feedback control is a type of integral control that has been recently shown to be a universal genetic topology that can achieve robust perfect adaptation (Briat et al, 2016) and has already been considered for regulation of metabolic pathways (Briat and Khammash, 2018). Therefore, the use of a genetic circuit implementing an antithetic integral feedback controller in combination with an extended metabolic biosensor seems a promising genetic system for pathway regulation.…”

“…However, it is becoming increasingly clear that expression variation may propagate to metabolites (Evans et al, 2020) leading to a negative impact production. It is expected that, in a stochastic scenario, our strategy including the antithetic controller would have a good performance (Briat et al, 2016). Finally, another limitation that challenges the application of the proposed approach is that it involves an invasive biosensor and therefore it is necessary to tune the circuit not only in order to obtain an appropriate dynamic range and response but also in order to keep a suitable conversion ratio of the product.…”

Robust and Structural Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks

“…A recent example is that of the antithetic integral feedback controller proposed in [3] (see also Fig. 1B) that has been shown to induce an ergodic closedloop network when some conditions on the endogenous network to be controlled are met; see also [17,18]. A major limitation of the ergodicity conditions obtained in [3,15,19] is that they only apply to networks with fixed and known rate parameters -an assumption that is rarely met in practice as the rate parameters are usually poorly known and context dependent.…”

Artificial Signal Feedback Network Mimicking Cellular Adaptivity

“…This observation shows that the signal transduction process had coupled with dynamic DNA assembly to detect external stimuli and transduce the detected signal into the output to evoke subsequent reactions, all of which represents an organism's adaptation to environmental change ( Figure S18). 5,[24][25][26] An adaptive system can both respond to an incoming stimulus and then recover to prestimulus level, enabling cells to continue sensing and responding to changes in their micromilieu. 4,27,28 To verify the returning of DNAzyme on the membrane surface after the cleavage of stimulus, the fluorescence intensity of Cy5-labeled DNAzyme and FAM-labeled trigger was monitored by confocal microscopy.…”