Mathematical Modeling of RNA-Based Architectures for Closed Loop Control of Gene Expression

Abstract

Feedback allows biological systems to control gene expression precisely and reliably, even in the presence of uncertainty, by sensing and processing environmental changes. Taking inspiration from natural architectures, synthetic biologists have engineered feedback loops to tune the dynamics and improve the robustness and predictability of gene expression. However, experimental implementations of biomolecular control systems are still far from satisfying performance specifications typically achieved by electrical or mechanical control systems. To address this gap, we present mathematical models of biomolecular controllers that enable reference tracking, disturbance rejection, and tuning of the temporal response of gene expression. These controllers employ RNA transcriptional regulators to achieve closed loop control where feedback is introduced via molecular sequestration. Sensitivity analysis of the models allows us to identify which parameters influence the transient and steady state response of a target gene expression process, as well as which biologically plausible parameter values enable perfect reference tracking. We quantify performance using typical control theory metrics to characterize response properties and provide clear selection guidelines for practical applications. Our results indicate that RNA regulators are well-suited for building robust and precise feedback controllers for gene expression. Additionally, our approach illustrates several quantitative methods useful for assessing the performance of biomolecular feedback control systems.

Distinct timescales of RNA regulators enable the construction of a genetic pulse generator

“…In TXTL there is no protein degradation, so this causes a pulse in the rate of GFP production. CRISPRi: clustered regularly interspaced short palindromic repeats interference; crRNA: CRISPR RNA; dCas9: dead Cas9; GFP: green fluorescent protein; I1-FFL: type 1 incoherent feedforward loop; STAR: small transcription activating RNA; tracrRNA: trans-activating crRNA; TXTL: transcriptiontranslation system [Color figure can be viewed at wileyonlinelibrary.com] combined with mathematical models to parameterize and understand RNA circuits (Agrawal et al, 2018;Hu et al, 2015;Hu, Takahashi, Zhang, & Lucks, 2018). TXTL is ideal for prototyping genetic circuit dynamics because it is quick and easy to use, requires minimal cloning, and shows good agreement with in vivo data , and recently it was used to characterize CRISPR nucleases and gRNAs .…”

In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller

“…Motivated by this analogy, various possible designs of such controllers have been discussed substantially in the context of biological systems. [13][14][15][16]26 The present work is inspired by our previous work, 26 in which we introduced a computational design based on RNA based controllers; no experimental validation was provided. Here, we start from that design, modifying it to allow for direct genetic regulation and provide an experimental validation.…”

“…For a case when the output is larger than the reference signal, free Y sequesters X to reduce the output. One of the key reasons that this controller is able to improve substantially upon that in 26 is that it implements an effective error computation through protein interactions; in contrast, RNA-based designs suffer from the fact that RNAs degrade much faster than proteins, making an effective error computation very hard to implement experimentally. 35 In contrast, the degradation of the proteins used in this work can be ignored.…”

“…Moreover, we started the model fitting manually with an initial guess of parameters derived from the literature. [23][24][25][26][27][28][29]35 Once we found the possible values that provide a qualitative agreement between the model and the measured response, we used an iterative least-squares fitting procedure to find a range of parameter values that gave us the best fit (see Methods). The means of the resulting parameters (Table 1) were then used along with the ODE model ( Fig.…”

“…By virtue of such advantages, several synthetic gene circuits have been implemented in TXTL with a successful modeling framework. [26][27][28][29] In this article, we constructed a synthetic biomolecular integral controller that precisely controls the expression of a target gene. Our strategy relies on a molecular sequestration reaction that enables error computation between the reference and the output signal while exploiting the natural interaction between the E. coli sigma factor σ28 and the anti-σ28, FlgM.…”