Multiobjective Identification of a Feedback Synthetic Gene Circuit

Abstract

Kinetic (i.e., dynamic) semimechanistic models based on the first principles are particularly important in systems and synthetic biology since they can explain and predict the functional behavior that emerges from the time-varying concentrations in cellular components. However, gene circuit models are nonlinear higher order ones and have a large number of parameters. In addition, experimental measurements are often scarce, and enough signal excitability for identification cannot always be achieved. These characteristics render the identification problem ill-posed, so most gene circuit models present incomplete parameter identifiability. Thus, parameter identification of typical biological models still appears as an open problem, where ensemble modeling approaches and multiobjective optimization arise as natural options. We address the problem of identifying the stochastic model of a closed-loop synthetic genetic circuit designed to minimize the gene expression noise. The model results from the feedback interaction between two subsystems. Besides incomplete parameter identifiability, the closed-loop dynamics cannot be directly identified due to the lack of enough input signal excitability. We apply a two-stage approach. First, the openloop averaged time-course experimental data are used to identify a reduced-order stochastic model of the system direct chain. Then, closed-loop steady-state stochastic distributions are used to identify the remaining parameters in the feedback configuration. In both cases, multiobjective optimization is used to address the parameter identifiability, providing sets of parameters valid for different state-space regions. The methodology gives good identification results, provides clear guidelines on the effect of the parameters under different scenarios, and it is particularly useful for easily combining time-course population averaged and steady-state single-cell distribution experimental data.

Modeling and Optimization of a Molecular Biocontroller for the Regulation of Complex Metabolic Pathways

“…The goal is to obtain a library of possible designs, each one corresponding to a different trade-off between the cost indices J 1 , J 2 . The resulting solutions are all equally optimal in the sense of Pareto ( Boada et al, 2019b ). When one of the objectives improves, the others necessarily deteriorate, so selecting the most appropriate solution depends on the designer.…”

“…Multiobjective optimization has already been demonstrated to be an appropriate tool for characterization of gene circuit parts ( Boada et al, 2019a ; Boada et al, 2019b ), and for the design of gene circuits with the desired behavior ( Boada et al, 2016 ; Boada et al, 2017b ; Boada et al, 2021 ). Here, we present an approach to use multiobjective optimization for the optimal tuning of the gene circuit parts composing the biocontroller and biosensor in a dynamic metabolic regulation feedback loop.…”

Characterization of Gene Circuit Parts Based on Multiobjective Optimization by Using Standard Calibrated Measurements

“…All of our constructions have constitutive expression of ap rotein of interest. [41,16] In addition, we modeled the cell population growth and its dilution effect [Eq. The key processes and assumptions considered for the reactions in Equation (9) during gene expression are as follows:T he cell contains enough free RNA polymerase (RNAP) to serve all active genes transcribing at ag iven moment;R NAP binding to each promoter is a fast reaction;t ranscription of genes is an irreversible reaction, so the transcription rate is an effective one;t ranslation is not as imple process.…”

“…(10)] that described the expression construct dynamics by using the law of mass action kinetics. [41,16] In addition, we modeled the cell population growth and its dilution effect [Eq. (10)].…”

“…[12] The multiobjective optimization design (MOOD) framework to perform model parameter estimation has been successfully used for the optimal design of gene networks, [13,14] complex systemsi dentification, [15] or closed-loop systemsi dentification. [16] It allows the following problems, which are difficult to tackle by using single-or weighted-objective optimizationa pproaches often found in syntheticg ene networks, to be addressed:1 )lack of identifiability,w hich is caused by overparametrization and multimodality of certain model parameters in the parameters space due to nonconvexity,s ince the MOOD approachc an provide all sets of parameters compatible with the objectives for optimization;2 )parameter selectionf itting, which is at rade-off between accuracy and model complexity or between multiple desired model performance specifications, since am ulticriteria decision-making (MCDM) strategy to select the most suitable solutionsi si ntegrated in the MOOD framework;3 )consideration of experimental context (e.g.,c ulture growth conditions) by including growth and experiment-relatedo bjectives, and4 )consideration of circuit contexts, sincet he estimation of parameters for ap art, or as et of parts, of interestc an be performed by using differentgene circuits that all share the parts of interest.…”