Mechanistic Models of Inducible Synthetic Circuits for Joint Description of DNA Copy Number, Regulatory Protein Level, and Cell Load

Abstract

Accurate predictive mathematical models are urgently needed in synthetic biology to support the bottom-up design of complex biological systems, minimizing trial-and-error approaches. The majority of models used so far adopt empirical Hill functions to describe activation and repression in exogenously-controlled inducible promoter systems. However, such equations may be poorly predictive in practical situations that are typical in bottom-up design, including changes in promoter copy number, regulatory protein level, and cell load. In this work, we derived novel mechanistic steady-state models of the lux inducible system, used as case study, relying on different assumptions on regulatory protein (LuxR) and cognate promoter (Plux) concentrations, inducer-protein complex formation, and resource usage limitation. We demonstrated that a change in the considered model assumptions can significantly affect circuit output, and preliminary experimental data are in accordance with the simulated activation curves. We finally showed that the models are identifiable a priori (in the analytically tractable cases) and a posteriori, and we determined the specific experiments needed to parametrize them. Although a larger-scale experimental validation is required, in the future the reported models may support synthetic circuits output prediction in practical situations with unprecedented details.

BioCRNpyler: Compiling Chemical Reaction Networks from Biomolecular Parts in Diverse Contexts

“…This has been explored in the literature using various approaches such as by direct mathematical comparison of mechanistic and phenomenological models [46][47][48] or by studying particular examples of reduced models.…”

“…45–47 Bridging the connections between the different modeling abstractions is a challenging research problem. This has been explored in the literature using various approaches such as by direct mathematical comparison of mechanistic and phenomenological models 48–50 or by studying particular examples of reduced models. 2 BioCRNpyler provides a computational approach using reaction schemas to easily change the mechanisms used in compilation from detailed mass-action to coarse-grained at various level of complexity.…”

A two-state ribosome and protein model can robustly capture the chemical reaction dynamics of gene expression

“…Reduced models are also useful to specify the desired objectives or the performance specifications of a system. To meet these objectives, the designer needs to map these reduced models to the level of system design and also mathematically characterize this mapping in order to analyze the system performance [17, 23]. Towards that end, it is important to explore the modeling assumptions of time-scale separation [9–11] and conservation laws [7, 12, 13] that are most commonly used in deriving reduced-order models for biological systems.…”

“…Similarly, f tl (•) could be a constant or a Hill function dependent on the transcriptional regulation mechanism [7]. Clearly, the parameters in this model and any parameters in the Hill functions all have empirical meanings but an analytical relationship with the mechanistic reaction rates is usually obscured [17]. Moreover, a closer analysis would show that such phenomenological models are only valid under certain assumptions and parameter regimes.…”

Computational Methods Enabling Next-Generation Bioprocesses

“…In this study, the author also proposes new reconstruction methods that leverage an increasingly common type of data in synthetic biology: population snapshots from microscopy or cytometry. Two additional contributions [4,5] tackle modelling issues. While Pasotti and colleagues focus on the derivation of mechanistic models of inducible circuits, Boeing and colleagues develop an aspect-oriented modelling framework that allows us to compose parts into circuits and study how they will interact with the host organism.…”