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Boolean logic and arithmetic through DNA excision (BLADE) is a recently developed platform for implementing inducible and logical control over gene expression in mammalian cells, which has the potential to revolutionise cell engineering for therapeutic applications. This 2-input 2-output platform can implement 256 different logical circuits that exploit the specificity and stability of DNA recombination. Here, we develop the first mechanistic mathematical model of the 2-input BLADE platform based on Cre- and Flp-mediated DNA excision. After calibrating the model on experimental data from two circuits, we demonstrate close agreement between model outputs and data on the other 111 circuits that have so far been experimentally constructed using the 2-input BLADE platform. Model simulations of the remaining 143 circuits that have yet to be tested experimentally predict excellent performance of the 2-input BLADE platform across the range of possible circuits. Circuits from both the tested and untested subsets that perform less well consist of a disproportionally high number of STOP sequences. Model predictions suggested that circuit performance declines with a decrease in recombinase expression and new experimental data was generated that confirms this relationship. Author summary: A major objective in synthetic biology is to predictably design and construct genetic circuits to control cellular functions. Although recent years have seen numerous advances towards this goal, Synthetic Biology is still mostly a microbial-centric discipline, and high performance genetic circuits are currently lacking in mammalian cells. Site-specific DNA recombinases Cre, Flp are among the most powerful genome engineering tools and form the basis of Boolean logic and arithmetic through DNA excision (BLADE), a platform that has the potential to revolutionise cell engineering for therapeutic applications in mammalian cells. Here, we develop the first mechanistic mathematical model of the 2-input BLADE platform and apply it by simulating the performance of 113 different circuits that have been constructed and tested experimentally. We demonstrate the predictive power of our model by simulating the performance of the 143 circuits that are yet to be tested. Our model is also capable of testing experimental hypotheses, revealing that the performance of synthetic BLADE circuits is sensitive to recombinase expression levels. We were able to confirm this computational result by generating new experimental data. [ABSTRACT FROM AUTHOR]

The circadian clock orchestrates biological processes so that they occur at specific times of the day, thereby facilitating adaptation to diurnal and seasonal environmental changes. In plants, mathematical modelling has been comprehensively integrated with experimental studies to gain a better mechanistic understanding of the complex genetic regulatory network comprising the clock. However, with an increasing number of circadian genes being discovered, there is a pressing need for methods facilitating the expansion of computational models to incorporate these newly-discovered components. Conventionally, plant clock models have comprised differential equation systems based on Michaelis-Menten kinetics. However, the difficulties associated with modifying interactions using this approach—and the concomitant problem of robustly identifying regulation types—has contributed to a complexity bottleneck, with quantitative fits to experimental data rapidly becoming computationally intractable for models possessing more than ≈50 parameters. Here, we address these issues by constructing the first plant clock models based on the S-System formalism originally developed by Savageau for analysing biochemical networks. We show that despite its relative simplicity, this approach yields clock models with comparable accuracy to the conventional Michaelis-Menten formalism. The S-System formulation also confers several key advantages in terms of model construction and expansion. In particular, it simplifies the inclusion of new interactions, whilst also facilitating the modification of regulation types, thereby making it well-suited to network inference. Furthermore, S-System models mitigate the issue of parameter identifiability. Finally, by applying linear systems theory to the models considered, we provide some justification for the increased use of aggregated protein equations in recent plant clock modelling, replacing the separate cytoplasmic/nuclear protein compartments that were characteristic of the earlier models. We conclude that as well as providing a simplified framework for model development, the S-System formalism also possesses significant potential as a robust modelling method for designing synthetic gene circuits. Author summary: Mathematical models have been widely employed as a complement to experimental work in elucidating the underlying mechanistic behaviour of the plant circadian clock. In this study, we investigate the use of a simplified modelling strategy, the S-System framework, to reduce the computational complexity of such models. We test the efficacy of our approach by constructing S-System versions of five established plant clock models, which we fit to synthetic and experimental gene expression data. We demonstrate that the S-System formulation can generate fits to expression data that are very similar to those of its more complex counterparts, yielding predictions with better accuracy in some cases. Our work reveals three principal benefits of the S-System formalism in modelling gene regulatory networks (GRNs) characterised by entrainable oscillations, typified by the circadian clock. Firstly, it enables new interactions to be incorporated in a very easy manner. Secondly, it facilitates the inference of unknown regulation types. Thirdly, it mitigates the parameter identifiability problem, thereby making it a suitable modelling method for designing GRN control circuits for synthetic biology applications. Taken together, our findings identify the S-System framework as a promising alternative approach for computational modelling of oscillatory GRN networks. [ABSTRACT FROM AUTHOR]

Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems. [ABSTRACT FROM AUTHOR]

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for the ubiquity of nonlinear dynamics in gene expression networks, and generate useful guidelines for the design of synthetic gene circuits. [ABSTRACT FROM AUTHOR]

Stable and robust oscillations in the concentration of adenosine 3', 5'-cyclic monophosphate (cAMP) are observed during the aggregation phase of starvation-induced development in Dictyostelium discoideum. In this paper we use mathematical modelling together with ideas from robust control theory to identify two factors which appear to make crucial contributions to ensuring the robustness of these oscillations. Firstly, we show that stochastic fluctuations in the molecular interactions play an important role in preserving stable oscillations in the face of variations in the kinetics of the intracellular network. Secondly, we show that synchronisation of the aggregating cells through the diffusion of extracellular cAMP is a key factor in ensuring robustness of the oscillatory waves of cAMP observed in Dictyostelium cell cultures to cell-to-cell variations. A striking and quite general implication of the results is that the robustness analysis of models of oscillating biomolecular networks (circadian clocks, Ca2+ oscillations, etc.) can only be done reliably by using stochastic simulations, even in the case where molecular concentrations are very high. [ABSTRACT FROM AUTHOR]