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Synthetic Biologists are increasingly interested in the idea of using synthetic feedback control circuits for the mitigation of perturbations to gene regulatory networks that may arise due to disease and/or environmental disturbances. Models employing Michaelis-Menten kinetics with Hill-type nonlinearities are typically used to represent the dynamics of gene regulatory networks. Here, we identify some fundamental problems with such models from the point of view of control system design, and argue that an alternative formalism, based on so-called S-System models, is more suitable. Using tools from system identification, we show how to build S-System models that capture the key dynamics of an example gene regulatory network, and design a genetic feedback controller with the objective of rejecting an external perturbation. Using a sine sweeping method, we show how the S-System model can be approximated by a linear transfer function and, based on this transfer function, we design our controller. Simulation results using the full nonlinear S-System model of the network show that the synthetic control circuit is able to mitigate the effect of external perturbations. Our study is the first to highlight the usefulness of the S-System modelling formalism for the design of synthetic control circuits for gene regulatory networks.

Measurement techniques in biology are now able to provide data on the trajectories of multiple individual molecules simultaneously, motivating the development of techniques for the stochastic spatio-temporal modelling of biomolecular networks. However, standard approaches based on solving stochastic reaction-diffusion equations are computationally intractable for large-scale networks. We present a novel method for modeling stochastic and spatial dynamics in biomolecular networks using a simple form of the Langevin equation with noisy kinetic constants. Spatial heterogeneity in molecular interactions is decoupled into a set of compartments, where the distribution of molecules in each compartment is idealised as being uniform. The reactions in the network are then modelled by Langevin equations with correcting terms, that account for differences between spatially uniform and spatially non-uniform distributions, and that can be readily estimated from available experimental data. The accuracy and extreme computational efficiency of the approach is demonstrated on a model of the epidermal growth factor receptor network in the human mammary epithelial cell.

Introduction of synthetic circuits into microbes creates competition between circuit and host genes for shared cellular resources, such as ribosomes. This can lead to the emergence of unwanted coupling between the expression of different circuit genes, complicating the design process and potentially leading to circuit failure. By expressing a synthetic 16S rRNA with altered specificity, we can partition the ribosome pool into host-specific and circuit-specific activities. We show mathematically and experimentally that the effects of resource competition can be alleviated by targeting genes to different ribosomal pools. This division of labour can be used to increase flux through a metabolic pathway. We develop a model of cell physiology which is able to capture these observations and use it to design a dynamic resource allocation controller. When implemented, this controller acts to decouple genes by increasing orthogonal ribosome production as the demand for translational resources by a synthetic circuit increases.

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.

Topological inference of biological interaction networks from experimental data is a fundamental research topic in the broad area of Systems Biology. Several algorithms presented in the literature have been devised in order to infer the topology of a network from time‐course data. The present work introduces a novel method for reverse‐engineering gene regulatory networks from time‐course experiments, which combines the instrumental variables technique for the identification of dynamical systems with a regularization strategy for dealing with over‐parametrized systems. Differently from least squares methods, the proposed approach can explicitly address the bias and nonconsistency issues that arise when dealing with time‐course measurements, thus yielding improved performance with respect to methods designed for steady‐state data. Moreover, the devised approach, which has been named RIVA (Reverse‐engineering of biological networks via Instrumental VAriables), can simultaneously exploit multiple time‐series, thus enabling one to get improved results by collecting and exploiting data from multiple experiments, and is computationally efficient, thus it can be also applied to large‐scale (in the order of thousands of nodes) networks. To analyze the applicability and effectiveness of RIVA, we performed several tests, both with simulated data and with experimental data, and compared the results against other state‐of‐the‐art inference methods designed for time‐series 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]

Background: In Saccharomyces cerevisiæ, structural bistability generates a bimodal expression of the galactose uptake genes (GAL) when exposed to low and high glucose concentrations. This indicates that yeast cells can decide between using either the limited amount of glucose or growing on galactose under changing environmental conditions. A crucial requirement for any plausible mechanistic model of this system is that it reproduces the robustness of the bistable response observed in vivo against inter-individual parametric variability and fluctuating environmental conditions. Results: We show how a control-theoretic analysis of the robustness of a model of the GAL regulatory network may be used to establish the model's plausibility in characterizing the persistent memory of different carbon sources, without the need for extensive simulations. Chemical Reaction Network Theory is used to establish that the proposed network model is compatible with structural bistability. The robustness of each of the two operative conditions against fluctuations of the species concentrations is demonstrated by studying the Domains of Attraction of the corresponding equilibrium points. Finally, we use a global robustness analysis method based on Semi-Definite Programming to evaluate the modification of the bistable steady states induced by multiple parametric variations throughout bounded regions of the parameter space. Conclusions: Our analysis provides convincing evidence for the robustness, and hence plausibility, of the GAL regulatory network model. The proposed workflow also demonstrates the power of analytical methods from control theory to provide a direct quantitative characterization of the dynamics of multistable biomolecular regulatory systems without recourse to extensive computer simulations. [ABSTRACT FROM AUTHOR]

Bistability is a system-level property, exploited by many biomolecular interaction networks as a key mechanism to accomplish different cellular functions (e.g., differentiation, cell cycle, switch-like response to external stimuli). Bistability has also been experimentally found to occur in the regulatory network of the galactose metabolic pathway in the model organism Saccharomyces cerevisiae. In this yeast, bistability generates a persistent memory of the type of carbon source available in the extracellular medium: under the same experimental conditions, cells previously grown with different nutrients generate different responses and get stably locked into two distinct steady states. The molecular interactions of the GAL regulatory network have been thoroughly dissected through wet-lab experiments; thus, this system provides a formidable benchmark to our ability to characterize and reproduce in silico the behavior of bistable biological systems. To this aim, a number of models have been proposed in the literature; however, we found that they are not able to replicate the persistent memory behavior observed in (Acar et al., ). The present study proposes a novel model of the GAL regulatory network, which, in addition to reproducing in silico the experimental findings, can be formally analyzed for structural multistability of the network, using chemical reaction network theory (CRNT), and allows the characterization of the domains of attraction (DA). This work provides further insights into the GAL system and proposes an easily generalizable approach to the study of bistability-associated behaviors in biological systems. [ABSTRACT FROM AUTHOR]