SYNBADm: a tool for optimization-based automated design of synthetic gene circuits

Automatic design of gene regulatory mechanisms for spatial pattern formation

Gene regulatory mechanisms (GRMs) control the formation of spatial and temporal expression patterns that can serve as regulatory signals for the development of complex shapes. Synthetic developmental biology aims to engineer such genetic circuits for understanding and producing desired multicellular spatial patterns. However, designing synthetic GRMs for complex, multi-dimensional spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given two-dimensional spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms-including the number of genes necessary for the formation of the target spatial pattern-we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover complex genetic circuits producing spatial patterns.

IDESS: a toolbox for identification and automated design of stochastic gene circuits

MOTIVATION

One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation.

RESULTS

In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks.

AVAILABILITY AND IMPLEMENTATION

IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise

Microorganisms (mainly bacteria and yeast) are frequently used as hosts for genetic constructs in synthetic biology applications. Molecular noise might have a significant effect on the dynamics of gene regulation in microbial cells, mainly attributed to the low copy numbers of mRNA species involved. However, the inclusion of molecular noise in the automated design of biocircuits is not a common practice due to the computational burden linked to the chemical master equation describing the dynamics of stochastic gene regulatory circuits. Here, we address the automated design of synthetic gene circuits under the effect of molecular noise combining a mixed integer nonlinear global optimization method with a partial integro-differential equation model describing the evolution of stochastic gene regulatory systems that approximates very efficiently the chemical master equation. We demonstrate the performance of the proposed methodology through a number of examples of relevance in synthetic biology, including different bimodal stochastic gene switches, robust stochastic oscillators, and circuits capable of achieving biochemical adaptation under noise.

Automated design of gene circuits with optimal mushroom-bifurcation behavior

Recent advances in synthetic biology are enabling exciting technologies, including the next generation of biosensors, the rational design of cell memory, modulated synthetic cell differentiation, and generic multifunctional biocircuits. These novel applications require the design of gene circuits leading to sophisticated behaviors and functionalities. At the same time, designs need to be kept minimal to avoid compromising cell viability. Bifurcation theory addresses such challenges by associating circuit dynamical properties with molecular details of its design. Nevertheless, incorporating bifurcation analysis into automated design processes has not been accomplished yet. This work presents an optimization-based method for the automated design of synthetic gene circuits with specified bifurcation diagrams that employ minimal network topologies. Using this approach, we designed circuits exhibiting the mushroom bifurcation, distilled the most robust topologies, and explored its multifunctional behavior. We then outline potential applications in biosensors, memory devices, and synthetic cell differentiation.

Robustness and innovation in synthetic genotype networks

Genotype networks are sets of genotypes connected by small mutational changes that share the same phenotype. They facilitate evolutionary innovation by enabling the exploration of different neighborhoods in genotype space. Genotype networks, first suggested by theoretical models, have been empirically confirmed for proteins and RNAs. Comparative studies also support their existence for gene regulatory networks (GRNs), but direct experimental evidence is lacking. Here, we report the construction of three interconnected genotype networks of synthetic GRNs producing three distinct phenotypes in Escherichia coli. Our synthetic GRNs contain three nodes regulating each other by CRISPR interference and governing the expression of fluorescent reporters. The genotype networks, composed of over twenty different synthetic GRNs, provide robustness in face of mutations while enabling transitions to innovative phenotypes. Through realistic mathematical modeling, we quantify robustness and evolvability for the complete genotype-phenotype map and link these features mechanistically to GRN motifs. Our work thereby exemplifies how GRN evolution along genotype networks might be driving evolutionary innovation.

On biological networks capable of robust adaptation in the presence of uncertainties: A linear systems-theoretic approach

Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1) in the presence of deterministic external and parametric disturbances and (2) in a stochastic setting. In all the cases, firstly, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that unlike the incoherent feed-forward network structures (IFFLP or opposer modules), the modules containing negative feedback with buffer action (NFBLB or balancer modules) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs whereas the IFFLP topology produces locally minimum variance while compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological networks.

Novel Ground-Up 3D Multicellular Simulators for Synthetic Biology CAD Integrating Stochastic Gillespie Simulations Benchmarked with Topologically Variable SBML Models

The elevation of Synthetic Biology from single cells to multicellular simulations would be a significant scale-up. The spatiotemporal behavior of cellular populations has the potential to be prototyped in silico for computer assisted design through ergonomic interfaces. Such a platform would have great practical potential across medicine, industry, research, education and accessible archiving in bioinformatics. Existing Synthetic Biology CAD systems are considered limited regarding population level behavior, and this work explored the in silico challenges posed from biological and computational perspectives. Retaining the connection to Synthetic Biology CAD, an extension of the Infobiotics Workbench Suite was considered, with potential for the integration of genetic regulatory models and/or chemical reaction networks through Next Generation Stochastic Simulator (NGSS) Gillespie algorithms. These were executed using SBML models generated by in-house SBML-Constructor over numerous topologies and benchmarked in association with multicellular simulation layers. Regarding multicellularity, two ground-up multicellular solutions were developed, including the use of Unreal Engine 4 contrasted with CPU multithreading and Blender visualization, resulting in a comparison of real-time versus batch-processed simulations. In conclusion, high-performance computing and client-server architectures could be considered for future works, along with the inclusion of numerous biologically and physically informed features, whilst still pursuing ergonomic solutions.

Synthetic Biology in Plants, a Boon for Coming Decades

Recently an enormous expansion of knowledge is seen in various disciplines of science. This surge of information has given rise to concept of interdisciplinary fields, which has resulted in emergence of newer research domains, one of them is 'Synthetic Biology' (SynBio). It captures basics from core biology and integrates it with concepts from the other areas of study such as chemical, electrical, and computational sciences. The essence of synthetic biology is to rewire, re-program, and re-create natural biological pathways, which are carried through genetic circuits. A genetic circuit is a functional assembly of basic biological entities (DNA, RNA, proteins), created using typical design, built, and test cycles. These circuits allow scientists to engineer nearly all biological systems for various useful purposes. The development of sophisticated molecular tools, techniques, genomic programs, and ease of nucleic acid synthesis have further fueled several innovative application of synthetic biology in areas like molecular medicines, pharmaceuticals, biofuels, drug discovery, metabolomics, developing plant biosensors, utilization of prokaryotic systems for metabolite production, and CRISPR/Cas9 in the crop improvement. These applications have largely been dominated by utilization of prokaryotic systems. However, newer researches have indicated positive growth of SynBio for the eukaryotic systems as well. This paper explores advances of synthetic biology in the plant field by elaborating on its core components and potential applications. Here, we have given a comprehensive idea of designing, development, and utilization of synthetic biology in the improvement of the present research state of plant system.

Automated Biocircuit Design with SYNBADm

SYNBADm is a Matlab toolbox for the automated design of biocircuits using a model-based optimization approach. It enables the design of biocircuits with pre-defined functions starting from libraries of biological parts. SYNBADm makes use of mixed integer global optimization and allows both single and multi-objective design problems. Here we describe a basic protocol for the design of synthetic gene regulatory circuits. We illustrate step-by-step how to solve two different problems: (1) the (single objective) design of a synthetic oscillator and (2) the (multi-objective) design of a circuit with switch-like behavior upon induction, with a good compromise between performance and protein production cost.

Automated engineering of synthetic metabolic pathways for efficient biomanufacturing

Metabolic engineering involves the engineering and optimization of processes from single-cell to fermentation in order to increase production of valuable chemicals for health, food, energy, materials and others. A systems approach to metabolic engineering has gained traction in recent years thanks to advances in strain engineering, leading to an accelerated scaling from rapid prototyping to industrial production. Metabolic engineering is nowadays on track towards a truly manufacturing technology, with reduced times from conception to production enabled by automated protocols for DNA assembly of metabolic pathways in engineered producer strains. In this review, we discuss how the success of the metabolic engineering pipeline often relies on retrobiosynthetic protocols able to identify promising production routes and dynamic regulation strategies through automated biodesign algorithms, which are subsequently assembled as embedded integrated genetic circuits in the host strain. Those approaches are orchestrated by an experimental design strategy that provides optimal scheduling planning of the DNA assembly, rapid prototyping and, ultimately, brings forward an accelerated Design-Build-Test-Learn cycle and the overall optimization of the biomanufacturing process. Achieving such a vision will address the increasingly compelling demand in our society for delivering valuable biomolecules in an affordable, inclusive and sustainable bioeconomy.

Reverse engineering genetic networks using nonlinear saturation kinetics

A gene regulatory network (GRN) represents a set of genes along with their regulatory interactions. Cellular behavior is driven by genetic level interactions. Dynamics of such systems show nonlinear saturation kinetics which can be best modeled by Michaelis-Menten (MM) and Hill equations. Although MM equation is being widely used for modeling biochemical processes, it has been applied rarely for reverse engineering GRNs. In this paper, we develop a complete framework for a novel model for GRN inference using MM kinetics. A set of coupled equations is first proposed for modeling GRNs. In the coupled model, Michaelis-Menten constant associated with regulation by a gene is made invariant irrespective of the gene being regulated. The parameter estimation of the proposed model is carried out using an evolutionary optimization method, namely, trigonometric differential evolution (TDE). Subsequently, the model is further improved and the regulations of different genes by a given gene are made distinct by allowing varying values of Michaelis-Menten constants for each regulation. Apart from making the model more relevant biologically, the improvement results in a decoupled GRN model with fast estimation of model parameters. Further, to enhance exploitation of the search, we propose a local search algorithm based on hill climbing heuristics. A novel mutation operation is also proposed to avoid population stagnation and premature convergence. Real life benchmark data sets generated in vivo are used for validating the proposed model. Further, we also analyze realistic in silico datasets generated using GeneNetweaver. The comparison of the performance of proposed model with other existing methods shows the potential of the proposed model.

Distilling Robust Design Principles of Biocircuits Using Mixed Integer Dynamic Optimization

A major challenge in model-based design of synthetic biochemical circuits is how to address uncertainty in the parameters. A circuit whose behavior is robust to variations in the parameters will have more chances to behave as predicted when implemented in practice, and also to function reliably in presence of fluctuations and noise. Here, we extend our recent work on automated-design based on mixed-integer multi-criteria dynamic optimization to take into account parametric uncertainty. We exploit the intensive sampling of the design space performed by a global optimization algorithm to obtain the robustness of the topologies without significant additional computational effort. Our procedure provides automatically topologies that best trade-off performance and robustness against parameter fluctuations. We illustrate our approach considering the automated design of gene circuits achieving adaptation.

Component Characterization in a Growth-Dependent Physiological Context: Optimal Experimental Design

Synthetic biology design challenges have driven the use of mathematical models to characterize genetic components and to explore complex design spaces. Traditional approaches to characterization have largely ignored the effect of strain and growth conditions on the dynamics of synthetic genetic circuits, and have thus confounded intrinsic features of the circuit components with cell-level context effects. We present a model that distinguishes an activated gene’s intrinsic kinetics from its physiological context. We then demonstrate an optimal experimental design approach to identify dynamic induction experiments for efficient estimation of the component’s intrinsic parameters. Maximally informative experiments are chosen by formulating the design as an optimal control problem; direct multiple-shooting is used to identify the optimum. Our numerical results suggest that the intrinsic parameters of a genetic component can be more accurately estimated using optimal experimental designs, and that the choice of growth rates, sampling schedule, and input profile each play an important role. The proposed approach to coupled component–host modelling can support gene circuit design across a range of physiological conditions.

Synthetic gene circuits for the detection, elimination and prevention of disease

In living organisms, naturally evolved sensors that constantly monitor and process environmental cues trigger corrective actions that enable the organisms to cope with changing conditions. Such natural processes have inspired biologists to construct synthetic living sensors and signalling pathways, by repurposing naturally occurring proteins and by designing molecular building blocks de novo, for customized diagnostics and therapeutics. In particular, designer cells that employ user-defined synthetic gene circuits to survey disease biomarkers and to autonomously re-adjust unbalanced pathological states can coordinate the production of therapeutics, with controlled timing and dosage. Furthermore, tailored genetic networks operating in bacterial or human cells have led to cancer remission in experimental animal models, owing to the network's unprecedented specificity. Other applications of designer cells in infectious, metabolic and autoimmune diseases are also being explored. In this Review, we describe the biomedical applications of synthetic gene circuits in major disease areas, and discuss how the first genetically engineered devices developed on the basis of synthetic-biology principles made the leap from the laboratory to the clinic.

An Automated Design Framework for Multicellular Recombinase Logic

Tools to systematically reprogram cellular behavior are crucial to address pressing challenges in manufacturing, environment, or healthcare. Recombinases can very efficiently encode Boolean and history-dependent logic in many species, yet current designs are performed on a case-by-case basis, limiting their scalability and requiring time-consuming optimization. Here we present an automated workflow for designing recombinase logic devices executing Boolean functions. Our theoretical framework uses a reduced library of computational devices distributed into different cellular subpopulations, which are then composed in various manners to implement all desired logic functions at the multicellular level. Our design platform called CALIN (Composable Asynchronous Logic using Integrase Networks) is broadly accessible via a web server, taking truth tables as inputs and providing corresponding DNA designs and sequences as outputs (available at http://synbio.cbs.cnrs.fr/calin). We anticipate that this automated design workflow will streamline the implementation of Boolean functions in many organisms and for various applications.

RNA-aptamers-in-droplets (RAPID) high-throughput screening for secretory phenotypes

Synthetic biology and metabolic engineering seek to re-engineer microbes into "living foundries" for the production of high value chemicals. Through a "design-build-test" cycle paradigm, massive libraries of genetically engineered microbes can be constructed and tested for metabolite overproduction and secretion. However, library generation capacity outpaces the rate of high-throughput testing and screening. Well plate assays are flexible but with limited throughput, whereas droplet microfluidic techniques are ultrahigh-throughput but require a custom assay for each target. Here we present RNA-aptamers-in-droplets (RAPID), a method that greatly expands the generality of ultrahigh-throughput microfluidic screening. Using aptamers, we transduce extracellular product titer into fluorescence, allowing ultrahigh-throughput screening of millions of variants. We demonstrate the RAPID approach by enhancing production of tyrosine and secretion of a recombinant protein in Saccharomyces cerevisiae by up to 28- and 3-fold, respectively. Aptamers-in-droplets affords a general approach for evolving microbes to synthesize and secrete value-added chemicals.Screening libraries of genetically engineered microbes for secreted products is limited by the available assay throughput. Here the authors combine aptamer-based fluorescent detection with droplet microfluidics to achieve high throughput screening of yeast strains engineered for enhanced tyrosine or streptavidin production.

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

Background

We consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs).

Methods

We present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems.

Results

We illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores).

Conclusions

These results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.

Automated Design Framework for Synthetic Biology Exploiting Pareto Optimality

In this work we consider Pareto optimality for automated design in synthetic biology. We present a generalized framework based on a mixed-integer dynamic optimization formulation that, given design specifications, allows the computation of Pareto optimal sets of designs, that is, the set of best trade-offs for the metrics of interest. We show how this framework can be used for (i) forward design, that is, finding the Pareto optimal set of synthetic designs for implementation, and (ii) reverse design, that is, analyzing and inferring motifs and/or design principles of gene regulatory networks from the Pareto set of optimal circuits. Finally, we illustrate the capabilities and performance of this framework considering four case studies. In the first problem we consider the forward design of an oscillator. In the remaining problems, we illustrate how to apply the reverse design approach to find motifs for stripe formation, rapid adaption, and fold-change detection, respectively.

Stochastic modeling and numerical simulation of gene regulatory networks with protein bursting

Gene expression is inherently stochastic. Advanced single-cell microscopy techniques together with mathematical models for single gene expression led to important insights in elucidating the sources of intrinsic noise in prokaryotic and eukaryotic cells. In addition to the finite size effects due to low copy numbers, translational bursting is a dominant source of stochasticity in cell scenarios involving few short lived mRNA transcripts with high translational efficiency (as is typically the case for prokaryotes), causing protein synthesis to occur in random bursts. In the context of gene regulation cascades, the Chemical Master Equation (CME) governing gene expression has in general no closed form solution, and the accurate stochastic simulation of the dynamics of complex gene regulatory networks is a major computational challenge. The CME associated to a single gene self regulatory motif has been previously approximated by a one dimensional time dependent partial integral differential equation (PIDE). However, to the best of our knowledge, multidimensional versions for such PIDE have not been developed yet. Here we propose a multidimensional PIDE model for regulatory networks involving multiple genes with self and cross regulations (in which genes can be regulated by different transcription factors) derived as the continuous counterpart of a CME with jump process. The model offers a reliable description of systems with translational bursting. In order to provide an efficient numerical solution, we develop a semilagrangian method to discretize the differential part of the PIDE, combined with a composed trapezoidal quadrature formula to approximate the integral term. We apply the model and numerical method to study sustained stochastic oscillations and the development of competence, a particular case of transient differentiation attained by certain bacterial cells under stress conditions. We found that the resulting probability distributions are distinguishable from those characteristic of other transient differentiation processes. In this way, they can be employed as markers or signatures that identify such phenomena from bacterial population experimental data, for instance. The computational efficiency of the semilagrangian method makes it suitable for purposes like model identification and parameter estimation from experimental data or, in combination with optimization routines, the design of gene regulatory networks under molecular noise.

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

From cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systems.