Multi-objective optimization framework to obtain model-based guidelines for tuning biological synthetic devices: an adaptive network case

Synthetic biology design principles enable efficient bioproduction of Heparosan with low molecular weight and low polydispersion index for the biomedical industry

Heparosan is a natural polymer with unique chemical and biological properties, that holds great promise for biomedical applications. The molecular weight (Mw) and polydispersion index (PDI) are critical factors influencing the performance of heparosan-based materials. Achieving precise control over the synthesis process to consistently produce heparosan with low Mw and low PDI can be challenging, as it requires tight regulation of reaction conditions, enzyme activity, and precursor concentrations. We propose a novel approach utilizing synthetic biology principles to precisely control heparosan biosynthesis in bacteria. Our strategy involves designing a biomolecular controller that can regulate the expression of genes involved in heparosan biosynthesis. This controller is activated by biosensors that detect heparosan precursors, allowing for fine-tuned control of the polymerization process. Through this approach, we foresee the implementation of this synthetic device, demonstrating the potential to produce low Mw and low PDI heparosan in the probiotic E. coli Nissle 1917 as a biosafe and biosecure biofactory. This study represents a significant advancement in the field of heparosan production, offering new opportunities for the development and manufacturing of biomaterials with tailored properties for diverse biomedical applications.

Optimal performance objectives in the highly conserved bone morphogenetic protein signaling pathway

Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in determining cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one context to another, despite the pathway connectivity remaining nearly constant. For instance, some cellular systems require a rapid response, while others require high noise filtering. In this paper, we examine how the BMP-Smad pathway balances trade-offs among three such systems-level behaviors, or "Performance Objectives (POs)": response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a Smad pathway model fit to human cell data, we show that varying non-conserved parameters (NCPs) such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics to identify optimal trade-offs among various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optimally tuned for each context.

Optimal Performance Objectives in the Highly Conserved Bone Morphogenetic Protein Signaling Pathway

Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in these cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one context to another, despite the pathway connectivity remaining nearly constant. For instance, some cellular systems require a rapid response, while others require high noise filtering. In this paper, we examine how the BMP- Smad pathway balances trade-offs among three such systems-level behaviors, or "Performance Objectives (POs)": response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a Smad pathway model fit to human cell data, we show that varying non-conserved parameters (NCPs) such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics to identify optimal trade-offs among various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optimally tuned for each context.

Functional Synthetic Biology

Synthetic biologists have made great progress over the past decade in developing methods for modular assembly of genetic sequences and in engineering biological systems with a wide variety of functions in various contexts and organisms. However, current paradigms in the field entangle sequence and functionality in a manner that makes abstraction difficult, reduces engineering flexibility and impairs predictability and design reuse. Functional Synthetic Biology aims to overcome these impediments by focusing the design of biological systems on function, rather than on sequence. This reorientation will decouple the engineering of biological devices from the specifics of how those devices are put to use, requiring both conceptual and organizational change, as well as supporting software tooling. Realizing this vision of Functional Synthetic Biology will allow more flexibility in how devices are used, more opportunity for reuse of devices and data, improvements in predictability and reductions in technical risk and cost.

Designing Biological Circuits: From Principles to Applications

Genetic circuit design is a well-studied problem in synthetic biology. Ever since the first genetic circuits─the repressilator and the toggle switch─were designed and implemented, many advances have been made in this area of research. The current review systematically organizes a number of key works in this domain by employing the versatile framework of generalized morphological analysis. Literature in the area has been mapped on the basis of (a) the design methodologies used, ranging from brute-force searches to control-theoretic approaches, (b) the modeling techniques employed, (c) various circuit functionalities implemented, (d) key design characteristics, and (e) the strategies used for the robust design of genetic circuits. We conclude our review with an outlook on multiple exciting areas for future research, based on the systematic assessment of key research gaps that have been readily unravelled by our analysis framework.

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

Achieving optimal production in microbial cell factories, robustness against changing intracellular and environmental perturbations requires the dynamic feedback regulation of the pathway of interest. Here, we consider a merging metabolic pathway motif, which appears in a wide range of metabolic engineering applications, including the production of phenylpropanoids among others. We present an approach to use a realistic model that accounts for in vivo implementation and then propose a methodology based on multiobjective optimization for the optimal tuning of the gene circuit parts composing the biomolecular controller and biosensor devices for a dynamic regulation strategy. We show how this approach can deal with the trade-offs between the performance of the regulated pathway, robustness to perturbations, and stability of the feedback loop. Using realistic models, our results suggest that the strategies for fine-tuning the trade-offs among performance, robustness, and stability in dynamic pathway regulation are complex. It is not always possible to infer them by simple inspection. This renders the use of the multiobjective optimization methodology valuable and necessary.

Trade-Offs in Biosensor Optimization for Dynamic Pathway Engineering

Recent progress in synthetic biology allows the construction of dynamic control circuits for metabolic engineering. This technology promises to overcome many challenges encountered in traditional pathway engineering, thanks to its ability to self-regulate gene expression in response to bioreactor perturbations. The central components in these control circuits are metabolite biosensors that read out pathway signals and actuate enzyme expression. However, the construction of metabolite biosensors is a major bottleneck for strain design, and a key challenge is to understand the relation between biosensor dose-response curves and pathway performance. Here we employ multiobjective optimization to quantify performance trade-offs that arise in the design of metabolite biosensors. Our approach reveals strategies for tuning dose-response curves along an optimal trade-off between production flux and the cost of an increased expression burden on the host. We explore properties of control architectures built in the literature and identify their advantages and caveats in terms of performance and robustness to growth conditions and leaky promoters. We demonstrate the optimality of a control circuit for glucaric acid production in Escherichia coli, which has been shown to increase the titer by 2.5-fold as compared to static designs. Our results lay the groundwork for the automated design of control circuits for pathway engineering, with applications in the food, energy, and pharmaceutical sectors.

Multi-Objective Optimization Tuning Framework for Kinetic Parameter Selection and Estimation

Semi-mechanistic kinetic (i.e., dynamic) models based on first principles are particularly relevant in biology, as they can explain and predict functional behavior that arises from varying concentrations of the cellular components over time. Here, we describe a computational tuning framework to facilitate both the selection of kinetic parameters for these models and its estimation from experimental data. On the one hand, the tuning framework uses multi-objective optimization to generate a model-based set of guidelines for the selection of the kinetic parameters. These parameter values are the required ones to provide a biological system with desired behavior, while fulfilling the design criteria encoded in the optimization problem itself. On the other hand, this framework can also be used to estimate the parameter values of biological systems from experimental data, once the optimization objectives had been defined appropriately. The methodology gives accurate identification results, as it provides clear orientation on the effect of the parameter values over the system's behavior even under different experimental scenarios. It is particularly useful for easily combining time-course-averaged data and steady-state distribution data. This protocol also addresses aspects related to the appropriate description of the kinetic models and the settings of the software tools. Therefore, it supplies for hands-on testing to evaluate the validity of the underlying technical assumptions of the biological kinetic models.

Evaluation of regional industrial cluster innovation capability based on particle swarm clustering algorithm and multi-objective optimization

With the progress of the times and the development of science, industrial clusters have been regarded by all countries in the world as one of the important ways to enhance regional competitiveness, and become an inevitable trend of industrial development. The research on the innovation ability of industrial clusters can not only maintain sustainable development of industrial clusters and obtain sustained competitive advantages, but also provide reference for the government's policy formulation of industrial clusters. This paper aims to study the evaluation of regional industrial clusters' innovation capability based on particle swarm clustering and multi-objective optimization. This paper uses the theory of industrial cluster innovation and takes regional industrial system as the empirical research object to establish a regional industrial system capability evaluation system, which is based on the selection of indicators, combined with analytic hierarchy process and factor analysis to evaluate industrial innovation capability. On this basis, the particle swarm clustering theory is used to verify the innovation ability and evaluation index system of industrial clusters, and provide a reference for the evaluation of the innovation ability of industrial clusters. This paper divides the regional cluster innovation capability into four aspects: innovation input capability, environment support capability, self-development capability and innovation output capability, and systematically analyzes the key elements and in the composition of innovation elements and their relationships. It then constructs the evaluation index system of regional cluster innovation capability. At the same time, this paper introduces clustering analysis algorithm and swarm intelligence algorithm into regional innovation evaluation, combines particle swarm optimization algorithm and K-means clustering algorithm, and optimizes particle swarm clustering algorithm by adjusting adaptive parameters and adding fitness variance. The experimental results of this paper show that from the results of the tested innovation potential of the three industrial clusters, industrial cluster F has the strongest innovation ability, with an evaluation coefficient of 0.851, followed by industrial cluster F, which has a value of 0.623. This result is consistent with the actual innovation status of the selected industry. From this point of view, the established particle swarm clustering model for evaluating the innovation capability of regional industrial clusters is reliable and can be used to evaluate the innovation capability of different industrial clusters.

Multi-objective optimization methods in novel drug design

Introduction: In multi-objective drug design, optimization gains importance, being upgraded to a discipline that attracts its own research. Current strategies are broadly classified into single - objective optimization (SOO) and multi-objective optimization (MOO).Areas covered: Starting with SOO and the ways used to incorporate multiple criteria into it, the present review focuses on MOO techniques, their comparison, advantages, and restrictions. Pareto analysis and the concept of dominance stand in the core of MOO. The Pareto front, Pareto ranking, and limitations of Pareto-based methods, due to high dimensions and data uncertainty, are outlined. Desirability functions and the weighted sum approaches are described as stand-alone techniques to transform the MOO problem to SOO or in combination with pareto analysis and evolutionary algorithms. Representative applications in different drug research areas are also discussed.Expert opinion: Despite their limitations, the use of combined MOO techniques, as well as being complementary to SOO or in conjunction with artificial intelligence, contributes dramatically to efficient drug design, assisting decisions and increasing success probabilities. For multi-target drug design, optimization is supported by network approaches, while applicability of MOO to other fields like drug technology or biological complexity opens new perspectives in the interrelated fields of medicinal chemistry and molecular biology.

Experimental evidence for constraints in amplitude-timescale co-variation of a biomolecular pulse generating circuit design

Understanding constraints on the functional properties of biomolecular circuit dynamics, such as the possible variations of amplitude and timescale of a pulse, is an important part of biomolecular circuit design. While the amplitude-timescale co-variations of the pulse in an incoherent feedforward loop have been investigated computationally using mathematical models, experimental support for any such constraints is relatively unclear. Here, the authors address this using experimental measurement of an existing pulse generating incoherent feedforward loop circuit realisation in the context of a standard mathematical model. They characterise the trends of co-variation in the pulse amplitude and rise time computationally by randomly exploring the parameter space. They experimentally measured the co-variation by varying inducers and found that larger amplitude pulses have a slower rise time. They discuss the gap between the experimental measurements and predictions of the standard model, highlighting model additions and other biological factors that might bridge the gap.

Extended Metabolic Biosensor Design for Dynamic Pathway Regulation of Cell Factories

Transcription factor-based biosensors naturally occur in metabolic pathways to maintain cell growth and to provide a robust response to environmental fluctuations. Extended metabolic biosensors, i.e., the cascading of a bio-conversion pathway and a transcription factor (TF) responsive to the downstream effector metabolite, provide sensing capabilities beyond natural effectors for implementing context-aware synthetic genetic circuits and bio-observers. However, the engineering of such multi-step circuits is challenged by stability and robustness issues. In order to streamline the design of TF-based biosensors in metabolic pathways, here we investigate the response of a genetic circuit combining a TF-based extended metabolic biosensor with an antithetic integral circuit, a feedback controller that achieves robustness against environmental fluctuations. The dynamic response of an extended biosensor-based regulated flavonoid pathway is analyzed in order to address the issues of biosensor tuning of the regulated pathway under industrial biomanufacturing operating constraints.

A robust multi-objective optimization framework to capture both cellular and intercellular properties in cardiac cellular model tuning: Analyzing different regions of membrane resistance profile in parameter fitting

Mathematical models of cardiac cells have been established to broaden understanding of cardiac function. In the process of developing electrophysiological models for cardiac myocytes, precise parameter tuning is a crucial step. The membrane resistance (Rm) is an essential feature obtained from cardiac myocytes. This feature reflects intercellular coupling and affects important phenomena, such as conduction velocity, and early after-depolarizations, but it is often overlooked during the phase of parameter fitting. Thus, the traditional parameter fitting that only includes action potential (AP) waveform may yield incorrect values for Rm. In this paper, a novel multi-objective parameter fitting formulation is proposed and tested that includes different regions of the Rm profile as additional objective functions for optimization. As Rm depends on the transmembrane voltage (Vm) and exhibits singularities for some specific values of Vm, analyses are conducted to carefully select the regions of interest for the proper characterization of Rm. Non-dominated sorting genetic algorithm II is utilized to solve the proposed multi-objective optimization problem. To verify the efficacy of the proposed problem formulation, case studies and comparisons are carried out using multiple models of human cardiac ventricular cells. Results demonstrate Rm is correctly reproduced by the tuned cell models after considering the curve of Rm obtained from the late phase of repolarization and Rm value calculated in the rest phase as additional objectives. However, relative deterioration of the AP fit is observed, demonstrating trade-off among the objectives. This framework can be useful for a wide range of applications, including the parameters fitting phase of the cardiac cell model development and investigation of normal and pathological scenarios in which reproducing both cellular and intercellular properties are of great importance.

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

Standardization and characterization of biological parts is necessary for the further development of bottom-up synthetic biology. Herein, an easy-to-use methodology that embodies both a calibration procedure and a multiobjective optimization approach is proposed to characterize biological parts. The calibration procedure generates values for specific fluorescence per cell expressed as standard units of molecules of equivalent fluorescein per particle. The use of absolute standard units enhances the characterization of model parameters for biological parts by bringing measurements and estimations results from different sources into a common domain, so they can be integrated and compared faithfully. The multiobjective optimization procedure exploits these concepts by estimating the values of the model parameters, which represent biological parts of interest, while considering a varied range of experimental and circuit contexts. Thus, multiobjective optimization provides a robust characterization of them. The proposed calibration and characterization methodology can be used as a guide for good practices in dry and wet laboratories; thus allowing not only portability between models, but is also useful for generating libraries of tested and well-characterized biological parts.

Multi-Objective Optimisation-Based Tuning of Two Second-Order Sliding-Mode Controller Variants for DFIGs Connected to Non-Ideal Grid Voltage

In this paper, a posteriori multi-objective optimisation (MOO) is applied to tune the parameters of a second-order sliding-mode control (2-SMC) scheme commanding the grid-side converter (GSC) of a doubly-fed induction generator (DFIG) subject to unbalanced and harmonically distorted grid voltage. Two variants (i.e., design concepts) of the same 2-SMC algorithm are assessed, which only differ in the format of their switching functions and which contain six and four parameters to be adjusted, respectively. A single set of parameters which stays valid for nine different operating regimes of the DFIG is also sought. As two objectives, related to control performances of grid active and reactive powers, are established for each operating regime, the optimisation process considers 18 objectives simultaneously. A six-parameter set derived in a previous work without applying MOO is taken as reference solution. MOO results reveal that both the six- and four-parameter versions can be tuned to overcome said reference solution in each and every objective, as well as showing that performances comparable to those of the six-parameter variant can be achieved by adopting the four-parameter one. Overall, the experimental results confirm the latter and prove that the performance of the reference parameter set can be significantly improved by using either of the six- or four-parameter versions.

System-level analysis of metabolic trade-offs during anaerobic photoheterotrophic growth in Rhodopseudomonas palustris

BACKGROUND

Living organisms need to allocate their limited resources in a manner that optimizes their overall fitness by simultaneously achieving several different biological objectives. Examination of these biological trade-offs can provide invaluable information regarding the biophysical and biochemical bases behind observed cellular phenotypes. A quantitative knowledge of a cell system's critical objectives is also needed for engineering of cellular metabolism, where there is interest in mitigating the fitness costs that may result from human manipulation.

RESULTS

To study metabolism in photoheterotrophs, we developed and validated a genome-scale model of metabolism in Rhodopseudomonas palustris, a metabolically versatile gram-negative purple non-sulfur bacterium capable of growing phototrophically on various carbon sources, including inorganic carbon and aromatic compounds. To quantitatively assess trade-offs among a set of important biological objectives during different metabolic growth modes, we used our new model to conduct an 8-dimensional multi-objective flux analysis of metabolism in R. palustris. Our results revealed that phototrophic metabolism in R. palustris is light-limited under anaerobic conditions, regardless of the available carbon source. Under photoheterotrophic conditions, R. palustris prioritizes the optimization of carbon efficiency, followed by ATP production and biomass production rate, in a Pareto-optimal manner. To achieve maximum carbon fixation, cells appear to divert limited energy resources away from growth and toward CO2 fixation, even in the presence of excess reduced carbon. We also found that to achieve the theoretical maximum rate of biomass production, anaerobic metabolism requires import of additional compounds (such as protons) to serve as electron acceptors. Finally, we found that production of hydrogen gas, of potential interest as a candidate biofuel, lowers the cellular growth rates under all circumstances.

CONCLUSIONS

Photoheterotrophic metabolism of R. palustris is primarily regulated by the amount of light it can absorb and not the availability of carbon. However, despite carbon's secondary role as a regulating factor, R. palustris' metabolism strives for maximum carbon efficiency, even when this increased efficiency leads to slightly lower growth rates.

Designing synthetic networks in silico: a generalised evolutionary algorithm approach

Background

Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes).

Results

The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction.

Conclusions

In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0499-9) contains supplementary material, which is available to authorized users.

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.

Multi-objective optimization of process conditions in the manufacturing of banana (Musa paradisiaca L.) starch/natural rubber films

Multi-objective optimization was used to evaluate the effect of adding banana (Musa paradisiaca L.) starch and natural rubber (cis-1,4-poliisopreno) at different ratios (1-13w/w) to the manufacturing process of biodegradable films, specifically the effect on the biodegradability, crystallinity and moisture of the films. A structural characterization of the films was performed by X-ray diffraction, Fourier transform infrared spectroscopy and SEM, moisture and biodegradability properties were studied. The models obtained showed that degradability vs. moisture tend to be inversely proportional and crystallinity vs. degradability tend to be directly proportional. With respect to crystallinity vs. moisture behavior, it is observed that crystallinity remains constant when moisture values remain between 27 and 41%. Beyond this value there is an exponential increase in crystallinity. These results allow for predictions on the mechanical behavior that can occur in starch/rubber films.