Which Metabolic Pathways Generate and Characterize the Flux Space? A Comparison among Elementary Modes, Extreme Pathways and Minimal Generators

Important efforts are being done to systematically identify the relevant pathways in a metabolic network. Unsurprisingly, there is not a unique set of network-based pathways to be tagged as relevant, and at least four related concepts have been proposed: extreme currents, elementary modes, extreme pathways, and minimal generators. Basically, there are two properties that these sets of pathways can hold: they can generate the flux space—if every feasible flux distribution can be represented as a nonnegative combination of flux through them—or they can comprise all the nondecomposable pathways in the network. The four concepts fulfill the first property, but only the elementary modes fulfill the second one. This subtle difference has been a source of errors and misunderstandings. This paper attempts to clarify the intricate relationship between the network-based pathways performing a comparison among them

Contractivity of a genetic circuit with internal feedback and cell-to-cell communication

[EN] We consider a realistic model of the synthetic gene circuit combining cell-to-cell communication system via quorum sensing, and a synthetic repressible promoter implementing intracellular negative feedback control. The circuit has been shown to increase robustness with respect to both extrinsic and intrinsic noise elsewhere. As a first step towards an analytic analysis, in this paper we use contraction theory to perform a stability analysis. From it, we infer the components of the circuit most affecting the rate of contractivity, using biologically sensible values of the circuit parameters.This research was partially funded by grant FEDER-CICYT DPI2014-55276-C5-1-R. Yadira Boada thanks grant FPI/2013-3242 of the Universitat Politècnica de València.Picó-Marco, E.; Boada-Acosta, YF.; Picó, J.; Vignoni, A. (2016). Contractivity of a genetic circuit with internal feedback and cell-to-cell communication. IFAC-PapersOnLine. 49(26):213-218. https://doi.org/10.1016/j.ifacol.2016.12.128S213218492

Sliding Mode Reference Coordination of Constrained Feedback Systems

[EN] This paper addresses the problem of coordinating dynamical systems with possibly different dynamics (e.g., linear and nonlinear, different orders, constraints, etc.) to achieve some desired collective behavior under the constraints and capabilities of each system. To this end, we develop a new methodology based on reference conditioning techniques using geometric set invariance and sliding mode control: the sliding mode reference coordination (SMRCoord). The main idea is to coordinate the systems references. Starting from a general framework, we propose two approaches: a local one through direct interactions between the different systems by sharing and conditioning their own references and a global centralized one, where a central node makes decisions using information coming from the systems references. In particular, in this work we focus in implementation on multivariable systems like unmanned aerial vehicles (UAVs) and robustness to external perturbations. To show the applicability of the approach, the problem of coordinating UAVs with input constraints is addressed as a particular case of multivariable reference coordination with both global and local configuration.Research in this area is partially supported by Argentine government (ANPCyT PICT 2011-0888 and CONICET PIP 112-2011-00361), Spanish government (FEDER-CICYT DPI2011-28112-C04-01), and Universitat Politecnica de Valencia (Grant FPI/2009-21)Vignoni, A.; Garelli, F.; Picó, J. (2013). Sliding Mode Reference Coordination of Constrained Feedback Systems. Mathematical Problems in Engineering. 2013:1-11. https://doi.org/10.1155/2013/764348S1112013Information consensus in multivehicle cooperative control. (2007). IEEE Control Systems, 27(2), 71-82. doi:10.1109/mcs.2007.338264Cao, Y., Yu, W., Ren, W., & Chen, G. (2013). An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination. IEEE Transactions on Industrial Informatics, 9(1), 427-438. doi:10.1109/tii.2012.2219061Interconnected dynamic systems: An overview on distributed control. (2013). IEEE Control Systems, 33(1), 76-88. doi:10.1109/mcs.2012.2225929Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of the IEEE, 95(1), 215-233. doi:10.1109/jproc.2006.887293He, W., & Cao, J. (2011). Consensus control for high-order multi-agent systems. IET Control Theory & Applications, 5(1), 231. doi:10.1049/iet-cta.2009.0191Liu, L. (2012). Robust cooperative output regulation problem for non-linear multi-agent systems. IET Control Theory & Applications, 6(13), 2142-2148. doi:10.1049/iet-cta.2011.0575Pitarch, J. L., Sala, A., & Arino, C. V. (2014). Closed-Form Estimates of the Domain of Attraction for Nonlinear Systems via Fuzzy-Polynomial Models. IEEE Transactions on Cybernetics, 44(4), 526-538. doi:10.1109/tcyb.2013.2258910Nuñez, S., De Battista, H., Garelli, F., Vignoni, A., & Picó, J. (2013). Second-order sliding mode observer for multiple kinetic rates estimation in bioprocesses. Control Engineering Practice, 21(9), 1259-1265. doi:10.1016/j.conengprac.2013.03.003Wu, L., Su, X., & Shi, P. (2012). Sliding mode control with bounded gain performance of Markovian jump singular time-delay systems. Automatica, 48(8), 1929-1933. doi:10.1016/j.automatica.2012.05.064Cao, Y., Ren, W., & Meng, Z. (2010). Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. Systems & Control Letters, 59(9), 522-529. doi:10.1016/j.sysconle.2010.06.002Cortés, J. (2006). Finite-time convergent gradient flows with applications to network consensus. Automatica, 42(11), 1993-2000. doi:10.1016/j.automatica.2006.06.015Rao, S., & Ghose, D. (2011). Sliding mode control-based algorithms for consensus in connected swarms. International Journal of Control, 84(9), 1477-1490. doi:10.1080/00207179.2011.602834Guo, P., Zhang, J., Lyu, M., & Bo, Y. (2013). Sliding Mode Control for Multiagent System with Time-Delay and Uncertainties: An LMI Approach. Mathematical Problems in Engineering, 2013, 1-12. doi:10.1155/2013/805492Garelli, F., Mantz, R. J., & De Battista, H. (2006). Limiting interactions in decentralized control of MIMO systems. Journal of Process Control, 16(5), 473-483. doi:10.1016/j.jprocont.2005.09.001Garelli, F., Mantz, R. J., & De Battista, H. (2007). Sliding mode compensation to preserve dynamic decoupling of stable systems. Chemical Engineering Science, 62(17), 4705-4716. doi:10.1016/j.ces.2007.05.020Picó, J., Garelli, F., De Battista, H., & Mantz, R. J. (2009). Geometric invariance and reference conditioning ideas for control of overflow metabolism. Journal of Process Control, 19(10), 1617-1626. doi:10.1016/j.jprocont.2009.08.007Revert, A., Garelli, F., Pico, J., De Battista, H., Rossetti, P., Vehi, J., & Bondia, J. (2013). Safety Auxiliary Feedback Element for the Artificial Pancreas in Type 1 Diabetes. IEEE Transactions on Biomedical Engineering, 60(8), 2113-2122. doi:10.1109/tbme.2013.2247602Gracia, L., Sala, A., & Garelli, F. (2012). A supervisory loop approach to fulfill workspace constraints in redundant robots. Robotics and Autonomous Systems, 60(1), 1-15. doi:10.1016/j.robot.2011.07.008Gracia, L., Garelli, F., & Sala, A. (2013). Integrated sliding-mode algorithms in robot tracking applications. Robotics and Computer-Integrated Manufacturing, 29(1), 53-62. doi:10.1016/j.rcim.2012.07.007Vignoni, A., Garelli, F., & Picó, J. (2013). Coordinación de sistemas con diferentes dinámicas utilizando conceptos de invarianza geométrica y modos deslizantes. Revista Iberoamericana de Automática e Informática Industrial RIAI, 10(4), 390-401. doi:10.1016/j.riai.2013.09.001Hanus, R., Kinnaert, M., & Henrotte, J.-L. (1987). Conditioning technique, a general anti-windup and bumpless transfer method. Automatica, 23(6), 729-739. doi:10.1016/0005-1098(87)90029-xMareczek, J., Buss, M., & Spong, M. W. (2002). Invariance control for a class of cascade nonlinear systems. IEEE Transactions on Automatic Control, 47(4), 636-640. doi:10.1109/9.995041Blasco, X., García-Nieto, S., & Reynoso-Meza, G. (2012). Control autónomo del seguimiento de trayectorias de un vehículo cuatrirrotor. Simulación y evaluación de propuestas. Revista Iberoamericana de Automática e Informática Industrial RIAI, 9(2), 194-199. doi:10.1016/j.riai.2012.01.00

A possibilistic framework for constraint-based metabolic flux analysis

<p>Abstract</p> <p>Background</p> <p>Constraint-based models allow the calculation of the metabolic flux states that can be exhibited by cells, standing out as a powerful analytical tool, but they do not determine which of these are likely to be existing under given circumstances. Typical methods to perform these predictions are (a) flux balance analysis, which is based on the assumption that cell behaviour is optimal, and (b) metabolic flux analysis, which combines the model with experimental measurements.</p> <p>Results</p> <p>Herein we discuss a possibilistic framework to perform metabolic flux estimations using a constraint-based model and a set of measurements. The methodology is able to handle inconsistencies, by considering sensors errors and model imprecision, to provide rich and reliable flux estimations. The methodology can be cast as linear programming problems, able to handle thousands of variables with efficiency, so it is suitable to deal with large-scale networks. Moreover, the possibilistic estimation does not attempt necessarily to predict the actual fluxes with precision, but rather to exploit the available data – even if those are scarce – to distinguish possible from impossible flux states in a gradual way.</p> <p>Conclusion</p> <p>We introduce a possibilistic framework for the estimation of metabolic fluxes, which is shown to be flexible, reliable, usable in scenarios lacking data and computationally efficient.</p

Validation of a constraint-based model of Pichia pastoris metabolism under data scarcity

<p>Abstract</p> <p>Background</p> <p>Constraint-based models enable structured cellular representations in which intracellular kinetics are circumvented. These models, combined with experimental data, are useful analytical tools to estimate the state exhibited (the phenotype) by the cells at given pseudo-steady conditions.</p> <p>Results</p> <p>In this contribution, a simplified constraint-based stoichiometric model of the metabolism of the yeast <it>Pichia pastoris</it>, a workhorse for heterologous protein expression, is validated against several experimental available datasets. Firstly, maximum theoretical growth yields are calculated and compared to the experimental ones. Secondly, possibility theory is applied to quantify the consistency between model and measurements. Finally, the biomass growth rate is excluded from the datasets and its prediction used to exemplify the capability of the model to calculate non-measured fluxes.</p> <p>Conclusions</p> <p>This contribution shows how a small-sized network can be assessed following a rational, quantitative procedure even when measurements are scarce and imprecise. This approach is particularly useful in lacking data scenarios.</p

Reduction of population variability in protein expression: A control engineering approach

[Abstract] Controlling protein expression level is of interest in many applications. Yet, the stochastic nature of gene expression plays an important role and cannot be disregarded. We propose a gene synthetic circuit designed to control the mean gene expression in a population of cells and its variance. The circuit combines an intracellular negative feedback loop and quorum sensing based cell-to-cell communication system. Our in silico analysis using stochastic simulations reveals significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback, and explain their different roles for different noise sources. Preliminary in vivo results agree well with the computational results.Comisión Interministerial de Ciencia y Tecnología; DPI2014-55276-C5-

Sliding mode reference coordination of constrained feedback systems

This paper addresses the problem of coordinating dynamical systems with possibly different dynamics (e.g., linear and nonlinear, different orders, constraints, etc.) to achieve some desired collective behavior under the constraints and capabilities of each system. To this end, we develop a new methodology based on reference conditioning techniques using geometric set invariance and sliding mode control: the sliding mode reference coordination (SMRCoord). The main idea is to coordinate the systems references. Starting from a general framework, we propose two approaches: a local one through direct interactions between the different systems by sharing and conditioning their own references and a global centralized one, where a central node makes decisions using information coming from the systems references. In particular, in this work we focus in implementation on multivariable systems like unmanned aerial vehicles (UAVs) and robustness to external perturbations. To show the applicability of the approach, the problem of coordinating UAVs with input constraints is addressed as a particular case of multivariable reference coordination with both global and local configuration.Facultad de Ingenierí

Output Feedback Linearization of Turbidostats After Time Scaling

"© 2019 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works."[EN] Turbidostats are a class of bioreactors gaining interest due to the recent availability of microscale and small-scale devices for characterization and scalingup of the biotechnological systems relevant in the biotech and pharma industries. The goal is to keep cell density constant in continuous operation. Thus, the control law, i.e., the substrate feeding strategy, must guarantee global or semiglobal convergence to an equilibrium point. However, their control is difficult due to the uncertain, time varying, and nonlinear nature of the processes involved. In this brief, we propose an adaptive control law that globally stabilizes the desired biomass setpoint. Furthermore, in a certain region of the state space, the controller linearizes the dynamic behavior after some time scaling. By this way, the orbits of the closedloop system are imposed by the designer. The intrinsic integral action of the gain adaptation rejects the parameter uncertainties. Moreover, the controller implementation only assumes the biomass concentration to be measured. Both the simulated and experimental results show the performance of the controller.This work was supported in part by the National University of La Plata under Grant 11-I127, in part by ANPCyT under Grant PICT2014 2394, in part by CONICET under Grant PIP112 2015 0837, and in part by MINECO/AEI/FEDER, UE under Grant DPI2014-55276-C5-1-R and Grant DPI2017-82896-C2-1-R. The work of F. N. Santos-Navarro was supported by ai2-UPV.De Battista, H.; Picó-Marco, E.; Santos-Navarro, FN.; Picó, J. (2019). Output Feedback Linearization of Turbidostats After Time Scaling. IEEE Transactions on Control Systems Technology. 27(4):1668-1676. https://doi.org/10.1109/TCST.2018.2834882S1668167627

Multiobjective Identification of a Feedback Synthetic Gene Circuit

© 2020 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Kinetic (i.e., dynamic) semimechanistic models based on the first principles are particularly important in systems and synthetic biology since they can explain and predict the functional behavior that emerges from the time-varying concentrations in cellular components. However, gene circuit models are nonlinear higher order ones and have a large number of parameters. In addition, experimental measurements are often scarce, and enough signal excitability for identification cannot always be achieved. These characteristics render the identification problem ill-posed, so most gene circuit models present incomplete parameter identifiability. Thus, parameter identification of typical biological models still appears as an open problem, where ensemble modeling approaches and multiobjective optimization arise as natural options. We address the problem of identifying the stochastic model of a closed-loop synthetic genetic circuit designed to minimize the gene expression noise. The model results from the feedback interaction between two subsystems. Besides incomplete parameter identifiability, the closed-loop dynamics cannot be directly identified due to the lack of enough input signal excitability. We apply a two-stage approach. First, the open-loop averaged time-course experimental data are used to identify a reduced-order stochastic model of the system direct chain. Then, closed-loop steady-state stochastic distributions are used to identify the remaining parameters in the feedback configuration. In both cases, multiobjective optimization is used to address the parameter identifiability, providing sets of parameters valid for different state-space regions. The methodology gives good identification results, provides clear guidelines on the effect of the parameters under different scenarios, and it is particularly useful for easily combining time-course population averaged and steady-state single-cell distribution experimental data.This work was supported by the European Union and Spanish Government, MINECO/AEI/FEDER under Grant DPI2017-82896-C2-1-R. The work of Y. Boada was supported by the Universitat Politecnica de Valencia under Grant FPI/2013-3242.Boada-Acosta, YF.; Vignoni, A.; Picó, J. (2020). Multiobjective Identification of a Feedback Synthetic Gene Circuit. IEEE Transactions on Control Systems Technology. 28(1):208-223. https://doi.org/10.1109/TCST.2018.2885694S20822328

Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise

[EN] Stochastic fluctuations in gene expression trigger both beneficial and harmful consequences for cell behavior. Therefore, achieving a desired mean protein expression level while minimizing noise is of interest in many applications, including robust protein production systems in industrial biotechnology. Here, we consider a synthetic gene circuit combining intracellular negative feed- back and cell-to-cell communication based on quorum sensing. Accounting for both intrinsic and extrinsic noise, stochastic simulations allow us to analyze the capability of the circuit to reduce noise strength as a function of its parameters. We obtain mean expression levels and noise strengths for all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in Escherichia coli. Our in silico experiments, validated by preliminary in vivo results, reveal significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback and highlight the differential role that they play in regard to intrinsic and extrinsic noise.his work was partially supported by the Spanish Government(CICYT DPI2014-55276-C5-1) and the European Union(FEDER). Y.B. thanks grant FPI/2013-3242 of UPV.Boada-Acosta, YF.; Vignoni, A.; Picó, J. (2017). Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise. ACS Synthetic Biology. 6(10):1903-1912. https://doi.org/10.1021/acssynbio.7b00087S1903191261