In this work, we present parameter estimation problem for Dynamic Flux Balance Analysis to study the production of ethanol by a mutant strain of the cyanobacterium Synechocystis sp. PCC 6803, as well as experimental data. This modified strain harbors the genes pdc and adhII from Zymomonas mobilis. The model includes two major components: (1) a dynamic model with mass balances for biomass, ethanol, nitrate, phosphate, internal nitrogen and phosphorus, and (2) a steady state genome-scale metabolic LP model. The biomass equation includes limiting functions for temperature and kinetics of growth inhibition by ethanol toxicity. Limitation of light by biomass accumulation is also taken into account. We formulate a dynamic parameter estimation problem with a weighted least-squares objective function, subject to dynamic mass balance equations at the bioreactor level and the intracellular LP model. The problem is solved in GAMS through a simultaneous optimization approach. Data set for parameter estimation were obtained in experiments performed over 73 h in batch liquid cultures. Numerical results provide useful insights on ethanol production by the genetic modified strain within the context of genomic-scale cyanobacterial metabolism.Fil: Laiglecia, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Planta Piloto de Ingeniería Química (i); Argentina. Universidad Nacional del Sur; ArgentinaFil: Estrada, Vanina Gisela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Planta Piloto de Ingeniería Química (i); Argentina. Universidad Nacional del Sur; ArgentinaFil: Vidal Vidal, Rebeca. Universidad de Sevilla. Consejo Superior de Investigaciones Cientificas; EspañaFil: Florencio, Francisco J.. Universidad de Sevilla. Consejo Superior de Investigaciones Cientificas; EspañaFil: Guerrero, Miguel G.. Universidad de Sevilla. Consejo Superior de Investigaciones Cientificas; EspañaFil: Diaz, Maria Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Planta Piloto de Ingeniería Química (i); Argentina. Universidad Nacional del Sur; Argentin

Diaz, Maria Soledad

Estrada, Vanina Gisela

Florencio, Francisco J.

Guerrero, Miguel G.

Laiglecia, Juan Ignacio

Vidal Vidal, Rebeca

English

LAReferencia - Red Federada de Repositorios Institucionales de Publicaciones Científicas Latinoamericanas

 CHEMICAL ENGINEERING TRANSACTIONS   VOL. 32, 2013 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Chief Editors: Sauro Pierucci, Jiří J. Klemeš Copyright © 2013, AIDIC Servizi S.r.l., ISBN 978-88-95608-23-5; ISSN 1974-9791                                                                                      Dynamic Flux Balance Analysis of a Genetic Engineered Cyanobacterium for Ethanol Production. Parameter Estimation Juan Laigleciaa, Vanina Estradaa, Rebeca Vidal Vidalb, Francisco J. Florenciob, Miguel G. Guerrerob , M. Soledad Diaz*,a a Planta Piloto de Ingeniería Química (PLAPIQUI), Universidad Nacional del Sur-CONICET, Camino La Carrindanga Km 7, Bahía Blanca 8000, Argentina b Instituto de Bioquímica Vegetal y Fotosíntesis, CSIC-Universidad de Sevilla, Av. Américo Vespucio 49, Sevilla E-41092, Spain sdiaz@plapiqui.edu.ar Chapter 1 In this work, we present a parameter estimation problem for Dynamic Flux Balance Analysis to study the production of ethanol by a mutant strain of the cyanobacterium Synechocystis sp. PCC 6803, as well as experimental data. This modified strain harbors the genes pdc and adhB from Zymomonas mobilis. The model includes two major components: (1) a dynamic model with mass balances for biomass, ethanol, nitrate, phosphate, internal nitrogen and phosphorus, and (2) a steady state genome-scale metabolic Linear Problem (LP) model. The biomass equation includes limiting functions for temperature and kinetics of growth inhibition by ethanol toxicity. Limitation of light by biomass accumulation is also taken into account. We formulate the dynamic parameter estimation problem with a weighted least-squares objective function, subject to dynamic mass balance equations at the bioreactor level and the intracellular LP model. The problem is solved in GAMS through a simultaneous optimization approach. The data sets for parameter estimation were obtained in experiments performed over 73 hours in batch liquid cultures. Numerical results provide useful insights on the ethanol production by the genetically modified strain within the context of genomic-scale cyanobacterial metabolism. 1. Introduction Cyanobacteria or blue-green algae constitute an ancient and diverse group (150 genera with about 2000 species) of autotrophic prokaryotes that played a crucial role in the atmosphere change from oxidative to reductive during the Precambrian period (Komarek, 2003). These microorganisms have developed adaptive mechanisms that allowed them to survive within a wide range of habitats, including freshwater, marine and terrestrial environments. They have a wide variety of morphologies, metabolism and cell structures and are very important in the nitrogen cycle in marine environments and in the dynamics of nitrogen and CO2 in the biosphere (Zehr et al., 2001). Cyanobacteria have been studied for a long time, they are considered as models of biological processes such as oxygenic photosynthesis which is the same process performed by higher plants. In the last decades they have attracted attention due to their potential to obtain commercially interesting products, such as biofuels and pharmaceuticals. Advances in metabolic engineering and synthetic biology based on gene sequence, biochemical and physiological data in public databases together with the constant improvement of mathematical tools can help speed the development of desirable phenotypes for production of several interesting bio-products (Picataggio, 2009). In this work we formulate a parameter estimation problem for Dynamic Flux Balance Analysis approach to study the production of ethanol by a mutant strain of the cyanobacterium Synechocystis sp. PCC 6803. We formulate a dynamic parameter estimation problem with a weighted least-squares objective function subject to dynamic mass balance equations at the bioreactor level and an intracellular LP model. The problem is solved in GAMS through a simultaneous dynamic optimization approach.  9552. System  Chapter 2 The system under study in this paper is the photosynthetic ethanol production by a mutant strain of Synechocystis sp. PCC 6803 obtained by Vidal Vidal (2009) in batch liquid culture. This modified strain harbors the genes pdc and adhB encoding for the enzyme pyruvate descarboxylase (EC 1.2.4.1), which catalyzes the non-oxidative decarboxylation of pyruvate to acetaldehyde and CO2 and the alcohol deshydrogenase II (EC 1.1.1.1), which participates in the reduction of acetaldehyde to ethanol. Both heterologous genes from Zymomonas mobilis are cloned under the control of the promoter of the endogenous gene petE in the Synechocystis mutant.  1. Methods 1.1 Dynamic Flux Balance Analysis Flux Balance Analysis (FBA) is a genome-scale constraint- based modelling approach for metabolic networks (Höffner et al. 2012) where the constraints are the steady state mass balances corresponding to metabolic fluxes (reactions) around each node (metabolite). The steady state assumption is justified by high reaction rates within the microorganism. In this way, the mass balances are described by a set of lineal equations,  (1) where A is the m (metabolites) x n reactions) stoichiometric matrix and  are the vector of flux (metabolic reactions of the network). To solve the intracellular fluxes and the uptake and secretion rates of the cell, a linear programming problem (LP) is formulated where the objective function is the maximization of the growth rate (Varma and Palsson, 1994). Solving the LP problem we obtain the metabolic flux distribution of the cell (Paulo et al., 2011). In order to describe the dynamics of the substrates, products and biomass concentrations and metabolic fluxes inside the cell we have extended FBA to a Dynamic Flux Balance Analysis approach, which allows modeling the interaction between the cellular metabolism and the environment (Höffner et al., 2012). Therefore, an LP problem is embedded within a dynamic model that takes into account mass balances for main substrates, products and biomass at the bioreactor level, allowing the inclusion of kinetic expression. 3.1.1 Dynamic mass balances  We formulate mass balances for external metabolites and biomass to model the environmental changes during Synechocystis growth by substrate consumption and biomass and product accumulation. We also include mass balances for internal phosphorus and nitrogen to model the storage of the main nutrients.  The resulting Differential Algebraic Equation (DAE) problem is as follows:   XkXdtdXd−= μ  (2) AXvdtdPO4PO4 −=  (3) XYdtdNOxn3 μ−=  (4) AXvdtdEE=  (5) PIPPPIPKPOPOUPdtdPIminmaxmaxP44max μ−−−+=  (6) NINNNINKNONOUNdtdNIminmaxmaxN33max μ−−−+=  (7) 956( ) ( )EfTfv*growth=μ  (8) ( )KIE11Ef+= (9) ( ) −=optopt TT1expTTTf (10)  Where, X, PO4, NO3, E, PI and NI represent biomass, phosphate, ethanol, nitrate, internal phosphate and internal nitrate, respectively. The net growth rate (μ)  is calculated affecting the maximum growth rate (*growthv ) by limiting functions for ethanol concentration and temperature. Table 1 shows description and values of the model parameters.  3.1.2 LP problem The internal metabolism is represented by the following optimization problem:  *growthb,vv  max  s.t.   (11) 0Av =  (12) 4POAPFUL v,v v  ,vvv ≠∀≤≤  (13) The intracellular and extracellular models are linked by growth rate, absorbed photon flux ( APFv ) and phosphorus uptake rate (4POv ). The model includes a limiting function for the light uptake that takes into account the decrease of light availability by biomass accumulation in the reactor. The phosphate uptake incorporates a kinetic expression depending on both external and internal phosphorus concentration. Bounds over these fluxes represent additional constraints for the inner problem.   ( )Ifvv *APFAPF ≤  (14) ( )Nfvv *POPO 44 ≤  (15) ( )minmaxminPPPPINf−−=  (16) ( ) −=optooptoII1expIIIf  (17) ( )( )pXKpXKexp1Iextexto−=  (18) 1.2 Experimental data Synechocystis sp. PCC 6803 was cultivated in BG-11 medium at 30 °C under continuous light (100 μE m-2 s-1) and air bubbling enriched with 1% CO2, which is considered as a CO2 rich medium. Liquid batch cultures were performed by duplicate for wild type and ethanol mutant strains for 73 h from the beginning of the exponential growth phase of growth. Biomass was estimated by OD730, Chlorophyll a concentration and total organic carbon. Nitrate and phosphate in the medium were measured by spectrophotometric methods and ethanol by an enzymatic method described by Kaplan and Ciotti (1957). 1.3 Parameter estimation problem Chapter 3 The parameter estimation problem for Synechocystis sp. PCC 6803 has the following general formulation:  957( ) ( )( ) ( )( )llN1iTll xtxWxtxpminp−−= =ϕ  (19) Chapter 4 Subject to DAE system Eqs. (2)-(10), which represent extracellular environment and the LP Eqs. (11)-(18) representing Synechocystis sp. PCC 6803 metabolism. UL ppp ≤≤  (20) ( ) ( ) ( ) ( ) mM868.6ON ,mM056.0OP ,mM046.0E ,l/g078.0X 030400 ====  (21) Chapter 5 Where lx  are DN  sets of experimental measurements obtained at time lt , and ( ) ( )[ ]TlTl tztx =  are the corresponding calculated differential variables for measured components. W is the weighting matrix for the least squares function (Eq. (19)). In this typical parameter estimation problem were defined data sets in each period, the state variables remains continuous over all periods, and parameters (p) are the same in all periods (Bard, 1974). pL and pU are the lower and upper bounds over the estimated parameter while X(0), E(0), PO4(0) and NO3(0) stand for initial conditions for the biomass, ethanol, phosphate and nitrate concentrations respectively. Chapter 6 In order to embed the outer optimization problem and the inner one, it is well known that the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary, to represent the intracellular model in this work, and transform the original bilevel problem into a single level one. The dynamic parameter estimation problem corresponding to component mass balance equations and path constraints is transformed into a NLP through orthogonal collocation (Biegler et al., 2006) the problem and is solved in (General Algebraic Modelling System, Brooke et al., 2011) with the CONOPT solver.  1. Results and Discussion We present the numerical results from solving the parameter estimation problem with a dynamic simultaneous approach for a batch ethanol production system for Synechocystis sp. PCC 6803 mutant.  The batch time was 73 h. The time horizon was discretized with 73 finite elements and 2 collocation points, resulting a NLP of 88,337 equations and 58,063 variables. Table 1 shows the optimal values for the estimated parameters.  Figures 1-4 show state variables profiles as compared to experimental data. There is good agreement between experimental data for Synechocystis biomass, nitrate and ethanol concentrations and predicted values. During the initial phase, the model accurately reproduces the behaviour of the phosphate concentration. However, from after 30 hours, the model predictions do not exactly agree with experimental data from phosphate dynamics. Pitt et al., (2010) and Burut-Archanai et al., (2011) reported that Synechocystis sp. PCC 6803 has two phosphate transport systems, Pst1 and Pst2. Pst1 is a low-affinity and high-velocity transporter, which predominates in high phosphate concentrations, while Pst2 is characterized by a high-affinity and low-velocity. In this study, we take into account only one phosphate uptake kinetic for high concentrations. Both kinetic will be included in future work through complementarity constraints (Raghunathan et al., 2006).           Table 1:  Parameters values used in model simulation and estimated parameter values. Symbol Description Value Units  kd                     [mortality rate] 0.033 [1/h] Estimated value Kext              [light extintion coefficient] 16.748 [m2/g] Estimated value Ki [constant inhibition constant] 310.135 [mM] Estimated value Ynx [nitrogen biomass yield] 1.228 [mM/g] Estimated value UPmax   [maximum phosphate uptake] 0.244 [mM/h] Fixed UNmax [maximum nitrogen uptake] 0.184 [mM/h] Fixed KP [half saturation constant for phosphate uptake] 4.44 [mM] Fixed KN [half saturation constant for nitrogen uptake] 2.82 [mM] Fixed  [maximum phosphate velocity rate] 0.184 [1/h] Fixed  [maximum light velocity rate] 150 [1/h] Fixed  9580 10 20 30 40 50 60 700.00.30.60.91.21.51.8  Experimental data  Simulation  Biomass concentration (g/l)Time (Hours) Figure 1. Biomass concentration for measured and predicted profiles.  0 10 20 30 40 50 60 700.000.010.020.030.040.050.060.07 PO4 concentration (mM)Time (Hours) Experimental data Simulation Figure 2. Phosphate concentration for measured and predicted profiles.   0 10 20 30 40 50 60 70345678  NO3 concentration (mM)Time (Hours) Experimental data Simulation Figure 3. Nitrate concentration for measured and predicted profiles.  9590 10 20 30 40 50 60 700.00.10.20.30.40.50.60.70.8  Ethanol concentration (mM)Time (Hours) Experimental data Simulation Figure 4. Ethanol production for measured and predicted profiles. 2. Conclusions In this work, we have coupled in a simultaneous framework the interaction between environment and intracellular metabolism of an ethanol producer mutant of Synechocystis sp. PCC 6803. The parameter estimation problem has been formulated within a simultaneous dynamic optimization framework within GAMS 23.0, with CONOPT shows good agreement with experimental data.  References Bard, Y., 1974, Nonlinear parameter estimation, Cambridge, MA: USA.Academic Press. Biegler, L. T., Cervantes, A., Waechter, A., 2002, Advances in simultaneous strategies for dynamic process optimization, Chem. Eng. Science, 57, 575–593. Brooke, A., Kendrick, D., Meeraus, A., Raman, R., 2011, GAMS, A User Guide. Washington, DC, USA. Burut-Archanai, S., Eaton-Rye, J.J., Incharoensakdi, A., 2011, Na+-stimulated phosphate uptake system in Synechocystis sp. PCC 6803 with Pst 1 as a main transporter, BMC Microbiol., 11, 225-232.  Höffner, K., Hatwood, S.M., Barton, P.I., 2012, A reliable simulator for dynamic flux balance analysis, Biotechnol Bioeng., 110, 792-802.  Kaplan, N. O., Ciotti, M. M., 1957, Enzymatic determination of ethanol, Methods in Enzymology, Academic Press., 3, 253-255. Komárek, J., 2003, Coccoid and colonial cyanobacteria, Freshwater Algae of North America, 59-116. Paulo, C., Di Maggio, J., Estrada, V., Diaz, M. S., 2011, Optimizing cyanobacteria metabolic network for     ethanol production, Computer Aided Chemical Engineering, 29, 1366-1370. Picataggio, S., 2009, Potential impact of synthetic biology on the development of microbial systems for the production of renewable fuels and chemicals. Curr. Opin. Biotechn, 20, 325-329. Pitt, F. D., Mazard, S., Humphreys, L., Scanlan, D. J., 2010, Functional characterization of Synechocystis sp. strain  PCC 6803 Pst 1 and Pst2 gene clusters reveals a novel strategy for phosphate uptake in a freshwater Cyanobacterium, J. Bacteriol., 192, 3512-3523. Raghunathan, A. U., Pérez-Correa, J. R., Agosin, E., Biegler, L. T., 2006, Parameter estimation in metabolic flux balance models for batch fermentation- formulation and solution using differential variational inequalities, Ann. Oper. Res., 148, 251-270.   Varma, A., Palsson, B. O., 1994, Metabolic flux balancing- Basic concepts, scientific and practical use, Bio-Technol., 12, 994-998. Vidal Vidal, R., 2009, Photosynthetic production of ethanol by the cyanobacterium Synechocystis sp. PCC 6803. PhD. Thesis, Universidad de Sevilla, Sevilla, Spain. Zehr, J. P., Waterbury, J. B., Turner, P. J., Montoya, J. P., Omoregie, E., Steward, G. F., Hansen, A., Karl, D. M., 2001, Unicellular cyanobacteria fix N2 in the subtropical North Pacific Ocean, Nature, 412, 635-638. 960

Dynamic Flux Balance Analysis of a Genetic Engineered Cyanobacterium for Ethanol Production: Parameter Estimation

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Dynamic Flux Balance Analysis of a Genetic Engineered Cyanobacterium for Ethanol Production: Parameter Estimation

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