(4b) Cybernetic Modeling for Metabolic Engineering and Reactor Optimization

The cybernetic approach offers a unique framework for dynamic modeling of metabolic systems by describing metabolic regulation as optimal response of the organism to changes in its environment by conserving its resources. The cybernetic framework, developed by Ramkrishna and his coworkers, has evolved over the last two decades and continues a remarkable growth. Classical cybernetic approaches which are based on a lumped view of metabolism and thus called lumped cybernetic models (LCMs) have been successful in predicting various uptake patterns of mixed substrates (e.g., Kompala et al., 1986). The current state of cybernetic modeling, presented by Young et al. (2008), has the significantly augmented capacity of dealing with large metabolic networks. Successful application of Young's model to mutant as well as wild-type strains is an example showing a great value of cybernetic models as a promising tool for metabolic engineering. Formulation of such an elegant model would, of course, require extensive measurements for the identification of multitudes of kinetic parameters in the model. Meanwhile, hybrid cybernetic modeling (HCM) has been introduced as an interesting alternative to Young's framework due to its simpler computational structure (Kim, 2005). HCM is able to handle larger networks by invoking the quasi-steady-state approximation for intracellular metabolites under which network is decomposed into a set of subnetworks called elementary modes (EMs). It is viewed in HCM that the total uptake flux is divided into individual fluxes through EMs. Taking into account of the whole set of EMs into HCM is, however, hindered by overparameterization.

This poster presents various innovative developments made by the author to make cybernetic models practically more useful not only for reactor optimization but also for metabolic engineering applications.

1. EM reduction for systematic formulation of HCM (Song and Ramkrishna, 2009; Song et al., 2009): Overparameterization is an intrinsic problem of HCM as it takes dynamic measurements of only extracellular metabolites for parameter identification while the number of EMs (and thus parameters) exponentially increases with the network size. To resolve this problem, we propose ?yield analysis,' a new method of extracting a subset of EMs essential for describing metabolic behaviors. Yield analysis can be defined as the analysis of metabolic pathways in yield space where the solution space is a bounded convex hull. A consistent way of choosing the unique, minimal active EMs among a number of possible candidates is presented. The proposed idea is tested in a case study of a metabolic network of recombinant yeasts fermenting both glucose and xylose.

2. Development of lumped HCM (L-HCM) for prediction of metabolic function from limited data (Song and Ramkrishna, 2010): Motivated by the need for a quick quantitative assessment of metabolic function without extensive data, we present an adaptation of the cybernetic framework, denoted as L-HCM, which combines the attributes of the classical LCM and the recently developed HCM. The basic tenet of L-HCM and HCM is the same, that is, they both view the uptake flux as being split among diverse pathways in an optimal way as a result of cellular regulation such that some chosen metabolic objective is realized. The L-HCM, however, portrays this flux distribution to occur in a hierarchical way, that is, first among lumped pathways, and next among individual EMs in each lumped pathway. The distribution of uptake flux at the first split is dynamically regulated according to environmental conditions, while the subsequent split is based purely on the stoichiometry of EMs. The resulting model is conveniently represented in terms of L-EMs which are fully identified with respect to yield coefficients of all products. These characteristics enable the model to account for the complete set of EMs for arbitrarily large metabolic networks despite containing only a small number of parameters which can be identified using minimal data. In a case study involving aerobic batch growth of Saccharomyces cerevisiae, LHCM is compared with LCM.

3. Prediction of "dynamic" behavior of knockout strains: In silico prediction of cellular response to gene knockouts is a challenging task as mutated strains often exhibit the significant change in uptake rate as well as in (relative) internal flux distribution. While constraint-based approaches including Flux Balance Analysis (FBA), Minimization Of Metabolic Adjustment (MOMA), and Regulatory On/Off Minimization (ROOM) have been applied to the simulation of knockout strains, they have no machinery to address the change of ?uptake rate? and thus their prediction is only about re-routing of intracellular fluxes for a given uptake rate. Consequently, these approaches might be useful with respect to ?yield,? but not reliable with respect to actual ?rate.? We present here a powerful methodology to predict the ?dynamic? behaviors of knockout mutants from limited metabolic data of wild-type strains using the L-HCM recently proposed by Song and Ramkrishna (2010). L-HCM makes a satisfactory prediction on dynamic behaviors of knockout strains as shown in various case studies. This proves the universal validity of the cybernetic regulatory mechanisms which work not only for wild-type strains as having been shown so far in various cases in the literature, but also for mutated strains as shown in this work.

4. Development of an automated software for dynamic metabolic modeling: An automated software for developing various dynamic metabolic models is developed using MATLAB and named as AUMIC which stands for AUtomated tool for Metabolic modeling Integrated with the Cybernetic regulatory mechanisms. While AUMIC is designed mainly for constructing cybernetic models including LCM, HCM, and L-HCM , it can also handle various other approaches to dynamic metabolic modeling such as lumped kinetic model (LKM), macroscopic bioreaction model (MBM) (Provost and Bastin, 2004), and dynamic flux balance analysis (dFBA) (Mahadevan et al., 2002) for comparative studies. LKM, MBM and dFBA can be considered as respective counterparts of LCM, HCM and L-HCM because of analogous features in each pair. In AUMIC, all of the foregoing approaches are subsumed as quasi-steady-state models which are formulated through consistent procedures within a unifying framework. Moreover, AUMIC provides the parameter identification routine so that one can develop their own models using specific experimental data. Finally, the results are quickly analyzed using the post-processing module. Conveniently, all tasks in AUMIC are performed using graphical user interface. Continuing efforts are being made towards developing AUMIC as an even more effective and advanced tool and its first version will be released soon for public use.

References :

Kim JI, Varner JD, Ramkrishna D. 2008. A Hybrid Model of Anaerobic E. coli GJT001: Combination of Elementary Flux Modes and Cybernetic Variables. Biotechnology Progress 24(5):993-1006

Kompala DS, Ramkrishna D, Jansen NB, Tsao GT. 1986. Investigation of Bacterial-Growth on Mixed Substrates - Experimental Evaluation of Cybernetic Models. Biotechnology and Bioengineering 28(7):1044-1055

Mahadevan R, Edwards JS, Doyle FJ. 2002. Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophysical Journal 83(3):1331-1340

Provost A, Bastin G. 2004. Dynamic metabolic modelling under the balanced growth condition. Journal of Process Control 14(7):717-728.

Song HS, Morgan JA, Ramkrishna D. 2009. Systematic Development of Hybrid Cybernetic Models: Application to Recombinant Yeast Co-consuming Glucose and Xylose, Biotechnology and Bioengineering 103(5): 984-102

Song HS, Ramkrishna D. 2009. Reduction of a Set of Elementary Modes Using Yield Analysis. Biotechnology and Bioengineering 102(2): 554-568

Song HS, Ramkrishna D. 2010. Prediction of Metabolic Function from Limited Data: Lumped Hybrid Cybernetic Modeling (L-HCM). Biotechnology and Bioengineering 106(2): 271-284

Young JD, Henne KL, Morgan JA, Konopka AE, Ramkrishna D. 2008. Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control. Biotechnology and Bioengineering 100(3):542?559.