Online automatic tuning and control for fed-batch cultivation

Performance of controllers applied in biotechnological production is often below expectation. Online automatic tuning has the capability to improve control performance by adjusting control parameters. This work presents automatic tuning approaches for model reference specific growth rate control during fed-batch cultivation. The approaches are direct methods that use the error between observed specific growth rate and its set point; systematic perturbations of the cultivation are not necessary. Two automatic tuning methods proved to be efficient, in which the adaptation rate is based on a combination of the error, squared error and integral error. These methods are relatively simple and robust against disturbances, parameter uncertainties, and initialization errors. Application of the specific growth rate controller yields a stable system. The controller and automatic tuning methods are qualified by simulations and laboratory experiments with Bordetella pertussis

Identification of metabolic engineering targets through analysis of optimal and sub-optimal routes

Identification of optimal genetic manipulation strategies for redirecting substrate uptake towards a desired product is a challenging task owing to the complexity of metabolic networks, esp. in terms of large number of routes leading to the desired product. Algorithms that can exploit the whole range of optimal and suboptimal routes for product formation while respecting the biological objective of the cell are therefore much needed. Towards addressing this need, we here introduce the notion of structural flux, which is derived from the enumeration of all pathways in the metabolic network in question and accounts for the contribution towards a given biological objective function. We show that the theoretically estimated structural fluxes are good predictors of experimentally measured intra-cellular fluxes in two model organisms, namely, Escherichia coli and Saccharomyces cerevisiae. For a small number of fluxes for which the predictions were poor, the corresponding enzyme-coding transcripts were also found to be distinctly regulated, showing the ability of structural fluxes in capturing the underlying regulatory principles. Exploiting the observed correspondence between in vivo fluxes and structural fluxes, we propose an in silico metabolic engineering approach, iStruF, which enables the identification of gene deletion strategies that couple the cellular biological objective with the product flux while considering optimal as well as sub-optimal routes and their efficiency.This work was supported by the Portuguese Science Foundation [grant numbers MIT-Pt/BS-BB/0082/2008, SFRH/BPD/44180/2008 to ZS] (http://www.fct.pt/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Metabolic map of wild-type <i>S.</i><i>cerevisiae</i>.

<p>Central carbon metabolism (orange), amino acids metabolism (blue), and extracellular metabolites (red). The graphs show the predicted reversibility scores using generating vectors for four out of 26 potentially reversible reactions for growth on glucose, glycerol, and acetate. A reversibility score of 0 indicates that the reaction is irreversible and 1 that the reaction may be active in both directions with equal flux on a particular substrate. The red line indicates the level of 0.5, below which all reaction directionalities are correctly predicted. The green line indicates the threshold of 0.05, above which a reversible reaction is split up into a forward and backward reaction in the approach based on generating vectors.</p

Predicted ethanol production for single reaction deletions in <i>S. cerevisiae</i> using OptGene in column two (Patil et al., 2005) and using iStruF in columns three and four.

<p>The biological objective (BO) is growth, the design objective (DO) ethanol production. Glucose uptake is 1. Growth is relative to the wild-type growth rate.</p

Procedure for finding targets of reaction deletions based on structural fluxes.

<p>The structural fluxes are computed from elementary modes (EMs, yellow) or from generating vectors (GVs, red) to facilitate larger-scale application. The yellow and red boxes are performed once to compute a biologically relevant set of structural fluxes for the wild-type (WT) network. The orange box presents the iterative computation of the structural fluxes for mutants with one or multiple reaction knockouts through re-computing the StruFs from the mode efficiencies that do not contain the deleted reaction(s) using Eqs. (3–5) without re-computing the EMs or GVs.</p

Biological objectives.

<p>Average Pearson correlation coefficient of the predicted structural fluxes versus measured ¹³C fluxes for different degrees of importance of biomass and ATP in the objective. <b>A.</b> for <i>E. coli</i> mutants <b>B.</b> for <i>S. cerevisiae</i> mutants.</p