Gene Expression Based Adaptive Fuzzy Control of Bioprocesses: State of the Art and Future Prospects Reinhard Guthke, Wolfgang Schmidt-Heck and Michael Pfaff* Hans Knoell Institute for Natural Products Research Beutenbergstr. 11a, D-07745 Jena, Germany Phone: +49-3641-656820, Fax: +49-3641-656825 email: {rguthke, wsheck}@pmail.hki-jena.de *BioControl Jena GmbH Wildenbruchstr. 15, D-07745 Jena, Germany Phone: +49-3641-675511, Fax: +49-3641-675512 email:
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ABSTRACT: An adaptive and predictive control strategy has been developed based on the model structure y = f(x(τ), u(t)). It determines an optimal control profile u(t) maximising y in depending on a variable x(τ) that can be measured or observed but can not be manipulated. The modelling procedure consists of two steps. First, the kinetics x(τ) and u(t) are modelled based on results of fuzzy clustering. Second, the function f(.) is modelled by a number of alternative approaches. The control strategy is applied to a two-stage industrial fermentation process. Here, y is the final antibiotic yield, u(t) is the time course of the substrate concentration during the main culture and x(τ) is the time course of a physicochemical variable such as pH that characterises the pre-culture. In the future, the pre-culture can be characterised on the molecular physiological level using biochip technology which allows for instance to monitor expression profiles xj of thousands of genes of the inoculated microbial population simultaneously. KEYWORDS: Data Based Modelling, Predictive Control, Antibiotic Fermentation, Biochip Technology
INTRODUCTION Advanced control strategies have been studied widely at laboratory and pilot scale to determine physiological state x dependent substrate feeding rates u(t,x) in biotechnological processes, e.g. microbial fermentations [1]. At industrial scale, however, due to the limited availability of robust sensors that measure x and the lack of valid and reliable process models dx/dt = f(x,u,t) these processes are more traditionally controlled either by open loop strategies where the feeding rate follows an off-line optimised time profile u(t) or by simple closed-loop strategies such as the PID-controller. In the latter case the control variable x is derived from physicochemical measurements, as for instance the pH, the dissolved oxygen pO2 or the respiration quotient RQ (= carbon dioxide evolution rate CER divided by the oxygen uptake rate OUR). The set points of such controllers may be shifted depending on process time t. According to the physiological state control concept [2] physicochemical measurements are joined with process time t using fuzzy rules that describe memberships of current process states to a certain process phases, e.g. lag phase, growth phase, transient phase, product formation phase [3]. These fuzzy rules that are derived from the experience of skilled operators describe the known features of process phases. For each phase i, a certain feeding profile function ui(t) or controller set point xsi has to be applied. Such control strategies do not consider any dynamic aspects and correlations of past, present and future physiological states of the bioprocess. Dynamic correlations, however, are intrinsic features of antibiotic fermentations and other bioprocesses that are characterised by “maturation” and “ageing”. The paper presents an adaptive and predictive control strategy, which is based on the model (1)
y = f(x(τ), u(t))⇒ max
Using this model, the current control profile u(t) in the second operation stage, the main culture, with 0 ≤ t ≤ tf, is adapted to the course x(τ) of the bioprocess in the first stage, the pre-culture, with t0 ≤ t 0. The optimal control profile u*(t) calculated by MLR is, due to its linearity, independent of x(τ). Therefore, this linear model without interaction of the input terms for the input variables is not suitable for adaptive optimal control. With the Artificial Neural Network (ANN) trained by a backpropagation algorithm the result of cross-validation has been found to be almost identical to the MLR result. The ANN as a non-linear model, however, is suitable for adaptive optimal control. The highest product yield y* was found for the optimised substrate concentration u*(t) adapted to a preculture characterised by the pH kinetics x of the first cluster (x=X1). This yield was 3.7% higher than that obtained for the "best" realised case (x = ximax(t), u = uimax(t)). For the other pH kinetics, different from the first cluster, the adapted optimal substrate concentration control profiles were quite different. Modelling by ANFIS showed that the number of fermentation runs was to small with respect to the 6 dimensional input vector. When, however, the dimension of the input vector was reduced, this resulted in poorer cross-validation results. In all cases studied (MLR, ANN, ANFIS), control constraints would have to be applied to obtain results of more practical relevance. The adequate modelling of these constraints is not trivial. This, however, was not the focus of this paper. It can be concluded that the optimal control profiles calculated by ANN and ANFIS strongly depend upon the course of the corresponding pre-cultures. Therefore, adaptive control strategies are necessary to control bioprocess main cultures depending on their pre-cultures. It can be expected that the off-line control method described in this paper is superior to more traditional on-line control methods u(t) = f(x,t), if the essential control variable x of the main culture is not on-line measurable robustly or observable. In general, xij does not have to be a time series. It may also be a vector of the expression intensities of the genes j in experiment or fermentation run i measured by DNA-chip technology. This technology is already available commercially for micro-organisms such as Escherichia coli and is under development for antibiotic producing Streptomyces species, in particular S. coelicolor [10, 11], S. hygroscopicus [in preparation] and Saccharopolyspora erythrea [12, 13]. The fuzzy clustering of E. coli gene expression data xij with j=1,… ,268 and i=1 and 2 for KX =3 clusters has been demonstrated previously [14]. Therefore, a certain gene expression pattern can also be characterised by a low dimensional parameter vector pX fitting the cluster based regression model eq. (2) to the observed data xij. Using (partially) supervised clustering and learning algorithms the obtained model structures will be more transparent. Experimental work is ongoing to apply the gene expression based adaptive and predictive control to substrate dosage rates of antibiotic fermentations.
ACKNOWLEDGEMENTS This work was supported by the Thuringian Ministry for Science, Research and Arts (TMWFK).
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