Semi-synthetic penicillins such as ampicillin and amoxicillin are among the most widely used antibiotics worldwide. The common industrial process, carried out at low temperatures (-30°C) using organochloride solvents, has been criticized for generating considerable amounts of non-recyclable waste (Bruggink and Roy, 2001). Alternatively, the synthesis of beta-lactam antibiotics through an enzyme-catalyzed process (using penicillin G acylase) may be carried out in aqueous medium, at room temperature (25°C) and almost neutral pH (Ospina et al., 1996). The enzymatic process known as kinetically-controlled synthesis (KCS) has its yields driven by a maximum transient and overcomes the necessity of organic (co-)solvents (Kasche, 1986). This approach has the potential to be a “green process” alternative to the common industrial process.

The use of a semi-continuous integrated reactor, where substrates are fed and product is crystallized (Kasche and Galunsky, 1995), may overcome the obstacles of KCS and it is a promising alternative for large-scale production based on an enzymatic process. Optimization of this reactor requires knowledge of the state variable transients (pH, temperature and concentration of substrates), such that selectivity and productivity may be maximized (Ribeiro and Giordano, 2005). An experimental monitoring and control system for ampicillin synthesis has been built including UV spectrophotometry and multivariate calibration (Ribeiro et al., 2008). The measurements need to be filtered and estimators must be designed to infer variables that are not directly measured such as the mass of antibiotic produced (in solid phase).

The present work focuses on online state estimation in enzymatic synthesis of ampicillin in a semi-continuous integrated reactor. Bayesian estimation via Sequential Monte Carlo sampling (SMC), such as Sampling Importance Resampling (SIR) has been shown to be feasible for online estimation in chemical engineering problems with highly non-linear but low dimensional systems (Chen et al., 2004).

The ampicillin process is nonlinear, comprising 7 states: total concentration of D(-)phenylglycine methyl ester, PGME, and 6-aminopenicillanic acid, 6-APA (substrates); total concentration of ampicillin and D(-)phenylglycine (desired and undesired products); volume of the aqueous phase; pH; and apparent enzyme activity. The system has 3 control variables (inputs): flow rates of EMFG, 6-APA and sodium hydroxide. Inputs also carry uncertainties and are dynamically driven by a proportional controller. The measured data (outputs) are: concentration of substrate and products in aqueous phase, and pH throughout time.

First, a simplified kinetic model from the literature (Ferreira et al., 2000) was fitted against experimental data generated in a batch reactor. Since the simplified model cannot fit the data for all range of concentration of substrate, only a specific region with more relevance to the process was used to fit the model. The aqueous phase plus the insoluble biocatalyst was assumed to be one pseudo-homogenous phase. Possible effects of gradients of concentration and pH within the biocatalyst particle and uncertainties of activity of the enzyme are lumped in the noise of the apparent enzymatic activity, which can be related to the dynamic effectiveness of reaction. Crystallization of products was assumed as soon as they reached their limit of solubility. Therefore, a possible metastable zone was neglected. Covariance matrices of the measurement noise were estimated from results of the fitting procedure. Some terms of the covariance matrices of the noises of the system were estimated and others were assumed based on prior information of the real system.

Secondly, evaluation of the SIR on the experimental data used to fit the model and a validation batch showed good agreement between predicted states and the states calculated by the fitted model. On the other hand, this approach also exhibited high sensitivity to modeling errors. Incorporation of initial condition uncertainties and noise term in the enzymatic activity appeared to overcome error modeling and gave better filtering results. In other words, it permitted to track a parameter related to the global effectiveness of reaction.

In a simulated semi-continuous integrated reactor, the SIR approach produced state estimates close to the simulated states and allowed good prediction of the mass of antibiotic crystallized. pH and concentrations were measured every 0.5 and 5 minutes respectively. The Monte Carlo state estimation method used 500 samples for each variable and the computation time was less than 3 seconds for each 30 seconds of real batch. Therefore, this approach may be used for online state estimation. Average results obtained after 35 runs showed a mean squared error (mse) between estimated and simulated values for concentration was 2.3x10-5 (mol.L-1)2 and an mse for pH was 1.4x10-4. Results obtained by using Extended Kalman Filter (EKF) for the same runs showed an mse value for the concentrations of 5.0x10-5 (mol.L-1)2 and an mse for pH of 16.8x10-4. However, the computation time for the SIR approach was 35 times greater than the time for EKF. In contrast to EKF, the SIR approach does not require simplifying assumptions about the probability density function of state variables or the dynamic models.

References:

Bruggink, A. & Roy, P. D. (2001), Synthesis of beta-Lactam antibiotics (Chapter I), Kluwer Academic Publishers, Netherlands.

Chen, W. S.; Bakshi, B. R.; Goel, P. K. & Ungarala, S. (2004), 'Bayesian estimation via sequential Monte Carlo sampling: Unconstrained nonlinear dynamic systems', Ind. Eng. Chem. Res. 43(14), 4012-4025.

Ferreira, A. L. O.; Goncalves, L. R. B.; Giordano, R. C. & Giordano, R. L. C. (2000), 'A simplified kinetic model for the side reactions occurring during the enzymatic synthesis of ampicillin', Braz. J. Chem. Eng. 17(4-7), 835-839.

Kasche, V. (1986), 'Mechanism And Yields In Enzyme Catalyzed Equilibrium And Kinetically Controlled Synthesis Of Beta-Lactam Antibiotics, Peptides And Other Condensation Products', Enzyme Microb. Technol. 8(1), 4-16.

Kasche, V. & Galunsky, B. (1995), 'Enzyme-Catalyzed Biotransformations In Aqueous 2-Phase Systems With Precipitated Substrate And/Or Product', Biotechnol. Bioeng. 45(3), 261--267.

Ospina, S.; Barzana, E.; Ramirez, O. T. & LopezMunguia, A. (1996), 'Effect of pH in the synthesis of ampicillin by penicillin acylase', Enzyme Microb. Technol. 19(6), 462--469.

Ribeiro, M. P. A. & Giordano, R. C. (2005), 'Variational calculus (optimal control) applied to the optimization of the enzymatic synthesis of ampicillin', Braz. Arch. Biol. Tech. 48, 19--28.

Ribeiro, M. P. A.; Padua, T. F.; Leite, O. D.; Giordano, R. L. C. & Giordano, R. C. (2008), 'Multivariate calibration methods applied to the monitoring of the enzymatic synthesis of amipicilin', Chemom. Intell. Lab. Syst. 90, 169--177.