Estimation of intracellular phosphate content in plant cell cultures using an extended Kalman filter

Phosphate is an essential nutrient that is usually taken up by plant cells rapidly and stored intracellularly. Currently, there is no convenient means for on-line sensing of the intracellular phosphate content in cultured plant cells. In this study, a state estimator for this important parameter in batch plant cell cultures was developed using extended Kalman filter (EKF) methodology. A non-linear kinetic model was constructed to describe the dynamics of intracellular phosphate uptake and utilization. For intracellular phosphate estimation, this model was found to be most sensitive to three parameters: the maximum specific growth rate (mu(max)), the maximum phosphate uptake rate (nu(max)), and the yield coefficient on oxygen (y(o)). The EKF algorithm coupled with the kinetic model and on-line oxygen uptake rate (r(o)) measurement was used successfully to track the intracellular phosphate content under different initial phosphate concentrations. The state estimator could also accurately predict the biomass concentration. When mu(max), nu(max), and y(o) were included in the state vector, tracking of intracellular phosphate was only slightly affected. The estimation system was found very stable as long as the measurement errors of the initial states, the r(o) measurement error, and the system error were respectively within 30%, 30%, and 50%. With a r(o) measurement interval as long as 12 h, accurate tracking of the intracellular phosphate content could still be attained using a discrete EKF. Apparently, the slow r(o) dynamics in plant cell cultures allows the use of a long measurement interval. Considering the difficulties encountered in the on-line sensing of intracellular phosphate using the chemical or nuclear magnetic resonance (NMR) methods, the EKF method coupled with simple on-line oxygen uptake rate measurement provides a promising means for sensing this important culture parameter on-line.