Multivariate Curve Resolution and Carbon Balance Constraint to Unravel FTIR Spectra from Fed-Batch Fermentation Samples

Abstract

The current work investigates the capability of a tailored multivariate curve resolution-alternating least squares (MCR-ALS) algorithm to analyse glucose, phosphate, ammonium and acetate dynamics simultaneously in an E. coli BL21 fed-batch fermentation. The high-cell-density (HCDC) process is monitored by ex situ online attenuated total reflection (ATR) Fourier transform infrared (FTIR) spectroscopy and several in situ online process sensors. This approach efficiently utilises automatically generated process data to reduce the time and cost consuming reference measurement effort for multivariate calibration. To determine metabolite concentrations with accuracies between ±0.19 and ±0.96·gL^-l, the presented utilisation needs primarily-besides online sensor measurements-single FTIR measurements for each of the components of interest. The ambiguities in alternating least squares solutions for concentration estimation are reduced by the insertion of analytical process knowledge primarily in the form of elementary carbon mass balances. Thus, in this way, the established idea of mass balance constraints in MCR combines with the consistency check of measured data by carbon balances, as commonly applied in bioprocess engineering. The constraints are calculated based on online process data and theoretical assumptions. This increased calculation effort is able to replace, to a large extent, the need for manually conducted quantitative chemical analysis, leads to good estimations of concentration profiles and a better process understanding.

Keywords: E. coli; alternating least squares; carbon mass balance constraint; fed-batch; fermentation; hybrid modelling; multivariate curve resolution; soft constraints.

Figure 1

Scheme of the MCR-ALS algorithm with inequality constraints applying MATLAB lsqlin function.

Figure 2

Proof of the initial estimation for the spectral air bubbles signature: in a known aqueous solution of glucose, ammonium and phosphate, air bubbles are present in one case and absent in another. On the left, the known spectral components S₀ do not consider the air bubble model. On the right, the air bubble model is integrated and the differences between concentrations estimated in medium with and without air bubbles are similarly close to the known concentrations.

Figure 3

The 264 infrared spectra acquired from approximately 50 h fed-batch fermentation.

Figure 4

Concentration profiles estimated by FTIR/MCR-ALS (solid lines) and reference measurements (dots). The two dashed vertical lines in each plot distinguish the three process phases: batch phase (left), feeding phase/biomass production (middle), induction phase (right).

Figure 5

Initial measurements of pure substances (dashed lines) and identified pure spectral components after 300 ALS iterations (solid lines).

Figure 6

Concentration profiles for glucose (left) and acetate (right), estimated without application of the carbon balance constraint.

Figure 7

Carbon recovery based on the final glucose and acetate estimations after 300 ALS iterations, without (left) and with (right) application of the carbon balance constraint (solid line). Carbon recovery calculated by offline determined glucose and acetate concentrations (+). The dot-dashed horizontal lines indicate the highest upper and lowest lower bounds, only enabled in the run displayed on the right. The dotted horizontal line is the theoretical recovery rate of 1. The vertical lines indicate the three process phases: batch, feeding and induction.