Linear constraint relations in biochemical reaction systems: I. Classification of the calculability and the balanceability of conversion rates

Abstract

Measurements provide the basis for process monitoring and control as well as for model development and validation. Systematic approaches to increase the accuracy and credibility of the empirical data set are therefore of great value. In (bio)chemical conversions, linear conservation relations such as the balance equations for charge, enthalpy, and/or chemical elements, can be employed to relate conversion rates. In a pactical situation, some of these rates will be measured (in effect, be calculated directly from primary measurements of, e.g., concentrations and flow rates), as others can or cannot be calculated from the measured ones. When certain measured rates can also be calculated from other measured rates, the set of equations, the accuracy and credibility of the measured rates can indeed be improved by, respectively, balancing and gross error diagnosis. The balanced conversion rates are more accurate, and form a consistent set of data, which is more suitable for further application (e.g., to calculate nonmeasured rates) than the raw measurements. Such an approach has drawn attention in previous studies. The current study deals mainly with the problem of mathematically classifying the conversion rates into balanceable and calculable rates, given the subset of measured rates. The significance of this problem is illustrated with some examples. It is shown that a simple matrix equation can be derived that contains the vector of measured conversion rates and the redundancy matrix R. Matrix R plays a predominant role in the classification problem. In supplementary articles, significance of the redundancy matrix R for an improved gross error diagnosis approach will be shown. In addition, efficient equations have been derived to calculate the balanceable and/or calculable rates. The method is completely based on matrix algebra (principally different from the graph-theoretical approach), and it is easily implemented into a computer program. (c) 1994 John Wiley & Sons, Inc.

Application of a mechanistic model as a tool for on‐line monitoring of pilot scale filamentous fungal fermentation processes—The importance of evaporation effects

“…All rights reserved Der Heijden et al, 1994). In this case the production of by-product is neglected, and assumed to be negligible.…”

Stoichiometric growth model for riboflavin‐producing Bacillus subtilis

“…Relying exclusively on stoichiometric relationships of biochemical reaction systems, stoichiometric network analysis yields information on elementary flux modes (Schuster et al, 2000) and provides important information which reactions are balanceable and calculable (van der Heijden et al, 1994). Adding information on biosynthetic precursor requirements enables one to identify vital, critical, and redundant reactions (Edwards and Palsson, 1999), calculate maximum theoretical yields (Sauer et al, 1998;Varma et al, 1993), or to examine objectives of metabolic flux distributions (See et al, 1996).…”

13 C-Labeled Gluconate Tracing as a Direct and Accurate Method for Determining the Pentose Phosphate Pathway Split Ratio in Penicillium chrysogenum

“…Table 1 shows the "measured" macroscopic parameters of the cultivation. Apart from an erroneous oxygen consumption rate, identified by rate balancing as described by van der Heijden et al (33), no major differences between the balanced and "measured" macroscopic rates were found. Note that the rate of gluconate uptake was just less than 5% of the rate of glucose uptake.…”