Can microbial growth yield be estimated using simple thermodynamic analogies to technical processes?

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Abstract

In view of the prime importance of the biomass yield in microbial growth for research, for environmental and for industrial applications some thermodynamic concepts are reviewed that were developed over the years in order to understand the large variations observed in this parameter and to predict it. Special emphasis is given to a comparison between cellular growth and an energy transducer, which uses an input of chemical or mechanical energy to drive a useful output reaction. It turns out that it is impossible to calculate energetic efficiencies and to predict biomass yield based on correlations of the latter because the very concept is plagued with internal inconsistencies. Nevertheless, the energy transducer model reflects at least qualitatively the compromise between two extreme types of metabolism that must have emerged during evolution. On one hand, one can imagine that microbial metabolism could dissipate most of the Gibbs energy contained in the substrates for generating large driving forces and thus fast metabolism, but this would result in small biomass yields. On the other hand, metabolism could maximize biomass yield but this would minimize the chemical driving forces and thus the growth rate. It appears that a certain range of values of Gibbs energy dissipation somewhere between these two extremes may have emerged during evolution. Correlations for estimating this range of Gibbs energy dissipation for specific microbial growth system have been developed. Based on a Gibbs energy balance, the wide variety of growth yields occurring in nature may be explained and roughly predicted.

Introduction

Biomass yield in cellular growth constitutes one of the key parameters in any scientific research project involving microbial cultures, since it determines the final biomass or cell concentration that may be obtained. The biomass or growth yield Yx/s is a sort of stoichiometric coefficient characterizing the growth efficiency of a given microbial strain and indicates how much dry biomass can be grown per amount of carbon and/or energy substrate consumed. It must be optimized imperatively in any biotechnological project, in order to produce reasonable amounts of biological material for scientific analysis and research. Optimizing biomass yield is also of prime importance in industrial biotechnology for obtaining large product amounts and synthesis rates, both of which determine the economic viability of any bioprocess. In view of the importance of this parameter this paper attempts to review the usefulness of simple thermodynamic concepts that were developed over time to make predictions about the biomass yield even before any experiments have been performed. From an engineering point of view, the most straightforward approach of analyzing cellular growth yield would consist in treating growth as an energy transduction characterized by a certain bioenergetic efficiency. Consequently, a special emphasis will be placed on exploring the usefulness of this approach in predicting biomass yields.

Several concepts for correlating and predicting biomass yields were recently compared with each other based on a database comprising over 200 results of individual experiments reported in the literature [1]. A large part of this database has originally been collected and published by Heijnen and van Dijken [2], but Liu et al. [1] completed the base with additional literature values and also with experimental results obtained in the first author's laboratory.

As a result, the database covers quite a range of different carbon and energy sources (Table 1), as well as a number of electron donors (energy sources) in autotrophic growth and also a number of different electron acceptors (Table 1). It covers hetero-organotrophic as well as autolithotrophic growth, cases without and with reverse electron transport, and also a large number of fermentations, in which no electron acceptors are present. (The carbon and energy sources are the compounds that supply, respectively, the carbon atoms and the energy necessary for growth. The latter is often also called “electron donor”. Many microorganisms use the same organic compound for both functions, but in other types of microbial growth they are different chemicals. This is imperatively the case for “autotrophic” growth, which is based on CO2 as the carbon source.)

The first observation one can make (cf. Fig. 1) is that the growth or biomass yields of all these experiments vary by two orders of magnitude. In Fig. 1 these biomass yields are plotted in terms of carbon mole of dry biomass obtained per carbon mole of carbon and/or energy substrate consumed as a function of the degree of reduction of the electron donor. Since a carbon-mole of a given chemical compound or of dry biomass contains by definition one mole, i.e. 12 g of carbon, C-molar biomass yields indicate directly what fraction of the carbon atoms contained in the original carbon and/or energy substrate ends up in the freshly grown biomass. The degree of reduction of γD of the electron donor for the catabolic reaction represents the number of electrons that would be transferred to oxygen if one C-mole of this substance was oxidized to CO2 and water, and it is a rough measure of the energy contained in the energy donor [3].

In view of the spectacular variation of growth yields from one type of microbial system to another, the questions arise why these yields vary so much, what the factors are that affect this yield and therefore are responsible for the variation, and whether it is possible, once these factors have been identified, to predict the value of biomass yields in given cases.

Section snippets

Gibbs energy change and microbial growth

The simplest thermodynamic analysis of microbial growth consists of considering the latter as a spontaneous process transforming a number of reactants or substrates into a range of products, one of which is the newly produced biomass (Fig. 2). According to classical thermodynamics, the Gibbs energy change associated with this transformation process must be negative. However, it is not immediately evident why growth is so spontaneous and how ΔG can be strongly negative because dry biomass may be

Theoretical concepts

It may be seen from Eq. (7) that increasing bioenergetic efficiencies correlates with increasing growth yields, but according to Eq. (4) also with a decrease of the negative value of the overall change of Gibbs energy. Since the negative value of ΔrG°, ΔrGa° and ΔrGb° in Eq. (6) represent the change of Gibbs energy per mole of advancement of, respectively the overall growth reaction, reactions (a) and (b), they may be interpreted as driving forces for the advancement of these reactions much in

Prediction of biomass yields based on Gibbs energy dissipation correlations

Heijnen and Van Dijken [2], [21] have pointed out already in the year 1992 and 1993 that efficiency measures are plagued with internal inconsistencies and cannot be used for correlating purposes. Since their values change dramatically as a function of how the anabolic reaction is formulated, as demonstrated by Fig. 7, Fig. 8, only efficiency values based on biochemically realistic individual biosynthetic reactions might bear a biological significance.

On the other hand, the relationship between

Conclusions

The wide variations of biomass yields among different microbial systems may be explained based on simple thermodynamic considerations. However, it is not possible to consider microbial growth as an energy transduction process, calculate energetic growth efficiencies and predict biomass yields based thereupon. Bioenergetic growth efficiency definitions depend on the way the lumped anabolic reactions are formulated. In order to carry any biological significance, they would have to be based on

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