Efficiency of growth and product formation 3. Introduction 3.2 Relationships between product formation and growth 3.3 Determination of maintenance energy requirement and maximum 3.4 Determination of P/o quotients 3.5 Metabolite overproduction and growth efficiency Summary and objectives
35 Efficiency of growth and product formation 3.0 Intrduction 3.1 Growth stoichiometry 36 36 3.2 Relationships between product formation and growth 3.3 Determination of maintenance energy requirement and maximum 42 biomass yield 48 3.4 Determination of P/O quotients 49 3.5 Metabolite overproduction and growth efficiency Summary and objectives 50 58
Chapter 3 Efficiency of growth and product formation 3.0 Introduction In order to develop a rational approach to improving rates of metabolite production, it is necessary to consider the fate of the nutrients that are required for its synthesis. However, overcoming the major flux control points within a metabolic pathway may not lead to metabolite overproduction if the energetic consequences of the alteration are unfavourable to the organism. nergetics In this chapter we will consider growth and product formation from an energetics perspective perspective. In the first part of the chapter, the stoichiometry of growth is considered in some detail. The relationships between product formation and growth are then described, together with approaches to determining key parameters of growth efficiency. Finally, classes of metabolites are defined, according to the relationships petween energy and metabolite synthesis. Examples of commercially significant products in each class are also discussed cquations describing growth and product formation stoichiometry are presented in this pter. These are intended to illustrate a quantitative approach to the study of efficiency of growth and product formation. You are not expected to recall all details of the equations rather the factors that need to be considered in such a quantitative analysis. If this approach is entirely new to you, we recommend Chapters 8-10 of the BIOTOL text Bioprocess Technology: Modelling and Transport Phenomena, which deals with the modelling of growth and product formation 3.1 Growth stoichiometry 3.1.1 Yield coefficients In any quantitative ass of growth and /or pro on, it is essential to link formation of microbial biomass and products with the utilisation of substrate and nutrients. In the case of microbial biomass production, the total amount of cell mass comew formed is often proportional to the mass of substrate utilised. Mathematically this is as the com responding ratio, or yield coefficient: △X x/s △s AX= amount of biomass produced As=amount of substrate consumed
36 Chapter 3 Efficiency of growth and product formation 3.0 Introduction In order to develop a rational approach to improving rates of metabolite production, it is necessary to consider the fate of the nutrients that are required for its synthesis. However, overcoming the major flux control points within a metabolic pathway may not lead to metabolite overproduction if the energetic consequences of the alteration are unfavourable to the organism. In this chapter, we will consider growth and product formation from an energetics perspective. In the first part of the chapter, the stoichiometry of growth is considered in some detail. The relationships between product formation and growth are then described, together with approaches to determining key parameters of growth efficiency. Finally, classes of metabolites are defined, according to the relationships between energy and metabolite synthesis. Examples of commercially significant products in each class are also discussed. Since process technologists rely on quantitative relationships, many seemingly complex equations describing growth and product formation stoichiometry are presented in this chapter. These are intended to illustrate a quantitative approach to the study of efficiency of growth and product formation. You are not expected to recall all details of the equations, rather the factors that need to be considered in such a quantitative analysis. If this approach is entirely new to you, we recommend Chapters 8-10 of the BIOTOL text ‘Bioprocess Technology: Modelling and Transport Phenomena’, which deals with the modelling of growth and product formation. energetics perspective 3.1 Growth stoichiometry 3.1.1 Yield coefficients In any quantitative assessment of growth and/or product formation, it is essential to link formation of microbial biomass and products with the utilisation of substrate and nutrients. In the case of microbial biomass production, the total amount of cell mass formed is often proportional to the mass of substrate utilised. Mathematically this is expressed as the corresponding ratio, or yield coefficient: yield coefficient where AX = amount of biomass produced AS = amount of substrate mnsumed
Efficiency of growth and product formation 37 Yield coefficients may be defined for different substrates in the medium and are usually based upon substrate change in units of mass or mol of substrate eg yo2 is used to relate the amount of biomass formed to the amount of oxygen consumed, so 9 g glucose 684 oxygen 27.2 Where yield coefficients are constant for a particular cell cultivation system, knowledge of how one variable changes can be used to determine changes in the other. Such stbichiom tre stoichiometric relationships can be useful in monitoring fermentations. For example, some product concentrations, such as Co leaving an aerobic bioreactor, are often the most convenient to measure in practice and give information on substrate consumption rates, biomass formation rates and product formation rates In practice, variations in yield factors are often observed for a given organism in a given medium. For example, yield coefficients often vary with growth rate. An explanation for these variations comes from a consideration of the fate of substrate in the cell, which can be divided into three parts: assimilation into cell mass · energy for growth; energy for maintenance energy for Energy for maintenance is the energy required for survival, or non-growth related mantuan purposes. It includes activities such as active transport across membranes and turnover (replacement synthesis)of macromolecules. Where a single substrate serves both as carbon and energy source, which is the case for chemoheterotrophic organisms used for biomass production, we can write: ASassimilation+ ASgrowth energy ASmaintenance energy As= the total amount of substrate consumed ASassimilation amount of substrate assimilated Sgrowth energy=amount of substrate consumed to provide energy for grwoth Asmaintenance energy=amount of substrate consumed to provide energy for maintenance Or, expressed as yield coefficients Yx/s=△X/△ Assimilation+△X/△ Sgrowth energy+△X/△ maintenance energy
Efficiency of growth and product formation 37 Yield coefficients may be defined for different substrates in the medium and are usually based upon substrate change in units of mass or mol of substrate eg, Ydo2 is used to relate the amount of biomass formed to the amount of oxygen consumed, so: Organism Pseudomonas fluorescens Substrate YXJ. 9 9-’ g mol-’ glucose 0.38 68.4 y*2 Where yield coefficients are constant for a particular cell cultivation system, knowledge of how one variable changes can be used to determine changes in the other. Such stoichiometric relationships can be useful in monitoring fermentations. For example, some product concentrations, such as COZ leaving an aerobic bioreactor, are often the most convenient to measure in practice and give information on substrate consumption rates, biomass formation rates and product formation rates. In practice, variations in yield factors are often observed for a given organism in a given medium. For example, yield Coefficients often vary with growth rate. An explanation for these variations comes from a consideration of the fate of substrate in the cell, which can be divided into three parts: assimilation into cell mass; energy for growth; energy for maintenance. Energy for maintenance is the energy required for survival, or non-growth related purposes- It includes activities such as active transport across membranes and turnover (replacement synthesis) of macromolecules. Where a single substrate serves both as carbon and energy source, which is the case for chemoheterotrophic organisms used for biomass production, we can write: AS = ASassimilation + &growth energy + &aintenance energy where AS = the total amount of substrate consumed Asassimilation = amount of substrate assimilated AS~OW~ energy = amount of substrate consumed to provide energy for grwoth &,&tenan- energy = amount of substrate consumed to provide energy for maintenance Or, expressed as yield coefficients:
Chapter 3 where AX is amount of biomass produced Yx/s is the yield coefficient Whereas the amount of substrate assimilated per unit of biomass formed (AX/ASassimilation)is constant regardless of the growth rate, the overall yield coefficient pendence (Yx/d is variable and dependent upon the environmental conditions within the culture To illustrate this growth rate dependence, consider two extremes: a culture growing at ts maximum specific growth rate will use most of its substrate for assimilation and rowth energy, whereas a stationary phase culture(non growing) will consume substrate for maintenance without any growth From the biotechnological process point of view, yield coefficient variability is extremely important and yield coefficients must, of course, be optimised Later in this chapter(section 3. 2. 1) we shall consider yield coefficients with respect to 3.1.2 Elemental material balances for growth The stoichiometry of growth and metabolism can also be described by elemental material balances. This approach can provide an insight into the potential of the organism for biomass or product production, and thus the scope for process An elemental material balance approach to growth stoichiometry requires an empirical formula for dry weight material The ratios of subscripts in the formula can be determined if the elemental composition of an organism growing under particular conditions is known. a unique cell formula can then be established by relating elemental composition to one gram-atom of carbon ieθ=1,thenα,阝,andδ are set so that the formula is consistent with known relative elemental weight content of the cells. The formula can be extended to include other elements to be a significant proportion of cell matel lemental analysis shows these macro-elements, such as phosphate and sulphur, if Complete the following statements 1)One C-mol of cells is the quantity of containing one gram-atom of 2)One C-mol of cells corresponds to the cell weight with the carbon subscript (e)taken as The missing words are: 1)cells and carbon 2)'dry' 'unity Use the data on elemental composition shown below to determine the empirical chemical form nd the formula weight for the yeast
38 Chapter 3 where AX is amount of biomass produced Yx/s is the yield coefficient Whereas the amount of substrate assimilated per unit of biomass formed (AX/GaSMrmkt,,,,,) is constant regardless of the growth rate, the overall yield coefficient (Y,,J is variable and dependent upon the environmental conditions within the culture. To illustrate this growth rate dependence, consider two extremes: a culture growing at its maximum specific growth rate will use most of its substrate for assimilation and growth energy, whereas a stationary phase culture (non growing) will consume substrate for maintenance without any growth. From the biotechnological process point of view, yield coefficient variability is extremely important and yield coefficients must, of course, be optimised. Later in this chapter (section 3.2.1) we shall consider yield coefficients with respect to product formation. 3.1 -2 Elemental material balances for growth The stoichiometry of growth and metabolism can also be described by elemental material balances. This approach can provide an insight into the potential of the organism for biomass or product production, and thus the scope for process improvement. An elemental material balance approach to growth stoichiometry requires an empirical formula for dry weight material: Ce Ha Op Ns growth rate dependence empirid fOm~Ia for dV biomass The ratios of subscripts in the formula can be determined if the elemental composition of an organism growing under particular conditions is known. A unique cell formula can then be established by relating elemental composition to one gram-atom of carbon, ie 8 = 1, then a, p, and 6 are set so that the formula is consistent with known relative elemental weight content of the cells. The formula can be extended to include other macro-elements, such as phosphate and sulphur, if elemental analysis shows these elements to be a significant proportion of cell material. n Complete the following statements: 1) One C-mol of cells is the quantity of containing one gram-atom of 2) One C-mol of cells corresponds to the cell weight with the carbon subscript (e) taken as The missing words are: 1) 'cells' and 'carbon'; 2) 'dry' and 'unity'. Use the data on elemental composition shown below to determine the empirical n chemical formula and the formula weight for the yeast
Efficiency of growth and product formation mposition(% by weight) Formula C HN O Bacterum4717813.7313 208 44.7628.531.21080.6 ? ? Atomic weights:C12011;H1.008;N,14.008;O,16.000P30.98;532.06 The empirical chemical formula is CH1.65 No16 O0.52 Po.01 So.005 and the formula weight is 24.6. For example, the subscript for O in the chemical formula is determined as allows:(312/16)/(447/12011) The formula weight is then calculated by multiplying the coefficients by the atomic weights and summing them. Thus(1x12011)+(1.008x1.65)+(14008×016)+(16x0.52)+(30.9x001) +(3206x0.05)=246 Now lets consider the elemental approach to stoichiometry for a relatively simple situation: aerobic growth where the only products formed are cells, carbon dioxide and water.The following formulas can be used if we consider the four main elements Cell material CHoOB Ns Carbon source CHro Nitrogen source HomNn stoichiometric We can now write the reaction equation by introducing stoichiometric coefficients for dCH,O,+bO2+cH,.N->CH,O, Ns+d'HO+eCOL E-3.1 e) since the coefficient of cells is taken as unity. The reaction equation can be used to establish relationships between the unknown coefficients by considering balances on he four elements as follows: H:ax+cl=a+2d ∏I Write material balances for the remaining two elements in the reaction equation CE-31) The material balances are O:ay+2b+cm=阝+d+2e
Efficiency of growth and product formation 39 composition (“A by weight) Empirical Fmuh CHNOPS chemical weight formula (C-mole of cells) Bacterium 47.1 7.8 13.7 31.3 666N0.2000.27 20‘8 Yeast 44.7 6.2 8.5 31.2 1.08 0.6 ? ? Atomic weights: C, 12.011; H, 1.00s; N, 14.008; 0,16.000; P, 30.98; S, 32.06. The empirical chemical formula is CH1.s N0.1600.52 Po.01 s0.00~ and the formula weight is 24.6. For example, the subscript for 0 in the chemical formula is determined as follows: (31.2/16)/(44.7/12.011). The formula weight is then calculated by multiplying the coefficients by the atomic weights and summing them. Thus (1 x 12.011) + (1.008 x 1.65) + (14.008 x 0.16) + (16 x 0.52) + (30.98 x 0.01) + (32.M x 0.005) = 24.6. Now lets consider the elemental approach to stoichiometry for a relatively simple situation: aerobic growth where the only products formed are cells, carbon dioxide and water. The following formulas can be used if we consider the four main elements: Cell material CHaOpNs Carbon source CH*o, Nitrogen source mmNn We can now write the reaction equation by introducing stoichiometric coefficients for all elements of the equation. stoichiometric coefficients a’ CH, 0, + b’ 02 + c’ I-h 0, N,, ---> CH, 0, Nc, + d‘ H20 + e’C02 E - 3.1 You should note that there are only five unkown stoichiometric coefficients (a’, b’, c’, d‘, e‘) since the coefficient of cells is taken as unity. The reaction equation can be used to establish relationships between the unknown coefficients by considering balances on the four elements, as follows: Ca’= 1 +e’ H. ak + c’I = a + 2d‘ n Write material balances for the remaining two elements in the reaction equation (E - 3.1). The material balances are: 0 a‘y + 2b’ + c’m = + d’+ 2e’ N: c’n = 6