Heijnen Et Al-1992-Biotechnolo1gy and Bioengineering

8/18/2019 Heijnen Et Al-1992-Biotechnolo1gy and Bioengineering

1/26

In Search of

a

Thermodynamic Description

of Biomass Yields for the Chemotrophic

Growth of Microorganisms

J.

J. Heijnen * and J. P. van Dijken

Depar tm ent of Biochemical Engineering and of 2Microbiolog and Enzymo logF

Delft Univ ersity of Technology, Julianalaan 6Z 628 BC Delft, The Netherlands

1

Received June 12, 1991Mccepted October 18,

1991

Correlations for the prediction of biomass yields are valu-

able, and many proposals based on a number of parameters

(YATP,

A ,,

v o ,V Gibbs energy efficiencies, and enthalpy

efficiencies) have been published. This article critically ex-

amines the properties of the proposed parameters wi th re-

spect to the general applicability to chemotrophic growth

systems, a clear relation to the Second Law of Thermody-

namics, the absence of intrinsic problems, and a require-

ment of only black box information. It appears that none of

the proposed parameters satisfies all these requirements.

Particularly, the various energetic efficiency parameters suf-

fer from major intrinsic problems. However, this article will

show that the Gibbs energy dissipation per amount of pro-

duced biomass (kJ/C-mol) is

a

parameter which satis-

fies the requirements without having intrinsic problems. A

simple correlation is found which provides the Gibbs energy

dissipation/(=-mol biomass as a function of the nature of

the C-source (expressed as the carbon chain length and the

degree of reduction). This dissipation appears to be nearly

independent of the nature of the electron acceptor (e.g., Oz,

NO3-,

fermentation). Hence, a single correlation can de-

scribe a very wide range of microbial growth systems. In

this respect, Gibbs energy dissipation is much more useful

than heat production/C-mol biomass, which is strongly

dependent on the electron acceptor used. Evidence is

presented that even a net heat-uptake can occur in certain

growth systems.

The correlation of Gibbs energy dissipation thus ob-

tained shows that dissipation/C-mol biomass increases

for C-sources with smaller chain length C,

+

C,), and

increases for both higher and lower degrees of reduction

than 4. It appears that the dissipation/C-mol biomass can

be regarded as a simple thermodynamic measure of the

amount of biochemical "work" required to convert the car-

bon source in to biomass by the proper irreversible carbon-

carbon coupling and oxidation/reduction reactions. This

is

supported by the good correlation between the theoreti-

cal ATP requirement for biomass formation on different

C-sources and the dissipation values (kJ/C-mot biomass)

found. The established correlation for the Gibbs energy dis-

sipation allows the prediction of the chemotrophic biomass

yield on substrate with an error of 13 in the yield range

0.01 to 0.80 C-mol biomass/(C)-mol substrate for aerobic/

anaerobic/denitrifying growth systems.

Key words: biomass yield chemotrophic growth Gibbs

energy dissipation thermodynamic efficiencies energy

convertor

* To

whom all correspondence should be addressed.

INTRODUCTION

Microbial growth occurs on a wide variety of com-

pounds (Table I) . For biotechnological processes of in-

dustrial interest, chemotrophic grow th

is most

relevant.

Phototrophic growth i s rarely exploited at present.

An

important parameter in biotechnological processes i s

Table

I.

A sample list of microbial growth systems.

Electron donor Electron acceptor

couple couple C-source

Organic

Oxalic acid/COz

Formic acid/COz

Glyoxalic acid/COz

Malic ac id/C02

Citric acid/COz

Pyruvic acid/C02

Succinic acid/COz

Gluconic acid/COz

Formaldehyde/COz

Glucose/COz

Lactic ac id/C02

Acet ic acid/COz

Mannitol/COz

Gly c e r o l /C0 2

2,3 Butanediol/acetoin

Et hanol/CO z

Methanol/COz

n-Alkanes/COz

Methane/COz

Inorganic

Organic

Fumarate/succinate

Pyruvate/lactate

Acetaldehyde/ethanol

Acetoine/ butanediol

Inorganic

Organic

Oxalic acid

Formic acid

Glyoxalic acid

Malic acid

Citric acid

Pyruvic acid

Succinic acid

Gluconic acid

Formaldehyde

Glucose

Lactic acid

Acetic acid

Mannitol

Glycerol

2,3 Butanediol

Acetoine

Ethanol

Methanol

n-Alkanes

Methane

Inorganic

coz

co

Biotechnology and Bioengineering,

Vol.

39,Pp. 833-858 (1992)

0

1992 John

Wiley &

So ns , Inc.

CCC

0006-3592/92/080833-026 04.00


2/26

the yield

YDx)f

biomass

(X)

on th e available substrate

(electron donor,

D). Yox

s defined a s C-mol of biomass

produced per amount of electron donor consumed (in

C-mol for organic or in moles for inorganic donors).

Hence,

YDx

s in C-mol/(C)-mol. Because of its prime

importan ce, biomass yield for many different microbial

systems has been studied extensively, and it is currently

known for a wide variety of substrates th at supp ort mi-

crobial growth. Yields can vary widely, wi thin t he range

of

0.01

to 1.0 C-mol biomass/(C)-mol electron donor,

and depend s t rongly on the microorgan ism and i t s

growth substrates.

In practice, an estimate of the expected biomass yield

in a process is frequently required before t he biochemi-

cal capabilities and properties

of

the microorganism(s)

are know n. Co nsidering the wide variety

of

potentially

useful microbial systems (Table I), this poses a difficult

problem. T he solution lies in th e selection

of

a parame-

ter which can be quantified from an established simple

correlation, and which can be used to calculate YDx.

Such a parameter should, however, preferably comply

with a number

of

general requirements. First, it

is

re-

quired that the parameter can

be

generally applied t o all

microbial growth systems. Second, it is well-known t hat

a theoretical upper limit also can be calculated for

Y D x

due to the Second Law

of

Thermodynamics. Thus, it

would be useful

if

the parameter itself has an u pper or

lower l imit which originates from the Second Law.

Thi rd, one often faces the problem

of

providing a n esti-

mate

of YDx

or a microbial system, for which the bio-

chemistry is not well-known. Hence, one must be able

to use the parameter without having information about

the intracellular biochemical properties

of

the micro-

organism (e.g. , electron transport chain or anabolic/

catabolic properties). The only information available,

known as

black box information,

would deal with the

carbon source, electron donor and acceptor, N-source,

and biomass composition. This information is generally

presented as a “black box” (Fig.

1,

which indicates the

consumption/production

of

said chemicals) , or as a

macrochemical equation which describes the material

balance for the production

of

1 C-mole biomass.’ Fig-

ure

1

contains a simple example

of

a black box and

the macrochemical equation for the aerobic growth

of

Pseudomonas oxalaticus

on oxalate with a yield

of

0.086

C-mol biomass/C-mol oxalate. Finally, such a

parameter should not suffer from intrinsic problems

(the nature

of

which will become apparent).

Because of its obvious importance, there have been

numerous attempts to establish biomass yield predic-

tions (Table IIA). This article will present a critical

evaluation

of

these attempts in relation to the above-

mentioned requirements. The negative results of this

evaluation prompted us to develop a more satisfying

parameter, based on the Gibbs energy dissipation per

unit

of

biomass produced.

Figure 1. Black box descriptio n of microbial grow th.

Table

IIA.

Models

for

the predic t ion of biomass yields.

Correla t ion Nature

of

based on Parameter the model

A T P

Available electrons

Oxygen

C ar bon

Gibbs energy

Gibbs energy

Gibbs energy

E nt ha l py

YATP Metabolic

YAW Black box

70 Black box

Y ,

Black box

7

B

Black box

Zc

Metabolic, energy convertor

7 H Black box

Metabolic, conservation

Table IIB.

yields.

Evaluat ion of the models for the predict ion of biomass

1. General ly

applicable Yes Yes

N o N o

Yes Yes Yes Yes

2. Relation to

Second Law

No No No

No

No

Yes Yes Yes

3. Black box No Yes Yes Yes Yes No Yes No

4.

Invar iant

to

frame of

reference of

G i bbsene r gy Y es

No

Yes

5

Invar iant to

choice

of

input /output

process

N o

- :

Not

relevant.

834

BIOTECHNOLOGY A ND BIOENGINEERING, VOL. 39, NO. 8, APRIL 5,

1992


3/26

Cr i ti ca l Eva luat ion o f Proposed Metho ds fo r the

Predict ion of Biom ass Yields

In 1949, Monod proposed the concept of the yield of

biomass on substrate.'l This yield was originally consid-

ered to be a characteristic constant of a microorgan-

ism for a specific substrate. Later, Herbert and Pirt

showed that the biomass yield was only constant at high

growth rates, and that the yield dropped at low growth

rates because of maintenance and/or endogeneous pro-

c e ~ s e s . ~ ~ , ~ ~ollowing these initial studies, maximal bio-

mass yields have been determined experimentally for

many microorganisms growing on a wide variety of

substrates (for reviews, see refs. 14, 18,

20,

and

23).

In

this article, only the so-called maximal biomass yield,

corrected for maintenance, designated by the symbol

YDX yield of biomass

(X)

on electron donor

(D)],

will be

considered.

The results of yield determinations have greatly stimu-

lated the search for parameters to correlate biomass

yields (Table IIA). A critical evaluation of these at-

tempts will be provided here. This evaluation will be

qualitative. For the quantitative relationships between

YDXand YATP,YAve,

q,,

K , TH,

qC,

qBB, r qEC nd a

critical comparison of the established correlations to

predict YATP,YAve, qo, K ,

TH q , q ,

and qEC, he

reader is referred to Reels:' We~terhoff:~ to~thamer,~~

and

battle^.^

In this section, the less-known general aspects of

these parameters will be elucidated in light of the re-

quirements described above (see Table IIB for sum-

mary). Initial attention

wil l

be given to chemical

efficiencies and, subsequently, the Gibbs energy and

enthalpy-based efficiencies will be dealt with.

C

BB

YATP,

YA ~,

0 ,

c

Bauchop and Elsden6 proposed the concept of express-

ing the yield of biomass in terms of consumed ATP

(YA~pn grams of biomass dry weight/mol ATP). This

concept, which is, in principle, applicable to any mi-

crobial system, has subsequently been extended by

Stouthamer3' and others. The effects of maintenance

and different C- and N-sources has been taken into ac-

count, and the theoretical

YATp

has been shown to vary

between

2

and 30 g/mol. A major problem is, however,

that there is often a gap of about 50% between experi-

mentally measured and the theoretically predicted YATp.

Moreover, for practical application, one needs detailed

biochemical knowledge about the ATP generated by the

specific microorganism to be able to calculate the

biomass yield, YDx. This concept can, therefore, not be

applied if one only has black box information. Further-

more, this parameter has no intrinsic limit based on the

Second Law.

Mayberry et al?' proposed the concept of biomass

yield

(YAve)

n terms of grams of biomass per mole avail-

able electrons (which is defined as the number of elec-

trons per C-mol electron donor upon combustion). These

electrons generate the Gibbs energy needed for micro-

bial growth. The idea is that, assuming a constant Gibbs

energy production per mole of electrons, the biomass

yield per mole of available electrons might be constant.

This parameter can be calculated for any microbial sys-

tem, and is generally applicable.

YAve

follows directly

from YDx, using only black box conservation relations

as shown by Roels,28and is therefore a true black box

parameter. The obvious limitation is that

YAve

is not

constant for different electron donors and acceptors.

For example, aerobic and anaerobic growth give a dif-

ference of a factor 4 to 5 in YAv,.This is due to the fact

that the Gibbs energy of combustion per available elec-

tron depends strongly on the electron donor/acceptor.

Furthermore, there is no intrinsic Second Law-based

limit for YAve.

Minkevich and EroshinZ3proposed the oxygen effi-

ciency

q,,

which is defined as the ratio of amount of

electrons conserved in biomass over the amount of elec-

trons available in organic substrate by aerobic combus-

tion to HC03-. Roels has shown that

q,

follows from

Y D ~sing only black box conservation relations. Hence,

q,

is a true black box parameter. An obvious limitation

is that q, can only be applied to aerobic systems and,

therefore, lacks general applicability. Also, there is no

intrinsic limit based on the Second Law.

Linton and Stephenson proposed that the carbon

yield of biomass on the C-source, Y,, could be used as a

parameter for growth. This is clearly a black box pa-

rameter which is identical to YDx for heterotrophic

growth. However, for autotrophic growth, this parame-

ter is always 1. Hence,

K

is not a generally applicable

parameter. Furthermore, there is also no intrinsic limit

based on the Second Law.

qBB

Roels proposed the use of the black box (BB) Gibbs

energy efficiency, qBB, s a correlating parameter for

microbial growth processes. (Fig. 3.7 in ref. 28). qBB

s

defined as the ratio between the sum of the Gibbs en-

ergy associated with

all consumed

chemicals (input)

and the sum of the Gibbs energy associated with all

produced

chemicals (output) (Fig. 1). The relation be-

tween

qBB

nd

Yox

can be calculated from a black box

approach, using elemental conservation principles and

the macroscopic Gibbs energy balance.28

The attractive features of this type of approach are

that it can be applied to any microbial system, needs

only black box information, and has a maximal limit of

1 due to the Second Law of Thermodynamics. This

limit of qBB= 1 leads directly to the theoretical maxi-

mal limit in YDxby substitution of qBB 1 in the equa-

tion between YDx and qBB.

An important aspect of energetic efficiencies is that

they, as well as being correlating parameters, are gener-

HEIJNEN AND VA N DIJKEN: THERMODYNAMICS OF MICROBIAL GROWTH

835


4/26

ally considered as a measure of thermodynamic process

performance. A high numerical value (e.g., vBB

90%),

indicates that only

10%

of the available Gibbs energy

has been lost, and hence indicates a good performance;

v B B

10% is then considered bad. Moreover, one intu-

itively expects that qBBncreases as YDxncreases, and

vice versa. However, energetic efficiencies are troubled

with intrinsic problems, which makes such an intuitive

interpretation improper, as will be shown below.

To use the qBB oncept, one has to choose a certain

frame of reference within which the G‘ibbs energy of the

chemical compounds is defined. This choice is com-

pletely independent of the specific process studied, and

normally one uses the “thermodynamic reference” (zero

Gibbs energy for elements at standard temperature and

pressure). However, other choices are possible. For ex-

ample, Roels has defined the “combustion reference” as

a particularly convenient choice.28Here, the Gibbs en-

ergy of 02 , C03-, H 2 0 , N-source, and H are de-

fined as zero at standard temperature and pressure. This

leads to a Gibbs energy of organic compounds which is

equal to the combustion Gibbs energy (Appendix A,

Table A-I). It is obvious that a meaningful thermo-

dynamic efficiency of a process should be independent

of

the choice

of

the frame of reference

of

the Gibbs

energy of the chemical compounds. To test this,

7’’

has been calculated for the above-mentioned 2 frames

of reference for a set of aerobic and a set of anaerobic

growth data (taken from Rutgers3’). Sample calculations

are presented in Appendix A. The results for 71”’ (ther-

modynamic reference) and 7 8 (combustion reference)

are listed in Table I11 and shown in Figure 2A (aerobic

growth) and Figure 2B (anaerobic growth) as a function

of the degree of reduction

(yD)

of the organic substrate/

electron donor. yD Is the fiumber of electrons liberated

upon oxidation of 1 C-mol of organic material to C02

or of 1 mol of inorganic material to its oxidized form.28

From Figures 2A and B and Table 111, the following

conclusions are obvious:

There is a large difference in the values of 17 1”” and

r/2BB

for the same microbial system.

For aerobic growth (Fig. 2A), a switch in the frame of

reference leads to a complete reversal of the efficiency

correlation and also in counterintuitive behavior. For

example, 77 8 for oxalate is much lower than for etha-

nol. In addition, vfB correlates with

YDx

in an intu-

itively expected way; a higher ~ 8 ~ives a higher YDx.

However, for

7

”” the behavior is completely reversed,

now oxalate has a very high efficiency and ethanol the

lowest. Also, a higher YDx corresponds with a lower

7

””,

which is quite counterintuitive.

For anaerobic growth (Fig. 2B) the obtained vBBorre-

lation (for both reference frames) is completely differ-

ent from that for aerobic growth. Apparently, different

correlations are found for different electron acceptors;

furthermore, a switch in reference frame no longer

gives such a dramatic change in behavior, as observed

in the aerobic case. However, now both frames of ref-

Table 111.

(9:”) and combustion frame of reference (7:”) or aerobic and anaerobic growth .”

Black box Gibbs energy efficiencies with thermodynamic frame of reference

YDX

J

,”” J ””

Substrate Composition

Y O

C-mol/C-mol

(-)

(-1

Pseudomonas oxalaticus (aerobic)

OxaIatez-

czo42-

Formate- CHOz-

Glyoxylate- CzH03-

Tartratez- C4H4062-

Malonate2- C3Hz042-

c itrate3- CsH5073-

Succinate2- c H 4 0 2 -

Acetate- CzH302-

Fructose C6 H 1 2 0 6

Glycerol C3HaO3

Et ha no l Cz H&

Klebsiella pneumoniae (anaerobic)

itr rate -

CsH50:-

Pyruvate- C3H303-

Gluconate- C6H1107-

Fructose C 6H

1 2 0 6

Glucose C6H

1 2 0 6

Dihydrox yacetone C3H6 03

Mannitol C6Hi406

Glycerol C3H803

Clostridium butyricum

(anaerobic)

Gluconate- CsHi107-

Glucose C6H1206

Mannitol C6H1406

1

2

2

2.5

2.7

3.0

3.5

4

4

4.66

6.0

3

3.33

3.66

4

4

4

4.33

4.66

3.66

4

4.33

0.086

0.162

0.220

0.280

0.238

0.390

0.385

0.406

0.505

0.569

0.558

0.073

0.083

0.121

0.173

0.176

0.150

0.154

0.093

0.143

0.176

0.151

0.83 0.31

0.66 0.30

0.68 0.40

0.64 0.45

0.62 0.39

0.62 0.55

0.51 0.49

0.46 0.46

0.40 0.50

0.39 0.50

0.20 0.40

0.95 0.96

0.93 0.95

0.90 0.93

0.87 0.93

0.84 0.92

0.83 0.92

0.86 0.94

0.86 0.95

0.90 0.93

0.84 0.91

0.87 0.93

836

BIOTECHNOLOGY AND BIOENGINEERING, VOL.

39,

NO. 8, APRIL

5,

1992


5/26

060

Y D X

0.40

0.20

0.00

7)-

0.90

-

-/erobic

Ps~udomnas

roloficus

-

I

I 1 I

1

2 3 4

5 6 7 0

YD

-

0.10

0.00

7)-

0.90

0.00

I I

1

0 1

2 3 4

5

6 7

8

Y D

( A)

I I I I I 1 I I

1

6 7 8

Y D

i

K/Cbsi . / /o

pneumonia*

Y

DX

Clorfridium bulyricum

060

0.80

0.70

0.60

0.50

0.40

0.30

0 .20

-

-

-

-

-

-

-

o.80

t

0.50

0.40

0.30

020

0.60O 1

-

-

-

-

0.101

\cL.

8 Vrs

0.00

I

I

I I

0

1 2

3

4 5 6

7

8

y o

(B)

Figure

2. Black box thermodynamic efficiency, T ~ , nd biomass yield on electron donor YDx)or microbial growth using a thermody-

namic frame of reference,

(qFB),or

a combustion frame of reference,

( T : ) ,

for C-sources with different degrees of reduction.

(A) Aerobic growth

(P seu dom on as oxa la~ icu s )~ ' ;

B)

anaerobic growth

(Klebsiella aerogenes

and

Clostridium butyricum).3'

erence do indicate that a higher YDx ives a lower qBB,

which is again counterintuitive.

From these results, it clearly follows that qBBs not a

meaningful process parameter because its value is very

sensitive to the chosen frame of reference. Also, coun-

terintuitive behavior is observed. These intrinsic prob-

lems are general properties of any black box efficiency,

which is defined as a ratio of total Gibbs energy input

and total Gibbs energy output. Therefore, qBB s not

considered to be

a

meaningful parameter

to

correlate

biomass yields in the light of the requirements outlined

in the introduction.

Roels proposed a second definition of a Gibbs energy

efficiency, which is often also considered to be a black

box efficiency [eq. (3.67) in ref. 281. This parameter, in

contrast to the qEB iscussed above, leads to a single

correlation which covers aerobic, denitrifying, and fer-

mentative systems. From a correlative point of view, this

parameter is more successful than

qBB,

However, it is

easily shown that this parameter is

not

a black box

Gibbs energy definition, but that it resembles an energy

convertor efficiency of Gibbs energy. This proposal is

dealt with in a paragraph below on Gibbs energy effi-

ciencies, qEC,ased

on

the energy convertor concept of

microbial growth. Furthermore, Appendix C explains

the difference between a black box and an energy con-

vertor efficiency, because these can easily be confused.

.I

In 1960, Battley introduced the concept of Gibbs en-

ergy conservation efficiency

qc

to

describe microbial

To calculate qc, two chemical reactions, the

conservative reaction and the nonconservative reac-

tion, are defined.

The conservative reaction, also called the growth

equation, is in fact the macrochemical equation (Fig. l),

whereby proper multiplication the stoichimetric coeffi-

cient of substrate becomes -1. Hence, the conservative

equation represents the mass/elemental balance of the

conversion of 1mol of substrate into biomass. From this

conservative reaction one can calculate AGc, the Gibbs

HEIJNEN AND VAN DIJKEN: THERMODYNAMICS OF MICROBIAL GROWTH

837


6/26

energy of the conservative reaction. Clearly,

(

-AGc) is

then the Gibbs energy dissipated in this reaction.

The nonconservative reaction describes the process

which occurs when

all

the substrate of the conservative

reaction (being

1

mol) is converted according to the

catabolic pathway used by the microorganism. For ex-

ample, for anaerobic growth of

Saccharomyces cere-

visiae on glucose, this is the conversion of

1

mol glucose

to ethanol and CO,; for its aerobic growth on ethanol,

this is the combustion of

1

mol ethanol to CO2 and

H 2 0 .This nonconservative reaction has a Gibbs energy

of AGNC. Hence, (-AGNc) is the maximum amount of

Gibbs energy which can be generated by the organism

by catabolizing all substrate.

In relation to the maximal available Gibbs energy

(-AGNC), the amount (-AGNC + AGc) represents then

a measure of the Gibbs energy, which has not been dis-

sipated. Hence,

7 =

(-AGNC + AGc)/(-AGNc) is the

fraction of the maximal available Gibbs energy which

has not been dissipated, but can be considered as con-

served into growth. Also, it is clear that in the hypo-

thetical case of thermodynamic equilibrium

AGc

=

0,

and therewith

qc

has a maximal value of

1.

Also, the qc

concept is generally applicable, and is not influenced by

different frames of reference of Gibbs energy for the

chemical compounds. Using this approach, Battley3 ob-

tained a useful correlation for aerobic and anaerobic

growth between

7

and the maximal available Gibbs

energy per C-mol of substrate. It is obvious that, in order

to apply qc, one must possess biochemical information

about the catabolic route, used by the organism, to

establish the nonconservative equation. Hence,

7

can-

not be considered as a black box parameter. Further-

more, an intrinsic problem appears to be that (

-AGNc)

represents the maximal available Gibbs energy if at1

substrate is catabolized.

In actuality, in heterotrophic growth, a part of the

substrate is always assimilated to biomass and only

a fraction of the substrate is catabolized to generate

Gibbs energy. Therefore,

7

appears not to represent

the actual energy metbolism, but must be considered as

an operational definition. Nevertheless, from an empiri-

cal point of view, the q concept leads to an interesting

correlation.

rlEC

Kedem and Kaplan proposed the general concept of a

linear Gibbs energy convertor to describe nonequilib-

rium processes in the late 1 9 6 0 ~ ' ~n the early 1980s this

concept was applied to describe microbial growth by

We~terhoff~~Fig. 3).

Basically, the overall growth process, represented

by the measured macrochemical reaction, is split into

2 processes. Each of these processes can be described

by a chemical reaction, the sum of which is equal to the

already known macrochemical equation. The first pro-

cess is a Gibbs energy-producing chemical reaction,

GIBBS ENERGY CONVERTOR DESCRIPTION OF MICROBIAL GROWTH

convertor

CATABOLISM 1 ANABOLISM

Gibbs energy Gibbs energy

u p t a k e

Y, =

O.Ce6)

- 5.315 C,Or

-

2.657 0.\

-

5.315

(0

\ /

ANABOLISM

+

3 4 3 k J

CATA0OLISU

- 1391

kJ

+

10.63

HCO;

/

- 0.5 c p y

- 0.2 FH:

\

0 . 1

yo

- 0s

K

ANABOLISM

-

0 5

C,O:

-

0

2

NH, -

0 1 H,O - 0 8

H'

+ 1

CH,O,,N,,

+ 0 8 0,

CATABOLISM

-

5 315 C,O:-

-

5 315 HO -

2

6 5 7 0, +10 63 HCO;

SUM MACROCHEMICAL EQUATION

-

5 815 C,O:-

-

0 NH,

- 5

415 HO

- 0

8

H

1

8 5 7

0,

+ 1 CH,,O,,N,, + 10 63 HCO;

Figure 3.

Gibbs energy convertor description

of

microbial growth

commonly identified as catabolism. The second process

is the chemical reaction which produces the biomass,

commonly called anabolism. This second process nor-

mally requires Gibbs energy. Now the ratio of the re-

quired Gibbs energy in anabolism to the produced Gibbs

energy in catabolism is a measure of the Gibbs energy

conservation, and is called the thermodynamic coupling

efficiency qEC f the convertor (EC from energy conver-

tor). Figure

3

shows an example to illustrate this con-

cept. From the Second Law, it follows directly that qEC

is maximally

1.

This concept can be generally applied,

and the value of

7

is not influenced by different

choices of frames of reference of Gibbs energy of the

chemical compounds, because qEC s a ratio of the

Gibbs energies of reaction of the defined anabolic and

catabolic processes.

Furthermore,

i t

has been shown, that an exact value

of qEC an be derived from a supposed optimization

criterion according to which the biomass energy conver-

tor For example, a maximal rate of bio-

mass formation at optimal efficiency gives

7

= 0.24.

Such efficiencies have subsequently been calculated for

many aerobic growth systems,43 uggesting that growth

has perhaps evolved toward maximal growth rates at

optimal qEC. he independence of

7

from the frame

of reference, in combination with the possible link to

an optimal criterion, makes the parameter

vEC

more

838

BIOTECHNOLOGY A ND BIOENGINEERING, VOL. 39, NO. 8,APRIL 5, 1992


7/26

interesting candidate than qBB

r

qc. However, close

inspection reveals a basic problem in the use of qEC.

This resides in the requirement to specify the chemical

reactions of catabolism (providing the Gibbs energy in-

put into the convertor) and anabolism (which contains

the conserved Gibbs energy and represents the conver-

tor output of Gibbs energy). As already stated, this boils

down to a split of the macrochemical reaction. Making

such a split presents 2 problems.

It is assumed that only black box information is avail-

able, and not specific biochemical knowledge about

the microbial system. Hence, only generally available

biochemical knowledge can be used. Within this

framework, many splits are still possible. Thus, it is of

importance to find out whether qECs sensitive toward

different splits.

The 2 processes resulting from a proposed split are

not independent. Their sum must equal the measured

macrochemical equation. Hence, a proposed catabolic

(or anabolic) reaction implicitly defines the corre-

sponding anabolic (or catabolic) reaction. In the litera-

ture, different proposals for the catabolic (or anabolic)

process have been made on the basis of generally

available biochemical arguments. However, the corre-

sponding implicitly defined anabolic

(or

catabolic)

process also has to be questioned from a general bio-

chemical viewpoint. Hence, it is of obvious interest to

study both the defined catabolic and anabolic pro-

cesses from a general biochemical point of view, for

the various proposed qEC efinitions.

To answer the first point,

3

different splits for aerobic

and anaerobic growth data sets have been made. It is

stressed that these splits are only for illustrative pur-

poses to test the qEC ensitivity toward different splits.

Appendix B shows the chosen splits and gives the cal-

culations. The results are shown in Table

IV,

Figure 4A

(aerobic growth), and Figure 4B (anaerobic growth). It

is clear that qEC s very sensitive to the chosen split.

Thus, it is important to take into account as much as

possible the generally available biochemical arguments

for a particular split in order to obtain a meaningful

thermodynamic efficiency qEC.

It is interesting to pay some attention to the various

proposed splits associated with the definitions given by

a number of proponents of qEC.

Roels implicitly proposed a qEC efinition (Appen-

dix D) which gave a useful correlation of aerobic, an-

aerobic, and denitrifying growth.28 A general anabolic

definition was proposed, which is equivalent to the

statement that biomass formation occurs from

COz

with

production of

Oz.

The virtue of this definition is that

there is always Gibbs energy

uptake

in this process,

which assures that 0 < qEC< 1. From a biochemical

point of view, it is clear that this anabolic process is very

unrealistic for heterotrophic growth systems (especially

the fermentative and the denitrifying systems). It is

now illuminating to see which implicitly defined cata-

bolic processes arise from Roels' anabolic definition

(Appendix D). For aerobic growth, one finds that the

catabolic reaction is the aerobic combustion of the

or-

Table IV.

and output processes for aerobic growth and anaerobic gr ~ w t h . ~ '

Gibbs energy convertor efficiencies vEC ith 3 different definit ions

of

input

YDX

:

:

11

F

Substrate YD C-mol/C-mol (-) (-) (-1

Pseudomonas oxalaticus (aerobic)

OxaIate2- 1

Formate- 2

Glyoxylate-

2

Tartrate*- 2.5

Malonate- 2.7

c itrate3- 3.0

Acetate-

4

Fructose

4

Glycerol 4.66

Ethanol 6.0

Klebsiella pneumonia e

(anaerobic)

Succinate2- 3.5

c itrate3-

3

Pyruvate- 3.33

Gluconate- 3.66

Fructose 4

Glucose

4

Dihydroxyacetone 4

Mannitol 4.33

Glycerol 4.66


(anaerobic)

Gluconate- 3.66

Glucose 4

Mannitol 4.33

0.086

0.162

0.220

0.280

0.238

0.390

0.385

0.406

0.505

0.569

0.558

0.073

0.083

0.121

0.173

0.176

0.150

0.154

0.093

0.143

0.176

0.151

0.246

0.169

0.233

0.233

0.200

0.268

0.164

0.085

-0.003

-0.170

-0.350

-0.014

-0.028

-0.086

-0.144

-0.125

-0.126

-0.094

-0.065

-0.100

-0.125

-0.094

-0.078

-0.055

-0.111

-0.042

+0.025

+0.017

+0.044

+0.053

-0.057

-0.045

-0.020

+0.035

-0.002

- 0.079

-0.144

-0.125

-0.123

-0.094

-0.069

-0.092

-0.125

-0.094

0.31

0.30

0.40

0.45

0.39

0.55

0.49

0.46

0.50

0 50

0.40

-0.157

-0.120

-0.119

-0.144

-0.122

-0.111

-0.115

-0.110

-0.139

-0.122

-0.115


839


8/26

0

60

Y D X

0 40

0 20

0.00

7)

0 50

0.40

0.30

0.20

0.10

0.00

-0 10

-0

20

0.00

-0.10

- 0 2 0

Pseudomonos oxolOt ,CuS

A e r o b i c

-

-

-

1

6

7

8

y o

3

4

5 .

. .

0 4 1

-0.30

yo

(A)

Klrbsrdla

pmumonia8

Clostndum bulyricum

Anaerobic

yoxo6 140

0.20

'

0001 I

o 201-lo

-0.30

0

2

3 5

6 7 8

y o

(B)

Figure 4. Gibbs energy convertor efficiency, T ~ ~ ,nd biom ass yield on electron donor, YDx) ,sing three different defin itions of input

and output (qFc,

qFc, qFc)

or C-sour ces with d ifferent degrees of reduction. (A) Aerobic growth

(P.

x a l a t i c u s ) ~ ' ;B) anaerobic growth

( K .

aerogenes and C. b ~ t y r i c u r n ) . ~ '

ganic substrate, which is biochemically quite acceptable.

This shows that an unrealistic anabolic reaction some-

times can lead to an acceptable catabolic reaction. How-

ever, the corresponding catabolic process for anaerobic

growth is unusual, being the partial oxidation, with 02,

of the substrate to fermentation products. In conclu-

sion, it appears that qEC s defined by Roels, although

providing a satisfying empirical correlation of microbial

growth, cannot be considered as a valid measure

of

thermodynamic process performance.

Westerhoff and Van Dam43 proposed, for aerobic

growth, an anabolic process (Appendix

E)

in which bio-

mass formation occurs from the organic substrate with

production of O2 (for substrates more oxidized than

biomass) or consumption

of

O 2 (for substrates more re-

duced than biomass). The O 2 production

is,

for hetero-

trophic growth, clearly unrealistic from a biochemical

point of view. Also the above-mentioned hypothesis that

growth has evolved to a maximal rate at optimal qEC

seems to be questionable, because the experimentally

found qEC= 0.24 is based on this biochemically unreal-

istic split.

In addition, a substantial Gibbs energy production is

obtained in the anabolic process for more reduced sub-

strates than biomass. This then gives the possibility of

negative values of

qEc.

The implicitly defined catabolic

reaction for aerobic growth is the combustion of the

substrate with 02 , hich is biochemically quite valid.

For anaerobic growth, it has been pointed out that

this anabolic definition is un re al i~ ti c, ~~nd it has been

proposed to replace O 2with

H2.

However, for fermenta-

tion processes without H 2 his proposal is again unsatis-

factory. In addition, the

qEc

correlation obtained for

anaerobic growth totally differed from aerobic

The question then arises whether one can formulate

an anabolic reaction equation which is based on bio-

chemical evidence. Such equations have indeed been

proposed.8 It is easily shown, however, that the Gibbs

energy of these anabolic reactions is invariably close to

zero, a fact which was already recognized by Battley' in

his studies of

qc

He proposed a similar anabolic reac-

tion where biomass is produced from organic substrate,

C 0 2 ,

and N-source, without involvement of

0 2

his

leads to partly C02 ixation for substrates more reduced

than biomass and C 0 2production for substrates less re-

duced than biomass. In fact, this proposal of anabolism

is identical to the anabolism used in split 2 (Appen-

dix

B).

Figure

4A

and B clearly show that is differ-

840

BIOTECHNOLOGY A ND BIOENGINEERING, VOL.

39,

NO.

8,

APRIL

5, 1992


9/26

rent for aerobic and anaerobic growth. Also qEC p-

pears to be close to zero for this anabolic proposal

where biochemistry is taken into account as much as

possible. This value of qEc= 0 does not correspond to

any optimization criterion.43

Before closing this section on Gibbs energy-based ef-

ficiency proposals, it is interesting to remark that, for

aerobic heterotrophic growth, qBBwith combustion ref-

erence), qE CRoels), and qc from Battley all give identi-

cal results. It appears that totally different concepts may

lead to exactly the same efficiency.

In conclusion, it appears that

qEC

annot be applied

as a biochemically meaningful measure of thermody-

namic process performance, given only black box infor-

mation. Extensive biochemical knowledge is required

for a useful application, and major intrinsic problems

are present.

Enthalpy Eff ic iencies

qH

Enthalpy efficiencies have been defined in analogous

terms as the previously discussed Gibbs energy efficien-

cies. Minkevich and EroshinZ3 nd Roels28proposed the

use of the black box efficiency using the combustion

reference for enthalpy values. Battley3 has proposed the

use of the heat efficiency derived from the conservation

concept of microbial growth. As with the Gibbs energy

efficiencies, these parameters are generally applicable.

However, they lack a theoretical upper limit based on

the Second Law. The Second Law does allow for heat-

uptake during growth, which would result in an en-

thalpy efficiency > 1. More serious is, however, that

the intrinsic problems which have been pointed out for

the various Gibbs energy efficiencies also apply to the

analogous enthalpy efficiencies.

Summarizing, it can be concluded that none of the pa-

rameters discussed above provide a satisfactory frame-

work for the correlation of microbial growth yields of

chemotrophic systems (Table IIB). Their range of appli-

cation is too limited

( y C

and v, ,most have no relation

to the Second Law of Thermodynamics

(YATp,

K ,

q,,

enthalpy efficiencies,

YAVe),

ome require biochemical

information (YATp,

qc,

vEC),nd intrinsic problems oc-

cur due to frames of reference (vBB),making a split

(vEC),

nd assuming catabolism of all substrate

(77).

In

the next section, another parameter, which can be used

to achieve a biomass yield correlation, will be presented.

This parameter fulfills the requirements mentioned in

the introduction.

Gibbs Energy Diss ipat ion Per C-Mol Biomass

Produced as a Predict ive Parameter for

Chemot roph ic Gro wt h

It has been suggested by Roels that the Gibbs energy

dissipation, which occurs per unit of biomass produced,

is perhaps constant for many C-sources, and probably

independent of the type of electron acceptor involved.28

If

0, '

s designated as the Gibbs energy dissipated

(kJ/m3 h) and biomass production (C-mol/m3 h) is repre-

sented by TAX, then Dsol/rAx rovides the Gibbs energy

which must be dissipated by the microbial system in

order to produce 1 C-mol of biomass from the available

C-source, electron donor, and electron acceptor. If

D;'/rAx is considered with respect to the requirements

mentioned in the introduction it appears that:

The dissipation of Gibbs energy can be calculated for

any microbial growth system.

The Second Law of Thermodynamics requires that

Dsol/rAxs positive, hence there is a theoretical lower

limit:

~ s o l / r A ~

0.

The value of

D;' / rAx

an be calculated from black box

information alone. RoelsZ8has shown that there is a

unique relationship between

YDx

nd

Dsol/rAx.

n fact,

Dso'/rAxs equal, but of opposite sign, to the reaction

Gibbs energy of the macrochemical reaction (Fig. 1,

Appendix F).

Df ' / r A x oes not suffer from the intrinsic problems

which were found for

qBB

nd qEc. t is clear (See Ap-

pendix F) that

Dsol/rAx

s independent of the chosen

frame of reference. Furthermore, there is no need to

provide a split in input and output processes for its

calculation; D;l / rAxcan be calculated directly from

black box information alone as represented in the

macrochemical equation (Appendix F).

It is clear that the parameter Dsol/rAxossesses all the

properties required to function as a thermodynamically

based, black box, predictive parameter for the calcula-

tion of biomass yields.

It must be remembered that the actual concentrations

of the reactants must be considered in order to calculate

meaningful values of Gibbs energy dissipation. This in-

formation is often not available. As a compromise, the

Gibbs energy at pH

7,

and otherwise standard condi-

tions (1 mol/L or 1 atm and 25 C), can be calculated.

This choice is indicated by the superscript 01 . Devia-

tions from the standard conditions generally exert a

limited effect. However, in some special microbial sys-

tems [e.g., anaerobic cultures with

lo-'

to lo-' atm Hz,

or systems with a low pH (e.g., pH l),or low values of

YDx],ignificant effects can occur which necessitate the

use of the actual concentration^.^^ A set of published

data for which chemotrophic microbial growth yield

(electron donor limited) has been measured in batch or

continuous culture has been collected. In these experi-

ments, well-defined mineral media were used and un-

known product formation was excluded by showing that

the carbon and redox balances were satisfied. Reliable

macrochemical equations could thus be calculated, giv-

ing reliable and meaningful values of

D:' / rAx .

A sample

calculation of

D,ol/rAx

s shown in Appendix

F.

The microbial systems used cover a wide range of

conditions (Table VA-H) which encompass:

A large variety of microorganisms.

Chemoheterotrophic (Table VA-G) and chemoauto-

trophic (Table 5H) growth.

HEIJNEN AND VAN DIJKEN: THERMODYNAMICS

OF

MICROBIAL GROWTH

841


10/26

Table VA. Biomass yield and Gibbs energy dissipation for the aerobic growth of Pseu-

domonas oxalaticus

on

different organic substrate^.^'

YDX

D,0’/rAx

Substrate Composition YO C-mol/C-mol k J/C-mol biomass

OxaIate2-

Formate-

Glyoxylate-

Tartrate2-

Malonate2-

itr rate'-

Succinate2-

Acetate-

Fructose

Glycerol

Ethanol

1

2

2

2.5

2.7

3.0

3.5

4

4

4.66

6.0

0.086

0.162

0.220

0.280

0.238

0.390

0.385

0.406

0.505

0.569

0.558

1048

1089

709

584

757

383

504

567

470

473

702

Table

VB. Biomass yields and Gibbs energy dissipation for aerobic growth of Candida

utilus

on

different organic s~ bstr ate s.~’

YOX D?lrAX


YO

C-mol/C-mol k J/C-mol biomass

Citrate-

Pyruvate-

Succinate2-

Gluconate-

Glucose

Xylose

Acetate-

Glycerol

Acetoin

2-3 Butanedic

Ethanol

3.0

3.33

3.50

3.666

4.0

4.0

4.0

4.666

5.00

5.50

6.0

0.411

0.434

0.448

0.559

0.595

0.490

0.455

0.692

0.424

0.446

0.617

340

396

366

296

327

497

455

316

845

890

592

Table VC.

denitrificans.

39s43

Biomass yield and Gibbs energy dissipation for aerobic growth of Paracoccus

YDX D ,”

TAX


YO

C-mol/C-mol

k

J/C-mol biomass

Formate-

C02H-

2 0.12

Malate2-

C4H40:- 3 0.42

Succinate2-

C4H40.t-

3.5 0.48

Gluconate-

C6H1107-

3.666

0.51

Mannitol

C6H1406 4.333 0.62

Methanol

CH40 6.0 0.54

1636

333

311

371

345

809

Table VD.

acidophilus. 7

Biomass yield and Gibbs energy dissipation for aerobic growth of Thiobacillus

YDX

D?/rAx


YO

C-mol/(C)-mol

k

J/C-mol biomass

Formate- COzH-

2 0.10

L-MalateZ-

C4H40:- 3.0 0.25

Pyruvate

-

C3H303- 3.33 0.32

Glucose

c

6H

1 2 0 6 4 0.40

Glycerol

C3H803 4.66 0.55

2058

880

704

717

512

Different C-sources, either more reduced or more oxi-

dized than biomass (with degree of reduction yDfrom

0 -+8) and C-sources with highly different carbon

chain lengths (from C1 o C6).

Different electron acceptors such as O2 Table VA-E),

NO3- (Table VF) and fermentation (Table VG).

A number of microbial systems where growth yield

data were measured for the same microorganism grow-

ing on a wide variety of electron donors

( =

C-source).

From the available biomass yield data, the values of

Gibbs energy dissipation

(DP’/rAx)

ere calculated (see

Appendix

6

for the procedure). The results are provided

84 2 BIOTECHNOLOGY A ND BIOENGINEERING, VOL. 39, NO.

8,

APRIL

5,

1992


11/26

Table VE.

erotrophic microorganisms on various organic substrate^.̂ ^ ̂ . ^

Biomass yield an d Gib bs energy dissipation for aerobic growth of various het-

YDX D?/rAx

Subst ra te Composi t ion

YO

C-mol/C-mol kJ/C-mol biom ass

OxaIate2-

Formate-

Malate2-

c i t r a t e3 -

Succinate2-

Gluconate-

Glucose

Lactate-

Acetate-

Formaldehyde

Manni tol

Glycerol

Propionate

Acetone

Ethanol

Methanol

Propanoi

n-A l kanes

Butane

M e t h a n e

1

2

3

3

3.5

3.666

4

4

4

4

4.333

4.666

4.666

5.33

6

6

6

6.13

6.5

8

0.07

0.18

0.375

0.365

0.400

0.51

0.61

0.51

0.41

0.47

0.56

0.67

0.480

0.445

0.53

0.54

0.575

0.57

0.445

0.55

1399

933

429

442

467

371

308

394

557

587

433

335

556

813

765

809

658

662

1061

1011

Table

VF.

ganisms

on

organic subst ra tes us ing NO3-/N2 as a~ ce pt o r . ~ '

Biomass yield an d G ibb s energy dissipation for den itr ifying growth of microor-

DPl/rAx

YDX kJ/C-mol

Microorganism Compound Composi t ion

YD

C-mol/C-mol biomass

Campylobacter

Paracoccus

denitrificans

Succinate2-

C 4 H 4 0 2 -

3.50 0.387 466

P. enitrificans

Gluconate-

C6H1107-

3.666

0.505 358

C. spu tum

L ac t a t e -

C3Hs03-

4 0.274 1064

P. denitrificans

Manni tol C6H1406

4.333 0.506 500

sputum F o r m a t e - C 0 2 H - 2

0.166 999

in Table 5A-H and Figures 5A-G. If one studies the

values of

D:'/rAX

for the various microbial systems, a

very simple correlation becomes evident (Fig. 6A). It

appears that

DsO1/rAx:

depends strongly on the degree of reduction and the

is only weakly dependent on the

electron acceptor.

for chemoautotrophic systems with an

electron donor

where reversed electron transport occurs, the required

dissipation is much higher than for chemoautotrophic

systems where reversed electron transport is absent.

Within both groups, the dissipation is influenced little

by the nature

of

the electron donor.

The effect of the degree of reduction of the C-source

is

clearly observed in Figures 5A-G. Figure 6A contains

all data. The data in these figures cover a very wide

spectrum of C-sources, microorganisms, and electron

acceptors. Nevertheless, the same pattern arises.

D:l / rAx

is minimal around yD = 3.5 to 4.5, and increases for

more reduced or more oxidized substrates. Moreover,

most Gibbs energy dissipation data for the different

microorganisms are fairly close. Typically,

D:' / rAx

is

carbon chain length of the

carbon source.

around 200 to 350 kJ/C-mol for yD

=

3.5 to 4.5, and

around 900 kJ/C-mol for

YD

= 0 to 2 and YD = 6 to 8 .

Systematic deviation from the typical average behavior

of microorganisms can, however, also be observed. For

example

Thiobacillus acidophilus

(Table VD) has a

much higher dissipation than most aerobic microorgan-

isms. One reason might be the low pH of 3.5, which

might increase dissipation. Another example is the an-

aerobic bacterium Butyribacterium methylotrophicum,

which has a significantly lower dissipation than most

fermentative microorganisms. The reasons for this are

not known.

The effect of the carb on chain length

of

the C-source,

as a function of its degree of reduction, is shown in

Figure 6A (based on the data of Table VA-H, without

T. acidophilus and B. methylotrophicum). For carbon

sources with the same number of C-atoms, one observes

the above-mentioned typical effect of its degree of re-

duction. Dissipation is minimal for the degree of reduc-

tion around 4 and increases on both sides. Table VI

contains the average dissipation values for a number of

C-sources.


843


12/26

Table

VG.

substrates.

Biomass yield and Gibbs energy dissipation

for

anaerobic growth

of

defined heterotrophic microorganisms on organic

Substratel

YDX D?/rAx

Ref. Microorganism electron Donor Composition

YD

C-mol/(C)-mol kJ/C-mol

31

31

31

31

31

31

31

31

31

31

31

9,40

1

45

45

1

1

1

1

33

33

33

33

33

33

33

33

33

34

34

34

35

Klebsiella pneumoniae


Methanobacterium AZ

M. formicicum

M. soehngenii

Methanosarcina barkeri

Butyribacterium m ethylofrophicum

Pelobacter propion icus

P.

carbinolicus

C. magnum

Saccharomyces cerevisiae

itr rate'-

Pyruvate-

Gluconate-

Fructose

Glucose

Dihydrox y-acetone

Mannitol

Glycerol

Gluconate

Glucose

Mannitol

HZ atm)

Formate-

Acetate-

Methanol

Hz/COz

co

Glucose

Methanol

Lactate

Acetoin

Butanediol

Ethanol

Propanol

Ethylene

Glycol

Acetoin

Butanediol

citrate3-

Glucose

Acetoin

Butanediol

Glucose

3

3.33

3.666

4

4

4

4.33

4.666

3.666

4

4.33

2

2

4

6

2

2

4

6

4

5

5.5

6

6

5

5

5.5

3

4

5

5.5

4

0.073

0.083

0.121

0.173

0.176

0.150

0.154

0.093

0.143

0.176

0.151

0.019

0.053

0.024

0.13

0.056

0.11

0.250

0.30

0.085

0.08

0.063

0.028

0.019

0.073

0.070

0.036

0.03

0.32

0.08

0.072

0.14

185

236

237

210

236

257

191

254

219

229

222

822

880

539

570

440

350

110

584

197

358

390

785

792

617

259

244

55

1

139

364

353

255

Table

VH.

Biomass yield and Gibbs energy dissipation for chemoautotrophic growth.

Ref.

D?lrAx

k J/C-mol

Microorganism Acceptor ( a t 4 -1 C-mol/mol biomass

Donor YO YDX

No

reversed electron transport systems

24 Methanobacterium arborophilus

34 Alcaligenes eutrop hus

22 Carboxydotrophic bact.

9,40

M . A Z

Reversed electron transport systems

30 Thiosphaera pantotropha

30 Thiobacillus neapolitanus

11

Thiobacillus ferrooxidans

27

Thiobacillus acidophilus

11 Thwbacillus ferrooxidans

39 Thiobacillus denitrificans

12

Thiobacillus ferrom'da ns

25 Nitrosomonas europaea

25

Nitrobacter

sp.

~ ~ ( 1 0 - ~ )

~ ~ ( 1 0 - ~ )

Hz(

o-')

co

szosz-

s20:

s20:-

s20sz

s402-

HS-

Fe2+ pH 1.6)

NH4+

N02-

8

8

8

8

14

8

1

6

2

0.015

0.13

0.16

0.019

0.16

0.16

0.22

0.23

0.41

0.30

0.010

0.06

0.017

1076

1267

1105

840

4627

4627

3237

3076

2761

2186

2927

4117

3892

It

appears that the carbon sources containing more

C-atoms (for the same degree of reduction) require less

Gibbs energy dissipation. For example, consider the

carbon sources with degree of reduction 4 (formalde-

hyde, acetate, lactate, dihydroxy-acetone, glucose, see

Table VI). It appears that DP1/rAxs halved when the

chain length of the carbon source increases from 1 to 3.

An analogous trend is observed for compounds with

degrees

of

reduction 2 to 2.5 (CO/formate, glyoxylate,

tartrate), 2.7 to 3 (malonate, malate, citrate), and

5

to

844

BIOTECHNOL OGY AND BIOENGINEERING,

VOL. 39,

NO. 8, APRIL

5, 1992


13/26

5.5 (ethyleneglycol, acetoin). It also appears that the

ef-

fect of carbon chain length is most significant between

1 to 4 carbon atoms. There is no large effect

if

one con-

siders 4 to 6 C-atoms.

The effect of a change in electron acceptor is rather

limited, as can be observed

if

one compares 02 , O3-,

and fermentation systems (Fig. 5A-E,

G,

and F). As a

first approximation, it appears that the Gibbs energy

7 .oo

0 50

0.00

ThiobaCl l luS

aCldODhllUB

aerobic

-

0

0

0

0

s

c?

s

m

a

v,

u

'0

i

0

0 00

Boo

A

0

0 1 2 3 4 5 6 7 6

1 - 0 0

Candad

Uto lug

aerobic

-

B

s

?i

a

-B

B

d

0.00

1 ' ' ' ' '

'

000

16

1200

800

400

0 1 2 3 4 5 6 7 6

degree o f reduc t i on deg ree o f reduct ion

O =O00

II_

000

16

1200

8

400

s

m

D

-B

z

i

B

(3

0 1 2 3 4 5 6 7 6

degree o f reduc t i on

( C )

0 1 2 3 4 5 6 7 8

degree

of

reduct ion

(D)

Figure 5. Biomass yield, YDX, nd Gibb s energy diss ipation as a funct ion of the degree of reduction of the C-source for differ-

ent carbon sources, electron acceptors, and microorganisms. (A) P. oxaht icus , aerobic, heterotrophic; (B) Candida

utilis,

aerobic, het-

e r o t r o p h i c ;

(C) Paracoccus

denitrificans, a e r o b i c , h e t e r o t r o p h i c ;

(D) Thiobaciffus

a c i d o p h i l u s , a e r o b i c , h e t e r o t r o p h i c ;

(E) chemohe t e r o t r oph i c mi c r oor gan isms , ae r ob i c ; (F) chemohe t e r o t r oph i c mi c r oor gan isms , den i t r i f y i ng ; (G) C hemohe t e r o t r o -

phic microorganisms, fermentative. (+) Aerobic;

(+)

denitrifying;

(B)

naerob ic systems.


OF

MICROBIAL

GROWTH

845


14/26

2 0 0 0

4 0 0

8

d

2 0 0 0

.=.

8

’ 1600

Y

1200

z

-B

8 0 0

400

3

d

+

+ +

+

0

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8


(E)


(F)

2000

0 1 2 3 4 5 6 7 8

degree

of

reduc t i on

G)

Figure 5.

(con t inued)

dissipation is independent of the external electron ac-

ceptor 0 2 ,

NO3-,

or fermentation. There appears to

be, however, a tendency that microbial systems which

do not use an electron transport chain (fermentative

growth) have less Gibbs energy dissipation than sys-

terns which do. The difference appears to be about 50

to 150 kJ/(C-mol biomass) (compare Fig.

5G w i t h

Fig. 5A-F).

The effect of a change in electron acceptor can be

illustrated nicely with data from Von Stockar and

B h - 0 ~ ~ ~ho measured substrate yield of yeast under dif-

ferent regimes of oxygen supply and ethanol production

846


39,

NO. 8, APRIL

5, 1992


15/26

Number

o f

carbon atoms

of

carbon source

YD

am

r

OD

2

0 '

4

I 1 5 7

Degree of reduction

of

carbon source

(A)

1 1 6 1

I

4

4 Erro r - 30

1, '

O F 4 I

400 800 1200 1600

Actual

dissipation (kJ/C-mol biomass)

(B)

Figure 6. (A) The ef fect of carbon source (carbon chain length and degree of reduction) on the

required G ibb s energy dissipation pe r C-mol biomass produce d. Solid l ine is the est imation accord -

ing to eq. (1).(*) Aerobic;

(+)

denitrifying; (D)naerob ic systems. (B) Compar ison between actual

and est imated [eq. l)]dissipation data (from Table

VA-H). (*)

Aerobic; (+) denitrifying;

(D)

n -

aerobic systems.

(Table VII). It can be seen that the biomass yield

YDx

changed strongly, but that D:'/rAx emained fairly con-

stant. Furthermore, it should be noted that the mea-

sured heat production per C-mol produced biomass was

not nearly as constant; there was a decrease by a factor

3.5 if the electron acceptor changed from aerobic to fer-

mentat on.

In relation to heat production per C-mol biomass for

different electron acceptors, another interesting feature

can be shown. It is known that the total Gibbs energy

dissipation in chemical reaction systems is due to the

sum of heat-related and chemical entropy-related Gibbs

energy dissipation. The total Gibbs energy dissipation

must be positive (Second Law), but there are no restric-

HEIJNEN AND VAN DIJKEN: THERMODYNAMICS OF MICROBIAL GROWTH 847


16/26

Table VI. Average Gib bs energy dissipation values (Dpl/rAx)or C-sources.

Carbon Dp’lrAX

C-source Degree of chain

No. of

kJ/C-mol SD

compound reduction length observations biomass

(%)

C o l a

COzh

OxaIatez-

co

Formate-

Glyoxylate-

T a r t r a t ez -

Maionate’-

Malate*-

itr rate'-

Pyruvate-

Succinate2-

Gluconate-

Formaldehyde

A ce t a t e -

Lactate-

Di hydrox yacetone

Glucose

Glycerol

Manni tol

Propionate

Et hyleneglycol

Acetoin

Butanediol

Acetone

Methanol

Ethanol

Propanol

n-Alkanes

Butane

M e t h a n e

0

0

1 o

2.0

2.0

2.0

2.5

2.67

3.0

3.0

3.33

3.5

3.66

4

4

4

4

4

4.66

4.33

4.66

5 O

5.0

5.5

5.33

6

6

6

6.13

6.5

8

1

1

2

1

1

2

4

3

4

6

3

4

6

1

2

3

3

6

3

6

3

2

4

4

3

1

2

3

6

4

1

9

3

2

1

5

1

1

1

2

5

2

5

6

1

4

2

1

8

4

5

1

1

3

3

1

3

4

2

1

1

1

3494

1061

1224

1105

1107

709

584

757

380

381

316

422

311

587

529

296

257

284

345

338

556

617

457

469

813

729

712

725

662

1061

1011

a

For

electron donor with reversed electron transfer.

For electron donor without reversed electron transfer.

tions on heat- or chemical entropy-related Gibbs energy

dissipation; each can be positive or negative. Table VIII

shows some data for aerobic and anaerobic growth with

glucose,

H2,

or acetate as electron donor, which use

glucose, C02,and acetate as C-source. It can be seen

that the total Gibbs energy dissipation,

D:l/rAx,

emains

very similar for the same C-source, with different elec-

Table

VIJ.

Biomass yield, heat production, an d Gibb s energy dis-

sipation for growth of yeast under aerobic, part ly anaerobic, and

anaerobic condition^?^

Gibbs energy

Measured dissipation

Biomass Ethano l heat production

(DsU1/rAx)

yield yield kJ/C-mol k J/C-mol

C-mol/C-mol C-mol/C-mol biomass biomass

0.57 0 339 332

0.52 0.082 313 307

0.40 0.228 250 306

0.23 0.440 160 312

0.19 0.512 114 230

0.14 0.566 95 255

tron acceptors. The relative contribution of heat- and

chemical-related Gibbs energy dissipation is, however,

quite different. During aerobic growth on glucose, there

is a small chemical entropy consumption, but nearly

all dissipation is due to heat. In anaerobic growth on

glucose, the main dissipation comes from chemical en-

tropy production which is due to the degradation of a

large molecule (glucose) into small fragments (ethanol

and

Con).

Because the total dissipation is more or less constant,

this results in much less heat production under anaero-

bic conditions. With aerobic growth on H2 , here is a sig-

nificant chemical entropy consumption, because small

molecules

( H 2 ,C02)

re converted into larger molecules

(biomass). This entropy consumption must be “paid for

by extra dissipation from heat production. This effect is

even more pronounced under anaerobic conditions

(4H2 + COz combine to give CH4+ 2Hz0),resulting

in a very large entropy consumption and, therefore, a

very large heat production. In contrast to glucose, the

use of H2as an electron donor gives a heat production

848

BIOTECHNOLOGY A ND BIOENGINEERING, VOL. 39, NO. 8, APRIL

5,

1992


17/26

Table

VIII.

contribution of heat- and chemical entropy-related dissipation.

Gibbs energ y dissipation and heat production

for

aerobic and anaerobic growth on glucose, H2, and acetate, and the relative

Dissipation due to

Ref.

Microbial

system

Chemical

YDx dissipation heat entropy

C-mol/(C)-mol kJ/C-mol k J/C-rnol k J/C-m ol

Cond itions donor biomass biomass biomass

Total

35 Saccharomyces cerevisiae Glucose /02

35 S. cerevisiae Glucose/

34 H Zbacterium

Hz + COz/Oz

aerobic

0.57

332 +339 -7

anaerobic

0.14 270 +95 +175

aerobic

0.13 1265

+

1686 -421

24 Methanobacterium arborophilus Hz + COz/CO2

anaerobic

0.015 1035 +3923 -2888

31 Pseudomonas oxalaticus Acetate/Oz

45 Methanobacterium soehngenii Acetate/CH4

aerobic 0.406 562 +593 -31

anaerobic 0.024 597 0 +687

per C-mol biomass under anaerobic conditions, which is

much higher than under aerobic conditions. Finally, for

microbial growth on acetate under aerobic conditions,

nearly all of the dissipation comes from heat produc-

tion, and there is only a small amount of chemical

entropy consumption. During anaerobic growth on

acetate (which is converted to C H4 and C02 /HC0 3- ),

there is a calculated net

hear uptake,

because the con-

version of acetate into gaseous C0 2and CH4 produces

so much entropy.

These results clearly show the inadequacy

of

heat pro-

duction as a correlating parameter for biomass yields,

because large changes are associated with a change in

electron acceptor. Furthermore, it is quite interesting to

see that microbial growth can possibly be accompanied

by heat uptake.

Different organic electron donors

have the same ef-

fect as different organic C-sources. During autotrophic

growth, it appears that there is a fairly constant value

of

DP'/rAx

f about 1000 kJ/C-mol for different electron

donors when reversed electron transfer is not required

(H 2, CO, Table VH). This value is in line with the

extrapolated values for a C-source (COz) where y = 0

(Fig. 6A). However, when reversed electron transport

is involved, a significantly increased value of

D P1 / r A x

of about 3000 to 4000 kJ/C-mol biomass is found

(Table VH). The nature of the electron donor (Fe2+,

NOz-, NH4+,S2032-, etc.) exerts no systematic influ-

ence. It is remarkable that , for photoautotrophic growth

of

Chlorella vulgaris,

a Gibbs energy dissipation of

3575 kJ/C-mol biomass occurs.15 This coincides with

the value for chemoautotrophic systems, which use

reversed electron transport.

DISCUSSION

It

is

evident that one can use

DP'/rAx

s a correlating

parameter to estimate microbial growth yields.

As

a first

approximation, one can conclude that

Dj) ' / rAx

s mainly

determined by the nature of the C-source and whether

reversed electron transport is required.

Table VI contains the average values of

DS' /rAx

hich

are found for a large number

of

C-sources.

Furthermore, a correlation has been found [eq. (l)]

which describes the data of Table VA-H for electron

donors when no reversed electron transport occurs.

D:'/rAX

=

200

+ 18(6 -

c)'

+ ExpC((3.8 - Y ~ ) ' } . ~ ~

(3.6 + 0.4C)I

(1)

For electron donors that necessitate reversed electron

transport one finds a constant value of

D F / r A x

f about

3500 kJ/C-mol. In eq. l),

C

is the number of C-atoms

and

ys

is the degree of reduction of the substrate

C-source.

Figure 6A shows how the correlation eq.

(1)

compares

to the data. Figure 6B shows the comparison of actual

and calculated [eq. l)] issipation values. It can be con-

cluded that eq.

(1)

gives the

D f l / r A x

alue for an arbi-

trary C-source with

30%

error. Hence, eq. (1) can be

used for nonlisted C-sources to calculate a first estimate

of

D : l / r A X .

t is now interesting to compare calculated

and measured biomass yield values. YDx an be calcu-

lated from

D P1 / r A x

or any particular microbial system

by a simple procedure (Appendix F). It should be kept

in mind that the relation between

YDx

and

D:l/rAX

is

nonlinear to such an extent that errors in

DP1/rAx

o lead

to smaller errors in Yox.Said calculation YDx rom

D : ' / r A x )

s, however, lengthy (Appendix F), and there-

fore, a simple mathematical relation has been derived

which gives

YDx

s a function of the Gibbs energy char-

acteristics of C-source, electron donor, electron accep-

tor, and biomass (J. J. Heijnen, manuscript submitted).

Figure 7A shows the result when the values of

D:'/rAx

from Table VI are used to calculate the

Y D x

alues of

the microbial systems

of

Table

VA-H.

Figure 7B shows


849


18/26

,

Y, measwed

( A)

1

1

0.1

0 0 1

0 0

1

0.1

1

Y, measwed

(B)

Figure 7.

(m) anaerobic systems. (A ) Average dissipation data from T able VI. (B) Calculated dissipation data from eq. ( 1 ) .

Comparison between actual (Table VA-H ) and est imated Y D X ata from D y / r A xvalues. (+) Aerobic; (+ ) denitrifying;

the result when

D, ' /rAx

s calculated fro m eq. (1). It can

be seen that YDXan be predicted w ith 13% erro r over a

YDx

ange from 0.01 to

0.8

C-mol biomass per (C)-mol

donor if the dissipation values

of

Table VI are used, and

with

19%

error if eq. (1) is used.

On the basis of these results, it appea rs that chemo-

trophic microbial gro wth ca n be characterized and pre-

dicted by the simple black box parameter D ; l / r A x .

T h e effect

of

C-sou rce, electron donor, and electron

acceptor on

D p l / r A x

an be summarized as follows. It ap-

pears that D: l / r A x is mainly dependent on the

C-source

used. Typically, the degree

of

reduction (0 to

8)

and

the C -chain length (1 to 6) exert a major influence. Val-

ues of D , l / r A x range between 150 and

3500

kJ/C-mol

biomass. Electron acceptor

02 , O3-,

fermentation)

has l i t t le o r no e f fec t on

D : l / r A x .

Organic electron

donors, which function as C-source (chemo heterotrophic

growth), have the same effect as organic C-sources.

With inorganic donors, where CO, i s the C-source

(chemoautotrophic growth), the effect of the electron

donor depends on the o ccurrence

of

reversed electron

transport. If this does not occur (e.g., H 2 , CO as elec-

tron donor) the value of Df1/ rAX

s

about

1000

kJ/C-mol

biomass, and seems to be independent of the electron

donor. When reversed electron transport does occur

(e.g., Fez',

N H 4 + ,

N O 2 - ,

SZO3*-,

tc . ) , the va lue of

D P / r A x is about 3500 kJ/C-mol biomass and , again, ap-

pears to be independent of the electron donor.

On e might wonder about th e origins of the observed

correlation (Fig. 6A). In th e opinion

of

the authors, the

correlation is th e result

of

th e fact that biochemical pro-

cesses are similar in all microorganisms. Depending on

the available C-source, a microbial system must carry

out many o r few biochemical reactions to arriv e at the

correct redox level and carb on chain length of the build-

ing blocks for biomass synthesis. A microbial system

which has

C 0 2

s its C-source must carry out more re-

duction reactions and carbon-carbon coupling reactions

th an a microbial system which uses glucose. Glucose is

much closer to th e redox level of biomass and the typi-

cal biomass building blocks which contains about

4

to

5

C-atoms. Thus, much more reaction steps, and hence

much m ore dissipation

of

Gib bs energy, are involved in

C 0 2 ssimilation tha n in glucose utilization. Analogous

reasoning applies to substrates such as formaldehyde or

methanol.

Similarly, the presence of an electron transport chain

02, O3-) results in somewhat more dissipation per

C-mol biomass compared with i ts absence (fermen-

tatio n). Th us, the e xtra facility of electron transport

phosphorylation requires fur the r chemical reactions, re-

sulting in the additional Gibbs energy dissipation of

about 50

to

150 kJ/C-mol. In the same way, the con-

sequence of reversed electron transfer is apparently an

additional dissipation of about

2500

k J/C-mol biomass,

as compared to autotrophic growth without reversed

electron transfer. Reversed electron transfer seems a

very costly process.

The Gibbs energy dissipated per C-mol produced

biomass thus appears to be a straightforward measure

850


39,

NO. 8, APRIL

5,

1992


19/26

Table IX. Com parison between the theoretical ATP requirement for biomass synthesis on

different carb on s o ~ r c e s , ~ ~ ~ ~nd found values of Gibbs energy dissipation (see Table VI).

YATP Theoretical

theoretical

ATP need Found

biomass production for biom ass

Gibbs energy

o n ATP synthesis dissipation

Carbon source g/mol ATP mol ATP/C-mol biom ass kJ/C-mol biomass

Glucose

28.8 0.85 280

Malate

15.4 1.69 380

Acetate

10 2.46 530

Ethanol

10 2.46 710

COZ a 6.6

3.73

1060

C 0 2

2.5 9.85

3500

a No

reversed electron transport.

Reversed electron transport.

of the amount of work required and spent to synthesize

biomass from a given C-source, electron donor, and

electron acceptor. As such, this parameter should re-

semble 1 / Y A T p , which provides the theoretically needed

amount of ATP to synthesize biomass from a specific

C-source.

Table

IX

and Figure

8

show a comparison of the theo-

retical ATP requirement for biomass synthesis in moles

ATP/C-mol b i o m a ~ s ' ~ , ~ ~nd the Gibbs energy dissipa-

tion values (in kJ/C-mol biomass) found for different

C-sources. There appears to be a very good correlation,

indicating that the parameter

D:'/rAx

can be considered

the thermodynamic equivalent of the biochemically-

based parameter 1/YATp.

Finally, some words of caution. The derived relation-

ship [Fig. 6A, eq.

l),

Table VI], which gives D, '/rAxor

various C-sources, will give only a first approximation

3500

3000

2500

=

2

2.5

of the biomass yield. It is bound to be of limited accu-

racy because the actual biochemistry involved has not

been taken into account. Of course, the absence of the

need for biochemical details is the attractive feature of

this approach, but it also limits the accuracy of yield

predictions.

This point is illustrated by the system where micro-

organisms convert sugar anaerobically to ethanol. Using

the present approach described here, one would esti-

mate a biomass yield of about 0.13. This is correct for

S. cerevisiae, but wrong for Zymomonas mobilis, where

YDx = 0.06.

The difference between the two microor-

ganisms is biochemical.

S.

cerevisiae employs the gly-

colysis route, which gives

2

mol ATP/mol glucose, while

Zymomonas mobilis

uses the Entner-Doudoroff path-

way, which generates only 1 ATP/mol glucose.

A second illustrative example is the aerobic growth of

microorganisms on formate. Biochemically, two differ-

ent types of microorganisms are known. The autotrophs

(such as P. oxalaticus or Paracoccus denitrijicans) oxi-

dize formate to COz, and subsequently assimilate the

COz to biomass. Typically, these microorganisms have

a biomass yield of about 0.14C-mol/C-mol, and a Gibbs

energy dissipation of about 1300 kJ/C-mol.

The heterotrophs (such as Pseudomonas sp.

1

or 135)

can assimilate formate directly to biomass without first

oxidizing it to COz. The yield obtained with hetero-

trophs is about

0.23

C-mol/C-molZ9 nd the Gibbs en-

ergy dissipation is about 600 kJ/C-mol biomass. Using

the approach described here, a yield of about

0.16

for

both formate systems would have been calculated.

ooov

, , , , ,

15.4

500

0

0

1 2 3 4 5 6

7

8

9 10

l /YA,p ( mo l ATP/C- mo l b io m a s s )

Figure

8.

ues. Data from Table

IX .

Comparison between ~/YATP nd found dissipation val-

CONCLUSION

It has been shown that all published parameters to es-

tablish a prediction for biomass yield are subject to

limitations and problems. Notably, the Gibbs energy ef-

ficiencies suffer from intrinsic problems. However, a

simple (and biochemically understandable) prediction

can be based on the Gibbs energy dissipation per C-mol

biomass produced. It is shown that, for a wide variety of


OF

MICROBIAL GROW TH

851


20/26

microbial growth systems, in which YDx aries between

0.01

and

0.80,

this method provides an estimated bio-

mass yield with an error of about 13%.

The authors thank Prof . K. van Da m, Prof .

U.

von Stockar,

and D r . H .V . W es t e r hof f f o r f r u i t f u l d i s cus s i ons , and

Dr .

L.

Rober t son for cor rect ion of the text .

NOMENCLATURE

yield

of

biomass on electron donor ( per mol or per C-mol

for carbo n compou nds) [C-mol/(c)-moll

yield of biomass on ATP (g/mol ATP)

yield of biomass on available electrons (g/mol electron)

carbon efficiency (-)

oxygen efficiency (-)

enthalpy efficiency

(-)

Gib bs energy efficiency from black box description

(-)

Gibbs energy efficiency from the conservation descrip-

t ion

(-)

Gibb s energy ef fic iency for Gib bs energy conver tor de-

scription

(-)

Gibbs energy diss ipat ion in microbial growth sys tems

(kJ/m3 h)

net production rate of biomass (C-mol/m3 h)

degree of reduction of electron donor (-)

degree of reduction

of

substrate

(-)

reaction G ibbs energy (kJ)

react ion Gibb s energy conservative react ion ( kJ)

reaction Gibbs energy nonconservative reaction (kJ)

APPENDIX A: CAL CULATION OF qBB

For microbial growth systems, one can form ulate the black box de-

scription if the electron acceptor, the N-source, and the yield of

biomass

on

the e lect ron donor i s known. Th is descript ion can be

presented in various ways, but i t is eas ies t to calcula te the macro-

chemical reaction equation. In this equation, biomass is formed

from the C -source , the N-source , and e lect ron acceptor . The s toi -

chiom etric coefficients follow from:

use of the elemental and electric charge conservation principles.

set t ing the stoichiometric coefficient of biomass to +l .

using the available yield value

of

biomass on C-source/electron

qB B an now be calcula ted f rom the macrochemical equat ion. T he

proced ure wil l be i l lustrated

for

the aerobic growth of Pseudomonas

oxulaticus and the anaerobic growth of Klebsiellu uerogenes

on

a

variety of organic carbon sources .

donor.

Aerobic Growth of Pseudomonas oxalaticus on

Oxalate as C-source

Given a yield of 0.086 C-mol biomass/C-mol substrate, and using

the fact that NH4+ s the N-source and 0 2 he electron acceptor,

whi le H2O and HC03- are produced, one can es tabl ish the follow-

ing macrochemical equ ation as the black box description (including

the react ion Gibbs energy AG

g).

For biomass, the composit ion

quoted by Roels is used.28 Th e stoich iometric coefficients follow

from charge, C , H, 0 , and N conservat ion.

-5.815CzO42-

-

0.2NH4'

-

0.8H'

-

1.85702 - 5 .42H z0

+ lCHI.gOo.~N0.z+ 10.63HC03- = 0

AG:'

= -1048 kJ

Th e compou nds wi th a negat ive s toichiomet ric coef f ic ient are ob-

viously consumed, whi le

Date post:	06-Jul-2018
Category:	Documents
Upload:	bo-fan
View:	219 times
Download:	0 times

Heijnen Et Al-1992-Biotechnolo1gy and Bioengineering

Documents