heijnen et al-1992-biotechnolo1gy and bioengineering
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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
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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.
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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-
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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
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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
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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
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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
Clostridium butyricum
(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
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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-
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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.
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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
Substrate Composition
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
Substrate Composition
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
Substrate Composition
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
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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.
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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
Clostridium butyricum
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
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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.
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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
degree o f reduc t i on
(E)
degree o f reduc t i on
(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
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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-
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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
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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
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,
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
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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
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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