Báo cáo khoa học: Super life – how and why ‘cell selection’ leads to the fastest-growing eukaryote doc

Super life – how and why ‘cell selection’ leads
to the fastest-growing eukaryote
Philip Groeneveld1, Adriaan H. Stouthamer1 and Hans V. Westerhoff1,2,3
1 Department of Molecular Cell Physiology & Mathematical Biochemistry, Netherlands Institute for Systems Biology, Vrije Universiteit,
Amsterdam, The Netherlands
2 The Manchester Centre for Integrative Systems Biology, Manchester Interdisciplinary Biocentre, School of Chemical Engineering
and Analytical Science, The University of Manchester, UK
3 Swammerdam Institute for Life Sciences, Netherlands Institute for Systems Biology, University of Amsterdam, The Netherlands

Keywords
highest eukaryotic growth rate; modular
control analysis; pH-auxostat selection;
surface-to-volume ratio optimization;
systems biology
Correspondence
H. V. Westerhoff, The Manchester Centre
for Integrative Systems Biology, SCEAS,
The University of Manchester, Manchester
Interdisciplinary Biocentre (MIB), 131
Princess Street, Manchester M1 7ND, UK
Fax: +44 161 306 8918
Tel: +44 161 306 4407
E-mail:
(Received 20 December 2007, revised 26
October 2008, accepted 3 November 2008)
doi:10.1111/j.1742-4658.2008.06778.x

What is the highest possible replication rate for living organisms? The
cellular growth rate is controlled by a variety of processes. Therefore, it is
unclear which metabolic process or group of processes should be activated
to increase growth rate. An organism that is already growing fast may

already have optimized through evolution all processes that could be optimized readily, but may be confronted with a more generic limitation. Here
we introduce a method called ‘cell selection’ to select for highest growth
rate, and show how such a cellular site of ‘growth control’ was identified.
By applying pH-auxostat cultivation to the already fast-growing yeast
Kluyveromyces marxianus for a sufficiently long time, we selected a strain
with a 30% increased growth rate; its cell-cycle time decreased to 52 min,
much below that reported to date for any eukaryote. The increase in growth
rate was accompanied by a 40% increase in cell surface at a fairly constant
cell volume. We show how the increase in growth rate can be explained by a
dominant (80%) limitation of growth by the group of membrane processes
(a 0.7% increase of specific growth rate to a 1% increase in membrane surface area). Simultaneous activation of membrane processes may be what is
required to accelerate growth of the fastest-growing form of eukaryotic life
to growth rates that are even faster, and may be of potential interest for
single-cell protein production in industrial ‘White’ biotechnology processes.

There is considerable interest in what determines the
rate at which reproductive growth occurs. This issue
is most intriguing for the ‘maximum’ growth rate
(Jgrowth-max) of the fastest independently replicating
organism, relatives of which are used commercially as
‘living factories’. The fastest-dividing organisms are
micro-organisms, and we limit our analysis to eukaryotic microbes, as they are most similar to cells of
higher organisms. The cell-cycle time of one of the
fastest-growing eukaryotes (i.e. a generation time of
70 min [1]) is still seven times longer than that of one
of the fastest-growing prokaryotes (i.e. a generation
time of < 10 min [2,3]). One of the known fastestgrowing microbial eukaryotes is the non-pathogenic
industrial yeast Kluyveromyces marxianus, which GRAS
status (‘generally recognized as safe’). For these reasons,
254

this organism has been chosen as an efficient vehicle
for single-cell protein production [4–7]. In this context,
we do not consider early transient cleavage during fast
embryonic growth of eukaryotes such as Xenopus
laevis [8]. Reproduction in terms of cell number by
cleavage is much faster but the net biomass remain
constant. Here, we refer to the highest reproduction
rate of cells in terms of the maximum specific growth
rate (lmax), which is expressed as an increase in net
flux of biomass, Jgrowth-rate, per unit of cell mass or
total protein, and equals ‘ln 2’ divided by the generation or cell-cycle time. The questions posed in this
study also address the minimum cell-cycle time.
The maximum (specific) growth rate refers to cellular biosynthesis during which all nutrients are supplied
in excess (i.e. substrate-saturated conditions relative to

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P. Groeneveld et al.

their transporter enzymes), and is therefore only
limited by the biological properties of the cell itself [1].
In so-called ‘rich’ media, substrate-saturated conditions
refer to the ample supply of undefined monomeric
nutrients in addition to provision of the main basic
carbon (C) and Gibbs free-energy (E) sources. In
defined ‘mineral’ media, cells have to synthesize these
monomers from the basic C ⁄ E sources together with
mineral salts and vitamins. If these biosynthetic pathways are insufficiently active (due to shortcomings of

any possible metabolic process within or coupled to
these pathways), the lmax on mineral medium will be
lower than that on rich medium. Under both conditions, control of lmax is solely determined by the biological properties or ‘dynamic hardware’ of the cell
itself, properties that may comprise at least four main
metabolic processes, i.e. catabolism, anabolism, maintenance and transport [9–11]. Each of these metabolic
groups consists of a network of interacting metabolic
pathways through which substrates flow, and by which
products, including new cell material, are formed. It is
unknown which individual process exercises the strongest constraints on the flux into new cell material, and
hence ‘controls’ lmax [12–14]. In baker’s yeast (Saccharomyces cerevisiae) for instance, the primary catabolic
pathway is glycolysis, and any of the components of
this pathway might have been expected to control glycolytic flux and growth. It has been shown, however,
that the control of the glycolytic enzymes on the glycolytic flux is rather small in this yeast. [15–19]. There is
substantial, but incomplete, evidence for a high control
of the glucose-uptake step on the yeast glycolysis
[16,19–21]. Control by glucose transport has been
shown to be limited in Salmonella typhimurium [22]. It
is a frequent observation that activation of single
aspects of cell metabolism fails to increase major fluxes
in the cell such as the growth rate [17,23,24]. This has
been attributed to a shift of the limitation to the
second most rate-limiting step [25]. Indeed, control
of fluxes is often distributed among several steps and
layers [26–31].
For biotechnologists, this is bad news, as further
increases of microbial productivity do not seem to be
as simple as over-expressing a single rate-limiting
enzyme. Although solutions to this problem have been
devised in principle, they require over-expression of
large proportions of the of cell metabolism to the same

strictly related [32] or to rather diverse [33] extents.
The enzymes that need to be over-expressed to the
same extent belong to a functional unit [34,35] or level
[36] of cell metabolism. Intracellular chemistry appears
to be organized in terms of such modules, which often
correspond to operons or regulons [37]. The cell itself

Control of highest eukaryotic growth rate

may modulate its fluxes by increasing the expression
level of such a regulon as a whole, through a single
transcription factor [38–40]. Consequently, a new
approach to bioengineering may be to first identify the
natural regulons of the host organism and then modulate their activities towards the desired effect [41].
Changes in the morphology of micro-organisms may
influence their physiology, because some cellular fluxes
depend primarily on cell volume and others on the cell
surface area [42]. This distinction plays an important
role in understanding why unicellular organisms are as
small as they are. With increased size, the surface-tovolume ratio decreases, and the supply rate of Gibbs
energy and chemical substrates becomes insufficient for
cytoplasm-based catabolic and anabolic processes [43].
With regard to identification of what limits the growth
rate of already fast-growing unicellular organisms,
membrane-located processes (or outer wall transport
[23]) are therefore possibly a major site of control. The
dynamic energy budget (DEB) model [44,45] reinforces
this viewpoint. It describes microbial growth as based
on cellular uptake capacity and volume. The former
is considered proportional to the cell surface and is

assumed to control growth proportionally. Thus variation in cell morphology may change the cell’s surfaceto-volume ratio and hence its specific growth rate.
In a similar vein, Hennaut et al. [46] have specifically shown for the three anabolic substrates arginine,
lysine and uridine that the relative uptake rates
decrease in proportion to the surface-to-volume ratio
in a series of isogenic multiploid strains of baker’s
yeast growing on defined medium enriched with these
monomers. Transport of these substrates is catalyzed
by constitutive permeases [47–49]. For substrates such
as methionine and leucine, for which transport is
inducible [50], such a decrease was not observed. The
results of the study by Hennaut et al. [46] imply that
the cytoplasmic membrane in a haploid strain is saturated (or nearly saturated) with these constitutive
permeases. With increasing ploidy, the cell surface may
become more and more limited for permease insertion,
as the increase in cell surface will fall short of the
increase in cell mass or cell volume. We surmise that if
the major site of control on growth rate indeed resides
in the module of membrane processes, and if the activity of these processes per cell increases with increasing
membrane surface area per cell, selection for increased
maximum growth rate (lmax) should yield strains with
increased surface-to-volume ratios.
Although substantial progress is being made with
regard to understanding of the modular organization
of cell metabolism [35,51], it is not yet feasible to predict how the module of membrane processes may

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P. Groeneveld et al.

be activated selectively. However, as the issue is one
of growth rate, it may be possible to manipulate the
organism to do this by itself. With this aim, the organism should be cultivated under conditions that select
for increased lmax. For already fast-growing microorganisms, it is difficult to perform such an experiment
under well-defined fermenter conditions. During batch
cultivation, there is only a limited time period during
which the cells are in steady state. At higher cell densities, factors other than lmax are selected for. The bestknown continuous culture system, the chemostat
[52,53], is not suitable because it is unstable at dilution
rates close to lmax. Of the suitable continuous culture
systems, such as the turbidostat, or permittistat [54]
and the pH-auxostat [55,56], we here chose the latter
to select for increased lmax.
A second uncertainty in our objective of selecting a
faster-growing variant of an already fast-growing
eukaryotic microbe is whether such a variant can exist
at all. Because of the maximum limit of diffusion-limited association, and because the complicated
chemistry of some biochemical reactions takes time,
there are maximum rates at which the processes synthesizing new cell material can operate. Making more
enzymes to catalyze these processes shifts but does not
eliminate the upper limit of growth rate, as the new
enzymes also have to be synthesized [57–59]. Consequently, due to limitations of chemistry, physics and
biocomplexity, there must be a ‘highest possible’ maximum specific growth rate for living organisms, i.e. a
‘lowest minimum’ cell-cycle time. As additional processes may well serve to enhance rates and efficiency,
this highest possible growth rate is unlikely to be
found in so-called ‘minimal organisms’, i.e. organisms
with the smallest possible genome [60] or in extreme

thermophiles [61], because both are associated with
slow growth. Yeasts from the genus Kluyveromyces,
however, constitute a case in point because of their
excellent (industrial) growth characteristics. K. marxianus, in particular, already has a high specific growth
rate (approximately twice as high as baker’s yeast), a
high aerobic biomass yield (because of its Crabtreenegative physiology [55,62]) and a high optimum
growth temperature (40 °C, which reduces the cooling
costs of large bioreactors) [15,63]. Therefore, K. marxianus may be close to the true ‘absolute’ maximum
growth rate, perhaps even too close for any further
increase to occur on defined medium conditions.
In this paper, we address four questions: (1) Can
one use the pH-auxostat to select for even faster-growing variants of fast-growing eukaryotic micro-organisms? (2) Can an industrially useful yeast such as
K. marxianus grow even faster than it already does?
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(3) What is the fastest possible growth rate for eukaryotic life on defined medium? (4) To what extent does
this indicate that the highest growth rate is controlled
by the surface-to-volume ratio? We report the selection
of a much faster-growing variant of K. marxianus with
an almost proportional increase in surface-to-volume
ratio. We developed a bimodular control analysis to
express growth control in quantitative terms for two
separate cellular groups (functional modules). Control
exerted by transport processes (module 1, including all
membrane-located processes) and that exerted by intracellular metabolism (module 2, including all cytoplasm-based processes) was defined and quantified.
In the present post-genomic era, the methodologies
presented here may offer a new integrative ‘top-down’
systems approach [10,64] for the identification of major
sites of control on cellular growth rate.

Results
General characteristics of a pH-auxostat
When continuous cultivation of microbial cultures at
maximum specific growth rate (lmax) is required for
and growth is accompanied by changes in pH,
pH-auxostat or ‘phauxostat’ culturing may be the
method of choice [56]. The pH-auxostat is a continuous culture system in which, unlike the chemostat, the
dilution rate can vary according to the properties of
the micro-organism. As in the chemostat, there is a
continuous supply of growth medium and an equal
continuous efflux of culture. The two fluxes are measured in terms of volume per unit time per unit volume
of the culture, i.e. the dilution rate, D. In the pH-auxostat, addition of fresh medium is coupled to pH control of the medium in the culture vessel. As the pH of
the culture drifts from a given set point, fresh medium
is added to bring the pH back to the set point. Thus,
this system has an external control loop that keeps the
pH difference between the culture vessel and the reservoir constant by adjusting the dilution rate. When the
difference in pH (DpH, defined as pH culture ) pH
reservoir, which in our set-up has a negative value),
the biomass concentration is determined only by the
buffering capacity of the inflowing medium (BCR,
defined as the amount of acid or base required to
change the pH of 1 L of the medium in the reservoir
to the pH of the medium in the culture vessel [56]),
provided that a constant number of protons are produced per unit biomass synthesized. The rate of
growth is independent of BCR and DpH, and
depends only on the conditions under which the
micro-organism is cultured and the properties of the

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Selection for highest cellular growth rate
(minimum cell-cycle time)
K. marxianus CBS 6556 was cultured in a pH-auxostat
growing on defined mineral medium with all nutrients
(essential vitamins and mineral salts with ammonium
as the main nitrogen source) in excess and with glucose
as sole carbon and Gibbs free-energy source. A few
hours after inoculation, the culture produced enough
protons to trigger the feed pump, supplying the culture
with fresh medium (pH 6.2), which kept the culture
pH constant at 4.5. From that point, a continuous
supply of fresh medium by the pH-controlled pump
and the removal of equal amounts of culture medium
by the fermenter overflow-outlet, keep all physiological
parameters constant in time. The average maximum
specific growth rate (lmax) of the yeast population,
measured online as the culture’s dilution rate (D), was
0.6 h)1, (g new biomass per g biomass per hour) and
appeared to be constant during the initial 60 h of cultivation (Fig. 1, Exp. 1). After this long stable period
(which corresponds to 50 generations), the culture’s
dilution rate suddenly began to increase, i.e. the average lmax increased from 0.6 to 0.8 h)1 within a period
of approximately 40 h. This second steady state
remained constant for more than three subsequent
days. The entire experiment was repeated more than
three times with essentially the same results. Another
of these experiments is also shown in Fig. 1 (Exp. 2),
exhibiting an increase of lmax from 0.57 to 0.79 h)1.
The ratios of the lmax values for the first steady state
to that for the second steady state in these long-term

pH-auxostat cultivations were 1.33 and 1.39 for the
two independent complete experiments.
The highest cellular growth rate remains stable
outside the pH-auxostat
To exclude any culture contamination with other
micro-organisms, e.g. with faster-growing prokaryotes,
liquid samples from the pH-auxostat were taken before
and after selection; both cultivars were identified as
K. marxianus CBS 6556 at the Centraal Bureau voor
Schimmel (CBS Delft). Nutrient variation between
both steady states was excluded by changing vitamin

A
Average cell size, diameter (µm)

micro-organism itself. By computerized feedback control, the dilution rate is adjusted so as to make the pH
independent of time. When all growth substrates are
supplied in sufficient excess and the BCR and DpH are
kept constant, a steady state at lmax can be maintained
at which the pH and biomass concentration in the culture vessel remain constant.

Control of highest eukaryotic growth rate

Average cell-size (diameter) Exp.2
D = µmax Exp.1
D = µmax Exp.2

B
µmax = 0.8 h–1

µmax = 0.6 h–1

Maximum specific growth rate, µmax (g·g–1·h–1)

P. Groeneveld et al.

Time (h)
Fig. 1. Specific growth rate and average cell size during two longterm pH-auxostat cultivations of K. marxianus. Right ordinate:
steady-state dilution rate that equals the culture’s average maximum specific growth rate (lmax) on defined mineral medium at
optimal culture conditions (i.e. saturated concentrations of all
growth substrates, full air supply, pH 4.5 and temperature 40 °C;
open diamonds, lmax for experiment 1; closed squares, lmax for
experiment 2). Left ordinate: change in average cell size (i.e. mean
cell diameter in lm as measured with a Coulter Counter particle
size analyzer) during the second long-term pH-auxostat cultivation
(closed circles, experiment 2). Inset: log of the percentage carbon
dioxide production and oxygen consumption during regulated batch
cultivation. Two batch cultures were inoculated with either selected
or initial K. marxianus colonies.

and mineral concentrations in control experiments; no
effect on the pattern of dilution rate was observed. In
addition, plated colonies of the initial K. marxianus
CBS 6556 strain (obtained during the first steady state)
and of the selected variant of our K. marxianus CBS
6556 strain (obtained during the second steady state)
were examined in subsequent regulated batch cultures
(as shown in the inset to Fig. 1). The selected population produced much more carbon dioxide over time, in
agreement with its increased growth rate. From the
gas exchange, we calculated the lmax value under batch

conditions. During the exponential growth phase, gas
exchange (oxygen consumption and carbon dioxide
production) should be directly proportional to the
maximum specific growth rate. The lmax for the
selected cells remained 0.8 h)1, and that for the initial
population was again 0.6 h)1. We also verified the stability of the new growth characteristics by frequently
re-plating a colony of the selected cells on defined
medium agar plates. The selected growth rate did not
revert to the initial value after re-plating more than 10

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P. Groeneveld et al.

times (see inset to Fig. 1). As shown in the inset to
Fig. 1, the re-plated colonies started in the pH-auxostat at a lmax of 0.8 h)1, whereas the lmax of cells from
the initial steady state remained at 0.6 h)1. Clearly,
the characteristics gained in the pH-auxostat were
inherited over more than 400 generations (assuming at
least 40 generations per plate) in a non-pH-auxostat
environment. Finally, we tested the stability of the
selected higher growth rate by glucose-limited chemostat cultivation; 120 h of steady-state glucose-limited
growth at sub-maximum rate (Dss = l = 0.2 h)1) did
not cause the selected growth performance of
K. marxianus to revert to the initial value (data shown

in [1]). Therefore, it was not likely that the increase in
lmax was caused only by an unknown, reversible
mechanism of cellular adaptation which occurred
under these rather special pH-auxostat conditions.
Morphology changes during selection for highest
growth rate
As can be seen in Fig. 1 (left ordinate), the average
cell-size distribution was constant during the initial
60 h of pH-auxostat cultivation. However, during the
sudden increase in dilution rate, the average cell size
(measured as relative cell diameter) increased in parallel with the increase in cellular growth rate. The

increase was accompanied by significant alterations in
the average cell-size distribution (see Fig. 2A). The distribution of the average cell-size increased within 40 h
in parallel with the increase in specific growth rate
each time after 60 h from the beginning of the steady
pH-auxostat cultivation. However, these data are just
a rough indication of the cell-size distribution in the
yeast population and could not be used to calculate
average relative changes in cell sizes. Therefore, we
used a phase-contrast microscope to measure the average relative changes in cell sizes within the yeast population. These microscopic observations accurately
revealed the cause of the alterations in gross cell-size
distribution: the average individual cell morphology
changed considerably during the selection for highest
growth rate. The cell shape changed from spheroid (or
ovoid) to an elongated cell form between the two successive pH-auxostat steady states (see Fig. 2B,C).
Although yeasts are usually regarded as discrete budding ovoid cells, some genera exhibit dimorphism by
producing mycelial or elongated growth forms under
certain environmental conditions [65]. Fig. 2 clearly
shows dimorphism of K. marxianus, i.e. transition

from round ovoid cell morphology to elongated filaments when selection for the highest specific growth
rate took place under defined optimal medium conditions in a pH-auxostat.

Cell-size distribution and morphology
during long-term pH-auxostat cultivation

Number of cells (10 6 cells·L–1)

A

B
b: bud or daughter
cell
m: mother cell

Steady state 1
µmax = 0.6 h–1
length spheroid (ls) = diameter (ds)

C
Steady state 2
µmax = 0.8 h–1

l = n· dc, f (with n = 6)

Average cell-size distribution (µm)
Fig. 2. Cell-size distribution (A) and morphology changes during long-term pH-auxostat cultivation at steady states 1 (B) and 2 (C) as determined using a Coulter counter particle size analyzer and observed under a microscope.

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Control of highest eukaryotic growth rate

The cell surface-to-volume ratio increased during
selection for the highest growth rate
We estimated surface-to-volume ratios based on microscopic observations. The calculations did not show
significant geometric changes in cell volumes (v) during
the alteration of cell morphology. (vspheroid = 0.113;
vcylinder = 0.104–0.120), nor in the biomass concentration of the culture (data not shown). We considered
the cell shape during the first steady state to correspond to that of round ovoid spheres (spheroid s, as
shown in the inset to Fig. 2B), and that during the
second steady state as elongated cells (cylinders, c,
or filaments, f, as shown in the inset to Fig. 2C).
We estimated the length (l) of elongated cells to
be approximately six times their diameter (d). As
described in Doc. S1, we estimated the volume and
surface area of the selected elongated cells in two
ways: by considering these cells as cylinders (c) with a
flat surface at both ends, or by considering these cells
as cylinder-like filaments (f) with both ends as half
spheroids. Accordingly, the surface-to-volume (s ⁄ v)
ratio of the two elongated cell types was estimated to
be between 1.44 and 1.50.
Quantification of growth control by outer
membranes versus intracellular processes
Had the growth rate been precisely proportional to the

s ⁄ v ratio, lmax would have increased by this same
factor i.e. between 1.44 and 1.50. The experimentally
determined increase in lmax of 1.33–1.39 was not
far from this ratio 1.44–1.50, suggesting that much
growth control might well reside in membrane-located
processes.
We then estimated how much growth control must
reside in the membrane processes to account for the
actual increase in maximum growth rate. For this, we
needed to define a quantifier for the extent of growth
control by the outer membrane. This quantifier is
called the control coefficient for growth control by
membrane processes, and is defined as the relative
increase in maximum growth rate for a 1% increase in
the activities of all membrane processes, or more precisely as:


d ln JgrowthÀmax
JgrowthÀmax

Cm
d ln m
where m refers to the activity of the membrane processes. Doc. S2 shows that this control coefficient is
related to the ratio of the relative increase in growth
rate and the relative increase in surface-to-volume ratio
um by:

l
Jgrowthmax
Cmmax % Cm

ẳ /m ỵ 1 /m ÞÁ

d ln lmax
d ln /m

l
where Cmmax refers to the control by membrane processes on the maximum ‘specific’ growth rate. Inserting
the experimental observations into this equation, and
assuming that the surface-to-volume ratio is 10%,
leads to an estimate for the control of maximum (specific) growth rate by the membrane processes of
0.8 ± 0.1. This implies that the control by cytoplasmic
processes must be 0.2 ± 0.1, i.e. the control by membrane processes exerted on the maximum specific
growth rate appears to be four times stronger than the
control by cytoplasmic processes. The response of the
maximum specific growth rate to an increase in surface
area should equal 0.8 ± 0.1 times that increase,
whereas the response of the maximum non-specific
growth rate (J) to such an increase should be
0.7 ± 0.1 times that increase (see Doc. S2, Eqn 14).

Metabolic flow distribution as a function
of growth rate and glucose availability
We further verified our findings by determining the
microbial physiology in the pH-auxostat and comparing the metabolic activity exhibited during selection for
highest lmax with that in glucose-limited chemostat
cultures. By using both culture systems, we were able
to measure the metabolic flows of K. marxianus as a
function of the full range of growth rates under
(defined) conditions of glucose limitation (chemostat)
and substrate saturation (pH-auxostat). The specific

cellular glucose and oxygen consumption rates,
together with the specific protein and carbon dioxide
production rates (qglu, qO2 , qCO2 and qp, respectively)
were determined for both culture systems. Stable
steady-state chemostat dilution rates (D = l) ranged
from 0.05 to 0.55 h)1 (Fig. 3).
The specific glucose uptake rates (qglu) ranged from
0.7 to 6.0 mmolỈg)1Ỉh)1 for the lowest to the highest
steady-state chemostat dilution rate, respectively. In the
pH-auxostat, stable glucose uptake rates started at
approximately 7 mmolỈg)1Ỉh)1 and increased in parallel
with the increase in lmax to 9 mmolỈg)1Ỉh)1, i.e. an
increase of approximately 30% as already shown in
Fig. 1 for the pH-auxostat dilution rate. The specific gas
exchange rates (qCO2 and qO2 ) in the chemostat ranged
from 2.3 to 16 mmolỈg)1Ỉh)1. During growth rate selection in the pH-auxostat, these increased from 17–18 to
23 mmolỈg)1Ỉh)1; a 30% parallel increase. All steadystate metabolic flows obtained before and after
pH-auxostat selection were in line with the chemostat
data, i.e. all flows corresponded to linear extrapolations

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P. Groeneveld et al.

Specific protein rate, qprotein (in g·g dw–1· h–1)

Specific rate rates (in mmol–1·g dry weight·h–1):

gas exchange (qgas); glucose consumtion (qglu);
Proton production (qH+)

Control of highest eukaryotic growth rate

Specific cellular growth rate (µ in g·g–1· h–1)
Fig. 3. Physiological properties of K. marxianus under glucose-limited chemostat conditions (solid lines: 0 < l < 0.55 h)1) and during
substrate-saturated conditions in a long-term pH-auxostat (dashed
lines: 0.57 < l < 0.8 h)1). Specific carbon production rate (qCO2 in
mmol per g dry weight per h; closed squares, chemostat; open
squares, pH-auxostat). Specific oxygen consumption rate (qO2 in
mmol per g dry weight per h; closed circles, chemostat; open circles, pH-auxostat). Specific glucose uptake rate (qglu in mmol per g
dry weight per h; closed diamonds, chemostat; open diamonds,
pH-auxostat). Specific protein biosynthesis rate (qp in g protein per
g dry weight per h; rightward-pointing open triangle, chemostat;
open triangle, pH-auxostat). Specific proton production rate (qHỵ in
protons per gram dry weight per h; closed inverted triangle,
pH-auxostat; not determined using the chemostat).

of the variation with specific growth rate observed in
the chemostat. They remained fully coupled to the specific cellular growth rate of K. marxianus. The specic
proton production rate (qHỵ ), which equals the ammonium uptake rate on defined medium (K. marxianus
produced one proton per ammonium ion consumed),
was calculated for the auxostat system only. The proton
stoichiometry was approximately 6 protons per gram
biomass. As can be seen from Fig. 3, much of the
ammonium consumed is incorporated into proteins
(qHỵ qp = 1). The respiration quotient (RQ =
DCO2 ⁄ DO2) remained 1.0, indicating a fully oxidative
catabolism, confirming the Crabtree-negative physiology of K. marxianus, i.e. no glucose fermentation to

ethanol (plus extra CO2 production) even at ultra-high
glucose uptake rates (i.e. under glucose saturation).
The carbon recovery during the sudden increase in
pH-auxostat dilution rate was and remained 100%.
Both datasets indicate that no products other than
biomass and CO2 were synthesized, confirming that the
specific flows of catabolism (qCO2 and qO2 ) and anabolism (lmax) remained fully coupled during selection
260

for the highest possible growth rate under defined
medium conditions.

Discussion
Background
Our study focused on the highest possible growth rate
of microbial eukaryotes. The main question was what
limits cellular growth rate under nutrient-saturated
defined medium conditions? As cellular metabolism is
structurally organized into functional entities [66,67],
our question was refined to what or which cellular regulon, functional module, pathway or process step is
insufficiently active and therefore responsible for
growth limitation? As control of flux is distributed
across various metabolic steps and hierarchical levels
[68], it is difficult to find limitation in just one single
pathway step; a ‘limitation’ may be an entire functional module of cell metabolism. If such a controlling
module could be localized at all, our further aim was
to quantify to what extent cellular growth rate was
controlled by such a module.
When K. marxianus was cultivated under mineral
nutrient-sufficient conditions with continuous selective

pressure on the maximum specific growth rate, we
observed a significant increase in lmax of approximately 30%. Although undefined rich media from
cheap bulk waste streams are often used in industrial
biotechnology, our approach of using mineral medium
is still relevant because less stable DNA vectors (precious vectors in high-copy numbers) are readily lost
after several generations of growth on rich media [15],
due to the lack of selective markers. K. marxianus is
used for the industrial production of commercially
attractive proteins [4–6]. To guarantee the sustainability of high-copy number vectors, more expensive selective mineral media with substrate markers are used.
The drawback of using mineral medium is often a
lower maximum growth rate, resulting in an increase
in cost-intensive bioreactor times. To optimize the
overall protein production process on mineral medium,
a higher maximum growth rate is called for. Therefore,
cell selection on mineral medium may help to increase
the microbial productivity of industrial single-cell
protein manufacturing. As shown in our study, the
pH-auxostat bioreactor can be used to select for cells
with the potential to grow faster. Stemmer [69] has
developed a method for rapid evolution of a protein
in vitro by means of DNA shuffling. Here, we showed
a rapid evolution of yeast cells in situ by pH-auxostat
cultivation for more than 50 generations. We call this
‘cellular selection’. Chemostats have also been shown

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P. Groeneveld et al.

to be useful for the selection of microbes. However,
selection is not for maximum growth rate alone; selection also occurs for an increased affinity for the limiting substrate (1 ⁄ Ks), depending on the dilution rate
[51,52]. In fact, selection in a chemostat often favors
the strain with the highest lmax ⁄ Ks ratio. When lowering bioreactor times on mineral medium, only the lmax
is of interest. Therefore, selection using a pH-auxostat
is preferable to selection in a chemostat when an
increased growth rate on mineral medium is called for.
However, the pH-auxostat can not be used for analysis
of growth-control on rich medium, as growth-associated
protons are not produced on rich medium, due to the
lack of sufficient proton-coupled ammonium uptake
(uptake of N-rich monomers instead of NH4+). In
addition to the pH-auxostat experiments presented
here, we used a CO2-auxostat to obtain steady-state
substrate-saturated (maximum) growth on rich undefined medium [1]. Under these conditions, we also
showed evolution towards a higher growth rate, but
this was not accompanied by an altered morphology.
We think that moving from defined to rich medium
shifts the control from input processes to internal processes, hence away from uptake. This would explain
the observation but these results do not constitute
evidence for our contention that there is less control
by uptake when growth of K. marxianus takes place in
rich medium. Koebmann et al. [70] found that the
prokaryotic growth rate is mainly controlled (> 70%)
by the demand for ATP. By using Escherichia coli in
which intracellular ATP ⁄ ADP levels could be modulated, they showed that the majority of the control of
bacterial growth rate resides in anabolic reactions, i.e.
cells growing on glucose-minimal medium are mostly
carbon-limited. By quantifying the concomitant change
in the cell’s surface-to-volume ratio and maximum

growth rate, we showed that our results are consistent
with control of the growth rate of one of the fastestgrowing eukaryotes, K. marxianus, mainly due to in
outer-membrane transport of carbon and ⁄ or Gibbs
free-energy substrates.
Highest eukaryotic growth rate
Our observation of microbial selection using an auxostat also addressed the second issue of our study, i.e.
whether one of the fastest-growing eukaryotes,
K. marxianus, can grow even faster on defined mineral
medium. The answer would appear to be yes. The
average cell-cycle time of the faster-growing population
was 52 min, which is among the shortest steady-state
cell-cycle time of any eukaryotic organism on defined
glucose ⁄ ammonium mineral medium, and is certainly

Control of highest eukaryotic growth rate

much shorter than that of the more minimalist Mycoplasma genitalium [60]. Figure 1 shows that the steadystate pH-auxostat dilution rate (D) increased from one
steady state to the new steady state, and lasted many
generations.
Importantly, an alternative scenario of a change in
metabolism with an induced additional acid and CO2
production at constant specific growth rate is refuted
by our observations. Here the special properties of the
pH-auxostat [56] are important: at steady state, the
dilution rate of the auxostat D equals the specific
growth rate of the cells (l), and a change in the specific rate of acid production at constant specific growth
rate is reflected by a change in biomass density in the
auxostat not by a change in dilution rate. We did
observe an increase in dilution rate from one steady
state to a next, proving that there was an increase in

specific growth rate. In the case of a change in metabolism at constant specific growth rate, enhanced acid
production by K. marxianus would have initiated with
higher carbon dioxide production. The semi-logarithmic plot shown in the inset to Fig. 1 would have
shown an upward-shift in gas production with parallel
straight slope indicating the same rate of the exponentional growth. In addition to the theory and our observations, there is ample evidence that this alternative
scenario must be rejected. For the two steady states,
we calculated 100% carbon recovery, indicating that
no carbon products (such as organic acids) were produced other than biomass and CO2, confirming full
oxidative metabolism of K. marxianus during the entire
experiment. In Fig. 3, all metabolic flows (including
carbon dioxide production) are shown in terms of
specific flow rates in mmolỈg)1 dry weight of biomass
per hour, and all such flows were fully coupled to
growth rate.
Another alternative reason for the increase in dilution rate, such as additional wall growth inside the
transparent fermenter vessel, was also rejected as no
extreme amounts of biomass were observed. If extreme
amounts of biomass had been stacked inside the fermenter vessel, wash-out of the entire culture would
have take place. Moreover, a fresh auxostat culture
inoculated with the selected strain always started
immediately at the elevated dilution rate, excluding an
increase in dilution rate due to wall growth.
The observed 30% increase in lmax from 0.6 to
0.8 h)1 (Fig. 1) was irreversible in the sense that cells
with the obtained higher growth rate did not return to
the initial value upon injection into a fresh pH-auxostat. This was also the case after frequent re-plating,
batch cultivation or intermittent use of a glucose-limited chemostat [1] at a sufficiently low dilution rate.

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The initial value of lmax of 0.6 h)1 was the mean of
two experiments. As can be seen in Fig. 1, a difference
of 5% was observed between the initial lmax for the
two separate experiments. As reported in Results, we
checked whether minor variations in additions of vitamins and essential minerals could have caused this, but
they did not affect the initial lmax. Our working explanation for this is the importance of the pre-induction
state of the cells; whether or not all enzymes of the
relevant pathways have already been induced depends
on the history of the cells put into culture. As can also
be seen in Fig. 1, after sufficient duration of steadystate pH-auxostat cultivation enabling selection, this
apparent difference in lmax diminished, resulting in
one of the fastest possible growth rates for eukaryotic
life on mineral medium (0.8 h)1). This result answers
our third question: an increased specific growth rate
of 0.8 h)1 shown for K. marxianus might be well the
fastest possible growth rate recorded thus far for
eukaryotic life on defined medium.
Auxostat cultivation is not a standard microbial
method for selection of cells. In contrast to serial batch
cultures or plate cultures, it allows long-term selection
for a higher growth rate under perfect steady-state
growth conditions [both in terms of the presence of
sufficient growth substrates (i.e. S ) Kms, with Kms as

the substrate concentration, S, at which the reaction
rate, V, is 0.5 Vmax) and absence of toxic products, P,
(i.e. P > Kmp, with Kmp as the product concentration,
P, at which the reaction rate, V, is 0.5 Vmax)]. The
intermittent stationary phases in serial batch cultures,
or the variations in substrates and products during
batch cultivation, would not provide the selective
steady-state conditions we required. Chemostat operation would not specifically select for the highest possible growth rate either, but at most for a maximum
growth rate specifically obtained during substratedependent, limiting cultivation in the chemostat, i.e. at
which the chemostat method is unfortunately unstable.
Therefore we used the pH-auxostat, in which cells
are able to grow as fast as they can under optimal
conditions for all medium components (all substrates
saturated and no toxic products).
Phenotypic adaptation or genetic evolution?
We tried to distinguish between adaptive and nonadaptive [71] evolutionary changes in the traits of
K. marxianus after cultivation for more than 50 generations at the highest growth rate. Measurements of
cell-cycle times for individual cells within populations
of cells growing under steady-state conditions in
homogeneous environments revealed considerable vari262

ability. Wheals and Lord [72] showed significant differences in specific growth rates within a population of
genetically identical (or very closely related) cells of
S. cerevisiae. Under pH-auxostat conditions, such
clonal variability may, in principle, have been the basis
of selection for cells with a higher growth rate. However, the reason for this variability in the distribution
of cell-cycle times is still unclear. Axelrod and Kuczek
[73] have ascribed clonal differences in growth rate to
potentially intrinsic, inheritable but non-genetic (epigenetic) differences between cells. Variation in cell-cycle
time has been ascribed to asymmetric partitioning of

biosynthetic material (other than chromosomal), which
may affect the rate at which cells traverse the cell
cycle, or G1 in particular [74]. Because of the epigenetic character of unequal partitioning, the value of
the increased growth rate should return to the lower
initial lmax value in a non-selective environment due to
the weaker cells (or relatively smaller daughter cells
with lower growth rates) being retained in the population. As shown in Fig. 2A, the average relative sizes of
the smallest two types of particles measured, assumed
to be daughter or mother cells, both increased to the
same extent during selection. Epigenetic selection for
the biggest daughter cells at the time of separation due
to asymmetric partitioning may have occurred. However, in our additional experiments, the characteristics
were inherited over more than 400 generations on
plates subjected to repeated batch cultivation (as
shown in the inset to Fig. 1) and for 40 generations at
a rather low dilution rate (D = 0.2, i.e. 25% of the
selected lmax) in a glucose-limited chemostat [1]. In
view of the observed steadiness of the higher growth
rate gained, it is unlikely that an increase due to the
proposed epigenetic inheritance by asymmetric distribution of biosynthetic cell material (i.e. on the basis of
bud size at separation) was the cause of our observations. In closed systems such as batch culture and
re-plating, newly born smaller cells did not reduce the
higher average lmax value of the selected population.
Consequently, variation in daughter cell size could not
account for the persistent increase in lmax.
Simulation of the flow dynamics during the selection
in the pH-auxostat supported this reasoning. Using
from the hypothesis that our yeast population contained cells with a variety of growth rates normally
distributed among the measured average growth rate
of 0.6 h)1 (ranging from 0.5 to 0.7 h)1), and that these

growth rates were inherited, produced a dilution
pattern (see D in Fig. 4A) that deviated from the
experimental data shown in Fig. 1. In this simulation,
sub-populations of cells with higher maximum growth
rates succeeded each other, and the sub-population

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Control of highest eukaryotic growth rate

Number of cells (cells·L–1) × 1011

A

Dilution rate, D (L·h–1)

Total amount of cells

B

Dilution rate, D (L·h–1)

Number of cells (cells·L–1) × 1011

Time, t (h)

Time, t (h)

Fig. 4. Simulations of the dilution rate (bold line, D) during pH-auxostat cultivation. (A) Each curve (dashed lines) represents the number of cells with one specific growth rate, indicated in the figure.
The simulation started with the assumption that the yeast population contained cells with a variety of maximum growth rates, all
normally distributed around the measured average maximum
growth rate of 0.6 h)1, ranging from 0.5 to 0.7 h)1. All growth rates
ranging from 0.5 to 0.7 h)1 with a standard deviation of 0.05 were
taken into account during simulation of D. For clarity, only the subpopulations of cells with growth rates of 0.59, 0.61, 0.64, 0.66,
0.69 and 0.71 h)1 are visualized. (B) Simulation of the dynamics of
the dilution rate (D) in the pH-auxostat during selection of cells arising by spontaneous mutation. The simulation was started at time
t = 0 using approximately 2.5 · 1011 wild-type cells and 15
mutants with a lmax of 0.6 and 0.8 h)1, respectively. The dilution
rate (D, bold line) equals the steady-state average maximum
growth rate of the yeast population (lmax); open triangles, number
of cells with average lmax = 0.6 h)1; open squares, number of cells
with average lmax = 0.8 h)1.

with the highest lmax value ultimately predominates
over slower sub-populations. Simulation of the dilution
rate (D) revealed a slow regular increase to a steady
state (see Fig. 4A) without a pre-steady state of 60 h
at a lower value. Therefore, the flow dynamics of the
selection of cells with a higher growth rate, distributed
around an average lmax value, did not concur with the
experimental data as shown in Fig. 1.

Non-Mendelian inheritance of extra-genomic information by an ancestral RNA-sequence cache, as has
been suggested by Lolle et al. [75] for Arabidopsis thaliana (and discussed in [76–78]), is also not a likely
mechanism for the inheritance of a stable higher
growth rate of K. marxianus.
Genetic variability as a more realistic explanation
for our observed increase in growth rate was considered. In yeast, spontaneous mutations occur at a low

frequency, approximately 10)4 to 10)8 per gene per
generation [79]. As the pH-auxostat population at the
beginning of the first steady state derived from a single
cell approximately 38 generations earlier, genetic heterogeneity must have existed. Starting from 5000 yeast
genes each undergoing spontaneous mutations at a
rate of 10)7 mutations per gene per generation, one in
50 cells should have been affected by a mutation after
38 generations (neglecting the effects of selection). If
one key regulatory gene needs to be mutated to obtain
an increase in maximum growth rate, one in
250 · 103 cells should have a mutation in that gene. If
one in ten thousand mutations in that gene has a positive effect, 4 · 10)10 cells out of a population should
have such positive ‘upward’ mutation. As shown in
Fig. 4B, simulation of the dynamics of the dilution
rate and these numbers of wild-type and mutant cells
concurred with the experimental data presented in
Fig. 1. In this simulation, we started with approximately 2.5 · 1011 cells at a lmax of 0.6 h)1 and
assumed that approximately 15 mutant cells (i.e. a
fraction of 0.6 · 1010) were present at the start of the
cultivation with an average lmax of 0.8 h)1. After 60 h
of pH-auxostat cultivation, the competition was completed in favor of the faster-growing cells within a period of approximately 40 h. This corresponds to the
experimental findings shown in Fig. 1. Consequently,
genetic diversity of K. marxianus that arose as a result of
in spontaneous mutations at normal rates may well have
been the cause of the increase in lmax during the longterm pH-auxostat cultivations. Based on our calculations of genetic variability and a simulation of the bioreactor flow dynamics, we conclude that the sudden
increase in growth rate after 50 generations has been
attained through mutation, rather than a slow epigenetic
selection of faster-growing cells at the beginning of the
culture.
Why would such a faster-growing mutant selected

by our auxostat not already have appeared in nature
by natural selection? The answer could be that natural surroundings change rapidly over time, causing
the selection pressure to variate over time without
allowing any selection of one particular microbial
trait to occur. Therefore, changing environments may

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not select at all, or not as fast, for one desired
microbial property as an auxostat. In contrast to natural habitats, an auxostat provides a monoculture
with a constant selection parameter, i.e. selection
pressure on the rate of cellular growth, sustained for
many generations.
Increase in the surface-to-volume ratio
Was amplification of membrane processes invoked
while growth rate was increasing? Where growth is
controlled by the transport capacity of a given permease, an increase in the surface-to-volume ratio (s ⁄ v)
could allow insertion of additional permeases. This
could increase the uptake capacity for all types of (catabolic or anabolic) nutrients, enabling the cell to grow
faster [80]. Therefore, growth rate is probably controlled indirectly by transport processes due to protein
crowding and space limitation in the cell membrane.
However, where growth is controlled by intracellular
enzyme activities, or when there is no space limitation

for a given (inducible) permease, or when molecular
sequestration and channeling [81] take place, such an
increase in s ⁄ v ratio should not be a consequence of
the increase in growth rate.
Cooper [82,83] and Planta [84] assumed that there is
no limitation to growth other than protein synthesis
and ribosome function. Our analysis did not use any
such assumption. It allows control of growth rate to be
distributed in any way within the cells’ entire metabolism, including steps of ribosome function such as competition between mRNAs for protein synthesis, amino
acid loading of tRNAs or the free energy (ATP) supply
for protein synthesis etc., as well as the s ⁄ v ratiodependent transport of anabolic and catabolic growth
substrates. If protein synthesis were the growth ratecontrolling sub-module for K. marxianus, then our
analysis method would still apply. In that case, however, we would not expect the observed increase in
surface-to-volume ratio to parallel the observed
increase in growth rate, but rather a decrease because
more ribosomes would be made at the cost of making
membrane.
The microscopic observations revealed the change in
morphology in greater detail (as shown in Fig. 2). The
relative average cell size (diameter) of K. marxianus
increased, while the morphology changed from spheroid ⁄ ovoid to elongated ⁄ cylindrical shaped filamentous
cells. These changes in cell geometry caused the cell’s
s/v ratio to increase. The s ⁄ v ratio and maximum
growth rate increased almost to the same extent, which
may indicate the existence of a putative growth-control
site. Indeed, our observations could be readily
264

explained if significant control of the growth rate on
mineral medium of the wild-type K. marxianus strain

resides in the cell surface. This is in accordance with a
major tenet of Rashevsky [85] and the dynamic energy
budgets (DEB) model [44], which has been extended to
mass budgets in biological systems [45].
More generally, when differences in growth rates are
observed within a single species concomitant with a
change in cell morphology, measurements of the s ⁄ v
ratio in particular may allow identification of important sites of growth control. Such changes in s ⁄ v ratio
may distinguish between transport processes and intracellular processes as ‘controllers’ of growth rate. In
our experiments, the maximum growth rate increased
by almost as much as the s ⁄ v ratio, indicating that the
yeast cell membrane is the site of major limitation of
the growth rate on defined glucose ⁄ ammonium minimal medium. This answered our fourth question: an
increase in relative membrane size occurs when the
cellular growth rate is increased. Probably, increasing
the cell’s s ⁄ v ratio can enhance the growth rate of
fastest-growing form of eukaryotic ‘life’, i.e. enhance
the maximum specific growth rate of K. marxianus on
defined medium.
Integrative systems biology: linking phenotype
to genotype
We developed a modular analysis of control [66] in
order to more precisely identify the site of control of
the highest eukaryotic growth rate. Our experimental
findings allowed us to discriminate between cell surface
and cell volume, thereby refining the effect of the s ⁄ v
ratio on growth. In addition to recognition of separate
locations of control, we extended the modular analysis
in order to more precisely quantify the control distribution of these two defined cellular entities (or functional modules). Our approach led to identification of
a subtlety that may be expected for living organisms;

control may be largely confined to one aspect of cell
function but rarely completely so. In total, 80% of the
control of the highest eukaryotic growth rate resided
in the membrane processes, but 20% of control
remained in the other, presumably cytoplasmic, processes. This 20% is certainly relevant, as it will increase
upon an increase in s ⁄ v ratio, and ultimately begin to
limit further increases in growth rate [67]. In general,
targeting sites of major control with inhibiting drugs
will enhance their effect on growth rate. The more
controlling-enzyme is inhibited, the larger its control
becomes in the system. Indeed, several important drug
targets controlling the growth rate, morphology and
virulence of pathogenic fungi (such as Candida spp.)

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P. Groeneveld et al.

have already been found in steps of the membranelocated sterol pathway [86].
Powell et al. [87] measured surface areas and cell
volumes for various S. cerevisiae generations, assuming
the cells to be ellipsoidal spheres. The so-called virgin
cells, which are the youngest yeast cells possessing only
one birth scar and no bud scars, and older yeast cells
up to the eighth generation, possessing eight bud scars,
were examined. Both the cell surface area and volume
increased with the increasing number of generations as
determined by the number of bud scars. Our calculation of s ⁄ v ratios on the basis of these data [87]
revealed a relative decrease in the s ⁄ v ratio of 24%

within the first eight generations (absolute s ⁄ v values
of 0.87–0.66 calculated from [87]). According to the
dynamic energy budget models of Kooijman [44,45],
this implies that the maximum rate of replicative
growth of individual cells should decrease proportionally by 24% within the first eight generations. According to our analysis presented here, and if transport
controls the growth rate of S. cerevisiae to the same
extent as for K. marxianus (i.e. 80%), a 20% decrease
in growth rate is predicted. Further measurements of
growth rate in individual cells will verify and locate
control sites for S. cerevisiae (or important pathogenic
fungi) using our quantitative estimates.
In our more precise analysis, we estimated that
control of the fastest eukaryotic growth rate at
defined mineral conditions, i.e. that of K. marxianus,
was located in the membrane (80%) and in cytoplasmic processes (20%). A significant goal in the postgenome era is to relate the annotated genome
sequence to the physiological functions of a cell.
Working from this digital core of information [88], as
well as from the available physiological and biocomplex information, it is possible to reconstruct complete metabolic networks [89,90]. In this study, we
demonstrate how ‘cell selection’ can help us to obtain
quantitative data enabling us to relate a selected optimized phenotype to the genome of industrial useful
yeast. Our approach opens the way for further analysis of membrane-located permeases by comparing the
optimized mutant with the wild-type strain at the
genomic level [91].
For the establishment of more efficient single-cell
protein production [5], ‘cell selection’ shows that even
the fastest-growing eukaryote can achieve a higher
growth rate when the s ⁄ v ratio is increased through
rapid cellular evolution and selection. This will significantly reduce reactor times while maintaining stable
vector copy numbers and facilitating downstream processing, thus increasing the overall microbial protein
productivity on defined selective medium.

Control of highest eukaryotic growth rate

Experimental procedures
Organism and culture conditions
A wild-type yeast strain of K. marxianus CBS 6556 was
obtained from the Centraal Bureau voor Schimmel cultures
(CBS Delft, The Netherlands) and maintained on YNB-glucose agar plates containing 6.7 gỈL)1 yeast nitrogen base
without amino acids (YNB, Difco, Lawrence, KS), 20 gỈL)1
glucose and 13 g L)1 agar (Oxoid Ltd, Basingstoke, UK).
In the pH-auxostat, K. marxianus was grown aerobically on
mineral medium, with glucose (saturated at 10–20 gỈL)1) as
the sole carbon and free-energy source, containing
10.0 gỈL)1 (NH4)2SO4 and 1.0 gỈL)1 MgSO4Ỉ7 H2O. This
medium was supplemented with 2 mL of a mineral stock
solution per liter medium, containing 15.0 gỈL)1 EDTA,
4.5 gỈL)1 ZnSO4Ỉ7 H2O, 3.0 gỈL)1 FeSO4Ỉ7 H2O, 0.3 gỈL)1
CuSO4Ỉ5 H2O, 4.5 gỈL)1 CaCl2Ỉ2 H2O, 1.0 gỈL)1 MnCl2Ỉ
4 H2O, 0.3 gỈL)1 CoCl2Ỉ6 H2O, 0.4 gỈL)1 NaMoO4Ỉ2 H2O,
1.0 gỈL)1 H3BO3 and 0.1 gỈL)1 KI (AppliChem GmbH,
Darmstadt, Germany) and with 2 mL of a vitamin stock
solution per liter medium, containing 0.05 gỈL)1 biotin,
1.0 gỈL)1 Ca-pantothenate and 1.0 gỈL)1 nicotinic acid. All
supplementary solutions were filter-sterilized.
K. marxianus was cultured in a 2-L fermenter with a
working volume of 1 L, and 100 mL of washed overnight
batch pre-culture was used to inoculate 900 mL sterile
mineral medium. Oxygen saturation was established by
airflow of 60–70 LỈh)1 through the culture, stirring at a
speed of 800 r.p.m. The buffer capacity of the pH-auxostat mineral medium was established by addition of phosphate 6.93 gỈL)1 KH2PO4 and 1.58 gỈL)1 K2HPO4, which

gives a 60 mm phosphate buffer with a pH of 6.1. Thus
the buffered medium contains all minerals, vitamins and
carbon and Gibbs free-energy substrates in sufficient
excess for the biomass of K. marxianus (biomass concentration is set by the buffer capacity and the proton stoichiometry) to propagate at its maximum specific growth
rate. The average pH of the fresh medium in the reservoir was adjusted with H2SO4 and ranged from 6.0 to
6.3. The buffering capacity of the fresh medium in the
reservoir was determined at laboratory temperature (20–
25 °C). The pH of the reservoir medium was determined
and the volume of 0.10 m HCl necessary to titrate
100 mL of that medium to the pH of the culture was
measured. With a phosphate concentration of approximately 60 mm, reservoir medium pH of 6.0–6.3 and
culture pH of 4.5 ± 0.1, the BCR was estimated at
15 mmol H+ L)1. The proton stoichiometry (h) was calculated as: h = BCR ⁄ x. The dry weight (x) of the culture
samples was determined by filtration over Sartorius membrane filters (pore size 0.2 lm) and subsequent drying at
100 °C. With a BCR of 15 mm and all medium compounds sufficiently provided (at saturated conditions), a
stable active biomass concentration of approximately

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2 gỈL)1 was maintained at an optimal growth temperature
of 40 °C. The rate at which fresh medium flowed from
the reservoir into the culture vessel responded to pH
changes in the culture vessel, and maintained the culture

pH at the optimal pre-set value of 4.5. By this method,
it was possible to maintain long-term continuous cultures
at a maximum specific cellular growth rate that was optimal with respect to all medium components and environmental conditions at constant pH, temperature and
biomass concentrations [1,56]. The rate of growth was
independent of the buffer capacity of the inflowing fresh
medium and the pH difference between culture vessel and
medium reservoir, and depended only on the properties
of the micro-organism itself, growing at maximum cellular speed (minimum cell-cycle time). The flow of effluent
medium from the culture vessel was measured online
using an electronic balance connected to a computer to
monitor the average culture’s dilution rate as a function
of time. Every 60 s, the weight on the balance was registered. During steady-state growth, the maximum specific
growth rate, lmax, was taken to equal the dilution rate
D (h)1).
For the additional glucose-limited chemostat cultures, we
lowered the glucose concentration in the mineral medium
to 2 gỈL)1 without addition of auxostat phosphate buffer.
In chemostat mode, the culture pH was kept at 4.5 by automatic addition of 2 m KOH or 1 m H2SO4, and was
checked daily to ensure it remained constant at the various
steady-state dilution rates (growth rates).

Determination of average cell size, distribution
and morphology
Cell number and size were determined by taking samples
from the culture and counting after dilution with Isoton
(Coulter Electronics, Harpenden, UK) using a Coulter
counter particle-size analyzer Multisizer II, with a 30-lm
orifice. The morphology and dimensions of the cells were
microscopically determined and compared with a standard.

Cellular protein content
The protein concentration of the cells was determined using
the Robinson–Hogden biuret method as described by
Herbert et al. [92]. BSA (Sigma-Aldrich Inc., St Louis, MO,
USA) was used as the standard, and extinction was
measured at k = 550 nm.

Determination of specific glucose uptake rate
In order to determine the amount of glucose consumed in the
auxostat, the residual glucose concentration in the culture
was measured. Approximately 10 mL of effluent medium
was rapidly (within a few seconds) passed through a filter of

266

0.2 lm porosity (Millipore Corp., Billerica, MA, USA). The
filtrates, free of yeast cells, were used for determination of
residual glucose by means of a standard glucose test (glucose
kit number 184047, Boehringer Mannheim GmbH, Mannheim, Germany). The specific rates of glucose consumption
(qglu) were calculated from qglu = [(Sr ) S) D] ⁄ x, where Sr is
the glucose concentration (in m) in the medium reservoir, S is
the glucose concentration in the culture vessel, D is the dilution rate (h)1) and x is the biomass concentration (gỈL)1).

Determination of specific oxygen uptake rate
and CO2 production rate
The specific oxygen consumption rate and carbon dioxide
production rate were obtained by measuring the gas composition of the inward and outward gas flows. Gas exchange
was determined by leading the inward and outward gas flows
through a mass spectrometer model MM 8-80F (VG Instruments Group Ltd, West Malling, UK). At steady state, the
O2 consumption and CO2 production of the culture were

confirmed to be constant over a long period of time
(minimum seven generations). The specific gas exchange rate
is given by qgas = (D%gas fg ⁄ 100) V Mvol, where qgas is the
specific O2 uptake rate or CO2 production rate (molỈg)1Ỉh)1),
V is the fermenter volume (L), x is the biomass dry weight
(gỈL)1), D%gas is the percentage gas exchange measured at
23 °C at which the molar gas volume (Mvol) is 24.282 L
(according to the Boyle–Gay Lussac law), and fg is the gas
flow (LỈh)1). The percentage carbon dioxide produced by the
culture is D%CO2 ¼ D%COout À D%COin ).
2
2

Computer simulations
The dynamics of the dilution rate (D) and the number of cells
(N) during pH-auxostat cultivation were simulated using
stella ii ( />intro.html). In the case of a variable amount of mutants with
a higher maximum specific growth rate at the initial pHauxostat cultivation, the following model descriptions were
used: Nmt (t) = Nmt (t ) dt) + (growthmt ) dilutionmt) dt,
Int Nmt = 15, growthmt = lmt Nmt, dilutionmt = D Nmt,
Nwt (t) = Nwt (t ) dt) + (growthwt ) dilutionwt) dt, Int
Nwt = 1 109, growthwt = lwt Nwt, dilutionwt = D Nwt,
D = (hmt lmt Nmt + hwt lwt Nwt) ⁄ BCR medium flow =
D 420, BCR = 16, hmt = 1.0667 10)10, hwt = 6.1538 10)11,
lmt = 0.78, lwt = 0.54, Ntotal = Nwt + Nmt, where the
subscripts mt and wt stand for mutant and wild-type cells,
respectively; t = time; dt = change in time; hmt = proton
stoichiometry per cell of mutant strain; hwt = proton stoichiometry per cell of wild type strain; BCR = buffer
capacity of the medium. We used the number of cells instead
of the concentration of biomass. As a consequence, we had

to reformulate the original proton stoichiometry (h in mmol
protons per gram biomass) as mmol protons per cell.

FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS


P. Groeneveld et al.

Control of highest eukaryotic growth rate

Acknowledgements
In memory of Fred Oltmann, Henk van Verseveld and
R. J. Planta. We thank Bas Kooijman (Theoretical
Biology, Faculty of Earth and Life Sciences, Vrije Universiteit Amsterdam, The Netherlands) for discussions
and advice. This study was supported in part by grants
from the Netherlands Foundation for Chemical
Research (SON) and Technology Foundation (STW)
with financial aid from the Netherlands Organization
for Advancement of Research (NWO) and through various grants from the EU-FP6 + 7 (Biosim, NucSys,
and Yeast Systems Biology Network) and Biotechnology and Biological Sciences Research Council.

10

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Supporting information
The following supplementary material is available:
Doc. S1. Estimations of surface to volume ratios.
Doc. S2. Modular metabolic control analysis of membrane versus cytoplasmic control.
This supplementary material can be found in the
online version of this article.
Please note: Wiley-Blackwell are responsible for the
content or functionality of any supplementary materials supplied by the authors. Any queries (other than
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