Super life – how and why ‘cell selection’ leads to the fastest-growing eukaryote Philip Groeneveld1, Adriaan H Stouthamer1 and Hans V Westerhoff1,2,3 Department of Molecular Cell Physiology & Mathematical Biochemistry, Netherlands Institute for Systems Biology, Vrije Universiteit, Amsterdam, The Netherlands The Manchester Centre for Integrative Systems Biology, Manchester Interdisciplinary Biocentre, School of Chemical Engineering and Analytical Science, The University of Manchester, UK 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: Hans.Westerhoff@manchester.ac.uk (Received 20 December 2007, revised 26 October 2008, accepted 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 [1]) is still seven times longer than that of one of the fastest-growing prokaryotes (i.e a generation time of < 10 [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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 255 Control of highest eukaryotic growth rate 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 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? 256 (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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 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 (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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 257 Control of highest eukaryotic growth rate 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 (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 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 cells·L–1) A B b: bud or daughter cell m: mother cell Steady state µmax = 0.6 h–1 length spheroid (ls) = diameter (ds) C Steady state µmax = 0.8 h–1 l = n· dc, f (with n = 6) Average cell-size distribution (µm) Fig Cell-size distribution (A) and morphology changes during long-term pH-auxostat cultivation at steady states (B) and (C) as determined using a Coulter counter particle size analyzer and observed under a microscope 258 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 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 JgrowthÀmax Cmmax % Cm ẳ /m ỵ /m ị 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 mmolỈg)1Ỉh)1 and increased in parallel with the increase in lmax to mmolỈg)1Ỉh)1, i.e an increase of approximately 30% as already shown in Fig 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 259 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 Physiological properties of K marxianus under glucose-limited chemostat conditions (solid lines: < 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) Specic 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 specific 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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 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 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 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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 261 Control of highest eukaryotic growth rate P Groeneveld et al 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 In this simulation, sub-populations of cells with higher maximum growth rates succeeded each other, and the sub-population 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 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 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 = 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 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, · 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 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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 263 Control of highest eukaryotic growth rate P Groeneveld et al 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.) FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 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 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 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 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 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 FEBS Journal 276 (2009) 254–270 ª 2008 The Authors Journal compilation ª 2008 FEBS 265 Control of highest eukaryotic growth rate P Groeneveld et al 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 gỈL)1 without addition of auxostat phosphate buffer In chemostat mode, the culture pH was kept at 4.5 by automatic addition of m KOH or 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 Computer simulations The dynamics of the dilution rate (D) and the number of cells (N) during pH-auxostat cultivation were simulated using stella ii (http://www1.union.edu/rices/STELLA/stella_ 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 = 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 + (Biosim, NucSys, and Yeast Systems Biology Network) and Biotechnology and Biological Sciences Research Council 10 References 13 Groeneveld P (1999) Control of specific growth rate and physiology of the yeast Kluyveromyces marxianus; a biothermokinetic approach Thesis, pp 1–324 (ISBN 909013010-1), Departments of Molecular Cell Physiology & Mathematical Biochemistry, Vrije Universiteit Amsterdam, The Netherlands Aiyar SE, Gaal T & Gourse RL (2002) rRNA promoter 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