Metabolic efficiency in yeast Saccharomyces cerevisiae in relation to temperature dependent growth and biomass yield

Author’s Accepted Manuscript Metabolic efficiency in yeast Saccharomyces cerevisiae in relation to temperature dependent growth and biomass yield Maksim Zakhartsev, Xuelian Yang, Matthias Reuss, Hans Otto Pörtner www.elsevier.com/locate/jtherbio

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S0306-4565(15)30018-8 http://dx.doi.org/10.1016/j.jtherbio.2015.05.008 TB1644

To appear in: Journal of Thermal Biology Received date: 26 January 2015 Revised date: 29 May 2015 Accepted date: 29 May 2015 Cite this article as: Maksim Zakhartsev, Xuelian Yang, Matthias Reuss and Hans Otto Pörtner, Metabolic efficiency in yeast Saccharomyces cerevisiae in relation to temperature dependent growth and biomass yield, Journal of Thermal Biology, http://dx.doi.org/10.1016/j.jtherbio.2015.05.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.


 

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Metabolic efficiency in yeast Saccharomyces cerevisiae in relation to temperature dependent growth and biomass yield Maksim Zakhartsev1,2,3#, Xuelian Yang4,2, Matthias Reuss2, Hans Otto Pörtner1 1

Alfred Wegener Institute for Marine and Polar Research (AWI), Bremerhaven,

Germany 2

Institute of Biochemical Engineering (IBVT), University of Stuttgart, Stuttgart,

Germany 3

Institute of Pharmacy and Molecular Biotechnology (IPMB), University of

Heidelberg, Germany 4

Beijing Engineering and Technology Research Center of Food Additives,

Beijing Technology & Business University, Beijing, China Keywords: temperature; growth rate; biomass yield on glucose; maintenance costs; product formation efficiency; ATP yield on substrate; intracellular ATP concentration; Running title: yeast temperature dependent batch anaerobic growth

 

Corresponding author: Dr. Maksim Zakhartsev, Plant Systems Biology, University of Hohenheim, Fruwirthstrasse 12, 70599 Stuttgart, Germany. T: +49 711 459 24771. [email protected]

 

Abstract Canonized view on temperature effects on growth rate of microorganisms is based on assumption of protein denaturation, which is not confirmed experimentally so far. We develop an alternative concept, which is based on view that limits of thermal tolerance are based on imbalance of cellular energy allocation. Therefore, we investigated growth suppression of yeast Saccharomyces cerevisiae in the supraoptimal temperature range (30-40°C), i.e. above optimal temperature (
 ). The maximal specific growth rate ( ) of biomass, its concentration and yield on glucose (   ) were measured across the whole thermal window (5-40°C) of the yeast in batch anaerobic growth on glucose. Specific rate of glucose consumption, specific rate of glucose consumption for maintenance ( ), true biomass yield on glucose  (   ), fractional conservation of substrate carbon in product and ATP yield on

glucose (   ) were estimated from the experimental data. There was a negative linear relationship between ATP, ADP and AMP concentrations and specific growth rate at any growth conditions, whilst the energy charge was always high (~0.83). There were two temperature regions where  differed 12-fold, which points to the existence of a ‘low’ (within 5-31°C) and a ‘high’ (within 33-40°C) metabolic mode regarding maintenance requirements. The rise from the low to high mode occurred at 31-32°C in step-wise manner and it was accompanied with onset of suppression of  . High  at supraoptimal temperatures indicates a significant reduction of scope for growth, due to high maintenance cost. Analysis of temperature dependencies of product formation efficiency and   revealed that the efficiency of energy metabolism approaches its lower limit at 26-31°C. This limit is reflected in the predetermined

   combination of   , elemental biomass composition and degree of reduction

of the growth substrate. Approaching the limit implies a reduction of the safety margin of metabolic efficiency. We hypothesize that a temperature increase above
 (e.g. >31°C) triggers both an increment in  and suppression of  , which together contribute to an upshift of   from the lower limit and thus compensate for the loss of the safety margin. This trade-off allows adding ten more degrees to
 and extends the thermal window up to 40°C, sustaining survival and reproduction in supraoptimal temperatures. Deeper understanding of the limits of thermal tolerance can be practically exploited in biotechnological applications.

Key-words: yeast; temperature dependent growth; energy metabolism; bioenergetics; growth efficiency; growth limitations;

Abbreviations: See section 9 for the complete list of abbreviations.

1. Introduction Yeasts are poikilothermic organisms and their life therefore depends on the temperature of their environment. The window of thermal tolerance of yeast from the genus Saccharomyces ranges between a lower permissive growth temperature (
 , i.e. temperature below which the cell division is not observed anymore and cell number stagnates) at approximately 3°C and an upper permissive growth temperature (
 ) at approximately 42°C, with an

 

optimal growth temperature (
 ; where the fastest growth rate of biomass is observed) at approximately 30-33°C (Piper, 1996; Salvado et al., 2011). The specific growth rate of biomass ( ) measured at different temperatures (T) rises exponentially from
 within the suboptimal or so-called physiological temperature range (i.e.
 

 ) to a maximum at
 and is suppressed in the range of supraoptimal temperatures (i.e.
 

 ) (Nielsen et al., 2003; Roels, 1983; Salvado et al., 2011). The objective of our research is a better understanding of the causes for growth suppression that occur at supraoptimal temperatures. Temperature exerts a pervasive effect on the metabolic system, i.e. it has no specific molecular target in a cell (at least within the physiological range) (Hochachka and Somero, 1973; Prosser, 1973). Historically, the chronic effect of temperature on metabolic systems has primarily been addressed through analyses of denaturation effects on metabolically important key-enzymes participating in the growth process, consequently influencing  (Esener et al., 1981b; Nielsen et al., 2003; Roels, 1983). This effect is described through irreversible enzyme denaturation:

µmax =

A exp ( −Eg / RT ) 1 + B exp ( −∆Gd / RT )

(1)

Where:  and  - pre-exponential constants;  - the activation energy of the growth process [ ];  - free energy change of protein denaturation [ ];  – universal gas constant [  ! "#];
– temperature ["]. In textbooks (Nielsen et al., 2003; Stephanopoulos et al., 1998) this equation is interpreted as an result of two counteracting processes in course of temperature increment: (i) increase of activity of fully functional enzymes and (ii) fractional

 

decrease of fully active enzymes (i.e. increase of denaturated ones), which progressively weaken growth rate, and this effect becomes most profound in supraoptimal temperature range. Nevertheless, this hypothesis has some shortcomings: (1) there is no experimental evidence that metabolically important enzymes of wild type yeast S. cerevisiae can be thermally denaturized at supraoptimal temperatures (i.e. 30-40°C). In fact, native proteins of studied yeast are thermally denaturized at temperatures far beyond this range (Figure 1). (2) Equation (1) describes temperature effects on a static system, because  and  are constants. This is in contrast to adaptive features of living organisms, where the amounts, composition, and kinetic features of enzymes are variables in the adaptation process. Moreover, it is hard to agree that at supraoptimal temperatures the major fraction of metabolic enzymes in a living cell would be denaturized and a cell would continuously cover the costs of their turnover (e.g. synthesis, reparation and degradation). Perhaps it is more adequate to interpret the lower term of the equation (1) in terms of temperature induced misfolding of proteins (Bava et al., 2004), which also leads to enzyme inactivation. However, misfolded proteins are repaired in an ATP-dependent process aided by chaperones (i.e. Hsp60, 70, 90 and 100). In this case, the chaperone content must increase in proportion to the fraction of misfolded proteins. At the same time, non-growth ATP expenses due to chaperones’ activity would also increase proportionally with temperature. However, according to our knowledge, there is no experimental evidence that chaperone content as well as non-growth ATP expenses linearly correlate with increasing temperature in the supraoptimal temperature range (for example (Zakhartsev et al., 2005)). Furthermore, the hypothesis of enzyme denaturation (reflected in equation (1)) does not take into account that enzymes are organized into homeostatically

 

regulated metabolic networks with hierarchical and metabolic control (Ruoff et al., 2007). According to Ruoff et al. (2007), the direct effect of temperature on the enzymes’ catalytic rate (described through the Arrhenius equation; as exemplified in (Zakhartsev et al., 2004b)) can be compensated by: (i) instantaneous changes in metabolite concentrations, which kinetically regulate enzyme activity; (ii) change in post-translational modifications; (iii) changes in enzyme or transporter concentrations (Cruz et al., 2012a), and (iv) changes in catalytic activity through the expression of isoenzymes (Zakhartsev et al., 2004a). The last two adjustments are achieved through alterations of gene expression (Zakhartsev et al., 2007), e.g. hierarchical regulation. These alterations cause a re-distribution of metabolic fluxes within the network and, consequently, (v) enhance kinetic regulation through temperature effects on metabolism (Ruoff et al., 2003; Ruoff et al., 2007). Thus, compensation of temperature induced metabolic activity via metabolic regulation seems to be a major regulatory mechanism. Substrate-limited growth of yeast S. cerevisiae in chemostats at different temperatures has revealed a dominant role of metabolic control as opposed to gene expression to compensate for temperature induced changes in glycolytic enzyme activity (Postmus et al., 2008; Tai et al., 2007b). A complimentary ‘regulation analysis’ demonstrated that around 85% of the increase in glycolytic flux during warming (30 vs. 38°C) was caused by changes in the metabolic environment of the glycolytic enzymes (Postmus et al., 2008). Neither a direct effect of temperature on enzyme catalytic rates nor an adaptive change in enzyme capacity through gene expression contributed much to the flux increase (Postmus et al., 2008). Similarities in the temperature dependencies of the catalytic capacities of glycolytic enzymes allow yeast to maintain metabolic homeostasis during circadian temperature cycles, thereby

 

avoiding extensive changes in enzyme levels through hierarchical regulation during temperature variation (Cruz et al., 2012b). Thus, the metabolic regulation of enzyme activities is one of the main homeostatic mechanisms during temperature variations. The effect of growth temperature is also reflected in the dynamics of yeast populations. In S.cerevisiae, the specific death rate ( ) increases with temperature. At supraoptimal temperature (39°C) it significantly concurs with declining growth rate resulting in decreasing biomass yield (van Uden, 1985; van Uden and Madeira-Lopes, 1976). In addition to  , the biomass yield decreases at supraoptimal temperature due to two effects that depress growth, which were identified in chemostat yeast cultures (van Uden and MadeiraLopes, 1976): (i) increased maintenance requirements by the viable fraction of the cell population and (ii) energy substrate dissipation by the non-viable fraction. It is noted for some microorganisms that an increase in growth temperature is accompanied by an increase in their maintenance costs. This was shown for S. cerevisiae and some other microorganisms (Esener et al., 1981a; Heijnen and Roels, 1981; Mainzer and Hempfling, 1976; Roels, 1983; Topiwala and Sinclair, 1971; van Uden and Madeira-Lopes, 1976; Verduyn et al., 1990). Maintenance costs are an integral part of cellular energy metabolism (equation (5)). Thus, during anaerobic metabolism, elevated maintenance costs result in increased flux of primary metabolites through glycolysis towards ATP formation without carbon assimilation in the biomass. This means that increase of non-growth associated processes would lead to higher end-product (e.g. CO2, ethanol, etc) formation and lower biomass yield (see equation (6))(Roels, 1983). Therefore, stimulation of maintenance rates through elevated temperature of cultivation

 

was suggested as one of the tricks for bioprocess optimization in the course of anaerobic yeast fermentation in order to maximize end-product formation (Roels, 1983). Taking these general considerations into account, we hypothesized that the growth rate of yeast in the supraoptimal temperature range (30-40°C) is constrained by the capacity of energy metabolism of the growing cells, i.e. their scope to increase energy turnover to cover costs on top of maintenance. This hypothesis is in agreement with the concept of “oxygen and capacity limited thermal tolerance” (OCLTT) developed for poikilothermic animals (Pörtner, 2002a, b). This concept states that indeed a progressive imbalance of cellular and whole organism energetics in metazoan poikilotherms sets the thresholds of their thermal tolerance in relation to their lifestyle. On the warm side of the thermal window, an imbalance between whole organism oxygen and cellular energy provision on the one hand and energy allocation to relevant performances on the other hand is initiated by a progressive increase in maintenance costs. This imbalance becomes suppressive for biomass growth due to a limitation in the functional capacity of mechanisms for energy and oxygen supply (Melzner et al., 2006; Pörtner, 2012). Temperature induced enzyme denaturation and protective stress responses (e.g. heat shock) usually take place at extreme temperatures (i.e.$
 ), which can be tolerated only for a limited period of time. Consequently, the question arises whether key elements of the OCLTT concept in terms of capacity of energy supply versus energy demand can also be applied to understand the temperature effects on growth of unicellular, immotile, eukaryotic, poikilothermic organisms under anaerobic conditions.

 

The growth bioenergetics of microorganisms can be directly quantified from their growth performance (rates and yields of biomass), exometabolite turnover and biomass concentration and its macromolecular composition (Cruz et al., 2012a; Roels, 1983; Verduyn, 1991; Verduyn et al., 1990). From an experimental point of view, the specific growth rate () of microbial biomass can be limited either by substrate availability (primary elements, energy-rich substrate, etc.) or by environmental factors (e.g. temperature, pH, inhibitors, etc.) (Verduyn, 1991). We therefore chose substrate-unlimited anaerobic batch growth on glucose as a sole carbon and energy substrate under different isothermal conditions. Anaerobic conditions allow direct quantification of the growth bioenergetics from input and output metabolic fluxes (Nielsen et al., 2003; Roels, 1983; Stephanopoulos et al., 1998; Verduyn et al., 1990; Villadsen et al., 2011). The aim of this pilot-research was therefore to study the effect of temperature on the rate of anaerobic, substrate-unlimited growth and biomass yield of the yeast Saccharomyces cerevisia in batch processes across the complete thermal window (5-40°C) and to find a possible link between growth suppression observed at supraoptimal temperatures with limitations that emerge from cellular energy metabolism. We interpret our findings in light of a recent analysis emphasizing that the complexity of organisms and the functional coordination between highest complexity functions are likely key in setting thermal tolerance limits (Storch et al., 2014).


 

2. Materials and methods 2.1

Yeast strain and medium

Baker’s yeast Saccharomyces cerevisiae haploid strain CEN.PK 113-7D (MATa, Ura3, His3, Leu2, Trp1, Mal2, Suc2) was kindly provided by Dr. Peter Kötter, Institute for Molecular Biosciences, Göthe University of Frankfurt, Germany. Mineral medium (so-called CEN.PK medium) was used for yeast cultivation (Verduyn et al., 1992): (NH%)&SO% 15 g/L, KH&PO% 9 g/L, MgSO%×7H&O 1.5 g/L, EDTA-Na& 45 mg/L, ZnSO%×7H&O 13.5 g/L, MnCl&×4H&O 3.0 mg/L, CoCl&×6H&O 0.9 mg/L, CuSO%×5H&O 0.9 g/L, Na&MoO%×2H&O 1.2 mg/L, CaCl&×2H&O 13.5 mg/L, FeSO%×7H&O 9.0 mg/L, H'BO' 3.0 mg/L, KI 0.3 mg/L, d-biotine 0.15 mg/L, Ca-D(+)panthotenate 3.0 mg/L, nicotinic acid 3.0 mg/L, myo-inositol 75.0 mg/L, thiamine hydrochloride 3.0 mg/L, pyridoxol hydrochloride 3.0 mg/L, p-aminobenzoic acid 0.6 mg/L. Additionally, ergosterol (10 mg/L) and Tween 80 (420 mg/L) were dissolved in ethanol (2.84 g/L) and added to CEN.PK medium as an anaerobic supplement. Throughout the experiments, the CEN.PK medium was used in two different modifications: (i) with glucose 15 g/L for batch experiments and (ii) with glucose 50 g/L for chemostat experiments. The content of primary elements in the medium was designed to support sustainable anaerobic yeast culture up to Cx = 15 gdw/L, where the latter depends on availability of the carbon source. The yeasts were pre-cultured aerobically on agar plates at 30°C from glycerol (15 %, v/v) stock. Some colonies were picked up and inoculated into 5 mL liquid aerobic CEN.PK medium for overnight aerobic incubation, which resulted in an optical density of the pre-culture of 0.1 optical units (OD(() = 0.1 O.U.) at 660 nm .



 

2.2

Growth conditions

2.2.1 Batch Pre-culture was inoculated into 300 mL of anaerobic CEN.PK medium with 15 g/L of glucose in flasks (500 mL). The anaerobic batch growth was performed in Aquatron® (INFORS HT, Switzerland) orbital water bath shakers (250 rpm) protected with gassing lids to control the gas atmosphere under constant nitrogen flow (0.5 L/h) through the shakers’ chamber (pO&=0%). Sampling was always carried out under the nitrogen stream. The growth temperatures varied between 4 and 40°C with ±0.1°C accuracy within each experiment. To achieve precise temperature control within a broad range, the incubator was additionally fitted with an externally refrigerated circulator (HAAKE F3 Fisons, Germany) via a cooling coil. Growth experiments were always run in duplicates (two flasks). 2.2.2 Chemostat Chemostat experiments were used only to measure adenylate (e.g. ATP, ADP and AMP) concentration in yeasts. Pre-culture was inoculated into 500 mL of anaerobic (or) aerobic CEN.PK medium with 15 g/L of glucose in a bioreactor (500 mL) and run in batch mode until * reached almost zero. Then, the process was switched into chemostat mode with 50 g/L glucose in feeding CEN.PK medium. The culture reached steady state conditions after 72 h and it was monitored by measurements off-gas from the bioreactor as well as by dry biomass measure. The dilution rates for different cultures were set between 0.05 and 0.25, stirring at 1000 rpm, external temperature control via a refrigerated circulator (HAAKE F3 Fisons, Germany) to 30°C, constant nitrogen (pO&=0%) or air (pO&=21%) flow (0.5 L/h) through the bioreactor). pH was controlled at 5.0 with 3 M NaOH and antifoam administrated at 0.05 mL/h.


 

2.3

Dry biomass

At defined time points, samples for dry weight of biomass (* ) were collected. 10 mL of the fresh culture was sampled and immediately filtered out on preweighed filters (0.2 µm) under vacuum conditions. The filtrate was washed three times with 10 mL ice-cold 0.9% NaCl solution and dried overnight at 115°C. 2.4

Parameters of biomass growth and efficiency of substrate utilization

The change in biomass dry weight was followed over time under isothermal +,-

conditions until it reached saturation (*

) (for an example see Figure 2). The

maximal specific growth rate ( ) was calculated from the exponential part of the experimental data by fitting to the following equation:

Cx ( t ) = Cx0 exp ( µmaxt )

(2)

Where: *. – initial concentration of the dry biomass /0 123;  – maximal specific growth rate of biomass [0  0 4#] or [54 ]. The goodness of fit R² • 0.98 was used as a quality criterion. Since batch growth reaches complete glucose depletion, the biomass yield on glucose (   ) was derived from the final dry biomass achieved in the batch +,-

(*

. ; for reference see Figure 2) and the initial glucose concentration (* )

as:

Yx / glc =

C xfinal 0 C glc

(3)

Consequently, specific rate of glucose consumption (6 ) that was achieved at  [0  0 4#] was:


 

rglc =

µ max Yx / glc

=

0 µ max C glc

C xfinal

(4)

When 6 is plotted as a function of  (Figure 3D) then the relationship of these quantities can be interpreted in terms of a linear equation:

rglc =

1 true x / glc

Y

µmax + mglc

(5)

 Where:   – true anaerobic yield of biomass on glucose [0 20 ];  –

specific rate of glucose consumption for maintenance processes [0  0 4#]  (Nielsen et al., 2003; Roels, 1983; Stephanopoulos et al., 1998).     is

the growth-associated term of the equation, whereas  is the non-growthassociated term (Nielsen et al., 2003; Roels, 1983; Stephanopoulos et al., 1998). Correspondingly, the biomass yield (   ) can be further expressed as described in (Nielsen et al., 2003; Stephanopoulos et al., 1998; Villadsen et al., 2011):

Yx / glc =

µ max µ max + mglc Yxtrue / glc

(6)

This equation explains the variation in biomass yield on glucose through the variation in growth rate and rate of glucose consumption for cellular maintenance.  If  ,  and   are known for anaerobic growth without an external

electron acceptor on a single source of carbon and energy, supported by ammonia as the nitrogen source and with excretion of a single or a single-ratio mixture of compounds, then fractional conservation of substrate carbon in


 

ethanol (78 ) as the major anaerobic end-product can be calculated as follows (Roels, 1983):

§ κ glc · § κ glc ¸η p = ¨ © κ etoh ¹ © κ etoh

ε etoh = ¨

§ κ x′Yxtrue m glcYxtrue / glc / glc + ¨1− κ glc µ max ·¨ ¸¨ true m Y ¹¨ 1 + glc x / glc ¨ µ max ©

· ¸ ¸ (7) ¸ ¸ ¸ ¹

Where:278 – fractional conservation of substrate carbon in ethanol [-]; 9 – degree of reduction of glucose (9 = 4) [:; *20<]; 98 – degree of reduction of ethanol (98 = 6) [:; *2:=4]; 9 98 – maximal theoretical fractional conservation of glucose carbon in ethanol [*2:=4*20<]; > – product formation efficiency [-]; 9? – generalized degree of reduction of biomass (9? = 4.2) [:; *2@]. The >  # approaches its upper limit=1.0 when  A B, whereas the minimal value will be at the lower limit of >  # when  A C (Roels, 1983): ­η pmax = lim η p ( µ max ) = 1 µ max → 0 °° ® min κ x′Yxtrue / glc °η p = lim η p ( µ max ) = 1 − µ max →∞ κ glc °¯

(8)

Thus, the value of >,- depends on intrinsic features of the biomass: carbon  and energy requirements (as reflected by   ), biomass composition (as

reflected by 9? ) and the substrate that is used as the carbon and energy source for growth under anaerobic conditions (9 ). Furthermore, the efficiency of ethanol formation (78 ) under anaerobic conditions allows approximate estimation (if other end-products are not taken in account) of ATP yield on glucose (Verduyn et al., 1990). Under anaerobic conditions, there is an equimolar relationship between ethanol formed and ATP synthesized.


 

Consequently, this feature can be used to assess ATP yield on glucose consumed if > is known (equation (7)). Maximal theoretical yield of ATP on glucose (   ) in anaerobic glycolysis is two moles of ATP formed per mole of glucose consumed when  = 0 and therefore:

­Yatp / glc = 2η p °° max max ®Yatp / glc = 2η p = 2.0 ° min min °¯Yatp / glc = 2η p

(9)

Where:   – ATP yield on glucose consumed [2
D20<]. 2.5

Adenylate contents

The quasi-steady state intracellular ATP concentration in yeast was always measured at early- or mid-exponential growth phase (for example see Figure 2). 1 mL of the culture was injected into 5 mL of pure methanol (pre-cooled to 80°C), vortexed and immediately placed into a -20°C thermostat. Methanol was decanted after cell precipitation by centrifugation (10E g, 10 min and -20°C). Then, 4 mL of boiling pure ethanol was added to the cell pellet, vortexed and kept at 80°C for 3 min, vortexing every minute. The extract-suspension was then evaporated in a rotational vacuum concentrator (Christ® RVC 2-33 IR, 4 mbar, 1300 rpm, ~1 h under 4°C) to dryness. The remains were re-dissolved in 500 µL of 10 mM phosphate buffer pH 7.0, vortexed vigorously and then 500 µL of chloroform was added, vortexed vigorously and centrifuged 10 min at 14×10³ g at 4°C. Then, 200 µL of the aquatic phase were collected and used for HPLC analysis. An Agilent 1200 Series HPLC system was used with a Supelcosil™ LC-18-T column (3 µm; 150×4.6 mm; Supelco, USA) guarded with a Supelcosil™ LC-18-T Supelguard™ (3µm; 20×4.0 mm; Supelco, USA). Buffer A: 100 mM phosphate buffer pH 6.0; 4 mM tetrabutylammonium disulfate


 

(TBAS). Buffer B: 30% methanol in 100 mM phosphate buffer pH 7.2 and 4 mM TBAS. The separation was performed in a linear gradient from 0 to 100% of B at 1.5%/min increments and a flow rate of 1 mL/min at 25°C (column thermostat). Detection was carried out at 260 and 340 nm. The separation method was calibrated using ATP, ADP and AMP (Sigma) as standards. The AXP content was expressed in µmol per gram of dry weight of biomass / 0 3 and the energy charge was calculated accordingly:

EC =

CATP + (0.5CADP ) CATP + CADP + CAMP

2.6

Data analysis

(10)

The experimental data of 
#(Figure 3A) were fitted to equation (1) and these fits were used as an analytical solution in subsequent calculations. Although the fitting provides accurate results (R2 = 0.93), it is nevertheless ambiguous and leads to wide standard errors of A and B due to their large values (Table 2). Therefore, one can simplify equation (1) to form F G H I :JK L
#M5 N O I :JK P
#Q, which provides an unambiguous fit of the same accuracy (R2 = 0.93). The experimental data in Figure 3B were fitted to equation (6) using calculated  values of   from equation (5), 
# as analytical solution from equation

(1) and 
# as analytical solution from equation (11). The total glucose consumption rate (Figure 3C) is a sum of glucose consumption rates for growth- and non-growth associated processes (equation  (5)). Therefore, the temperature dependence of 6 values at experimental


 

temperatures were fitted to equation (5) using temperature dependences of  (equation (1)) and  (equation (11)). The runs-test for linearity proved the validity of linear regression for analysis of experimental data in Figure 3D. The parameters of the linear equations (both slopes and intersects) between two lines were compared using an F-test in GraphPad Prism (V5.0) to compare independent fits with a global fit that shares the selected parameter. The values of  at experimental temperatures (Figure 3C) were calculated  . The temperature from equation (5) using experimentally derived 6 and  

dependence of  (Figure 3C) was fitted to the Boltzmann sigmoid equation, which was used only as an analytical solution:

low glc

mglc = m

+

(m

high glc

low − mglc )

§ T −T · 1 + exp ¨ 0.5 ¸ © slope ¹

(11)

 – low specific rate of glucose consumption for maintenance Where:  8,8 [0  0 4#] was accepted from linear analysis presented in Figure 3D; 

– high specific rate of glucose consumption for maintenance [0  0 4#] was accepted from linear analysis presented in Figure 3D; RK: – slope of the transition of the sigmoid between low and high maintenance costs;
.ST – temperature at halfway point between low and high maintenance costs [°C];
– temperature [°C]. The values of > (equation (7)) at experimental temperatures (Figure 3F) were fitted to a two-phase exponential decay equation, because it provided a better fit than a one-phase exponential decay:


 

­span fast = (η pmax −η pmin ) α fast ° ° max min ®spanslow = (η p −η p ) (1 − α fast ) ° min °¯η p = η p + span fast exp ( −k fast µmax ) + spanslow exp ( −kslow µmax )

(12)

Where: > and >,- are from equation (8); U+V – the fraction of the span (from > to >,- ) accounted for the faster of the two components [-]; +V and WL ]. The fit was used only for presentation purposes. V  – rate constants [

The runs-test for linearity proved the validity of linear regression for the analysis of experimental data in Figure 4A to B. See Table 2 for the numerical values of parameters.

3

Results and Discussions

. All batch experiments were started at * = 15 g/L in CEN.PK anaerobic . medium. This * was chosen to avoid growth limitation by accumulating

ethanol and other end-products during batch growth. Maximal theoretical yield of ethanol under anaerobic conditions when  = 0 is two moles of ethanol per . mole glucose consumed, which would correspond to about 7.6 g/L once * is

depleted. This expected ethanol concentration is much below the value that limits the growth rate of yeast under anaerobic conditions (Hoppe and Hansford, 1982). All results on yeast’s growth in anaerobic shaking flasks in batch mode under different isothermal growth conditions are summarized in Table 1. The reported values are given as mean ± min/max (n = 2).


 

3.1

Effect of growth temperature on XYZ[ and biomass concentration

The temperature dependence of  is presented in Figure 3A.
 was observed at around 31°C, after which the  decreased steeply at supraoptimal temperatures. Equation (1) was used to fit the experimental data and parameters are listed in Table 2. The temperature dependence of the final concentration of the dry biomass that +,-

was achieved in the batch (*

, see Figure 2 for definition) is presented in +,-

Figure 3B. The temperature dependence of * +,-

shape form with a maximum *

has an asymmetric bell-

\]S^_* # = 2.11 [0 1 ] (or   \]S^_* # =

0.141 [0 0 ]) and unequal slopes of the shoulders, where the supraoptimal temperature shoulder is steeper than the suboptimal. The biomass yield on glucose was calculated using equation (3) and plotted along the right axis of the graph in Figure 3B. The upper limit of this function is the true anaerobic yield of  biomass on glucose (   =0.1409 [0 0 ]), which is depicted as a

horizontal line in Figure 3B. This value is also used in equation (5) as slope of the lines (Figure 3D). 3.2

Effect of temperature on the specific rate of glucose consumption

The specific rates of glucose consumption (6 ) at experimental temperatures were calculated using equation (4) (Figure 3C). ). The greatest 6 was observed at 33°C [6 ^^_* # = 2.917 [0  0 4#]] (Table 1). Plotting 6 against  revealed a linear relationship between two of these quantities in accordance with equation (5) (Figure 3D). Linear regression analysis accompanied with a statistical test revealed the presence of two temperature regions where the linear relationship differs significantly: (i) 5-31°C and (ii) 3340°C. These two lines have equal slopes (F=0.1686 (1,9)), but differ

  

significantly in their intercepts (F=36.8 (1,9)). The slope of the line is the reciprocal value of the true anaerobic biomass yield on glucose (equation (5))  and is constant across all isothermal growth temperatures, slope = 5   =   7.096 [0 0 2] or   = 0.1409 [0 0 2] (Table 2).   determined in

this study corresponds to the value published earlier for the anaerobic batch growth of Saccharomyces cerevisiae (Roels, 1983). It can be concluded that for the formation of yeast biomass under anaerobic conditions the true or stoichiometric requirement for glucose is the same at any growth temperature. This is therefore an intrinsic feature or constant that is related to the biomass  composition of the given organism. This aspect of   is reflected as the

upper functional limit of  
# at Figure 3B (horizontal dotted line) and slope of the lines at Figure 3D. Thereby, the growth-associated term of equation (5)  (i.e.     .) is always proportional to the specific growth rate of the

biomass and therefore changes with temperature. The intercepts of the regression lines with the y-axis are the specific rates of glucose consumption for maintenance purposes (i.e.  ).  is the nongrowth associated term of the linear equation (5) and can be interpreted as various non-growth associated metabolic processes that consume ATP without contributing to a net synthesis of biomass (e.g., maintenance of concentration gradients and electron potential gradients; futile cycles; turnover of macromolecules, and other processes of endogenous turnover of the biomass (Roels, 1983; Stephanopoulos et al., 1998)).  differs approximately 12-fold 8,8

 between the two T-regions ( = 0.0603 vs.  = 0.7058 `0  0 4#a).

Reconstructed values of  (derived from re-arranged equation (5), using 6  and   ) plotted as a function of growth temperature show a step-wise


 

increase of  at 31.8°C (
.ST , equation (11), Figure 3C, Table 2). Thereby, we can distinguish two states of metabolic requirements for maintenance: •

 Low-maintenance requirements between 5-31°C at  = 0.0603

`0  0 4#a •

8,8

High-maintenance requirements between 33-40°C at  = 0.7058 `0  0 4#a

The transition between the two states occurs within a narrow temperature range of 31-32°C (
.ST, Figure 3C, Table 2). Since this transition is a key metabolic event in temperature dependent growth, the reasons for this transition are discussed in section 3.6.2. For better identification of the links among different metabolic processes, the transition temperature for  (i.e.
.ST ) was also depicted as a vertical dotted line in Figure 3A-C and E. This clearly indicates that the onset of suppression of both  and 6 occurs at
.ST . The existence of low- and high- maintenance modes in anaerobic yeast metabolism and associated ethanol formation was described previously (Roels, 1983). Thus, at growth temperatures above
.ST yeast consumes significantly more glucose for maintenance than in the suboptimal temperature range. For 8,8

 example, at
 (i.e. 40°C) 6 falls to such low level that  comprises

almost 50% of the 6 value. Analysis of the temperature dependency of  leads to the following observations: 1. There are two distinct metabolic states of maintenance requirements: low 8,8

 and high (e.g.  and  ).

  , 2.  (b = low, high) does not correlate with temperature within

corresponding temperature ranges.  3. Within a temperature range that is characterized by  , warming

stimulates  , whereas within a temperature range that is 8,8

characterized by  , warming suppresses  . Maintenance costs are an intrinsic part of the growth process (Esener et al., 1981a; Nielsen et al., 2003; Roels, 1983; Stephanopoulos et al., 1998). However, extra maintenance costs can be caused by different additional stimuli (temperature, pH, osmotic pressure, high salts, toxicants, drugs, metabolic impairment, etc.). One of the well-studied triggers of extra maintenance costs in yeasts are weak acids (acetic, propionic and benzoic acids). Under high concentration of an acid, there is extra ATP consumption for homeostatic regulation of intracellular pH, which is being acidified by an acid. This demands extra amounts of energy/carbon substrate and correspondingly leads to a reduction of biomass yield on the substrate (Verduyn et al., 1990, 1992). There is thus a positive linear correlation between the extracellular concentrations of the weak acids and the rates of glucose consumption for maintenance and correspondingly a negative linear correlation with biomass yield on glucose (Verduyn et al., 1990, 1992). However, in our experiment, we observed only two distinct values of glucose consumption rates for non-growth associated maintenance and they do not correlate with temperature within corresponding , at Figure 3C). This reflects the distinct difference in temperature ranges (

the causes of additional maintenance costs elicited by extracellular acids and the temperature dependent maintenance costs observed here. We assume that the transition between low and high energy demand phases of maintenance

 

follows a steep exponential function within a narrow temperature range, in similar ways as the exponential rise in aerobic maintenance costs seen in animals within wider temperature ranges (Mark et al., 2002; Van Dijk et al., 1999). Another popular hypothesis on temperature induced molecular damages centers on plasma membrane fluidity (i.e. integrity) as a main cause for an exponential rise in energy expenses. The hypothesis states that a temperature induced ‘gel-to-liquid’ phase-transition of the phospholipid bilayer might cause a loss of membrane integrity and, as a consequence, results in ion leakage, which correspondingly leads to extra ATP consumption to regain the trans-membrane ions and proton gradients. Experiments showed, however, that the temperature of the lipid phase-transition of native membranes of yeast S. cerevisiae is not an acute step-wise event, but rather an event that is stretched over a wide temperature range. For example, the phospholipid bilayer of yeast S. cerevisiae grown at 25°C began its phase-transition (gel-to-liquid) at 9°C and ended it at 15°C, with an average phase-transition temperature of 12°C (Laroche et al., 2001; Laroche and Gervais, 2003). Increasing the extracellular osmotic pressure (e.g. with glycerol) shifted the average phase-transition temperature upwards, but at the same time widened the temperature range. For example, at an osmotic pressure of 133 MPa phase-transition began at 14°C and ended at 33°C, with a mean phase-transition temperature of 23.5°C (Laroche et al., 2001; Laroche and Gervais, 2003). Additionally, it was shown that the temperature range of the phase transition at any osmotic pressure (between 1.3 and 133 MPa) always covered the 4-22°C temperature window (Laroche et al., 2001; Laroche and Gervais, 2003). High temperature (40°C) resulted in liquidification of the native membrane of yeasts (Simonin et al., 2008) and led to cell death.

 

Mortality of yeast cells exposed to a combination of thermal and osmotic treatments is related to leakage of cellular components through an unstable membrane when lipid phase-transition occurs (Laroche et al., 2005; Simonin et al., 2008). Simonin et al. (2008) concluded that the change in membrane fluidity is the critical event, which is important, but it must be accompanied by an osmotic stress to evoke cell death. Thus, reduction of cell viability at supraoptimal temperatures (Simonin et al., 2008) and the temperature induced death rate ( ) as discussed in (van Uden, 1985; van Uden and Madeira-Lopes, 1976) might involve a critical change in membrane fluidity. If we assume a positive correlation between growth temperature and loss of membrane integrity in the supraoptimal temperature range, then there must be a proportional increase in maintenance costs to meet the requirements of ion and pH homeostasis. However, this does not match the observation of a stepwise transition as in our experiments (Figure 3C). Consequently, we cannot exclude a role for membranes in contributing to maintenance costs but cannot relate the observed stepwise shift in  to a sudden loss of membrane integrity. 3.3

Effect of growth temperature on biomass yield on glucose

Temperature induced variations in biomass yield on glucose (   ; Figure 3B) can be interpreted in terms of equation (6).   depends on temperature induced changes in both, the specific growth rate ( ) and the specific rate of  glucose consumption for maintenance processes ( ).   on the other

hand remains constant for all growth conditions and this is presented as a functional limit in Figure 3B (horizontal line) and Figure 3D (slope of the lines). Moving from the optimal temperature region towards both extreme temperatures (5 and 40°C), the decrease of  mainly defines the decrease

 

of the biomass yield on substrate (equation (6)). Theoretically, this decrease, paralleled by the rise in maintenance costs, should be accompanied by a corresponding increase in the conversion of organic matter into end-metabolite yields (e.g. ethanol, CO2, etc.) and heat yield, i.e. yeast metabolism should become more dissipative. Additionally, at supraoptimal temperatures (i.e. > 31°C) the superposition of a strong decrease in  and a 12-fold increase in  both contribute to steeper slopes of these changes in the warmth. 3.4

Effect of growth temperature on the fractional conservation of glucose in ethanol and ATP yield on glucose

Based on a well elaborated macroscopic analysis of microbial growth (Roels, 1983), we have calculated the fractional conservation of carbon from glucose in ethanol (78 ), although ethanol was not directly measured in this research. The 78 is ethanol formation efficiency from glucose calculated as the percentage of product formation efficiency (> ) from the maximal theoretical yield of ethanol on glucose (9 98 ). The > can be calculated if the biomass elemental composition (9? ), biomass specific growth rate ( ), true biomass  yield on glucose (   ) and rate of glucose consumption for maintenance

( ) are known (equation (7)) in anaerobic growth on glucose as the sole carbon and energy substrate. The > was used for further analysis and assessment of the efficiency term. The > -values at experimental temperatures were calculated using experimental data listed in Table 1. These values were fitted to equation (7) (and presented as Figure 3E) using temperature dependencies of  (equation (1)),   (equation (11)) and a constant value of   from equation (5). The > -value

can vary between a functional upper limit at 1.0 when  G B (> ) and a

 

functional lower limit when  G C (>,- ; equation (8), Figure 3F). In our experimental conditions the >,- was 0.85, which corresponds exactly to the value known for yeast anaerobic growth on glucose in batch mode (Roels, 1983). Correspondingly, limiting values of > are reflected in limiting values of  ,the ATP yield on glucose (   = 2.0 and   = 1.7; equation (9)). These

limits were depicted as horizontal dotted lines in Figure 3E and F. The >,value indicates the lowest possible ratio between (i) the fraction of substrate invested into biomass formation (as a carbon source) and (ii) the fraction of substrate invested into energy generation to support synthesis and turnover of this amount of biomass, i.e. growth. > has a high value at 5°C and then decreases with increasing temperature/growth rate and approaches its lower limit at 26-31°C. Further warming towards
 (
c
 ) resulted in a sudden upshift of > from its lower limit (Figure 3E and F). Non-linear analysis of > as a function of  (equation (12); Figure 3F) revealed that there were two temperature regions where >  # differed  and significantly. These temperature regions correspond exactly to the  8,8

 maintenance metabolic modes shown in Figure 3C and D. Between 5 and 31°C, yeasts operated under the low-maintenance-requirements metabolic  mode ( ), where a temperature increase from 5 to 31°C stimulated an

increase in  , 6 and   and a decrease of the efficiency of anaerobic energy metabolism (> and   , correspondingly). > and   approached their lower functional limit at ~26-31°C (i.e. at
 ). At supraoptimal temperatures (i.e. 33-40°C), yeasts switched to high-maintenance-requirements 8,8

metabolic mode ( ), which is accompanied by suppression of  , and

  

corresponding reduction of 6 and   . In the same time, > and   become upshifted from their lowest values. The observed metabolic events at various temperatures can be assessed in light of Roels (1983) overview of the methods of maximization of end-product formation in anaerobic microbial cultures by means of optimization of the following growth parameters interconnected through equation (7): •

Decrease of . This can be achieved by (i) transferring the microbial process from batch to chemostat mode and running the process at lower dilution rates; (ii) continuous culturing with cell recycling; (iii) growth limitation by lack of essential elements (N, P, etc.); (iv) cell immobilization.

•

Increase of  . This can be achieved by (i) increasing operation temperature of the bioprocess; (ii) increasing salt concentration; (iii) creation of mutants or use of other microorganisms with intrinsically higher  .

•

 Decrease of   . Use other less efficient microorganism.

Thus, we see an analogy of observed metabolic adjustments in yeasts in the supraoptimal temperature region (i.e. both decreasing  and increasing  ) with the strategy of maximization of end-product formation in anaerobic  microbial cultures. However,   remained constant, since this is an intrinsic

feature of biomass composition. It is likely that the supression of  at supraoptimal temperatures is triggered by increased energy demands for maintenance. Correspondingly, we assume that the purpose of temperature induced metabolic adjustments observed at supraoptimal temperatures is to increase the efficiency of energy metabolism. Efficiency of energy metabolism

   ,descends to its lower limit (>,- = 0.85 or   = 1.7) at 26-31°C and further

warming triggers these metabolic adjustments to upshift from the lower efficiency limit at the expense of growth. Perhaps this is a trade-off to survive at supraoptimal temperatures and thus to extend the thermal window through reduced productivity and enhanced passive tolerance. 3.5

Effect of temperature on energy status

The intracellular adenylates (AXP = ATP + ADP + AMP) were measured in two metabolic modes: anaerobic and aerobic. In anaerobic batch growth AXP were always sampled during the early exponential growth phase (for example see Figure 2). Aerobic chemostat cultures were additionally performed to measure AXP contents under different steady state growth rates. In both metabolic modes (anaerobic and aerobic), we observed a negative linear relationship between specific growth rate and corresponding AXP content in the cells: the faster the cells grow the lower the AXP concentration is (Figure 4). This observation is not surprising since it is known that yeast’s glycolytic rate measured as glucose consumption and ethanol production rates in semipermeabilized cells negatively correlates with ATP concentration in yeast S. cerevisiae (Larsson et al., 1997). From this can be concluded that higher material fluxes through the metabolic system (supply and demand units coupled through the energy metabolism) are triggered by low ATP concentration (Hofmeyr, 1997; Hofmeyr and Cornish-Bowden, 2000; Koebmann et al., 2002; Kroukamp et al., 2002; Reich and Selkov, 1981). Under aerobic conditions, the intracellular ATP content is almost twice as high as under anaerobic conditions (app. 7 vs. app. 4 µmol ATP/gdw). This difference is defined by the inactive state of mitochondria in anaerobic yeasts, which was

 

experimentally proven by using permeabilized cells (Theobald et al., 1997). It was shown that the ATP pool observed in anaerobic yeasts is exclusively cytoplasmatic (Theobald et al., 1997). ATP and all other components in the adenylate pool (i.e. AXP) showed a proportional reduction in their concentrations with an increase in growth rate (Figure 4A and B). As a consequence, the cellular energy charge (EC; equation (10)) remained constant under all conditions tested (0.83; Figure 4C), reflecting that energy status is under strong homeostatic control at any growth conditions tested. 3.6

Trade-offs in energy budget: maintenance versus growth

Two key metabolic event were observed in the supraoptimal temperatures: (i) suppression of specific growth rate (i.e.  ) and (ii) step-wise increase of the specific rate of glucose consumption for maintenance (i.e.  ). High maintenance costs cause the steep decline of scope for growth at temperatures above
 . The mechanism of this trade-off is unclear. It is rather unlikely that  suppression is solely thermodynamically driven as follows from equation (1) (see reasoning in Introduction). We rather hypothesise that  suppression in supraoptimal temperatures is a coordinated and controlled process. The growth suppression allows cellular energy balance to be maintained at values sustaining crucial functions in supraoptimal temperatures and extends the thermal window. Through this trade-off ten more degrees are added to
 and the width of the thermal window (i.e. 30-40°C). 3.6.1 Growth rate In fact, microorganisms use different molecular mechanisms to down-regulate the growth rate at high growth temperatures. Biomass growth is a result of

  

counteracting synthesis and degradation rate-processes of proteins as a major biomass constituent. Thus, if the temperature stimulates the rate of protein synthesis through direct thermodynamic effect (described by the Arrhenius equation), then the net-rate production can be reduced through: (i)

down regulation of the expression of genes involved in ribosomal biogenesis (e.g. reduction of a number of working ribosomes) (Farewell and Neidhardt, 1998; Pizarro et al., 2008; Tai et al., 2007a; Tai et al., 2007b);

(ii)

increasing rate of protein degradation (e.g. ATP-dependent proteolysis in proteasomes (Farewell and Neidhardt, 1998; Hilt et al., 1993; Hilt and Wolf, 1995) or elevated expression of genes related to protein folding and degradation in the course of the heat shock response in yeast (Causton et al., 2001; Eastmond and Nelson, 2006; Gasch et al., 2000));

(iii)

increasing rate of mRNA degradation. Reduction of half-life of proteins and mRNA is a well known side-effect in the course of different stress-responses (Farewell and Neidhardt, 1998; Kresnowati et al., 2006; Yost and Lindquist, 1991).

3.6.2 Maintenance rate Cellular maintenance processes require the consumption of ATP without contributing to a net synthesis of biomass (Roels, 1983; Stephanopoulos et al., 1998). Some of these costs are proportional to the rate of growth (e.g. macromolecule turnover, etc.) and enter into the growth-associated term of equation (5). Baseline maintenance, which we denoted as  , might be related to the activity of ATP-dependent transporters maintaining trans-


 

membrane gradients, electrochemical gradients, futile cycles, change in half-life of macromolecules, ATP-dependent molecular reparation with chaperons and others. Batch aerobic growth of yeast S. cerevisiae at supraoptimal temperatures (30-39°C) for example resulted in an overall increase in membrane-associated H+-ATPase activity (Pma1) with growth temperature (Viegas et al., 1995). We can thus assume that the maintenance processes are involved in setting cellular conditions to be favourable for growth. Based on our estimates, we expect that anaerobic yeast become more heat dissipative in the supraoptimal temperature range (33-40°C) than in the suboptimal range (5-31°C). It was suggested recently (De la Fuente et al., 2013) that in dissipative metabolic networks a cellular enzymatic activity selforganizes in a set of different enzymatic reactions (i.e. metabolic core). The active metabolic core adjusts the internal metabolic activities to the external change by means of metabolic fluxes and structural plasticity. The state of the metabolic core is governed by attractor-states with the capacity to store functional metabolic patterns, which can be recovered correctly from specific input stimuli (De la Fuente et al., 2013). Thus, we hypothesize that increasing temperature might stimulate the transition of the metabolic core to another attractor-state where the entire metabolic network becomes more dissipative. This transition can trigger the mechanisms that suppress growth rate (by cell division) and thus maintain energy status. Perhaps using this strategy, the metabolic system sustains structural integrity and reproduction at supraoptimal temperatures.

 

4

Conclusions

Our data show that the thermal window of yeast as a unicellular eukaryotic organism is shaped by similar principles as recently elaborated as the OCLTT concept for animals. It was shown that the biomass yield (   ) varied with temperature due to changes in maximal specific growth rate through cell divisions ( ) and non-growth maintenance expenses ( ), whereas the  true yield of biomass on glucose (   ) was constant over the entire thermal

window (5-40°C). We observed two temperature regions with different nongrowth maintenance requirements: (i) ‘low’ within 5-31°C and (ii) ‘high’ within 33-40°C, with an acute step-wise transition between them at approximately 31.5°C. The ATP yield on glucose (   ) reaches its functional lower limit at 26-31°C, whereas in the supraoptimal temperature range (33-40°C) it is upshifted from its lower limit by means of elevated  and suppressed  . Temperature induced changes in  and  in supraoptimal temperatures seem to be coupled and controlled. It is expected that yeast metabolism becomes more heat dissipative at supraoptimal temperatures. We conclude, there must be molecular mechanisms, which adjust the rates of  and  to energy demand in order to sustain survival and reproduction within supraoptimal temperatures. There was a negative linear relationship between specific growth rate () and the intracellular quasi-steady state concentration of AXP (ATP, ADP, AMP), which sustained energy status (EC at appr.0.83) under any growth conditions. We therefore do not expect that the hypothesized tradeoff is initiated by an acute change in intracellular ATP content. The suppression of  and elevation of  at supraoptimal temperatures maintains cellular energy status and thereby contributes to extending the thermal window. This

 

trade-off widens the thermal window by ten degrees added to
 (i.e. 3040°C). Additional experiments are required in order to further analyse these relationships and hypotheses.

5

Acknowledgments

The authors would like to thank the following research groups and their institutions for supporting this project and work carried out: the integrative ecophysiology division at the Alfred Wegener Institute (AWI, Bremerhaven, Germany), the group of Prof. Matthias Reuss at the University of Stuttgart (Germany) and the group of Prof. Stefan Wölfl at the University of Heidelberg (Germany). This research was partially funded by the European transnational research initiative through the Systems Biology of Microorganisms (www.sysmo.net) project – Microorganism Systems Biology: energy and Saccharomyces cerevisiae (SysMO:MOSES). Special thanks to Dr. Birgit Obermüller (Iceberg Translation, UK) for the English grammar revision.

6

Vitae Dr. Maksim Zakhartsev has graduated in 1992 from Far Eastern State University (Vladivostok, Russia) with a diploma in biochemistry. In 2003, he has graduated with Ph.D. in biochemistry from University of Antwerp (Belgium) where he has conducted research in scope of CLICOFI project. This research has centred on

temperature adaptation of poikilothermic organisms. In 2003, he took up a research and teaching position at Jacobs University (Bremen, Germany), where he gained experience in methods of metabolic engineering. A position at the

 

Alfred Wegener Institute (Bremerhaven, Germany) followed and inspired the work presented here. During two further post-doc positions at the Universities of Stuttgart and Heidelberg (Germany), he has gained experience in mathematical analysis and modelling. Dr. Xuelian Yang has graduated in 2009 from Nanjing Tech. University with Ph.D in Biochemical Engineering. During the postgraduate study, she was involved in research project related to mathematical modeling of energy metabolism of yeast Saccharomyces cerevisae in Institute of Biochemical Engineering (Stuttgart,Germany). She has finished her post-doc position at Nanjing Technical University in 2011. After that, she works at Beijing Technology and Business University (Beijing, China) as a teacher and researcher. Prof.Dr. Matthias Reuss. University Education & Degrees – 1970, Ph.D. (Dr.Ing.) in Chemical Engineering from the Technical University of Berlin; 19711976 Research Assistant in the Department of Biotechnology at the GBF Braunschweig; 1977-1987 Professor of Biochemical Engineering Technical University of Berlin; from 1988 – 2009 (retirement) Professor of Biochemical Engineering and Director of the Institute of Biochemical Engineering at University Stuttgart; 2006-2013 Director of the Centre Systems Biology at University Stuttgart. 2010-2013 NGI Distinguished Visiting Scientist (Kluyver Centre Delft and NICSB Amsterdam) in The Netherlands.

 

Honors & Awards – Fellow of the International Institute of Biotechnology; 1992 Research award of the State of Baden-Wuerttemberg; 2006 Doctor honoris causa TU Delft, The Netherlands. Prof.Dr. Hans-O. Pörtner studied at Münster and Düsseldorf Universities where he received his PhD and habilitated in Animal Physiology. As a Research and then Heisenberg Fellow of the German Research Council he worked at Dalhousie and Acadia Universities, Nova Scotia, Canada and at the Lovelace Medical Foundation, Albuquerque, NM. Currently he is Professor and Head of the Department of Integrative Ecophysiology at the Alfred Wegener Institute for Marine and Polar Research, Bremerhaven, Germany. He acts as an associate editor “Physiology” for Marine Biology and as a co-editor of the Journal of Thermal Biology. He is a Coordinating Lead Author of IPCC WGII AR5, chapter Ocean Systems and a member of the author teams for the WGII Summary for Policymakers and Technical Summary, as well as a member of the Core Writing Team for the IPCC AR5 Synthesis Report. His research interests include the effects of climate warming, ocean acidification, and hypoxia on marine animals and ecosystems with a focus on the links between ecological, physiological, biochemical and molecular mechanisms limiting tolerance and shaping biogeography and ecosystem functioning.

7

Tables

Table 1

 

Experimental and estimated features of temperature-dependent anaerobic batch growth of yeast Saccharomyces cerevisiae CEN.PK113-7D on mineral medium with 15 gglc/L of initial glucose concentration. All values are given as average ± max/min (n = 2). +,-

5

0.008

± 0.001

1.10

± 0.07

0.073

± 0.005

0.102

± 0.003

0.049

± 0.002

0.923

± 0.005

10

0.030

± 0.008

1.45

± 0.02

0.096

± 0.002

0.312

± 0.093

0.099

± 0.033

0.899

± 0.002

15

0.068

± 0.013

1.64

± 0.01

0.110

± 0.001

0.616

± 0.124

0.136

± 0.029

0.885

± 0.001

18.5

0.115

± 0.030

1.92

± 0.03

0.128

± 0.002

0.898

± 0.217

0.080

± 0.006

0.866

± 0.002

22.5

0.167

± 0.039

1.91

± 0.10

0.127

± 0.007

1.301

± 0.238

0.117

± 0.039

0.866

± 0.007

26.3

0.250

± 0.020

2.11

± 0.02

0.141

± 0.002

1.780

± 0.162

0.017

-

0.854

-

  2 [mol ATP/mol g glc] 1.84 ± 0.010 1.80 ± 0.003 1.77 ± 0.001 1.73 ± 0.004 1.73 ± 0.014 1.70 -

30

0.319

± 0.006

1.97

± 0.10

0.132

± 0.007

2.425

± 0.115

0.218

± 0.047

0.865

± 0.002

1.73

31

0.379

± 0.010

2.00

± 0.01

0.133

± 0.001

2.843

± 0.094

0.147

± 0.024

0.860

± 0.001

1.72

33

0.309

± 0.013

1.59

± 0.08

0.106

± 0.005

2.917

± 0.269

0.723

± 0.174

0.889

± 0.005

1.77

34

0.258

± 0.075

1.59

± 0.02

0.106

± 0.001

2.434

± 0.681

0.599

± 0.148

0.889

± 0.001

1.78

35

0.242

± 0.043

1.52

± 0.02

0.102

± 0.001

2.376

± 0.324

0.658

± 0.074

0.892

± 0.003

1.78

37.5

0.195

± 0.030

1.36

± 0.04

0.091

± 0.002

2.159

± 0.384

0.772

± 0.173

0.905

± 0.002

1.81

40

0.111

± 0.034

1.02

± 0.06

0.068

± 0.004

1.623

± 0.399

0.834

± 0.157

0.929

± 0.004

1.85

T [°C]

 [h-1] a

  [gdw/gglc] c

* 2 b [gdw/L]

6 [gglc/(gdwÂh)] d

+,-

 – maximal specific growth rate; *

 [gglc/(gdwÂh)] e

> [-] f

– final dry biomass achieved in the

batch;   – biomass yield on glucose; 6 – specific rate of glucose consumption;  – specific rate of glucose consumption for maintenance; > – product formation efficiency as percentage of the maximal theoretical yield;   – ATP yield on consumed glucose. a,b,c

experimental values;

d

according to equation (4),

e

 derived from equation (5) using known 6 and   ,

± 0.005 ± 0.002 ± 0.011 ± 0.002 ± 0.002 ± 0.005 ± 0.009

   f

according to equation (7),

g

according to equation (9).

Table 2 Main estimated parameters Equation (1) for 

(5)

8,8  > >,   ,    

(8) (9) (11)

(12) for low maintenance requirements

(12) for high maintenance requirements

8

Parameter    e     

8,8 
.ST RK: > >,U+V +V V  > >,U+V +V V 


Value 18 8.9877×10 111900 5.8935×1050 296900 0.1409 0.0603

±s.e.m. too wide 15170 too wide 1487 0.003 0.040

0.7058 1.0 0.852 2.0 1.704 from eq. (5)

0.053

from eq. (5) 31.83 0.4526 from eq. (8) from eq. (8) 0.5953 234.5 9.322 from eq. (8) from eq. (8) 0.8553 7.493 1.52×10-16 equals to
.ST from eq. (11)

Units /d3 / 3 /d3 / 3 `0 0 a `0  0 4#a `0  0 4#a /d3 /d3 /2
D 20<3 /2
D 20<3

0.414 0.195

/_*3

7.419 88.37 2.462

/d3 WL 3 / WL 3 /

0.7622 6.027 -

/d3 WL 3 / WL 3 / /_*3

Figures

Figure 1 Midpoint temperature of the thermal unfolding (
 ) of proteins of wild-type yeast Saccharomyces cerevisiae. The data (m = 14, number of studied proteins; with

  

n = 203, number of database entries) were collected from the ProTherm database (Thermodynamic database for proteins and mutants (Bava et al., 2004); http://www.abren.net/protherm/) using advanced search criteria: source = Saccharomyces; mutations = wild type; denaturation method = thermal; measures = DSC, CD, fluorescence. (A)
 s of specific proteins (m = 14; average ±s.d.). The number in brackets next to the protein name is the number of database entries per this particular protein. (B) Complete set of
 s for those proteins whose ±s.d. overlapped with the supraoptimal region of temperatures for growth of yeast S. cerevisiae (30-40°C; shaded area).

Figure 2 An example of anaerobic batch growth of biomass of yeast Saccharomyces cerevisiae CEN.PK 113-7D in a shaking flask at 26.3°C. The shaded area indicates conditions where the culture has reached maximal specific growth rate ( ). Correspondingly, samples for ATP, ADP, AMP measurements were taken at time points within this area. All calculated parameters are according to equations (2) to (4).

Figure 3 Temperature dependencies of different growth parameters during anaerobic batch growth of yeast Saccharomyces cerevisiae CEN.PK 113-7D on glucose: (A) The maximal specific growth rate ( ) was fitted to equation (1); (B) The +,-

final concentration of biomass achieved in batch (*

) during anaerobic

growth. The experimental value of the biomass yield on glucose (   ;

 

equation (3)) was fitted to equation (6); (C) The specific rate of glucose consumption (6 ), data points at experimental temperatures were calculated according to equation (4) and fitted to equation (5); glucose consumption rate for maintenance ( ; calculated from equation (5), assuming known  , 6  and   ) was fitted to equation (11). (D) The linear relationship between 6  and  . The slopes (i.e. 5   ; equation (5)) of the lines in both T-regions

(5-31°C and 33-40°C) are the same (F-test, F=0.1686 (1,9)), whereas the intercepts (i.e.  ; equation (5)) are ~12-fold different; (E) Temperature dependence of efficiency of substrate carbon conservation in product (> ; equation (7)) and ATP yield on glucose (   ; equation (9)). (F) Dependencies of > on  were fitted to equation (12). The horizontal dotted line depicts the lower limit of > (>,- , equation (8)), which is the same for both curves, whereas the decay constants are different. The vertical dotted line in all panels depicts the transition temperature between (
.ST, equation (11)) low and high maintenance requirements.

Figure 4 Quasi-steady state intracellular concentrations of ATP, ADP and AMP (*fgh i *fjh i *fkh ) under (A) aerobic and (B) anaerobic growth rates that were modulated by different means: temperature in batch (marked as “batch”) or glucose limitation in chemostat (marked as “chem.”) at different temperatures. (C) Energy charge (equation (10)) as a function of specific growth rate () under different growth conditions. The horizontal line depicts the averaged energy

  

charge and the shaded area is lRS m. (D) List of linear equations which describe relationships among *fnh and .

9

Abbreviations







*fgh 

 !"#$!

/20 3

* 

% 

`0 12a

. * 

% 

`0 12a

*. 

&!'  

/0 123

*+,- 

&&!'  

/0 123

  

"#$! !% 

/2
D 20< 23

  

!% 

`0 0 2a

   

 !% 

`0 0 2a

 

*&%+'

/0  0 o 4#223/54 3



&%+'

/0  0 o 4#223

 

&&%  &

`0  0 o 4#22a

6 

&&%  

`0  0 o 4#22a

78 

&,&% '

/*2:=4 * 20<23

> 

! &&&%&' *',&  !  !%&! &
-' 

/d3

+%'&
-' ! 

/0, 3

!+%'&





(!

)



9, 

/:;*2b 3

.%'/ 0,  0' mp


  :=4

'



0<

% 



4

' 

/43



 & 




 

/_*3

J







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