Flux of O2 affects apparent optimal concentrations of O2 in suspensions of bacteria respiring microaerobically

J. theor. Biol. (1985) 115, 93-102

Flux of 02 Affects Apparent Optimal Concentrations of 02 in Suspensions of Bacteria Respiring Microaerobically FRASER J. B E R G E R S E N t AND J E A N - C H A R L E S TRINCHANT:[:

t CSIRO Division of Plant Industry, GPO Box 1600, Canberra A . C . T 2601, Australia and ~. Laboratoire de Biologic V~gdtale, Facult~ des Sciences et des Techniques, Parc Valrose, 06034 Nice, France (Received 21 November 1984) Calculations of the flux of 02 at very low concentrations in aqueous suspensions of bacteria show that different substrate-induced 02 demands may induce apparently different optima for O2-related activities. This arises from different concentration gradients near to the bacterial surfaces. These effects are illustrated from published experimental data showing apparently different optimal concentrations of 02 for nitrogenase activity of bacteroids isolated from root nodules of haricot bean, according to whether glucose or succinate were supplied as exogenous substrate. Profiles of 02 concentration within the spherical domain occupied by each bacterium were calculated for each of the experimental conditions discussed. Special attention was given to the effects of the presence of the macromolecular O2-carrying protein leghaemoglobin, which diminishes the 02 concentration gradients within the sphere of solution occupied by each bacterium. 1. Introduction

The importance of microaerobic metabolism in bacteria has been emphasized recently, especially for diazotrophs in which the requirements for 02 as a terminal electron acceptor for energy-producing pathways, frequently conflicts with the sensitivity to O2 of the nitrogenase complex (Robson & Postgate, 1980; Bergersen, 1982, 1984). In the root nodules of legumes, microaerobic conditions prevail (i.e. the concentration of free dissolved 02 is << l p.M; e.g. Appleby, 1969; Bergersen, 1982) and the O2 requirements of large numbers of intracellular bacteria are met by small diffusive fluxes of free-dissolved 02 greatly augmented by a diffusive flux o f oxyleghaemoglobin. The net effect is that adequate fluxes of 02 are available for the bacteria at very stable (Stokes, 1975) low concentrations ( < 2 0 n M ) . Leghaemoglobins are present in the host cell cytoplasm (e.g. Robertson et Address for correspondence: Dr F. J. Bergersen, CSIRO Division of Plant Industry, GPO Box 1600, Canberra ACT 2601, Australia. 93 0022-5193/85/130093 + l0 $03.00/0

(~ 1985 Academic Press Inc. (London) Ltd

94

F.J.

BERGERSEN

AND

J.-C.

TRINCHANT

al., 1978) and in some cases also within the intracellular compartments enclosing groups of bacteroids (Bergersen & Appleby, 1981). Leghaemoglobins from soybean nodules have been purified and their OE-binding kinetics measured (Imamura, Riggs & Gibson, 1972; Wittenberg, Appleby & Wittenberg, 1972). They have been used subsequently to study 02 consumption and nitrogenase activities of microaerobic suspensions of bacteroids and of other diazotrophic bacteria, in which diffusive fluxes of free, dissolved O2 would be restricted and difficult to measure (Bergersen & Turner, 1979, 1980; Bergersen, Kennedy & Hill, 1982; Hill, Turner & Bergersen, 1984; Emerich et al., 1980). Trinchant & Rigaud (1981) and Trinchant, Birot & Rigaud (1981) found apparently different optimal 02 concentrations for nitrogenase activity of suspensions of bacteroids prepared from haricot bean (Phaseolus vulgaris) and soybean (Glycine max), according to whether the exogenously supplied carbon substrate was a sugar (glucose or sucrose) or an organic acid (succinate). Further, there were differences in the apparent optima when leghaemoglobin was present or absent and there were also effects of bacterial concentration. In this paper we present a model of some of the features of microaerobic 02 supply using as the primary source of data the results of Trinchant & Rigaud (1979, 1981) and Trinchant et al. (1981) with bacteroids from root nodules of haricot bean. 2. Data and Description of the Models

The experimental data are derived from results of several different types of experiment (see Table 2 below). They are summarized below. ( 1) Shaken assays contained about 20 mg (dry wt) of bacteroids in 2.0 ml of 25 mM phosphate buffer, with 02 dissolved from a gas phase containing 1.3-10.7 kPa ( 10-80 mmHg) 02. In these assays, optimal nitrogenase activity was obtained at about 4 kPa 02 with glucose present, but at about 9 kPa with succinate (Trinchant & Rigaud, 1979). Similar results were reported by Trinchant et al. (1981). (2) Stirred suspensions containing 2.5 mg (dry wt) of bacteroids in 4.0 ml of buffer, with dissolved OE monitored by an 02 electrode. In these experiments, the concentration of dissolved O2 optimal for nitrogenase activity was 3 ttM with glucose and about 9 ttM with succinate (Trinchant & Rigaud, 1981). (3) In the third type of experiment, at very low concentrations of free, dissolved O2, bacteroids (1-2 mg dry wt) were suspended in 4.0 ml of buffer containing glucose or succinate and 80 ~M ferrous-oxyleghaemoglobin. In

02 OPTIMA

IN

MICROAEROBIC

SUSPENSIONS

95

these experiments the concentration of free dissolved 02 in the bulk o f the suspension was calculated from observations of the proportional oxygenation (Y) of the leghaemoglobin, monitored spectrophotometrically. With glucose the optimum concentration of 02 for nitrogenase activity was 5 nM whilst with succinate, maximum activities were obtained at 20 nM or higher (Trinchant et al., 1981). The c o m m o n feature of all of these experiments is that with sucrose or glucose as substrate, optimum 02 concentrations for nitrogenase activity were about 25-30% of those required when succinate was supplied. The calculations from the model will show that, at least in part, the difference arises from the three to four-fold difference in demand for O2 when succinate replaces glucose or sucrose as exogenous substrate. The model considers the approximation in which diffusion of 02 between two concentric spheres is calculated (Crank, 1975). The inner is a sphere of radius 0.66 x l0 -4 cm, having a volume equivalent to a bacteroid (Table l). The outer sphere has a volume equivalent to the volume of solution occupied by one bacteroid in the respective suspensions. The model also assumes that there is an optimum concentration (S) of dissolved 02 at the bacterial surface for the activity of some metabolic process within the organism (such as nitrogenase activity), which can be monitored independently.

3. Profiles of 02 Concentration in Suspensions IN D I L U T E S U S P E N S I O N S W I T H N O O 2 - C A R R I E R P R E S E N T

For the surface concentration (S), the profile of concentration ( C ) within the sphere of solution occupied by each bacterium is C=S+dC

(1)

where, from Crank (1975) d C - Q ( b - a)' 41r D a b

(2)

where d C represents a differential change in concentration with respect to the bacterial surface; C = the concentration o f 02 at any point within the sphere of solution (moles cm-3); a = the radius o f a sphere equivalent in volume to a bacterium (cm) ; b = the radius of the sphere of solution occupied by a bacterium (cm), or o f some intermediate radius within the sphere; Q = the respiratory 02 flux per bacterium (moles sec-I); D = t h e diffusion coefficient in the solution for free, dissolved 02 (cm2sec -l) and r = t h e radial distance from the centre of the bacterium (cm).

1

k2

Lb + 02 ~ LbO2

kt

(iii) For the reaction

(i) Diffusion coefficient ( D ) for free O2, dissolved in water (ii) Diffusion coefficient (Dp) for leghaemoglobin in water

C Valuesfor constants

(i) With succinate (ii) With glucose (iii) With no added substrate

B Respiratoryfluxes of 0 z

(ii) Dry weight (iii) Properties of suspensions: (a) 10mg (dry wt)/ml: volume/cell radius (b) 0.5 mg (dry w t ) / m h volume/cell radius

(i) (a) Volume (b) Radius of equivalent sphere

A Bacteroids

Parameter

cells/mg

k 2 = 4.4 sec-i K = kz/k ~= 0.04 x 10-9 moles cm -3

k 1 = 118 × 109 moles -~ cm 3 sec -~

Wittenberg et al. (1972)

Estimated from values for myoglobin (Wittenberg, 1970)

1.0× 10-6 cm2 sec -j

Trinchant & Rigaud (1979, Fig. 3)

Arnold (1930)

moles O z cell -I sec -~ 0.33 × 10-Is 0.10× 10-Is 0.08 × 10 - 1 8

from A. (ii)

as for CB1809, Bergersen (1982, Table 15)

Source

2.35 x 10-5 cm 2 sec -I

nmoles 02 min-~ (rag dry wt) ~ 40 12 9.2

2 x l0 -9 cm3/cell 6-2 × 10 -~ cm

5 x 10 -II cm3/cel! 2.3 × 10-4 cm

2 × 10 9

1.2 x 10 -12 cm3/cell 0.66 x 10 -4 cm

Values

Numerical values used in the calculations: the reaction temperature was 30°C f o r suspensions o f bacteroids prepared f r o m root nodules o f haricot

TABLE

02 OPTIMA IN MICROAEROBIC SUSPENSIONS

97

The solution to these equations is illustrated in Fig. l(a) and (b) for a suspension of 0.5 mg (dry wt)/ml of haricot nodule bacteroids with glucose or succinate as substrates, using the data listed in Table 1. The profile of concentration of dissolved 02 (Fig. l(b)), was calculated from consideration of a series of values of b. The higher 02 demand in the presence of exogenous succinate requires a greater concentration gradient. If S is small (say 1-5 riM), different supply concentrations (at the surface of each sphere of solution) will be required in order to provide an identical concentration of 02 (S) at the bacterial surface. If S is large (say 1-5 ~M) then these differences would be imperceptible, although still present. When calculations are made for different concentrations of bacteria, which give different values for b, the concentrations of free dissolved 02 needed to maintain a constant concentration at the bacterial surfaces are of course also different (e.g. Table 2). This effect was observed in the experiments on which these calculations were based (Trinchant, unpublished). Nevertheless, the ratios of the required 02 concentrations in the presence of glucose and succinate remain constant and similar to the ratio of the rates of 02 consumption with the respective substrates (Table 2). IN DILUTE S U S P E N S I O N S

IN THE P R E S E N C E O F O X Y L E G H A E M O G L O B I N

Unlike the above case, when an O2-carrying protein is present, it is necessary to specify the delivered 02 concentration, since the magnitude of facilitation of 02 flux by the carrier depends upon the degree of its oxygenation and hence upon the concentration of free, dissolved 02 and the affinity for O2 of the carrier. It will be seen from Fig. 1 that an assumed optimum delivery concentration of 1 nM free 02 fits well with the data of Trinchant et al. (1981) for the nitrogenase activity of haricot bacteroids in a suspension of 80 tXM partially oxygenated leghaemoglobin. Now, in a zone of macromolecular carrier-facilitated flux, the total flux (Q) is given by Q - - Qfacilitated -t- QfreeO2

(Wyman, 1966).

As before (equation (2)) -4

Qrreeo2 -

ab

7rDb-~

dC.

In the spherical domain surrounding each bacterium, the facilitated flux is essentially the flux of oxygenated carrier arising from the difference in oxygenation between the outer surface of the sphere and the bacterial

oo

~D

Experimental

11.8 13-0 16.1 8.9

4.7 5.6 3.3

9.7 8.5 9 25t

4.0 4.5 3 6

4.3

40

12

Substrate: Glucose Succinate

2-7

2.9

2-8

2.7

:~ = 2.85

2.4 1.8 3.0 4.2

3.3

Ratio (succinate/glucose)

Source of data

& Rigaud (1979, Fig. 2) et al. (1981, Fig. 6) & Rigaud (1981, Fig. 4) et al. (1981, Fig. 4)

This paper

Trinchant Trinchant Trinchant Trinchant

Trinchant & Rigaud (1979, Fig. 3)

t Near-maximum rate. ~: 02 consumption with glucose or succinate as in line 1, with 1 nM free, dissolved 02 at the bacteroid surface.

Outermost concentration of free, dissolved 02 (nM), for O2 consumption~t with respective substrates: (a) No carrier, 20mg (dry wt) bacteroids ml -I (b) No carrier, 10mg (dry wt) bacteroids ml-I (c) No carrier, 0.5mg (dry wt) bacteroids ml-I (d) +80p.MLb, 0.5mg (dry wt) bacteroids ml-Z

Calculationsfrom the model

(b) IJ.M dissolved O z no carrier (c) nM dissolved 02 LbO2 present

O z consumption [nmoles O2 (mg dry wt) -~ min -I] 02 concentration for optimal nitrogenase activity: (a) gas phase (kPa)

Parameter

Comparison of experimental data for bacteroids isolated from nodules of haricot, with calculations from the model

TABLE 2

O 2 OPTIMA

IN

MICROAEROBIC

SUSPENSIONS

99

surface where 02 is consumed. Thus

ab C p d Y Qfacilitated=4"rrDp~_Q

(3)

where: Cp = the concentration of the carrier; Dp = the diffusion coefficient of the carrier; Y = the fractional oxygenation of the carrier; d Y = difference in Y between a and b. Now, in the reaction carrier+O2 .

kI

" carrier :: 02

k2

in which C is the concentration of free, dissolved O2 and K is the ratio Y- C+-~

k2/kl,

(C+K)2.

and d Y = d

Now the total flux may be written

Q=

4 D ab KdC ~- p ~ _ a C p ( c + K ) 2

L

-

+

ab 4zrD~_adC

(

)

and

Q(b-a)

dC -

(5)

K

4~'ab~pLp('-"r" C + K)2

+D

For suspensions of bacteroids from haricot nodules (Table l) in solutions containing 80 ~M leghaemoglobin, profiles of concentration of free dissolved 02, within the sphere occupied by each bacterium, were obtained by calculating dC for various values of a and b in equation (5), outwards from 1 nM 02 at the bacterial surface. In doing this, it was necessary to first consider the boundary layer, immediately adjacent to the bacterial surface, within which the concentration of free 02 is not in equilibrium with leghaemoglobin. The flux of 02 in this boundary layer is approximately described by the diffusion equation for free 02 (equation (2)). The thickness of the boundary layer is described by Stokes (1975) as Ar=

[

o

1

k , Cp ~ll-- Y ) .J

"

(6)

100

F.

J.

BERGERSEN

AND

J.-C.

TRINCHANT

Figure l(c) describes the diffusion p a t h w a y a n d Fig. l ( d ) shows the profiles of c o n c e n t r a t i o n of free dissolved 02 w h e n either s u c c i n a t e or glucose was supplied. First of all, for the s a m e 02 fluxes, lower c o n c e n t r a tions of free, dissolved 02 are r e q u i r e d at the o u t e r surface of the sphere a n d s e c o n d l y , the c o n c e n t r a t i o n of free 02 is m u c h m o r e u n i f o r m w i t h i n the sphere, w h e n l e g h a e m o g l o b i n is present. The profiles of O2 c o n c e n t r a t i o n

6

5

4

3

2

1

0

1

2

3

4

5

6

16

16

d~ ~2 'o × lO

12

:~

10 ~I

8

x

+ 4

0

6

5

4

5

2

I

0

T 2

3

4

5

6

rlcm XT0-a)

FIG. 1. Diagrammatic presentation of the models for a suspension of bacteroids containing 0.5 mg dry wt ml-', in which each bacteroid (shown as a dark sphere of radius 0.66 x 10-4 cm, whose volume is that of a bacteroid) occupies a sphere of solution of radius 6.2 x 10.4 cm. The concentration (S) of free, dissolved 02 at the bacteroid surface is considered to be l riM. Where no 02 carrier is present the diffusion of O~ is described by equation (2), giving the concentration profiles shown in (b). In the presence of 80 txM ferrous leghaemoglobin, there is a boundary layer extending 0.52-0.55 x 10.4 cm from the bacteroid surface (L). Within this layer diftusion is described by equation (2). Beyond the boundary layer, the facilitated flux of 02 is described by equation (4), generating the concentration profiles shown in (d). In (b) and (d) the solid lines indicate the profiles for succinate and dashed lines those for glucose as exogenous substrates. w i t h i n the b o u n d a r y layer n e a r the bacterial surface, are identical with the profiles in this l o c a t i o n where l e g h a e m o g l o b i n is absent. A g a i n , with l e g h a e m o g l o b i n p r e s e n t (Fig. l ( d ) ) as w h e n it was a b s e n t (Fig. l ( b ) ) , the different 02 d e m a n d s g e n e r a t e d by the two substrates lead to differences in c o n c e n t r a t i o n s o f free 0 2 r e q u i r e d at the o u t e r surface o f the sphere, to m a i n t a i n the same c o n c e n t r a t i o n (1 nM free 02 in Fig. I) at the bacterial surface. This difference is a l m o s t entirely d u e to the differential c o n c e n t r a tion d r o p across the b o u n d a r y layer.

02

OPTIMA

IN

M I C R O A E R O B I C

101

SUSPENSIONS

4. Discussion

The calculations presented show that, when considering aspects of microbial physiology related to respiration of suspensions with dissolved 02 in the range of 1-100nM, it is necessary to take into account the fall in concentration near the bacterial surfaces. The dimensions of this fall depend on the magnitude of the 02 flux. Therefore, if there are experimentally imposed differences in flux, different concentrations will be required in the bulk of the solution to maintain a constant concentration near the surfaces of the bacteria. In the work considered in this paper, this had the effect of appearing to produce different optimal 02 concentrations for nitrogenase activity, according to whether succinate or glucose was supplied. Similar effects may be responsible for the different 02 concentration optima seen in the work of Patterson, Peterson & LaRue (1983, Fig. 2). An interesting feature of the results discussed is that the differences caused by substrate in apparent optimum 02 concentrations for nitrogenase, were seen even when the concentrations for 02 supplied were far from being in equilibrium with conditions close to the bacteria (e.g. compare gas phase 02 levels with no-gas-phase, leghaemoglobin experiments; Table 2). In the nM 02 concentration range, a correction for the drop in concentration near to bacterial surfaces should be applied in estimates of app. K, for 02. An example is shown in Fig. 2, data are given for one experiment with bacteroids from soybean nodules, in which respiration was measured 16 15

(o)

14

L_ -~ o E ET

c

(b)

15

0

7 ea~

12

o T

I1

E

10

cE 'c_

14

012

~Dh 0 1 0 0 08 006 004

9 8 0

2'0

6'0 nM 0 2

80

i

- 0 14

- 0 I0 - 0 0 6 - 0

L,J

opp KS-1

020 0"02

i

i

006

i

i

0.10

i

014

( nM 02) -1

FIG. 2. Effects of the fall in concentration of free dissolved 02 near to bacterial surfaces on estimates of apparent K~ for 02. (a) Data for an experiment (Bergersen & Turner, 1980) in which bacteroids from soybean nodules respired 02 in the presence of 10 mM succinate and 90 ~M partially oxygenated leghaemoglobin. (b) Lineweaver-Burk plot giving estimate of apparent K~. • • O2 concentration in the leghaemoglobin-facilitated zone (see Fig. l(c)); © - - - O 02 concentration corrected for the drop across the b o u n d a r y layer near to the bacterial surface.

102

F. J. B E R G E R S E N

A N D J.-C. T R I N C H A N T

w i t h 90 ~M l e g h a e m o g l o b i n a n d 1 0 m M s u c c i n a t e p r e s e n t ( B e r g e r s e n & T u r n e r , 1980). U n c o r r e c t e d d a t a g a v e a n e s t i m a t e o f a p p . Ks o f 9-4 riM. W h e n t h e d a t a w e r e c o r r e c t e d to c o n c e n t r a t i o n s at t h e b a c t e r o i d s u r f a c e b y a p p l y i n g e q u a t i o n s (2), (5) a n d (6), (as in Fig. l ( c ) a n d ( d ) ) t h e e s t i m a t e w a s 7-8 riM, a r e d u c t i o n o f 1 7 % . In b o t h c a s e s Vmax r e m a i n e d t h e s a m e a n d r 2 f o r t h e L i n e w e a v e r - B u r k p l o t was > 0 . 9 8 . A n e v e n l a r g e r d i f f e r e n c e w o u l d r e s u l t in c a s e s w h e r e n o 0 2 c a r r i e r was s u p p l i e d . H o w e v e r it is v e r y difficult to m e a s u r e 0 2 c o n c e n t r a t i o n in t h e nM r a n g e w i t h o u t t h e p r e s e n c e o f l e g h a e m o g l o b i n ( B e r g e r s e n & T u r n e r , 1979). The authors thank G. L. Turner and W. J. Muller for checking calculations. F.B. thanks the University of Nice for assistance with travel which facilitated the collaboration of the authors. REFERENCES APPLEBY, C. A. (1969). Biochim. Biophys. Acta 188, 222. ARNOLD, J. H. (1930). J. Am. Chem. Soc. 52, 3937. BERGERSEN, F. J. (1982). Root Nodules o f Legumes: Structure and Functions. Chichester, UK: Research Studies Press/J. Wiley and Sons. BERGERSEN, F. J. (1984). In: Advances in Nitrogen Fixation Research (Veeger, C. & Newton, W. E. eds), p. 171. The Hague: Nijhoff/Junk. BERGERSEN, F'. J. & APPLEBY, C. A. (1981). Planta 152, 534. BERGERSEN, F. J. & TURNER, G. L. (1979). Anal. Biochem. 96, 165. BERGERSEN, F. J. & TURNER, G. L. (1980). J. gen. Microbiol. 118, 235. BERGERSEN, F. J., KENNEDY, C. & HILL, S. (1982). J. gen. Microbiol. 128, 909. CRANK, J. (1975). The Mathematics of Diffusion, 2nd edn. p. 89. Oxford: Clarendon Press. EMERICH, D. W., ALBRECHT, S. L., RUSSELL, S. A., CHING, TEM. & EVANS, H. J. (1980). PI. Physiol. 65, 605. HILL, S., TURNER, G. L. & BERGERSEN, F. J. (1984). J. gen. Microbiol. 130, 1061. 1MAMURA, T., RIGGS, A. & GIBSON, Q. H. (1972). J. biol. Chem. 247, 521. PATTERSON, T. G., PETERSON, J. B. & LARUE, T. (1983). PI. Physiol. 72, 695. ROBERTSON, J. G., WARBURTON, M. P., LYTTLETON, P., FORDYCE, A. M. & BULLIVANT, S. (1978). J. Cell. Sci. 30, 151. ROBSON, R. L. & POSTGATE, J. R. (1980). Ann. Rev. Microbiol. 34, 183. STOKES, A. N. (1975). J. theor. Biol. 52, 285. TRINCHANT, J-C. & RIGAUD, J. (1979). Physiol. Veg. 17, 547. TRINCHANT, J-C. & RIGAUD, J. (1981). Physiol. Plant. 53, 511. TRINCHANT, J-C., BIROT, A. M. & RIGAUD, J. (1981). J. gen. Microbiol. 125, 159. WITTENBERG, J. B. (1970). Physiol. Rev. 50, 449. WITTENBERG, J. B., APPLEBY, C. A. & WI'I-I'ENBERG, B. A. (1972). J. biol. Chem. 247, 527. WYMAN, J. (1966). J. biol. Chem. 241, 115.