Vol. 57, No. 7APPLIED AND ENVIRONMENTAL MICROBIOLOGY, JUIY 1991, p. 2033-20380099-2240/91/072033-06$02.00/0Copyright C 1991, American Society for Microbiology

Biochemical Basis for Whole-Cell Uptake Kinetics: Specific Affinity,Oligotrophic Capacity, and the Meaning of the Michaelis Constant

D. K. BUTTON

Institute of Marine Science and BiochemistrylMolecular Biology Program,University ofAlaska, Fairbanks, Fairbanks, Alaska 99775

Received 25 February 1991/Accepted 22 April 1991

Formulations are presented that describe the concentration dependency of nutrient-limited transport andgrowth in molecular terms. They relate the rate of transport at steady state through a two-sequence process,

transport and metabolism, to ambient concentrations according to the amounts and kinetic characteristics of thetwo rate-limiting proteins in these sequences. Sequences are separated by a metabolic pool. A novel feature ofthese formulations is the translation coefficient, which relates the transport rate attained at given ambientnutrient concentrations and membrane transporter characteristics to the nutrient concentrations sustained in themetabolic pools. The formulations, termed janusian kinetics, show that hyperbolic kinetics are retained duringindependent changes in transporter and enzyme contents or characteristics. Specific affinity (aA) depends stronglyon the amount and kinetic characteristics of the transporters; it is also mildly affected by the amount andcharacteristics of the rate-limiting enzyme. This kinetic constant best describes the ability to accumulate substratefrom limiting concentrations. Maximal velocity (Vm,,) describes uptake from concentrated solutions and can

depend strongly on either limiting enzyme content or the associated content of transporters. The whole-cellMichaelis constant (KT), which depends on the ratio of rate-limiting enzyme to transporter, can be relativelyindependent of change in aA and is best used to describe the concentration at which saturation begins to occur.

Theory specifies that good oligotrophs have a large aA for nutrient collection and a small Vm. for economy ofenzyme, giving a small KT. The product of the two constants is universally rather constant so that oligotrophy isscaled on a plot of aA versus KT, with better oligotrophs toward one end. This idea is borne out by experimentaldata, and therefore typical small difficult-to-culture aquatic bacteria may be classified as oligobacteria.

The affinity of organisms for substrates sets the concen-trations of nutrients in aquatic systems, as well as interspe-cies competitiveness. This affinity is usually expressed as aMichaelis constant for transport (KT) by analogy to enzymekinetics (18) and does not account for changes in thetransporter content of the cells. Other theories describenutrient kinetics from the cellular content of the limitingnutrient (7), whole-culture activity versus KT (12), andmolecular collision frequency (1). Law and Button used theinitial slope of the curve of nutrient uptake rate per unit ofbiomass versus nutrient concentration as a measure ofaffinity (17); this was called the specific affinity, was formu-lated in terms of the number of transporters (3), and is one ofthe two primary kinetic constants for uptake (5). Specificaffinity is the best indication of the ability of microorganismsto collect substrate from a dilute solution (11), and growthrates can be estimated directly from it as well. The otherkinetic constant is maximal velocity (Vmax) (Table 1), themaximal rate of uptake per unit of biomass. Vmax is oftentaken as an indication of transporter characteristics, whichrestricts the range of possible influence on KT given normallimits of enzymatic binding constants (15). I presumed thatVmax is strongly influenced by the transporter content of thecell membrane (2) and therefore is an influential determinantof KT. While specific affinity theory accounts for the influ-ence of the transporter content of the cells on the rate ofuptake, saturation phenomena are not inherently accommo-dated, and the influence of rate-limiting cytoplasmic en-zymes is neglected. The purpose of this paper is to definesubstrate uptake from concentration in terms of the amountsand kinetic characteristics of the transporters and metabolicenzymes involved.

MATERIALS AND METHODS

The influence of molecular components on kinetic con-stants was examined by plotting formulations derived byusing a computer. Kinetic data for toluene dihydrodiolmetabolism were obtained by using the marine isolate Pseu-domonas sp. strain T2 at 10°C and measuring oxygen con-sumption with an oxygen electrode and biomass with aCoulter counter, as previously described (21). The data foralanine were obtained in the same way except that rateswere computed from particulate radioactivities that accumu-lated at the expense of ["4C]alanine, as described previously.

RESULTSTheory: the model. The rate of nutrient accumulation by

whole cells depends on the transporter content of the cellmembrane (1). At steady state with the external substrate Aconcentration (A,) constant, the rate of nutrient accumula-tion also depends on the rate of cytoplasmic substrateremoval from the cytoplasm. Therefore, transport dependson the content and kinetic characteristics of enzymes in-volved in the removal of Ac, which are taken as thecharacteristics of the enzyme at the slow step. A model ofuptake mediated in this way is shown in Fig. 1. Substrate isaccumulated from a concentration outside the cell to aconcentration in the cytoplasm by a transporter at concen-tration T in the cell membrane. Enzymes then convertcytoplasmic substrate to metabolic product (Pc) at a rate thatdepends on the concentration of the rate-limiting enzyme(Ec), as well as Ac. Kinetic characteristics of the transporterare set by the associated rate constants. For the simplemechanism shown below the rate constants can be groupedas a Michaelis constant for the transporter (KO), which

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TABLE 1. Nomenclature

Symbol Description Units

0aA Specific affinity for A Liters per gram of cells. hourAc Concentration of A in cytoplasm Grams per liter of cytoplasmAo Concentration of A outside cell Grams per literEC Concentration of rate-limiting enzyme Grams per liter of cytoplasmk, Rate constant Liters per gram of transporter per gram of membrane hourk3 Rate constant Hour-'KC Michaelis constant for EC Grams per liter of cytoplasmKO Michaelis constant (outside) for T Grams per literKT Whole-cell Michaelis constant for transport Grams per literKm Michaelis constant for an enyzme Grams per literL Translation coefficient Hour-'PC Metabolic product of A Grams of A per liter of cytoplasmRMx Ratio constant Grams of membrane per gram of cellsRCX Ratio constant Grams of cytoplasm per gram of cellsT Transporter concentration Grams of transporter per gram of membraneTA Transporter-substrate complex Grams of transporter-substrate complex per gram of

concentration membranev Concentration-dependent uptake rate Grams of A per liter- hourVI Maximal rate for transport Grams of A per gram of cells hourV2 Maximal rate for metabolism Grams of A per gram of cells hourVmax Maximal rate for whole cells Grams of A per gram of cells hourp. Specific rate of growth Hour-'Am Maximal growth rate Hour-'X Biomass Grams per literYXA Yield (dXI-dAo) Dimensionless

relates outside substrate concentration to the portion oftransporters that remain occupied: KO = (k2 + k3)/kl. Therate of nutrient transport per unit volume of a culture (v)depends on its substrate-free transporter content, T RMx X,where RMX is the ratio of membrane to biomass and X is themass of cells. When outside nutrient concentrations arelarge, most of the transporters are in a transporter-substratecomplex (TA), and the maximal rate per unit of biomass (V1)is

V1 = k3 TA RMx (1)

At low substrate concentrations the rate of accumulationalso depends on the concentration-dependent frequency ofsuccessful collisions with transporters as given by the sec-ond-order rate constant, kl. At intermediate nutrient con-centrations only some of the transporters are occupied withsubstrate, and saturation kinetics prevail. The rate of sub-strate uptake by whole cells is almost universally observedto be hyperbolic with respect to concentration, and depar-tures are explained by transporter heterogeneity (9), poolloading (16), and systematic changes in organism composi-tion because of changes in the growth rate (20). Saturationkinetics give the initial rate (no product inhibition) as

- membrane -

outside cytoplasmiccell pool fluid

A_kl

- rTA k3 Ac - Ec - Pc

FIG. 1. Model of a nutrient-limited growing cell, showing keynutrient accumulation components. See Table 1 for nomenclature.The conditions assume a steady state in which internal and externalconcentrations are constant and rates are normalized to biomass.

V V1 AOX KO + AO

(2)

before metabolic pools have had time to fill. During nutrient-limited growth, such as that found in continuous cultures andmost aquatic systems, the concentration of substrate in themetabolic pools drives both anabolic and energy-yieldingpathways and therefore sets the rate of growth. This sub-strate concentration then reflects the equilibrium amongsubstrate supply as given by equation 2, losses due tometabolic removal and leakage, and any product inhibitionwhich may occur. Assuming this for usual intercellularconcentrations and therefore for usual cytoplasmic concen-trations of limiting substrate, removal is primarily enzymaticthrough limiting cytoplasmic enzyme concentration, and therate of removal from the cytoplasm is Michaelian. Then anychange in the concentration of cytoplasmic substrate is givenby the difference between rates of input and output:

Change in cytoplasmic transport of Ao output ofAconcentration of A into cytoplasm from cytoplasm

(3)dAc

Rcx dtV1 Ao

Ko + AOV2 AC

Kc + AcThe ratio of cytoplasm to biomass (RCX) normalizes

cytoplasmic and external concentrations, giving units ofgrams of A per gram of cells hour for each function. Theoutput or third function of equation 3 is identical to equation2 except that V2 = kCEcA RCX, where kc is the catalyticconstant for EC and Kc is the associated Michaelis constant.At steady state the change in Ac is zero and the input andoutput terms are equal.

Coupling of external substrate concentration to cytoplasmicsubstrate concentration. Equation 3 gives the rate of sub-strate accumulation at the substrate concentration-depen-

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dent steady states between external substrate and cytoplas-mic substrate. It covers the range of growth rates betweenzero and the maximal growth rate (Um). Using the rateconstant definition of V1 requires either neglecting leakage(i.e., loss of cytoplasmic substrate because of imperfectretention by the cell membrane) or taking equation 2 as anexpression of net transport. Equation 3 can then be solvedwith the aid of a formulation that gives substrate concentra-tion in the third function in terms of the rate of transportaccording to the second function. Then rate, which is thesame through all of the functions, is tied in the third functionto external substrate concentration by the second function.To do this, I defined a new function called the translationcoefficient (L). This function gives the relationship betweenthe rate of transport per unit of biomass (vIX) and thecytoplasmic substrate concentration. Relationships like thishave been explored by using isotope relaxation procedures;these give unidirectional fluxes that attend substrate-limitedgrowth (4). For phosphate-limited continuous culture ofRhodotorula rubra there was a monotonic increase in theconcentration of cytoplasmic phosphate with both a net rateof phosphate uptake and a unidirectional inward flux ofphosphate (20). This concentration tended toward a maxi-mum at 10 mM as additional transport was used to satisfy anincreased phosphate content at high growth rates. Thisincreased phosphate content was reflected by a decreasedcell yield (YXA) with growth rate (,u), a change that alone wassufficient to produce hyperbolic uptake kinetics that wereunrelated to saturation. The present model assumes that thecells have a constant composition, cytoplasmic substrateconcentrations aside. This is more nearly correct for usualcarbon and energy substrates than for phosphate because thephosphate content of cells can be quite variable and RCX andYXA become constant rather than growth rate-dependentvariables requiring formulation. In either case the uptakerate and the specific rate of growth are interdependent:

V= (4)YXA

Assuming that the linear relationship between cytoplasmicsubstrate concentration and the rate of substrate uptakeobserved for phosphate holds, uptake is related to cytoplas-mic substrate concentrations by:

v = LXRcxAc (5)

When a value of 0.6 was used for RCX, the translationcoefficient for phosphate was 2.5 h-1.Rate equation. Transport can now be related to cytoplas-

mic concentration over a range of nutrient-limited rates ofgrowth at steady state. Substituting the second or transportterm of equation 3 into equation 5 gives

v V1Ao=K0+A0 = AcRcxL (6)X Ko + Ao

and solving for Ac

V1 Ao= (Ko + Ao) RcxL (7)

relates cytoplasmic concentrations to external concentra-tions through the kinetics of transport. Substrate is utilizedfrom the cytoplasm at a rate given by the third or outputfunction of equation 3. At steady state this concentration isset by the external substrate concentration through equation

wl-

cc)

J

0

w

0 20 40 60 80 100

SUBSTRATE CONCENTRATION AOFIG. 2. Plot of equation 10, showing changes in whole-cell

kinetic constants caused by changes in transporter and enzymeconcentrations. For curve 1 T = 500 and EC = 11 arbitrary units. Forcurve 2 T = 20 and EC = 45 arbitrary units. The values for thetransporter and enzymatic Michaelis constants were identical (50units).

7. Substituting this output term into equation 7 relates theoutput to uptake:

v V2 Ac

X Kc + Ac

V1 AoV2 Ko + AO

V1 AoKc +

Ko + AO0

(RCXL

(8)

Rcx L)

which reduces to

v V1V2 Ao(9)

X KcRcx Lo (Ko + Ao) + V1Aoor in the form of usual kinetic expressions

v V1V2 Ao(10)

X KcRcxLKo + (KcRcxL + V1)Ao

Kinetic curve shape. The form of equation 10 shows thatuptake kinetics can remain hyperbolic even when the rate iscontrolled by two independent components, transporterconcentration (7) and limiting cytoplasmic enzyme content.It also shows that the rate of uptake at all nutrient concen-trations depends on the concentrations as well as the kineticcharacteristics of the two proteins because they are compo-nents of both V1 and V2 (equation 1). Thus, a change in T or

Ec changes constants that define the position of the curve, as

specified by specific affinity for A (a' ) and Vmax, but not itsshape. This is demonstrated by the two plots of equation 10shown in Fig. 2, for which the enzymatic and transporterMichaelis constants and conversion factors were all heldconstant. The only changes were in the enzyme and trans-porter contents. The Ec increased by a factor of 4 in curve 2compared with curve 1, while T was 25-fold smaller. Thisresulted in a 2.6-fold decrease in a', while Vmax remainedessentially constant. The whole-cell Michaelis constant for

transport, KT, increased by a factor of 6.3. Double-recipro-cal plots (data not shown) confirmed that both curves are

VMAX 2

0 VMAX 1

1 X//CU~~rve 2

UKT1 KT 2 KcCt&2

-t

--t

-

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hyperbolic. Other plots showed that specific affinity dependsstrongly on the amount and kinetic characteristics of thetransporters, with some dependence on the amount andcharacteristics of the rate-limiting enzyme as well. Becauseof the dual control of flux by T and Ec, relationships such asequation 3 are referred to as janusian kinetics after Janus,the two-faced Roman god of gates.

Kinetic constants in molecular terms. The kinetic constantsof equation 10 specify the change in specific uptake rate (v/X)with respect to concentration. To obtain these constants inmolecular terms, let a = V1 V2, b = KC RCX L KO, and c =KCRCX L + Vl. Then differentiation of equation 10 writtenas the fraction

d(vlX) aAodAo b + cAo

(11)

by parts gives

d(v/X) (v. duldx) - (u . dvldx)dA0 (12)

dAo v2where u = a Ao and v = b + c Ao and

d(vlX) (b + cAo)a - acAodAo (b + CAO)2

a acAob + cAo (b + CAo)2 (13)

Specific affinity by definition is the slope of equation 10 at Ao= 0, or alb from equation 13:

d(vlX) V1V2

dAo A KoKcRcxL (14)

which has the units of a second-order rate constant (liters pergram of cells hour). By substituting in the molecular defi-nitions for V, (equation 1) and V2:

(k3TA RMX) (kcEc A Rcx)a= (15)A

KCRCX L KOEquation 15 shows that specific affinity depends on theamount of cytoplasmic enzyme as well as the amount oftransporter, expressed here in their bound forms (TA andEC A); unbound forms are accounted for in the rate constantdefinitions of KT and KC. The role of EC in specific affinitycan be visualized by considering a cell without cytoplasmicenzyme. At the steady state of sustained uptake, the rate ofsubstrate collection and thus the specific affinity are zero.The major dependence of specific affinity is probably ontransporter content rather than on cytoplasmic enzyme, asshown in Fig. 2 and by data reviewed by Abbott andNelsestuen (1); the relative contributions of T and Ec to aAare specified by L.

Vmax is the asymptote of equation 10 where Ao = co orfrom equation 13 where Vmax = alc gives

V1V2Vmax - KcRCXL + V1, (16)

which is the maximal specific flux (grams of A per gram ofcells hour) or rate at saturation.The Michaelis constant for transport is obtained in molec-

ular terms from the fact that kinetic curves from coupled

sequential reactions, such as the one shown in Fig. 1 andplotted in Fig. 2, remain hyperbolic. Therefore, these kinet-ics can be represented by the traditional hyperbolic relation-ship.

V'max Ao Vmax Ao Xv= =.

KT + AO KT + AO (17)where the prime in Vmax indicates traditional units of time'.The derivative at AO = 0 iS Vmax/KT, which is the specificaffinity. Rearranging

KT = V.max/a'and substituting in equations 16 and 17 gives

( V1V2 A

KCRcx L + V1, KOKCRCX L( V1V2 KCRCXL + V,KoKcRcx L)

(18)

(19)

which has units of concentration. Inspection indicates thatKT depends strongly on the Michaelis constant for thetransporter (KO) and on the reciprocal of the transportercontent (through Vj). This is confirmed by the simulationsshown in Fig. 2.The concentration dependence of rate is given above by

equation 10. As previously demonstrated (5), rate can nowbe written in terms of the primary whole-cell kinetic con-stants Vnmax and a' by combining equations 17 and 18:

aAVmax AoXv =

Vmax + ao Ao(20)

At low substrate concentrations equation 20 reduces to theoriginal specific affinity relationship

v=a- XAo (21)

which is convenient for estimating the specific affinitieswhen the abilities of laboratory or environmental popula-tions to collect substrate are evaluated. These abilities cannow be considered in molecular terms.

Oligotrophy. Low-substrate-concentration-adapted aquaticorganisms are often thought of as having small Michaelisconstants. To understand oligotrophic strategy in molecularterms, equation 18 can be written in the form

(22)Vmax = ao KTBecause of the direct relationship between V11rax and Imax,as indicated by the limits of equation 4, and since ILmax iSthought to vary by less than a factor of 10 for most pelagicbacteria, a reciprocal relationship between the specific af-finity and the whole-cell Michaelis constant is expected. Toexplore this reciprocity, equation 22 was converted to loga-rithmic form, and available data from the literature wererecomputed and plotted (Fig. 3). The data included from mylaboratory are for toluene dihydrodiol and alanine withPseudomonas sp. strain T2. While KT values spanned arange of 106, the deviation from the mean values predictedby equation 22 was within a factor of 5. Unusual substrates,such as 3-methylcatechol (data point 1), and copiotrophs,such as Saccharomyces cerevisiae (data point 2), appear atthe lower left in Fig. 3, while good substrate-oligotrophcombinations, such as Aeromonas hydrophila and arginine(data point 12), are at the top right. The high value for A.hydrophila could be an overestimate due to rate supplemen-

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O4

z LU_3

//

50.

03/ 4/~~~~0

1 2 3 4 5 7

1 gIL Ilp.gIL

-LOG MICHAELIS CONSTANT KT

FIG. 3. Plot of equation 22 as log a7 = log Vmax - log KT. Dataare shown for 3-methylcatechol (data point 1), asparagine (datapoint 2), fructose (data point 3), methylphenol (data point 4),p-chlorophenol (data point 5), glucose (data point 6), glycerol-3-phosphate (data point 8), and toluene (data point 9), (all recomputedfrom reference 3), as well as for toluene dihydrodiol (data point 7)(this paper), alanine plus Pseudomonas sp. strain T2 (this paper),glucose (data point 10) (23), and arginine (data point 12) (23). Thedashed line gives possible values for an organism having a IUmax of0.1 h-1 and a yield of 1 g of cells per g of substrate used (slope, 1.0).

tation by exogenous substrate (10). However a typical ma-rine bacterium was recently isolated in my laboratory (22) bygrowth from single cells in unsupplemented seawater. Pre-liminary data showed that there was linear uptake of 14C-labeled mixed amino acids over time with a specific affinityof 5,000 liters (g of cells h)-1, so such values appear to beattainable for carbon sources. These small, low-DNA-con-tent cultures remain difficult to maintain, and associated KTinformation and taxonomic information are not yet available.However, the data in Fig. 3 are sufficient to support theconcepts expressed in equation 22 (the concept of a recip-rocal relationship between specific affinity and the Michaelisconstant, the traditional idea that good oligotrophs havesmall Michaelis constants, and the novel concept that olig-otrophic capacity is best expressed by a large specific affinityin combination with a small Michaelis constant).

DISCUSSION

Translation coefficient. A key feature ofjanusian kinetics iscoupling of the kinetic properties of membrane transport tothe kinetic properties of whole cells. This coupling wasfacilitated with the translation coefficient, L, a function thatrelates membrane transport to substrate concentration in thecytoplasmic pools; the faster the transport, the higher theconcentration. The pool concentration is a steady-statevalue and is affected by substrate losses through metabolismand leakage, as well as the chemical potential from Acgenerated by membrane transport. Formulation of L fromfirst principles currently appears untractable because thisfunction depends on several processes that are far fromequilibrium, which increases the difficulty of the thermody-namics required. However, technology is available for cred-ible formulation from experimental measurements. Like cellyield, the translation coefficient is a species-dependent vari-able that depends on the system, nutrient concentrations,and transport rates in question. Equation 5 appears to be a

sufficient definition for improved descriptions of transportkinetics.Pathway kinetics. Janusian kinetics incorporate an as-

sumption that the kinetics are hyperbolic with respect toconcentration through each of two enzyme sequences (trans-port and metabolism). Kell and Westerhoff (14) believe thatall enzymes in a sequence share in the control of rateaccording to the relative sizes of their flux control coeffi-cients, terms that are directly affected by metabolic as wellas kinetic control. Cleland (6) described flux through a singlemultistep enzyme according to the distribution of enzymeforms by using the analogy of conductance and formulationsof electrical pathways. Newsholme and Crabtree (19) de-scribed sequences in which a "flux generating enzyme,"which is usually the initial enzyme of a nonbranched path-way and operates near saturation (near V2), sets the rate.The model of these latter authors is closest to the modelpresented in this paper, in which the rate-limiting enzyme isidentified as one enzyme of a sequence of enzymes that areassociated with the largest concentration of substrate com-pared with Km and therefore results in a "bottleneck" to theflow. Then, according to the law of limiting factors, it sets arate that is influenced only by the concentration of substrateand the amount of product inhibition arising from succeedingsteps. The kinetics of the pathway largely reflect the amountand kinetics of this enzyme. According to the Cleland model,influences of adjacent enzymes are reflected as changes inthe apparent kinetic constants for the rate-limiting enzyme,and the overall concentration-velocity relationship over thepathway remains hyperbolic, as it does for the two-compo-nent sequence described above.

Oligotrophy and the Michaelis constant. The traditionalassociation of small Michaelis constants with oligotrophy(13) is supported by the data described above, but the106-fold variation in KT is too large to be accounted for bychanges in binding constants (15) according to Michaelis-Menten theory. Janusian kinetics provide an improved ex-planation. Consider the case of a hypothetical oligotrophhaving a great deal of transporter and little rate-limitingenzyme. At low substrate concentrations cytoplasmic poolsof substrate are filled to usual concentrations. These poolconcentrations normally drive small quantities of flux-gen-erating enzymes at near-maximal rates to conserve protein.Because the enzyme quantities are small, they truncate ratesat which transported substrates can be processed, with ECoperating at near Vmax. At slightly higher external substrateconcentrations, but far below KO, EC attains Vmax9 anincreased external concentration of substrate has no effecton the steady-state rate of transport, the growth rate ismaximal, and the result is a very small Michaelis concentra-tion (KT). At external substrate concentrations approachingKO, pool substrate concentrations become excessive, asituation to which many typical aquatic bacteria may suc-

cumb, causing the common difficulties experienced in at-tempts at cultivation.

Copiotrophs, on the other hand, contain large amounts ofcytoplasmic enzyme for rapid metabolism, and growth rateis not substrate saturated until large values of Ao are

experienced so that KT becomes large. Therefore, the cross-

ing kinetic curves of oligotrophs and copiotrophs (8) are

explained as differences in ratios of T to Ec, not enzymaticor transporter properties. In considering small Michaelisconstants alone, it is unclear whether the associated organ-ism has a large amount of transporter or a small amount ofrate-limiting enzyme, and its ability to survive at low sub-strate concentrations remains in question. Vmax data are

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required as well. However, specific affinities directly quan-

tify substrate flux from small concentrations (AO < KT) andbest describe the ability to accumulate substrate from limit-ing concentrations. Maximal velocity describes uptake fromconcentrated solutions and can depend strongly on eitherlimiting enzyme or transporter content. The whole-cell Mi-chaelis constant depends on the ratio of rate-limiting enzymeto transporter, is a weak function of a' , and is best used todescribe the concentration at which saturation begins.

Oligotrophic capacity is now amenable to a new definition.The position on the plot of specific affinity versus Michaelisconstant is the clearest measure. Thus, a good oligotrophcan be identified as having, first and foremost, a largespecific affinity and, second, a product of the specific affinityand the Michaelis constant for transport which is large as

well. Because of the high specific affinities found for thesmall, low-DNA-content bacteria that are typical of seawa-

ter as determined by dilution culture techniques (22), theseorganisms, which have been referred to as ultramicrobacte-ria, minibacteria, dwarfs, and somnicells, might more appro-priately be called oligobacteria.

Janusian theory also helps explain metabolite leakage.When presented with moderate amounts of toluene, Pseu-domonas sp. strain T2 induces large amounts of at least twomembrane-associated proteins (unpublished data), and 60 to80% of the substrate is leaked as metabolic products (21).These proteins increase the specific affinity, and the leakageis presumably due to insufficient downstream enzymes toaccommodate the atypically large concentration of cytoplas-mic intermediates that result. Thus, when marine bacteriaare challenged with atypically large amounts of hydrocarbonduring an oil spill, unusual degradation products can beexpected to accumulate in the water.Reduction of uptake and metabolism kinetics to quantities

and characteristics of specific transporters and proteins isseen as a useful step in ecological theory because both thenumbers and the concentrations of substrates utilized can berelated to the numbers and quantities of proteins needed forprocessing. Thus, the biosynthetic costs of these proteinsare directly and independently reflected in the kinetics of thetransport and metabolic components, kinetics which cancombine in an infinite number of ways to give the whole-cellMichaelis constant with which we are so familiar. Also,when this distribution ratio of proteins becomes adjustableto suit a changing environment, the additional overhead ofmetabolic control becomes necessary, a cost which could beabsent in oligobacteria. Most importantly, janusian theoryprovides a framework to relate the kinetic properties ofwhole cells to the molecular properties of organisms, what-ever they may be.

ACKNOWLEDGMENTS

I appreciate the assistance of B. R. Robertson and the suggestionsof Z. Kowalik.

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an important consideration for membrane-associated enzymes.

Fed. Am. Soc. Exp. Biol. J. 2:2858-2866.2. Button, D. K. 1983. Differences between the kinetics of nutrient

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4. Button, D. K., and P. J. Kinney. 1980. Unidirectional fluxdetermination during nutrient limited microbial growth by theisotope relaxation rate induced in continuous culture, p. 269-278. In B. Sikyta, Z. Fencel, and V. Polacek (ed.), Continuouscultivation of microorganisms. Proceedings of the 7th Sympo-sium. Czechoslovak Academy of Sciences, Prague.

5. Button, D. K., and B. R. Robertson. 1989. Kinetics of bacterialprocesses in natural aquatic systems based on biomass asdetermined by high-resolution flow cytometry. Cytometry 10:558-563.

6. Cleland, W. W. 1975. Partition analysis and the concept of netrate constants as tools in enzyme kinetics. Biochemistry 14:3220-3224.

7. Droop, M. R. 1968. Vitamin B12 and marine ecology. IV. Thekinetics of uptake, growth and inhibition in Monochrysis lutheri.J. Mar. Biol. Assoc. U. K. 48:689-733.

8. Dugdale, R. C., B. H. Jones, Jr., J. J. Maclsaac, and J. J.Goering. 1981. Adaptation of nutrient assimilation. Can. Bull.Fish. Aquat. Sci. 210:234-250.

9. Futi, M. 1978. Experimental systems for the study of activetransport in bacteria, p. 8-41. In B. Rosen (ed.), Bacterialtransport. Marcel Dekker, New York.

10. Geller, A. 1983. Growth of bacteria in inorganic medium atdifferent levels of airbome organic substances. Appl. Environ.Microbiol. 46:1258-1262.

11. Gottschal, J. C. 1985. Some reflections on microbial competi-tiveness among heterotrophic bacteria. Antonie van Leeuwen-hoek 51:473.

12. Healey, F. P. 1980. Slope of the Monod equation as an indicatorof advantage in nutrient competition. Microb. Ecol. 5:281-286.

13. Hirsch, P. M., Y. S. Bernhard, Y. S. Cohen, H. W. Ensigh,H. W. Jannasch, A. L. Koch, K. C. Marshall, et al. 1978. Lifeunder conditions of low nutrient concentrations. Group reporton strategies of microbiological life in extreme environments.Verlag Chemie, New York.

14. Kell, D. B., and H. V. Westerhoff. 1986. Metabolic controltheory: its role in microbiology and biotechnology. FEMSMicrobiol. Rev. 39:305-320.

15. Krout, J. 1988. How do enzymes work? Science 242:533-539.16. Krupka, R. M. 1989. Testing transport models and transport

data by means of kinetic rejection criteria. Biochem. J. 260:885-891.

17. Law, A. T., and D. K. Button. 1977. Multiple-carbon-source-limited growth kinetics of a marine coryneform bacterium. J.Bacteriol. 129:115-123.

18. Monod, J. 1942. Recherches sur la croissance des culturesbacteriennes. Hermann, Paris.

19. Newsholme, E. A., and B. Crabtree. 1981. Flux-generating andregulatory steps in metabolic control. Trends Biochem. Sci.6:53-56.

20. Robertson, B. R., and D. K. Button. 1979. Phosphate-limitedcontinuous culture of Rhodotorula rubra: kinetics of transport,leakage, and growth. J. Bacteriol. 138:884-895.

21. Robertson, B. R., and D. K. Button. 1987. Toluene induction anduptake kinetics and their inclusion in the specific-affinity rela-tionship for describing rates of hydrocarbon metabolism. Appl.Environ. Microbiol. 53:2193-2205.

22. Schut, F., B. R. Robertson, and D. K. Button. 1991. Abstr. Gen.Meet. Am. Soc. Microbiol. 1991, N-17, p. 248.

23. van der Kooj, D., and W. A. M. Hijnen. 1988. Nutritionalversatility and growth kinetics of an Aeromonas hydrophilastrain isolated from drinking water. Appl. Environ. Microbiol.54:2842-2851.

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