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Microbiology and Molecular Biology Reviews, September 1998, p. 646-666, Vol. 62, No. 3
Swiss Federal Institute for Environmental
Science and Technology (EAWAG), CH-8600 Dübendorf,
Switzerland
1092-2172/98/$04.00+0
Copyright © 1998, American Society for Microbiology. All rights reserved.
Growth Kinetics of Suspended Microbial Cells: From
Single-Substrate-Controlled Growth to Mixed-Substrate
Kinetics
and
SUMMARY
INTRODUCTION
EXPERIMENTAL APPROACHES AND KINETIC DATA AVAILABLE
Quality of Experimental Data
Laboratory cultivation techniques versus conditions in the
environment.
Problems of measuring growth-controlling substrate
concentrations.
Kinetic Models and Data Processing
Monod-type kinetics.
(i) Kinetic and stoichiometric parameters.
(ii) Biological meaning of µmax,
Ks, and smin.
Alternative kinetic expressions.
Some comments on the choice of models and fitting exercise.
Parameter identifiability.
Variations in Kinetic Parameters
Intrinsic versus extant kinetics.
Feast and famine ends of an organism's kinetic properties.
(i) Long-term adaptation from high to low substrate
concentrations and vice versa.
(ii) Implications for growth of microbial cells in the
environment.
SUBSTRATE MIXTURES AND MIXED CULTURES
Utilization of Mixtures of Carbon Sources
Kinetic Effects during Utilization of Defined Substrate
Mixtures by Pure Cultures
Experimental data.
(i) Continuous cultivation.
(ii) Batch cultivation.
Kinetic models.
Effect of enzyme expression patterns.
(i) Fixed catabolic enzyme level.
(ii) Regulated catabolic enzyme level.
(iii) Threshold for enzyme induction.
Kinetics of Multiple-Nutrient-Controlled Growth
Biodegradation Kinetics: Effects during Utilization of
Complex Substrate Mixtures by Mixed Cultures
Effect of uncharacterized DOC on utilization of pollutants.
Kinetics of multicomponent substrate removal.
Influence of initial substrate-to-biomass ratio.
Catabolic capacity.
CONCLUDING REMARKS AND OUTLOOK
ACKNOWLEDGMENTS
REFERENCES
SUMMARY
 Top NextReferences
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Growth kinetics, i.e., the relationship between specific growth rate and the concentration of a substrate, is one of the basic tools in microbiology. However, despite more than half a century of research, many fundamental questions about the validity and application of growth kinetics as observed in the laboratory to environmental growth conditions are still unanswered. For pure cultures growing with single substrates, enormous inconsistencies exist in the growth kinetic data reported. The low quality of experimental data has so far hampered the comparison and validation of the different growth models proposed, and only recently have data collected from nutrient-controlled chemostat cultures allowed us to compare different kinetic models on a statistical basis. The problems are mainly due to (i) the analytical difficulty in measuring substrates at growth-controlling concentrations and (ii) the fact that during a kinetic experiment, particularly in batch systems, microorganisms alter their kinetic properties because of adaptation to the changing environment. For example, for Escherichia coli growing with glucose, a physiological long-term adaptation results in a change in KS for glucose from some 5 mg liter
1 to ca. 30 µg liter1. The data suggest that a dilemma exists, namely, that either "intrinsic" KS (under substrate-controlled conditions in chemostat culture) or µmax (under substrate-excess conditions in batch culture) can be measured but both cannot be determined at the same time. The above-described conventional growth kinetics derived from single-substrate-controlled laboratory experiments have invariably been used for describing both growth and substrate utilization in ecosystems. However, in nature, microbial cells are exposed to a wide spectrum of potential substrates, many of which they utilize simultaneously (in particular carbon sources). The kinetic data available to date for growth of pure cultures in carbon-controlled continuous culture with defined mixtures of two or more carbon sources (including pollutants) clearly demonstrate that simultaneous utilization results in lowered residual steady-state concentrations of all substrates. This should result in a competitive advantage of a cell capable of mixed-substrate growth because it can grow much faster at low substrate concentrations than one would expect from single-substrate kinetics. Additionally, the relevance of the kinetic principles obtained from defined culture systems with single, mixed, or multicomponent substrates to the kinetics of pollutant degradation as it occurs in the presence of alternative carbon sources in complex environmental systems is discussed. The presented overview indicates that many of the environmentally relevant apects in growth kinetics are still waiting to be discovered, established, and exploited.
INTRODUCTION
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"The study of the growth of bacterial cultures does not constitute a specialised subject or a branch of research: it is the basic method of microbiology."
J. Monod, 1949
Microbial growth kinetics, i.e., the relationship between the specific growth rate (µ) of a microbial population and the substrate concentration (s), is an indispensable tool in all fields of microbiology, be it physiology, genetics, ecology, or biotechnology, and therefore it is an important part of the basic teaching of microbiology. Unfortunately, the principles and definitions of growth kinetics are frequently presented as if they were firmly established in the 1940s and during the following "golden age" in the 1950s and 1960s (the key publications are those of Monod [166, 167, 168], Hinshelwood [102], van Niel [252], Novick and Szilard [181], Herbert et al. [101], Málek [155], Pfenning and Jannasch [193], Fencl [67], Pirt [194], Powell et al. [200], and Tempest [243, 251], culminating in the book by Pirt [195]). This state of affairs is probably the consequence of a stagnation in this area during the past three decades, in which the interest of many microbiologists was attracted by rapidly developing areas such as molecular genetics or the biochemistry of the degradation of xenobiotics. However, it might also be the consequence of certain frustration from the many attempts that had been made to obtain coherent experimental data (127; for a historical overview, see reference 114). This state is also reflected by the fact that only a few review articles (e.g., references 34, 36, 79, 173, 182, and 211) and one monograph (187) that primarily deal with growth kinetics per se and its problems were published within the last two decades. In contrast, considerable attention has been paid to the modeling aspects of both growth and substrate removal (biodegradation) kinetics (recently reviewed in references 3, 20, 18, 66, 86, 178, 208, 218, and 228).
Although some of these authors dealing with microbial growth kinetics started to emphasize the ecological point of view, they almost totally neglected the facts that in nature microorganisms grow mostly with mixtures of substrates (87, 88), that growth may not be controlled by only a single nutrient but by two or more nutrients simultaneously (57, 183, 214, 255), and that kinetic properties of a cell might change due to adaptation (unfortunately, only preliminary data for such changes have been published [e.g., references 104, 110, 134, and 212]). How little these topics were considered to be of importance to microbial ecology may be seen from the fact that all major microbial ecology textbooks (and monographs) (e.g., references 31, 69, 108, 171, and 240) ignore these subjects. However, recent more ecologically oriented studies in the area of microbial growth and biodegradation kinetics demonstrated that many fundamental questions in this field are still waiting to be discovered, established, and exploited (reviewed in reference 58).
Our intention was to present here a critical overview on microbial growth kinetics with respect to the current state, the recent advances that have been made, and its possible future developments. However, we kept in mind Monod's warning that "it would be a foolish enterprise, and doomed to failure, to attempt to reviewing briefly a `subject' which covers our whole discipline. Unless, of course, we considered the formal laws of growth as a method for their own sake, an approach which has repeatedly proved sterile" (167). Therefore, we focus here on growth and growth-linked biodegradation kinetics of suspended heterotrophic cultures where the substrates are available in the bulk liquid; such systems are experimentally more easily accessible than heterogeneous ones (in Fig. 1, the various aspects of cell growth that are frequently dealt with in the literature are shown). Nevertheless, one can envisage that much of the information presented here on, for instance, mixed-substrate growth or threshold concentrations can be also applied to the conditions prevailing in biofilms (176, 177, 206, 227). By necessity rather than choice, most of the issues discussed here are approached from the perspective of classical kinetics, where we restrict ourselves (with few exceptions) to the description of model systems that are well defined with respect to the microorganisms used, substrates, and growth conditions. Such studies offer a conceptual framework within which a number of observations concerning the growth of microbial cells and the fate of chemicals in real, complex systems (e.g., activated sludge biocenoses, microorganisms cultured for biotechnological purpose, and free-living aquatic microorganisms) may be rationalized, although they result mostly in unstructured models. Because of the large body of literature that is available on many of the aspects treated here (particularly on single-substrate-controlled kinetics), the list of references presented cannot be complete but is, in many instances, a personal selection that allow us to illustrate a particular issue.
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EXPERIMENTAL APPROACHES AND KINETIC DATA AVAILABLE
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Quality of Experimental Data
To validate a theory, experimental data of sufficient quality are needed. In this respect, however, most of the experimental data published on the relationship between specific growth rate and concentration of growth-controlling substrates are inadequate (for the use of the terms "growth-controlling" and "growth-limiting" substrate, see "Kinetic models and data processing" below). Typically, they exhibit a considerable degree of scattering (129, 166, 212, 213) that makes it virtually impossible to validate different models statistically. This can be attributed primarily to (i) the experimental cultivation systems used to collect the data and (ii) poor selectivity and sensitivity of analytical methods for measuring low concentrations of the growth-controlling substrates. The latter point represents a limitation in the analytical techniques used which may be overcome eventually; therefore, we will address this aspect only shortly (the problems have been discussed previously [128, 224, 226]). However, the first point is of primary importance because in this respect many conceptually different approaches are found in the published literature to collect the experimental data (182).
Laboratory cultivation techniques versus conditions in the environment. Microbial growth kinetics of suspended cells have been investigated in the laboratory in batch, continuous-culture, or fed-batch systems. Although, in theory (264), the last technique should overcome some of the disadvantages which hamper the conventional methods of batch and chemostat cultivation (discussed below), it has never been routinely used to experimentally estimate kinetic parameters (e.g., µmax and Ks), and therefore we will not discuss this approach in more detail.
In batch-culture experiments, either the consumption of the growth-controlling substrate or the increase in biomass concentration was monitored as a function of time. Inherent in this system is that the cell's environment and hence the cell's composition and physiological state change during the experiment (this has already been recognized and discussed in the classical studies by Kluyver [124], Málek [155], Herbert [100], Tempest [242], Koch [125, 126], and Tempest and Neijssel [245]). However, in continuous culture, an equilibrium concentration of the growth-controlling substrate is established independently of culture density and time. This allows the culture to grow at the set dilution rate by maintaining stable environmental growth conditions and hence the same physiological state. Therefore, in an ideal continuous culture, more precise, reproducible, and statistically relevant data can be collected than those obtained from batch cultures (137, 224). However, the constancy of all physicochemical parameters similarly represents artificial growth conditions as those imposed by a closed batch-culture system, and therefore the classical continuous-culture system is also not appropriate to study a number of microbial kinetic phenomena as they occur in the environment. In this respect, the situation of an organism under natural conditions most probably resides somewhere between the closed batch-culture and open continuous-culture systems (discussed in reference 114). In addition to studies performed with defined elements in batch or chemostat cultures, the kinetics of biodegradation of specific compounds has been investigated in complex systems consisting of undefined mixtures of cultures and substrates, e.g., in natural and technical environments directly or in laboratory microcosms (37, 108, 187). Such data are preferentially used to model processes in wastewater treatment plants or environmental compartments (83, 97, 98). Unfortunately, with the techniques presently at hand, it is extremely difficult to carry out kinetic experimental studies in such ecosystems and it is virtually impossible to obtain information at the single-cell level directly (for more details, the reader is referred to the following sections on mixed cultures and mixed substrates). At this point, the reader should be reminded that
as a result of the
slow hydrolysis of particulate organic matterthe growth of
heterotrophic microorganisms in most ecosystems is controlled by the
availability of carbon and energy substrates (reviewed in references
58, 90, and 169; note that
evidence that the removal of "solubilized" and bioavailable
substrates is not a limiting factor in the activated-sludge process had
already been reported in the 1960s [185]). Therefore,
it is the growth in carbon-limited continuous culture, mostly under
(slow) transient conditions or sometimes close to steady-state
conditions, that probably resembles the growth conditions experienced
by microorganisms in nature most of the time. In such a laboratory
system, the rate of hydrolysis is simulated by the rate of supply of
the growth-controlling substrate. We are convinced that defined
laboratory studies with mixed substrates and pure and mixed cultures
performed in continuous culture is one of the most appropriate
experimental approaches to understanding the kinetic and physiological
behavior of microorganisms in their natural environment (discussed in
references 58, 103, 112, and
170).
Problems of measuring growth-controlling substrate concentrations. To overcome the analytical difficulties of determining (low) growth-controlling substrate concentrations, kinetic experiments [i.e., determination of the µ = f(s) relationship] carried out in batch cultures mostly relied on indirect methods of obtaining data. The obvious reason for this is that the exact determination of the growth-controlling substrate concentration was and still is difficult whereas determination of the specific growth rate is quite easy (224, 270). Typically, specific rates of growth were measured (by determining cell number by plating or optical density) at different substrate concentrations which, in turn, were estimated either by calculation from the biomass produced and a growth yield factor (166) or simply by calculation from known dilution factors (129, 226).
To obtain kinetic data directly, either nonspecific or specific analytical techniques were used to measure concentrations of growth-controlling substrates. However, these methods not only have particular advantages but also have their specific limitations. The simple and cost-effective nonspecific methods, i.e., summary parameters such as dissolved organic carbon (DOC) removal, oxygen consumption (oxygen uptake rate or biological oxygen demand), and CO2 evolution (26, 38, 270), provide in the best case (i.e., DOC) kinetic information on the process of ultimate biodegradation, including the degradation of perhaps transiently excreted metabolites (see Fig. 1, where the different ranges of definition of biodegradability are indicated). Unfortunately, such methods cannot discriminate between different substrates in a mixture. In addition, these nonspecific methods are less sensitive (typically, detection limits are in the milligram-per-liter range). Therefore, they are less suitable for ecologically oriented studies, where one usually wants to obtain information on the effects on growth of low concentrations of particular substrates in mixtures. Alternatively, either the removal of an individual growth-controlling (i.e., parent) compound by a sensitive substrate-specific analysis (224) or the disappearance or production of 14C-labeled chemicals can be assessed (48, 115, 192, 233). The latter (high-cost) method has been successfully used for in situ measurements or at very low concentrations (micrograms per liter and lower) when other sensitive analytical techniques were not available. With respect to degradation kinetics, it should be pointed out that when the kinetics of the utilization of the parent compound is followed by specific analysis, only information on the primary degradation of this compound is obtained.Kinetic Models and Data Processing
Monod-type kinetics. During the last half century, the concepts in microbial growth kinetics have been dominated by the relatively simple empirical model proposed by Monod (166). The Monod model (equation 1) differs from the "classical" growth models (74, 256, 257, 205) in the way that it introduces the concept of a growth-controlling ("limiting") substrate.
It should be added that, confusingly, the terms "nutrient limitation" and "nutrient-limited growth" have been used in microbiology to describe two completely different growth phenomena. First, they are used in a stoichiometric sense to indicate that a certain amount of biomass can be produced from a particular amount of nutrient (or element, or substrate), i.e., that in a culture medium the availability of this nutrient determines the cell density which can be achieved (Liebig's law). Second, these terms are also used to indicate that the microbial growth rate (µ) is dictated by the (low) actual concentration of a particular substrate(s), as described, for example, by Monod's model (equation 1). For clarity, in this review we consistently use the term "nutrient-controlled" growth to describe the latter situation and use the term "limitation" to refer to stoichiometric aspects of growth (159, 214).(i) Kinetic and stoichiometric parameters. For most applications, it has turned out that growth or degradation phenomena can be described satisfactorily (usually based on a visual and not a statistical judgment) with four parameters, the two kinetic parameters, µmax and Ks, and the two stoichiometric parameters, YX/s and smin, as discussed below.
Monod's model relates the growth rate to the concentration of a single growth-controlling substrate [µ = f(s)] via two parameters, the maximum specific growth rate (µmax), and the substrate affinity constant (Ks) (the nomenclature used throughout, is listed in Table 1). Since growth is a result of catabolic and anabolic enzymatic activities, these processes, i.e., substrate utilization or growth-associated product formation, can also be quantitatively described on the basis of growth models (see, e.g., reference 94 and the excellent overview given in reference 13). The link between growth and substrate utilization has already been made by Monod (166), who linearly related the yield coefficient (YX/s; equation 2)a measure for the conversion efficiency of a growth
substrate into cell materialto the specific rate of biomass growth
(µ) and the specific rate of substrate consumption (q)
(equation 3).
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(ii) Biological meaning of µmax, Ks, and smin. A comment on the biological meaning of the parameters Ks, µmax, and smin, which are used to characterize microbial growth for given growth conditions, is necessary. Whereas the interpretation of µmax as the maximum specific growth rate is straightforward, the biological meaning of Ks is less obvious. Although, the Monod equation is mathematically analogous to the formula that was proposed by Michaelis and Menten (43) to describe enzyme kinetics, the meaning of the two parameters Ks and Km is quite different. Monod had already stressed (167) that there is no relationship between the Ks (affinity constant used in his growth model, which represents the substrate concentration at µ = 0.5µmax) and the Michaelis-Menten constant Km. In contrast to Michaelis-Menten kinetics, which is used to describe a process catalyzed by a single enzyme, Monod kinetics describes processes (both growth and growth-linked biodegradation) of a more complex nature in which many enzyme systems are involved (Fig. 1). Therefore, the still frequently used habit of describing the kinetics of growth or growth-associated biodegradation as "Michaelis-Menten-type" kinetics is not correct. Only in some special cases, when cell growth is controlled by the rate of active transport of a substrate, may Ks be considered to be similar to the Michaelis-Menten constant (Km) for the permease carrier (see, e.g., references 22 and 23). The value of 1/Ks is interpreted as a reflection of the affinity of the cell towards a substrate.
The existence of smin can be justified on the basis of the maintenance energy concept that can be easily explained by thermodynamic reasoning (194, 220). A consequence of this concept is the existence of a finite concentration or flux of an energy or carbon substrate at zero growth rate. In a system that is open with respect to the supply of substrate, this results in a finite concentration of the energy or carbon source at D = 0 h1 (this concept has also been verified experimentally
for single-substrate-controlled growth [135, 154, 226, 222,
246, 263]). It should be pointed out that such thresholds
should not be observed in closed systems like batch cultures
(246), because the maintenance requirement of cells implies
continued utilization until all available substrate is exhausted.
Alternative kinetic expressions. The first kinetic principle proposed for microbial growth by Penfold and Norris in 1912 (189), namely, that the relationship between µ and s is best described by a "saturation" type of curve, i.e., that at high substrate concentrations the organisms should grow at a maximum rate (µmax) independent of the substrate concentration, has been widely accepted. Although Monod's model (equation 1) fulfills this requirement, it has been criticized in the past in various respects. In particular, its systematic deviations of µ at low substrate concentrations, where the actual growth rate lies above the prediction, and at high substrate concentrations, where µmax is approached too slowly, were a matter of much debate (see particularly reference 199). The fact that even Monod's own data (166) did not indisputably support his proposed mathematical formula gave rise to many more studies. A variety of other mathematical expressions have been put forward to describe this hyperbolic curve (reviewed in references 182, 200, and 224). However, the development of structured (mechanistic) models for quantifying microbial growth kinetics is still limited because the mechanism of cell growth is very complex and is not yet completely understood (for a review of structured models, the reader is referred to reference 178). Therefore, most of the proposed growth models are unstructured and empirical. In principle, three methods were used to design such refined equations for the growth kinetics of suspended cells: (i) incorporating additional constants into the original Monod model that provided corrections of, for instance, substrate or product inhibition, endogenous metabolism (maintenance), substrate diffusion, or the dependence of µmax on the biomass density (5, 41, 44, 94, 99, 173, 195, 200, 199, 226); (ii) proposing different kinetic concepts, resulting in both empirical (24, 94, 239, 241, 266) and mechanistic (50, 133, 178) models; and (iii) describing the influence of physicochemical factors on the Monod growth parameters (39, 73, 135, 201).
Some of the recent attempts to create a general kinetic model that will be valid over a wide range of growth conditions, are represented by the equation proposed by Tan et al. (239), which includes the Monod, Moser, and multiple Monod equations as special cases, or by the powered Monod equation (equation 6) proposed by Heijnen and Romein (94). By including the exponent n, the model of Heijnen and Romein model was said to take into account the influence of variable enzyme concentrations. The fact that intracellular enzyme concentrations exert an important influence on overall growth kinetics has been already discussed (22, 23, 130). (Note that this powered Monod equation differs from the growth model proposed by Moser [cited in reference 199]; the influence of enzyme regulation on the kinetics of growth is discussed in more detail below.)
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(
(
(
(Some comments on the choice of models and fitting exercise. Although increasing model complexity often results in improved curve fitting, the most appropriate model should be selected on the basis of statistical considerations (discussed in references 127 and 208). Unfortunately, there is evidence that complex equations (e.g., models described in the previous section under points i and ii) have often been constructed in an attempt to explain a set of experimental data that exhibited so much scatter that it was impossible to discriminate between the different models (127, 182, 200, 212, 213, 224). Monod was aware of the inadequate quality of his data, and he reasoned that: "several different mathematical formulations could be made to fit the data. But it is convenient and logical to adopt a hyperbolic equation" (167). This leads to the conclusion that there is a need to acquire reproducible data of better quality (reproducible data from continuous culture were presented in, for example, references 135 and 224) and that it seems a fruitless exercise to develop new models as long as it is not possible to discriminate between them on the basis of the experimental data. One should be also aware that the development of unstructured models has, perhaps, reached its maturity and that much effort will therefore now be channeled into the development and verification of structured models (66, 178). However, the experimental effort expended to generate data that are required by the structured models will be enormous (i.e., data are needed that provide information on the mechanism of biomass growth and its composition). Although both the analytical and computational facilities for the advancement of such models are well developed, it will still be difficult to find the necessary balance between avoiding unnecessary complexity and ensuring sufficient reality.
Parameter identifiability. When the Monod model (equation 1) is directly fitted to a set of experimental data, Ks values are known to vary with µmax (the question of whether and to what extent the observed changes in Monod kinetic parameters are a result of this high correlation between them is still unanswered). This means that the two parameters are not completely independent but "draw" each other during the fitting procedure. For example, changing µmax in such a fitting exercise will also immediately lead to a small adjustment of Ks, and not, as one would expect theoretically, that they can be varied independently (discussed in reference 151). Therefore, it was proposed that the µmax/Ks ratio is a better parameter to assess the advantage in competition for a nutrient(s) at low concentrations (93). This ratio, also referred to as specific affinity, bridges the kinetics of enzymatic substrate uptake and microbial growth (comprehensively analyzed by Button [33-35]). It has been frequently pointed out that any combination of the two parameters that results in the same µmax/Ks ratio will fit equally well in the parameter estimation routine (the practical problems of the parameter identifiability for growth models containing "Michaelis-Menten-type" nonlinearities and the optimal experimental design are discussed in references 40, 208-210, and, recently, 258). In particular, it was stressed that it is almost impossible to obtain reliable kinetic parameters from a single batch substrate depletion curve. The reason for this is that for initial substrate concentrations much higher than the effective Ks, which is usually the case in batch cultures, the fitting procedure becomes insensitive to changes in Ks and, consequently, Ks values differing by several orders of magnitude could successfully describe the experimental data. Thus, µmax is the only parameter that rigidly fixes the growth behavior in batch culture (this statement is based on our personal experience but has also been discussed in references 66, 86, and 210).
Additionally, it should be pointed out that it has been demonstrated (43) that transformations of the original data by using, for instance, the Eadie-Hofstee, Lineweaver-Burk, or "direct linear" plots significantly affect the estimated kinetic constants. Therefore, it remains an open question whether some of the observed changes in kinetic parameters are a product of a tendentious data evaluation procedure rather than a reflection of reality (see, for instance, Fig. 3 and 5 in reference 179).Variations in Kinetic Parameters
Of all the different models that have been proposed, the Monod relationship (equation 1) is the one that has been most frequently used to describe microbial growth kinetics in both pure (reviewed in references 34, 182, and 224) and mixed (83, 196) culture systems. Therefore, the two "organism constants," µmax and Ks, dominate the literature and are discussed in the following sections of this review. Astonishingly, there is a considerable lack of consistency in the Monod parameters reported even for a specified combination of an organism and a substrate. Williams (268), who simulated the uptake kinetics by an undefined mixed culture, concluded that "departure from the predictions of Michaelis-Menten equation cannot be attributed simply to the fact that the population is heterogeneous." A typical example of the state of information on the kinetic properties exhibited by a particular microorganism are the data available for Escherichia coli growing with glucose. The Ks values reported vary over more than 3 orders of magnitude (Table 2; Fig. 3), and it should be stressed that the case of E. coli does not stand alone; similar examples can be found for or Cytophaga johnsonae (104) and Klebsiella pneumoniae (212).
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) and chemostat (
) cultures are given. The numerical
values and references are listed in Table Based on the discussion so far, it is evident that there are many different reasons for this variability. Those that seem to be the most important are the culture history, parameter identifiability, and quality of the experimental data (for a comprehensive review from an engineering point of view, the reader is referred to reference 79). Here, we would like to concentrate on the changes which are linked in one or another way to the experimental setup and the physiological state of the cell (but see also "Substrate mixtures and mixed cultures" below).
Intrinsic versus extant kinetics. As discussed above, the enormous variations in reported kinetic constants cannot be satisfactorily explained by strain differences or other (technical) deficiencies, but it is very likely that they depend to a considerable part "not only on s(t) but also on the history of the culture, in particular on the way in which `s' has varied in the past" (200). Hence, during a kinetic experiment, the physiological state of a culture can change and may exhibit so-called "intrinsic" or "extant" kinetic properties (this nomenclature has been proposed by Grady et al. [79]). The intrinsic parameters depend only on the nature of the substrate, the type of bacterial culture, and the set environmental (physicochemical) conditions, and they are considered to be independent of culture history and therefore reproducible. In contrast, the extant kinetic properties are a reflection of cell's history, the organism's intrinsic characteristics, and the currently existing environmental conditions; they are therefore variable and difficult to reproduce. (Note that a similar concept was already outlined by Powell in 1967 [199], who proposed an instantaneous specific substrate consumption rate that is related to both the substrate concentration and organism's physiological state.)
In most experimental systems that are used to determine kinetic parameters of microbial cultures, the physiological state of the cells changes during the experiment; hence, the culture will always exhibit extant kinetic properties. In the course of the experiment, the exhibited kinetic characteristics will move toward the intrinsic values that can be achieved under the given specific environmental conditions (temperature pH, etc.). With respect to the Monod parameters, it appears either that a culture is able to improve the µmax, when it is "trained" during repeated growth in batch culture with a corresponding loss in affinity towards the previously growth-controlling substrate (45), or, alternatively, that during cultivation in continuous culture it improves its ability to scavenge the growth-controlling substrate by decreasing Ks with the loss of capacity to grow at the maximum possible rate (134, 224). We are not aware of any experimental evidence showing that a culture simultaneously exhibited both the intrinsic µmax and Ks (arbitrarily defining "intrinsic" as the "best" possible value, i.e., the highest possible µmax and the lowest Ks); hence, only one of these parameters can be determined experimentally at a time. Such an understanding would extend the definition of intrinsic properties as originally proposed by Grady et al. (79). To date, the discussion of whether intrinsic or extant kinetic parameters are better suited to describe the biodegradation processes and to predict the fate of organic compounds in nature and engineered systems is still under way (86, 180). Unfortunately, most of the kinetic data reported in literature were determined somewhere between the two well-defined kinetic properties discussed above (150). Such data must therefore be interpreted with caution. To judge the quality and meaningfulness of the reported parameters, it is at least necessary to know the exact conditions of the experimental approach used. Hence, as is the case for cellular composition (100), with respect to kinetic properties we also have to recall that "...bacterial cells are able to change themselves phenotypically to such an extent that it is quite impossible to define them chemically (or structurally or functionally) without reference to the growth environment" (243).Feast and famine ends of an organism's kinetic properties. To survive and compete successfully in nature, most microorganisms are able to meet many of the environmental challenges by adjusting their cellular composition with respect to both structure and metabolic function (198). Regardless of whether these adaptive changes occur at the phenotypic level, the genotypic level, or both, it is logical that they also affect the growth and/or biodegradation kinetic properties exhibited by a cell. For example, microorganisms are able to adapt to growth at different extracellular substrate concentrations by drastically adjusting their key kinetic properties (in Monod terms, µmax and Ks), and the strategies that have been reported for both gram-negative and gram-positive microorganisms include the following: (i) a single uptake system that exhibits different kinetic properties depending on the concentration of its substrate is used (so-called multiphasic kinetics [7, 179]); (ii) the microorganisms switch between two or more transport systems of different affinity, as observed for different sugars (68, 95, 96) or for glycerol and ammonia (244) (such changes can include the modification of outer membrane components [68]); and (iii) other less well defined changes can be used, such as variations in the catabolic and/or anabolic capacity (the "metabolon"), as suggested by Kurlandzka et al. (140).
These modes of adaptation considerably differ in the time frame within which changes take place (discussed in reference 66). Whereas a multiphasic system will react instantaneously, the switch between different transport systems can proceed relatively quickly, i.e., within few minutes to hours; however, adaptation at the population level (e.g., evolution and enrichment of more competitive mutant strains) is predisposed to long-term changes. Two fundamentally different approaches are used at present to study the physiological changes taking place in microorganisms when the availability of particular substrate becomes restricted: (i) the starvation approach (i.e., behavior in the complete absence of a particular nutrient in batch culture [123, 131, 160, 161]), and (ii) slow growth at very low nutrient concentrations (as occurs, for example, during continuous cultivation [58]). It must also be stressed that there are distinct differences in the processes that occur during growth at different substrate concentrations, such as starvation (i.e., the total absence of a particular nutrient), steady-state growth under substrate control, and growth with excess substrate (i.e., control by the quality rather than the quantity of nutrients). However, neither of these approaches is able to exactly reproduce the growth and starvation conditions that microorganisms experience in ecosystems. Nevertheless, it has been recently argued that from the ecological point of view the continuous culture method seems more relevant because it resembles the growth under oligotrophic conditions (170). Therefore, the information obtained by this approach is used in the discussions in the following sections.(i) Long-term adaptation from high to low substrate
concentrations and vice versa.
For a number of bacterial strains,
it has been observed that during long-term cultivation in a
carbon-controlled continuous culture, although the culture was already
in steady state with respect to the biomass concentration, the residual
substrate concentration decreased, implying that the affinity for the
substrate increased (104, 129, 212). A systematic study of
this phenomenon was performed for E. coli grown at different
growth rates in a glucose-limited continuous culture (134),
and it was shown for the first time that the process of adaptation is
reproducible and proceeds faster at low than at high growth rates (Fig.
4). Assuming that the Monod model can be
applied, the data imply that the affinity constant for glucose
(Ks) decreased from approximately a few
milligrams per liter during batch-growth conditions to some 30 µg
liter1 at steady state in continuous culture (134,
224). It should be pointed out that the end point of adaptation
with respect to the kinetic properties of the cell was always identical
and was independent of the culture history (i.e., the intrinsic kinetic properties with respect to the substrate affinity were reproducibly achieved, apparently independently of dilution rate
[134]).
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); data for
independent continuous cultures are shown for D = 0.6 h
and 
). Adapted from reference
(ii) Implications for growth of microbial cells in the environment. During their life cycle many heterotrophic microorganisms encounter habitats that differ markedly in the spectrum and concentration of available nutrients (55, 216, 272), in addition to environmental parameters such as pH or temperature. For example, when the bacterium E. coli leaves its primary habitat, the nutrient-rich (copiotrophic) anaerobic intestine of warm-blooded animals and humans with an ample supply of carbonaceous compounds (153, 215), it has to adapt to its nutrient-deficient (oligotrophic) secondary habitat (water, soil or sediment), where concentrations of carbon and energy compounds are typically in the low micromolar or even nanomolar range and the availability of carbon and energy sources restricts the growth of heterotrophic microbes (6, 58, 169, 170, 175). It is obvious that a particular organism can successfully compete in both environments only if it can change and appropriately adapt its kinetic properties. This suggests that the kinetic properties of a microbial cell cannot be described by a single set of kinetic constants as has been done up to now. The experimental data reported in the literature for Ks and µmax of E. coli during growth on glucose (Table 2; Fig. 3) clearly indicate that this bacterium can exhibit different kinetic properties. This is schematically shown in Fig. 3, which suggests that a microbial cell can adjust its kinetic properties within a certain window of the Ks-µmax plane. All these observations support the statement (158) that categorizing bacteria according to the nutrient concentration (141, 197) as "typical" oligotrophs or copio(eu)trophs (and additional categories that were introduced by Horowitz et al. [105]) is arbitrary. In this respect, the observations reported long ago by ZoBell and Grant (275, 276), namely, that the ability to use nutrients at high or low concentrations is also dependent on the compound used as the test substrate, indicate that oligotrophy and copiotrophy are vaguely defined and documented concepts (see especially the excellent discussion in reference 223).
SUBSTRATE MIXTURES AND MIXED CULTURES
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Often, the observed degradation for a particular compound in soil or water samples follows a rather simple pattern. However, such die-away studies are essentially black-box systems and therefore difficult to interpret. A few years ago, Grady et al. commented on the state-of-understanding of such complex systems as follows: "...efforts to model systems of practical complexity may be premature at this time..." because first, "...data must be available upon which model development can be based" (80). It follows from the information presented and discussed earlier in this review that a systematic experimental approach is needed to elucidate the main principles of microbial growth kinetics and describe them in quantitative terms. Indeed, this is especially important when investigating the growth of mixed cultures with mixed substrates. For this reason, after a brief description of the situation in environmental systems, the problem will be approached here starting out from the growth of pure cultures with defined mixtures of substrates and moving toward the more complex situation of mixed cultures utilizing mixed substrates.
Utilization of Mixtures of Carbon Sources
Traditional kinetics are based on the assumption that a single compound (e.g., a particular carbon source, such as glucose, or a nitrogen source, such as ammonia) is controlling the rate of growth of a microbial cell. This concept has been investigated, tested, and confirmed for cultures cultivated under defined conditions in the laboratory with synthetic or mineral media, where each of the physiologically required nutrients is supplied in the form of a single compound, as discussed above. In contrast to the laboratory, growth in ecosystems proceeds under more complex conditions where microorganisms are faced with mixtures of compounds that can fulfill a particular nutritional function. This is probably best illustrated for heterotrophic microbial cells and the carbon substrates they use for growth. In almost all ecosystems, the availability of carbon and energy sources is extremely restricted (169, 170) and carbon is available in the form of a myriad of different compounds, all of them at concentrations of a few micrograms per liter or lower. These compounds originate mainly from the hydrolysis of particulate organic matter or are excretion products of higher organisms and, recently, to an increasing extent also from xenobiotic chemicals released into the environment (122, 174, 175, 219). Together with temperature, this pool of carbon compounds is known to control the growth rate of the heterotrophic microbial population in ecosystems (169) (unfortunately, the two parameters are difficult to separate because as well as the microbial growth rate, temperature affects the hydrolysis rate of polymeric carbon sources and therefore their availability). It should be pointed out that it is not only the actual concentration of compounds in the environment that has to be taken into account when assessing its role for microbial growth but also its rate of turnover. For example, the rapid turnover of glucose in seawater indicates that this sugar is probably one of the major substrates of many free-living heterotrophs in this ecosystem (121, 171, 204).
Under such conditions, one would expect no significant growth if cells were specialized for one of the many available carbon compounds (249, 250), as suggested by the principle of diauxic growth (e.g., for pure cultures [166] and for mixed cultures [71, 236]). There is overwhelming experimental evidence that carbon starvation or slow growth in carbon-limited continuous culture provokes the expression of many carbon catabolic enzyme systems, although the appropriate carbon sources are absent (2, 27, 78, 225, 221, 237), resulting in cells that are able to immediately utilize these carbon substrates if they become available in the environment. In addition, over the last two decades, many studies published by different research groups have provided evidence that under such conditions heterotrophic microorganisms do not restrict themselves to the utilization of a single carbon source but are simultaneously assimilating many of the carbonaceous compounds available in their environment, even mixtures of carbon sources that normally provide diauxic growth at high concentrations (a growth behavior referred to as mixed-substrate growth [88, 160] and recently summarized in reference 58). For example, Pseudomonas aeruginosa was reported to grow with a mixture of 45 carbonaceous compounds, each added to tap water at a concentration of 1 µg of carbon per liter, whereas none of these compounds supported growth on its own at this concentration (249, 250).
All the evidence outlined above indicates that in addition to improved substrate affinity (see the previous section on adaptation), the potential to utilize different carbon substrates simultaneously has to be taken into account when considering microbial competition at low environmental concentrations (125, 160; bacterial substrate transport strategies and environmental fitness are reviewed in reference 89). There are now numerous examples in the literature that demonstrate this catabolic versatility and flexibility of microbial cells, not only when growing under carbon- and energy-limited conditions but also for growth in carbon-sufficient batch cultures (reviewed in reference 58). This of course raises the question whether and how the traditional kinetic concepts based on growth rate control by a single substrate can be applied to the environmental situation where a cell (or mixed microbial population) is most probably utilizing several carbon compounds simultaneously.
Kinetic Effects during Utilization of Defined Substrate Mixtures by Pure Cultures
Experimental data. Unfortunately, kinetic studies involving mixed substrates in batch culture are currently restricted to effects reported on the specific growth rate. As far as we are aware, systematic experimental kinetic data for mixed-substrate growth were obtained only from studies in carbon-controlled continuous cultures with defined mixtures of carbon substrates.
(i) Continuous cultivation. The first experimental evidence for an influence of the simultaneous utilization of mixtures of carbon substrates on kinetics of growth was reported by Law and Button (142). When a Corynebacterium strain was grown in carbon-controlled chemostat culture with various mixtures of glucose and amino acids at a constant growth rate, the steady-state concentrations of glucose were lowered in the presence of the amino acids. This was later confirmed by other investigations in a carbon-controlled chemostat culture, when it was reported that the steady-state concentration of a particular substrate became reduced during mixed-substrate growth conditions (8, 61, 160, 191, 267). Although in all these studies the concentration of only one of the carbon substrates supplied to the culture was reported, usually because no suitable analytical methods were available to detect the other substrates, the data suggested that this effect was not limited to only one of the substrates but that it might be a general phenomenon.
Recently, an improved method for the analysis of reducing sugars (224) allowed a more detailed investigation (137, 148). This method allowed the reliable determination of the free concentrations of a variety of reducing sugars in carbon-limited chemostat cultures of E. coli in the low microgram per liter range (e.g., for glucose, quantification of reducing sugars in the culture medium was possible down to concentrations of 2 µg liter1). The method, including all necessary tests done
to ensure that no significant amounts of sugars were consumed
during sample collection, has been described in detail (145,
224).
To test the general validity of the pattern of reduced steady-state
concentrations of individual substrates during mixed-substrate growth,
E. coli was grown in a carbon-controlled chemostat culture at fixed growth rate with mixtures of up to six different sugars, all
of them supporting growth when supplied on their own (65, 148). As expected, all the sugars were utilized simultaneously, whether mixtures of two, three, or six sugars were supplied in the
feed. In all experiments the steady-state concentrations of the sugars
were reduced during mixed-substrate growth compared to those measured
during growth with single sugars. Furthermore, the concentrations of
the individual sugars approximately reflected their contribution to the
total substrate supplied to the culture, whereas the steady-state
concentration of total carbon remained approximately constant. An
example of this behavior is given in Fig.
5a, which shows the steady-state
concentrations measured during growth of this bacterium with mixtures
of glucose, galactose, and fructose at a dilution rate of 0.3 h1. In this particular experiment, fructose always
contributed some 33% to the total carbon concentration in the
feed medium whereas the contribution of glucose and galactose
varied. Accordingly, the steady-state concentration of fructose was
virtually constant, while the residual concentration pattern for the
two other sugars reflected their proportion in the feed medium.
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1) compared to that for glucose (ca. 30 µg liter1). However, the steady-state concentrations of
the two carbon substrates were lower than during single-substrate
growth and reflected their contribution in the feed (Fig. 5b; see also
the following section on kinetic models for mixed-substrate
utilization). A similar effect was observed during growth of the
methylotrophic yeast Kloeckera sp. strain 2201 with mixtures
of glucose plus methanol, where the concentration of DOC varied at a
constant dilution rate (the total carbon concentration essentially
followed that of methanol because the glucose concentration was always below the detection limit of 2 mg liter1 [see Fig.
6c]).
It should be pointed out that the observed dependence of the
steady-state substrate concentration on the concentration of the
particular substrate in medium feed (i.e., mixture composition) does
not contradict the well-known chemostat theory which states that the
steady-state substrate concentration is not affected by the
concentration of substrate in medium feed and, hence, biomass concentration (99, 101) and which has been verified only
recently (224). This prediction was based on the assumption
that only a single substrate is controlling growth. In contrast, for
the simultaneous utilization of mixtures, not only the total substrate (carbon) concentration but also the composition of the mixture in the
feed becomes relevant. Also, during mixed-substrate utilization, steady-state concentrations are independent of the total carbon concentration in the medium feed, but this statement is now restricted to each of the specific mixtures.
(ii) Batch cultivation. Under typical batch growth conditions, where carbon sources are supplied at concentrations of grams per liter, diauxic or sequential utilization of mixtures of carbon substrates is usually considered to be the rule rather than the exception. Surprisingly, the list of experimental data presented recently (58) clearly demonstrates that in the presence of high substrate concentrations the simultaneous utilization of two or more different carbon sources is commonly observed for both bacteria and yeasts, independent of whether growth occurs under aerobic, anaerobic, mesophilic, or thermophilic conditions. From the information available, it seems that carbon sources that on their own support only low to medium maximum specific growth rates are utilized together.
Even incompatible combinations of substrates (such as, e.g., glucose and galactose for E. coli), which lead to diauxic growth behavior when supplied at high concentrations, are often consumed simultaneously in batch culture when their initial concentrations are lowered into the milligram-per-liter range (32, 145, 147, 152, 248). Frequently, an increase in the maximum specific growth rate was observed when a culture was exposed to mixtures of carbon sources in comparison to growth with either of these substrates as single carbon sources (29, 92, 202, 271). It should be added that this stimulation is not restricted to growth with mixtures of carbon substrates but was also reported for mixed electron acceptor utilization. For instance, the growth of Thiosphaera pantotropha with molecular oxygen and nitrate as terminal electron acceptors was reported to lead to an increase in the specific growth rate compared to that observed during cultivation of this bacterium with either nitrate or oxygen alone (207). Similar effects have been observed in continuous culture, resulting in increased critical dilution rates during mixed-substrate growth (29, 152, 231). Although the increase in the specific growth rate seems to be a common effect, it is not yet possible from the limited data available to quantitatively predict the extent of stimulation of the specific growth rate. Nevertheless, it seems logical to assume that in such cases the rate of utilization of the individual substrates are limiting the supply of carbon into anabolic pathways and that consequently two or more catabolic pathways operating at the same time are able to better feed or even saturate anabolism, resulting in an increased maximum growth rate.Kinetic models. Because carbon substrates are most often utilized simultaneously under the carbon- and energy-controlled environmental conditions, several compounds together, not a single compound, will control the growth rate. Therefore, one must ask whether it is possible to describe mixed-substrate growth by combining the kinetic relationships determined for individual substrates during single-substrate-controlled growth or whether it is necessary to develop alternative mathematical models to describe growth under such conditions.
Although every microbiologist knows from practical experience that the growth rate is influenced by the complexity of the medium composition (see, e.g., references 80 and 217), the single-substrate growth models discussed above have been commonly used for describing bacterial growth and competition under more complex or even environmental conditions (76, 83, 97, 98, 139, 272). In the line with this single-substrate approach is the fact that most of the models for mixed-substrate growth that have been published were originally designed to describe the sequential or diauxic utilization of substrates in batch culture (and therefore contain inhibition terms). Nevertheless, several proposalsusually derived by combining two or
more (modified) Monod termswere made to describe the utilization of
both homologous (21, 25, 75, 132, 231, 272, 274) and
heterologous (9, 11, 12, 17, 144, 156, 162) combinations of
substrates; for more detail, the reader is referred to the
section on kinetics of multiple-nutrient-controlled growth,
below). Some of these models were also applied to growth with
substrate mixtures in chemostat cultures (75, 231, 274). Whereas these models could be easily tested for batch-culture growth, the authors were unable to prove their validity for
mixed-substrate growth in the chemostat because of the lack of data
on steady-state concentrations of growth-controlling substrates.
Unfortunately, only few of these models can be extended to more than
two substrates. Furthermore, a serious drawback is that most of them
contain no upper limit for µmax. This implies that the
more components that are used, the higher the resulting
µmax, until it becomes unrealistic. For instance, the
model proposed by Bell (21), which describes the total
substrate uptake rate or growth rate on mixtures of carbon substrates
as the sum of individual Monod terms, gives a good fit to the
experimental data of Lendenmann et al. (148) for growth with
mixtures containing two sugars. However, for mixtures containing three
or more sugars, the specific growth rates predicted from the
experimentally measured sugar concentrations are far too high
(147). A totally different approach to modeling bacterial growth with mixtures of substrates (i.e., a cybernetic model
consisting of mass balance and rate equations describing growth,
maintenance, and enzyme synthesis) was presented by
Ramkrishna and coworkers (16, 247). However, these
models were not tested rigorously with good experimental data.
Hence, there are few realistic published "multisubstrate" models
which describe the specific growth rate as a function of the individual
concentrations of more than two simultaneously utilized carbon
substrates (25, 137, 147). A first set of experimental data,
namely, the steady-state concentrations determined during growth of
E. coli with mixtures of up to six sugars (148), was used to evaluate the applicability of several models
(148). A new phenomenological model proposed by Lendenmann
et al. (148) (equation 7a), which was subsequently found to
fit the data best for growth with most mixtures, allows the prediction
of steady-state substrate concentrations during mixed-sugar utilization
(si) if the "intrinsic" Monod parameters of
single-substrate growth (i.e., when
s100%,i can be calculated from
Ks,i measured in chemostat culture
and µmax,i in batch cultures) and the
contribution of the particular substrate to the total substrate
(s0,i) are known. Recently, this
model was applied to the experimental data for growth of E. coli with mixtures of 3-PPA and glucose (137). To
obtain a good fit, it had to be rewritten in a more general form in
which the contribution of the individual substrates
(Ri) was expressed in the terms of either Gibbs
energy, carbon content of the substrates, or moles of oxygen needed for
their combustion (whereas the originally proposed model was based on
weight contributions of individual substrates). Thus, the initial
concept proposed for growth with mixtures of sugars (147)
was extended to the growth of E. coli with mixtures of glucose and 3-PPA, two substrates that differ with respect to their
chemical structure, carbon content, degree of carbon reduction, and
metabolic pathways involved in their degradation (equation 7b)
(137).
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(7a) |
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1; for the exact
derivation of this model, the reader is referred to reference
147).
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1 (i.e., two-thirds of the maximum specific growth
rate). In this culture, steady-state concentrations of the six sugars
were between 10 and 50 µg liter1 whereas the
corresponding concentrations for growth with single sugars at this
dilution rate were between 140 and 250 µg liter1
(148).
Effect of enzyme expression patterns. It has been frequently pointed out that for growth of a microbial strain in continuous culture, the steady-state extracellular concentration of the growth-controlling substrate and the content of the enzymes involved in transport and catabolism of this substrate influence each other (reviewed in references 34 and 211). This implies that the kinetic properties exhibited by a microbial cell for a particular substrate should be intimately linked to the expression levels of enzymes involved in the metabolic pathway of this substrate. Consequently, the regulatory pattern should be known to predict the resulting steady-state substrate concentrations.
We would like to discuss this question here for the case of mixed-substrate growth of a microbial culture in a chemostat at a constant dilution rate when supplied with different proportions of two carbon substrates. This is done because experimental data are available for this case. However, this line of thinking not only is valid for this particular case but also can be applied to growth with either a single substrate or more complex mixtures. As simplifying preliminaries, we assume that the growth yields for the two substrates are not markedly different and that for each of the substrates the specific consumption rate (qs) can be described by the Monod model, i.e., qs = qmax [s/(Ks + s)]. It should be pointed out that in this case, the specific consumption rate for a substrate is linearly related to its proportion in the substrate mixture fed. Essentially, three different regulation strategies for the synthesis of catabolic enzymes in a pathway can be postulated and are described below.(i) Fixed catabolic enzyme level. Let us first assume that regulation is such that the intracellular levels of the different enzymes in the pathway (and therefore also the cellular maximum specific substrate consumption capacity, qmax) are not affected by changes in the composition of the substrate mixture supplied. Two different patterns can now be anticipated for the residual concentration of a substrate in response to the changes in the supplied mixture, depending on whether the pathway operates in the saturated or nonsaturated region. In the latter case, an almost linear relationship between the steady-state substrate concentration and the mixture composition is expected, whereas the former situation will result in a distinctly nonlinear relationship (Fig. 6d).
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(ii) Regulated catabolic enzyme level.
An altogether
different regulation strategy can be postulated, namely, that the
cellular concentration of enzymes in a catabolic pathway is subject to
regulation and in some manner is dependent on the individual flux of
the particular carbon substrate (the different options are
schematically outlined in Fig. 6f). An experimental verification of
this hypothesis was given by the results obtained for the
methylotrophic yeast Kloeckera sp. strain 2201 during simultaneous utilization of glucose and methanol in a carbon-controlled continuous culture at constant growth rate (63, 64). During growth with low proportions of methanol (less than 50% [wt/wt]), the
cells used the strategy of regulating the amount of enzyme in the
pathway in order to sustain the increasing carbon flux (Fig. 6c), as
demonstrated for the specific activity of alcohol oxidase, the first
enzyme in the pathway for methanol in this yeast. This resulted in an
essentially constant external methanol concentration of 1.2 mg
liter1. However, when the flux of carbon through the
methanol pathway exceeded 50%, all enzymes of the pathway were fully
induced, and to support the increase in the specific methanol
consumption rate necessary to maintain the growth rate, the external
methanol concentration increased to approximately 70 mg
liter1. A similar pattern, also suggesting a close link
between kinetics and the regulation of enzyme levels, has been reported
recently for the steady-state concentration of hydrogen during
mixotrophic growth of Acetobacterium woodii with different
ratios of hydrogen plus lactate in the chemostat (191).
(iii) Threshold for enzyme induction.
A third strategy
might be that at low concentrations of a potential substrate the cells
are not expressing the catabolic enzymes necessary to utilize the
substrate and that a certain threshold concentration of this compound
has to be reached until induction occurs. This regulatory pattern was
observed for growth of E. coli with 3-PPA in combination
with glucose in carbon-limited continuous culture (134,
138). When the culture was supplied with very low 3-PPA
concentrations (<3 mg liter1) in the inflowing medium,
the enzymes (or at least some of them) necessary for its degradation
were not induced, and consequently 3-PPA was not utilized (Fig. 6b and
e). When the concentration of 3-PPA in the medium feed was increased
above 3 mg liter1, the synthesis of enzymes for 3-PPA
degradation was induced and the cells were utilizing this compound
together with glucose. Interestingly, once the enzymes were induced,
the cells were able utilize 3-PPA down to concentrations lower than
those required to trigger the induction.
Kinetics of Multiple-Nutrient-Controlled Growth
Most microbiologists still support the view that only one specific compound (e.g., glucose, or ammonia) can limit, i.e., control, the rate of growth at any one time. This contrasts with the substantial body of literature presented in the preceding sections on the simultaneous utilization of homologous substrates, where the basic principles of growth kinetics with mixtures of carbon sources was presented. Indeed, an interaction of two nonhomologous substrates (mostly a carbon source and a nitrogen source) at the kinetic level has been predicted based on theoretical reasoning and a number of models have been proposed in the literature to describe this behavior (10, 11, 17, 84, 144, 156, 162). Although kinetic experimental studies on this aspect of growth are extremely scarce, a number of reports that demonstrate such an interaction can be found in the literature. The first experimental indications that more than one nutrient may stoichiometrically limit growth had been published in the early 1970s (42, 56, 91, 106, 143, 144, 162, 186, 191, 230). Over the last decade, clear experimental proof has been given for the existence of dual-nutrient-limited (e.g., C and N or C and P) growth regimes during cultivation of bacteria, yeasts, and algae in the chemostat on the basis of culture parameters and the composition and physiological properties of the cells (1, 51, 59, 60, 82, 164, 186, 190, 203, 214).
Although there is now convincing evidence that stable multiple-nutrient-limited regimes exist and one would expect that the rate of growth within this region would be controlled by two or more nutrients at the same time, the kinetic relationship between concentrations of the growth-controlling nutrients and growth rate has not yet been elucidated. The only kinetic data reported to date are those by Rutgers et al. (214) for the simultaneous control of the growth rate of K. pneumoniae by glucose and ammonia in continuous culture (Fig. 7). Their data clearly demonstrate the (stoichiometrically) dual-nutrient-limited zone of growth at different dilution rates and the steady-state concentrations for glucose and ammonia, indicating that they control the growth together. Unfortunately, the scattering of the data is such that they do not allow a comparison of different models on a statistical basis. Therefore, the kinetic interaction of two nonhomologous growth-controlling substrates remains to be elucidated, and experimental confirmation of whether one of the many models proposed in the literature can describe the specific growth rate under such conditions is required.
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Biodegradation Kinetics: Effects during Utilization of Complex Substrate Mixtures by Mixed Cultures
In the fields of environmental engineering and microbial ecology, Monod kinetics, which were originally derived from laboratory experiments with pure cultures and single substrates, are frequently applied to describe the behavior of undefined mixed cultures growing with single substrates or complex substrate mixtures (83, 180, 264). In this case, the growth parameters used (Ks, µmax, and for growth-linked biodegradation kinetics, YX/s) represent overall values reflecting the growth constants of the many different strains with respect to the multicomponent substrate and the frequencies and concentrations of both the different substrates and microbial strains (a survey of Ks values for mixed populations of activated sludge was published by Pitter and Chudoba [196]). Consequently, µmax and Ks are not constants but variables in time that depend on the composition of the biocenosis and physiological state of the strains responsible for growth and substrate consumption (72, 188).
Effect of uncharacterized DOC on utilization of pollutants. In virtually all ecosystems, even oligotrophic ones, the concentration of accessible uncharacterized DOC is high enough to support considerable bacterial growth (109, 249, 250, 251). Hence, assuming simultaneous utilization of DOC together with pollutants, one must ask how uncharacterized DOC influences the rate and extent of pollutant degradation (3). The die-away curves in Fig. 8 present a straightforward theoretical calculation which gives an idea of the changes in the shape of a pollutant depletion curve (from convex to S shaped) for the case where different proportions of uncharacterized DOC are utilized simultaneously with the compound of interest. Consistent with the experimental data presented by Simkins and Alexander (229), the rate of degradation of the pollutant was enhanced and the acclimation phase was shortened when the growth of the population was supported by supplementary carbon sources. When the consumption rate of uncharacterized DOC was at least 10 times higher than that of the simultaneously utilized pollutant, the shape of the pollutant removal curves did not change any more and hence degradation became independent of the uncharacterized DOC (these effects are also dependent on the Ks values for both the pollutant and for DOC).
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Kinetics of multicomponent substrate removal.
The
substrate removal kinetics as formulated by Grau et al. (81)
(equation 9) represent a useful tooloften verified
experimentallyto describe in a simplified way the complex
substrate patterns during biodegradation experiments carried out in
batch cultures. It is assumed that the concentrations of individual
substrates in a complex mixture decrease linearly (i.e., zero-order
kinetics) until the substrates are exhausted. Thus, the overall DOC
removal rate, i.e., the sum of the individual removal rates, becomes a function of the ratio of the remaining number of components in the
mixture to the number of components initially present. If the mixture
contains a large number of components, the ratio of the number of
components remaining in the mixture to the initial number can be
approximated by, for instance, the ratio of concentrations S/S0, usually determined as DOC. To reflect the
decrease in the rate of substrate removal due to the decreasing number
of components as a function of time, the exponent n
(corresponding to an "order of reaction" similar to that of
chemical reaction kinetics) was introduced. With this exponent, it was
possible to fit any substrate depletion curve. Integration of this
model for n = 1 or n = 2 yields first-
or second-order kinetic equations, i.e., the multiple-substrate removal
kinetics most commonly found in the literature. For the initial
degradation period during which all substrates are still present in the
mixture, the overall removal pattern resembles Monod kinetics.
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Influence of initial substrate-to-biomass ratio. The majority of the methods reported in the environmental engineering literature for determination of kinetic parameters rely on simple and rapid batch cultivation or die-away experiments (86, 117, 196, 264). Unfortunately, the outcome of such kinetic experiments is highly influenced by the ratio of initial substrate to biomass concentration (S0/X0). For instance, it was recommended to use low S0/X0 ratios when conducting batch testing for determination of kinetic parameters used for the mathematical modeling of wastewater treatment plants (40). On the other hand, Kappeler and Gujer (117) advocated the use of very high S0/X0 ratios for estimation of the maximum specific growth rate of heterotrophic biomass by a respirometric method. This latter setup was criticized for delivering unrealistic values of maximum specific growth rates that do not reflect the kinetic properties exhibited by the microbial community in the environment from which it was removed (180); nevertheless, the meaning of the kinetic parameters determined at high S0/X0 ratios is obvious because they reflect the ultimate reactor performance under defined growth conditions (i.e., intrinsic kinetic properties, as discussed in reference 79). All this indicates that kinetic parameters determined by batch cultivation methods should be applied with caution (86).
The S0/X0 ratio has also been identified as an important parameter affecting the shape of growth-linked biodegradation curves determined in the laboratory. As far as we are aware, this issue was first discussed during the 1960s by Gates and Marlar (70), and later it was presented systematically by Simkins and Alexander (228) and Pitter and Chudoba (196). Dependent on the S0/X0 ratio chosen, simplification of the integrated Monod equation leads to six "new" kinetic expressions for the description of substrate disappearance. The resulting six models are (i) zero order, (ii) Monod (no growth), (iii) first order, (iv) logistic, (v) Monod (growth), and (vi) logarithmic. Unfortunately, the differences in the shape of the curves resulting from these models are usually minute, and in most cases it is difficult to statistically distinguish the different models when applied to experimental data (115). It should be pointed out that several of the presently available software packages allow us to solve differential equations by both numerical and analytical methods. Hence, the relevance of such simplifications of the original Monod model must be questioned today because the different models mainly introduce additional kinetic constants and in this way make the comparison of data from different studies even more difficult.Catabolic capacity. Unless pollution is heavy, the dominance of a particular strain with the ability to degrade this pollutant is rarely observed. Usually only a fraction of the microbial cells present have the potential to degrade a certain compound, and, furthermore, these strains are unevenly distributed and do not represent a constant fraction of the population. Likewise, the degree of induction of the catabolic enzyme system(s) responsible for the degradation can vary and usually is not known and cannot be determined easily. Therefore, kinetic measurements in undefined mixed cultures are a "black-box" approach. As a result, the kinetic parameters are usually assigned to the total biomass, not to its active part.
Whereas it is well accepted that only a fraction of the population is able to degrade a certain compound (chemical), it is less well known that the relevant catabolic enzymes are (because the cells are growing with substrate mixtures and not with single carbon sources) most probably only partially induced (as shown in Fig. 6) (15, 58). Consequently, the catabolic capacity (C) of a mixed population is a product of the number of active organisms (Ni) responsible for the substrate utilization and their respective degree of induction (Ii) (equation 10).
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CONCLUDING REMARKS AND OUTLOOK
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All of us teach and apply the well-established microbial growth kinetics almost daily. The principles seem to have been worked out long ago, and we feel little urge to question them. As a result, to most of us the field of microbial growth kinetics has become a (boring and stale) necessity rather than a field of active research. This review is an attempt to critically evaluate and discuss the foundation upon which the presently used kinetics for describing microbial growth and biodegradation processes are built (more information on historical aspects and the development of growth kinetics can be found in reference 114). Although certainly an important goal of this review was to make the reader aware of some of the most important deficiencies in this area (many of them are due to experimental difficulties), a major goal was also to indicate how to avoid the most common pitfalls and to suggest directions in which future developments might (or should) go.
One of the main messages of this review is certainly that for the description of growth of pure cultures with single growth-controlling substrates under ideal conditions, the widely applied kinetic model based on Monod's original proposal (or slight modifications thereof) is a solid basis. This was recently confirmed by using data of adequate quality for growth of E. coli with glucose (Fig. 3). However, it has also become clear that the two parameters used in the Monod model, Ks and µmax, are not constants but can vary. In the case of the substrate affinity exhibited by E. coli for glucose, the range within which Ks can change is enormous (and the data in the literature indicate that other organisms also behave in this way). Hence, we must accept that it may never be possible to describe the kinetic properties of a microbial cell with a single set of constants. After accepting this, it becomes of great interest to know the boundaries of the feast-and-famine kinetic properties of an organism, how they are influenced by the physiological conditions, growth substrates and so on, and what the timescale of such an adaptive response is and to elucidate the molecular and genetic events that are responsible for this process.
A first insight into growth kinetics under more complex conditions is provided by the recent results obtained for the kinetics of growth controlled by more than one carbon source (i.e., during mixed-substrate growth). Clearly, the kinetic data presented here for E. coli and the methylotrophic yeast strongly suggest that simultaneous utilization of carbon sources will, as a rule (rather than an exception), result in reduced steady-state concentrations of all substrates. This strategy allows a nutritionally "multicompetent" organism to utilize the available growth-controlling resources more efficiently (i.e., to lower the concentrations). Theoretically, this should allow the utilization of compounds at concentrations at which they will no longer support growth on their own (i.e., below their threshold concentration for growth). Under carbon-controlled conditions, the ability to grow with several carbon substrates simultaneously should result in enhanced competitiveness over an organism that is able to utilize only one or a few of the substrates present. Indeed, there are a number of reports in the literature showing that nutritionally versatile strains outcompeted specialist strains under mixed-substrate growth conditions (54, 77, 232). Although the actual concentrations of the substrates were not measured in the culture in any of these cases, it seems the most plausible explanation that competition occurred at the level of substrate concentration. In contrast to the traditional competition of two organisms for a single substrate, competition under mixed-substrate growth conditions is still in its infancy (76), although it is obviously an area of crucial importance for understanding the growth behavior of microbial strains in ecosystems. Considering in addition the ability of microbial strains to modulate their kinetic properties according to the growth environment, one can predict that there is still a lot to discover.
Finally, it should be pointed out that we have so far always considered that growth of a microbial culture is controlled by homologous nutrients, i.e., nutrients that fulfill the same physiological function (e.g., as a carbon source). However, it has been demonstrated within the last decade that microbial growth can be stoichiometrically limited at the same time by two or more heterologous nutrients, for example by carbon and nitrogen (57, 58), and there is now considerable evidence that under such conditions growth is probably also controlled by these nutrients. To date, the subject of multiple-nutrient-controlled growth has been addressed only theoretically (10, 17), and the few data that presently exist (214) do not allow one to draw conclusions on the kinetic relationship between the concentrations of growth-controlling nutrients and growth rate. However, the observation that in aquatic ecosystems the growth of algae and bacteria is probably frequently controlled by several nutrients simultaneously and not by a single nutrient (183, 184, 254) points out the ecological relevance of multiple-nutrient-controlled growth.
It is not difficult to foresee that this information will be most important for understanding and successful application of growth kinetics in more complex environments than just laboratory cultures.
ACKNOWLEDGMENTS
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We thank numerous colleagues for helpful discussions, and we particularly thank Matthias Bally, Václav Chaloupka, Andres Käch, Urs Lendenmann, and Anita Mock for careful experimental measurements upon which the theoretical considerations are based. We also thank H. Harms, K. Demnerova, and A. J. B. Zehnder for critically reviewing the manuscript. K.K. is also indebted to P. Grau and J. Chudoba for introducing her to the "classical" mode of growth kinetics as well as to T. Egli for introducing her to the "postclassical" modes.
We are grateful for the support provided by Swiss Federal Institute for Environmental Science and Technology (EAWAG). The research on mixed-substrate kinetics was financed by the Swiss National Science Foundation (projects NF-3.474.-083, 31-9210.87, 31-30004.90, 31-30004.90/2). Financial support for the work on NTA came from both the Research Commission of ETH Zürich (project 0.330.089.86) and Lever (Switzerland)/Unilever Merseyside (England).
FOOTNOTES
* Corresponding author. Mailing address: EAWAG, Ùberlandstrasse 133, CH-8600 Dübendorf, Switzerland. Phone: 41-1-823 5158. Fax: 41-1-823 5547. E-mail: egli{at}eawag.ch.
Present address: Vitamins and Fine ChemicalsBiotechnology, F. Hoffmann-La Roche Ltd., CH-4070 Basel, Switzerland.
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Microbiology and Molecular Biology Reviews, September 1998, p. 646-666, Vol. 62, No. 3
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