COMMENT
Limnol. Oceanogr., 31(2), 1986, 453-456
Q 1986, by the American Society of Limnology
and Oceanography,
Inc.
Affinity of organisms for substrate
The dilute nature of nutrients in aquatic
systems has resulted in particular attention
to the ability of microorganisms to sequester substrate. This ability is described in
terms of affinity-a
term which has been
defined in at least 18 ways (Button 1985).
According to my dictionary, affinity is an
attractive force between two substances or
particles (Webster’s 1976: S.V. “affinity”).
Traditionally
it was thought of as a binding
constant (Guldberg and Waage 1879). The
concept of a Michaelis constant K, (Michaelis and Menten 19 13) stems from the
observation of rates of enzymatic processes
which saturate and the idea that the constant reflects the ratio of rate constants for
substrate binding and release. Monod ( 1942)
observed that the rates of growth of bacteria
also followed saturation kinetics and used
the Michaelian relationship as a convenient
descriptive vehicle. Later when describing
substrate transport he considered the organisms to be at steady state (i.e. transport
components at equilibrium
with substrate)
and applied Michaelian theory. Affinite was
taken as a ratio of the rate of substrate-release/substrate-binding
by Rickenberg et al.
(1956), which led to the persistent and questionable (Button 1983) concept that the affinity of an organism for a substrate is related to (reciprocal of) a Michaelis constant
K,. Rather than rates of binding/release,
substrate accumulation has to do with the
number of transporter molecules and their
effective receptive area, the nutrient concentration at these receptors, and the electrochemical potential across the organism
surface (Skulachev 1984).
Analyses of nutrient dynamics in aquatic
systems and the substrate sequestering ability of osmotrophic organisms require data
that specify the rate of transmembrane
transport at a given substrate concentration
and biomass. Saturation is not in question
since concentrations of ambient substrates
seldom approach K,, the concentration at
half-maximal transport rate. When working
on the mechanism of maltose transport by
a Staphylococcus (Button et al. 1973b), we
noticed that usual rates of radioactive substrate accumulation
amounted to a very
small flux. Subsequent studies with phosphorus- and carbon-containing
nutrients
yielded uptake rates that were usually insufficient to account for observed growth at
given concentrations;
however, modification of protocol minimized this dilemma.
Rates at low nutrient concentration
were
second-order in substrate and biomass so
that the intervening rate constant was taken
as a measure of the ability of the organisms
to transport nutient. This whole-organismbased rate constant was called the affinity
by Law and Button (1977). The adjective
“specific” was added later to suggest a base
of biomass as in specific growth rate and to
distinguish from “apparent affinity” which
included a threshold term (because it was
calculated from growth kinetics) together
with yield (Robertson and Button 1979).
Adjectives such as “apparent” and “growth”
should probably be dropped because they
lack the theoretical base which makes affinity an attractive parameter. Often only one
of several products of nutrient transport is
measured, such as radioactivity
accumulated or a metabolic product released. Then
the transport apportioned to a particular
product is designated the partial affinity
(Button and Robertson 1986), a term which
is useful for balancing fluxes while retaining
precision in definitions.
Because of historical intermingling
of
growth and transport kinetics with Michaelis-Menten-Henri
kinetics, concentrationdependencies of microbial processes are traditionally tied to IS,. Michaelian kinetics
specify rate as a precisely hyperbolic-shaped
453
454
Comment
function of concentration. These kinetics are
often manipulated as in enzyme kinetics because resulting reciprocal plots of precisely
Michaelian profiles are linear and ease analysis. Although departure from linearity in
reciprocal plots is often taken as a measure
of ambient substrate concentration or Michaelis constant (Pick et al. 1984), inhibition of various sorts (Cleland 1970), numbers of transport systems (Azam and Hodson
198 l), thresholds, and other phenomena interfere. For example the region of curvature
in specific-growth-rate/substrate-concentration curves can be set by the nature of a
changing scale (Robertson and Button 1979).
Thus if an organism consumes additional
nutrient to form a particular biomass at a
high growth rate rather than a low one,
thereby becoming enriched in that nutrient,
and if the nutrient uptake rate is calculated
from the rates of growth together with the
yield associated with each, then the plot of
nutrient uptake on concentration will curve
down toward horizontal
because of the
combined demands for substrate due to both
increased synthesis of biomass and synthesis of biomass enriched in substrate.
Another sort of nonsaturation-dependent
curvature can be obtained in transport relationships if uptake rates are normalized
to the nutrient content of the biomass. For
example if uptake rates are based on particulate nitrogen (Dugdale et al. 198 1) and
the nitrogen content of the cell increases
with growth rate (the expected situation for
all nutrients: Droop 1983), then measurements of uptake rates at high nitrogen concentrations
(and correspondingly
high
growth rates) will depend on less biomass
than at low concentrations of nitrogen. Again
the uptake kinetic curve will bend down toward horizontal. If limiting nutient or its
products fill rate-limiting
steps along the
pathway at the concentrations
observed,
saturation can add to the curvature observed in either of the above examples.
Sometimes these influences can dominate
curvature more than do effects of saturation
(Robertson and Button 1979).
Healey ( 1980) suggested use of the parameter V,,,IK, (maximal uptake rate/nutrient
concentration at half-maximal rate) to compare uptake capabilities of microorganisms.
This term was originally used in enzyme
kinetics, where I//K, expresses the fastest
possible successful combination rate of substrate with enzyme (Cleland 1970) where V
is the maximal rate of catalysis. Goldman
and Glibert (1983) referred to this parameter as the affinity. If I’,,, is defined in terms
of substrate transport rate per unit biomass
and the kinetics are perfectly hyperbolic,
then V/K, is equivalent to our original definition of affinity, the initial slope of a plot
of rate vs. substrate concentration, because
the slope passes through the point V,,,, K,
(Button 1979). However multiple transport
systems tend to straighten Michaelian curves
(Button 1983) and V,,, values are often indeterminate (Button et al. 1973a). A preferable general definition of the affinity remains a,, the constant that relates uptake
rate v to both concentration, Aout, of substrate A and to biomass X as defined by
v = a,A,,,X.
(1)
Units are liters g-cells-l h-l, ones preferred
because they are general, adhere to the Webster’s (1976) definition of the force between
a substance and particle, define both the
substance and the particle, and have a theoretical base (see below). Units of per cell
persist (Paris et al. 198 1) and are compatible
with Webster’s (1976) defintion, but these
present an inadequate comparative index of
nutrient sequestering power because of inter- and intraspecies variation in cell size.
Currie and Kalff (1984) reported affinities
in units of liters mol-l h-l because rate was
reported in mass substrate taken up per mass
of substrate in the organisms. But internal
substrate does not effect uptake, the organisms do. Various other common ways of
reporting maximal rate such as doublings
per day or substrate mass cell-’ h-l result
in equally peculiar units for reported values
of V/K.
The theoretical base of affinity is that the
second-order rate constant for each transporter molecule or complex involved at the
rate limiting step for accumulation of the
substrate in question can be expressed in
terms of molecular rate constants, put on a
per gram cell basis, and summed to give the
affinity as defined by Eq. 1 (Button et al.
198 1). Rates are either measured at concentrations where saturation is insignificant
or extrapolated to conditions of zero satu-
Comment
ration as indicated by a”,, or else measured
at higher concentrations where the concentration at which the affinity is measured is
defined by a superscript. All three of these
values are usually identical within experimental error. In practice, data fit to a hyperbola from which the initial slope is calculated give a slightly larger value for aoA
than if the value is obtained from the initial
slope of a plot of v against A,,, for reasons
not completely understood.
The Michaelis constant for transport, in
contrast, is taken as a measure of the concentration where the resistance of substrate
flow into the organism is impeded by substrate (or its products) already contained in
the internal transport sequence. The Michaelis constant for growth Kp is a mixed
term which compares the affinity of the organism for substrate with its maximal rate
of growth. There does appear to be a correlation between the Michaelis constant for
transport K, and the maximal rate of transin most published data. Although
Poti
vmax
presently based on an incomplete understanding of the molecular mechanisms of
active transport, this correlation is seen as
a reflection of the strength of the forces between transporter and the intermediate form
of substrate during movement into the cell.
Acting on the intermediate form, the same
forces could be involved both in collecting
untransported intercellular substrate and in
retarding its intracellular release. Expressed
as rate constants usual to enzyme kinetics
(Cleland 1970), the term for release appears
in the numerator of definitions for both K,,,
so the correlation could have a
and
vrnax,
mechanistic base. What specific affinity adds
to the kinetics of transport by organisms is
provision for recognizing the characteristics
and content of the transporters involved;
whereas in enzyme kinetics the analogous
term is “enzyme content,” which is dropped.
Affinity values are of use in considering
aquatic processes because of their theoretical base and because they give an absolute
measure of nutrient processing at specific
nutrient concentrations and biomass. However nutrient kinetic data in the literature
are often without an indication of biomass
so that the value cannot be calculated. Where
biomass is given, variation among calculated affinities seems to be quite large; a
455
factor of 4 X lo4 for glucose, lo5 for ammonium, 4 x lo3 for phosphate, 3 x lo4
for oxygen, and lo3 for vitamins (Button
1985). Although the state of induction for
substrate (such as a hydrocarbon) can have
a marked effect on affinities for certain substrates, in most cases workers have apparently utilized organisms cultured and attuned for nutient uptake studies. Because of
large variation in aA values, the fact that
they are usually very small as compared to
uptake requirements, and the fact that we
have difficulty in observing uptake rates that
attain calculated values, reported variations
in affinity values appear to contain substantial underestimates. On the other hand the
affinity calculated from turnover rates (tR)
of amino acids in seawater reported by Ferguson and Sunda (1984), assuming a biomass of 2 X 1O-l3 g bacterium-l, was aA =
t&l=l = 1,700 liters g-cells-l h-l. This is the
highest value for a carbon source reported,
and the Michaelis constants for tranport at
< l-6 nM were about lo3 lower than those
usually observed for bacterial isolates. A
speculative explanation is that most marine
bacteria have large affinities and transport
constants and are unculturable because they
lack sufficient metabolic controls for laboratory culture.
Wheeler et al. (1982) noticed the effect of
pool loading on uptake, which was particularly apparent in their unmanipulated
kinetic plots at a series of incubation times.
A specific affinity for ammonium uptake by
phytoplankton of 403 liters g-cells-’ h-l can
be computed from their data. Bell (1983)
measured the utilization
of algal extracellular products by bacteria, but specific affinity calculations from those data were
complicated by the probability that bacterial populations measured with spread plates
underestimated the effective biomass. The
specific affinity of phytoplankton
can often
be computed from existing data by estimating the chlorophyll
content of the organisms. If we use a value of 0.2% chlorophyll wet weight, then the specific affinities
for ammonium
found by Carpenter and
Dunham (1985) range around 400 liters gcells-’ h-l, but only 2 1 for phosphate as
reported by Pick et al. (1984).
A test of the significance of the measured
uptake rate to a population is that the max-
Comment
456
imal specific growth rate (p) obtainable at
any particular affinity and substrate concentration (not to be confused with the maximal specific growth rate at saturation, pm,,)
is simply
P = aA&, GA
(2)
where YXA is the yield of biomass produced
from the substrate consumed. I hope that
future publications
utilizing
uptake and
growth kinetics will be sufficiently complete
so that the specific affinity of the population
can be determined and that the value will
be subjected to a test of absolute significance
as presented by Eq. 2. Then the importance
of a particular substrate concentration can
be ascertained.
D. K. Button
Institute of Marine Science
University of Alaska
Fairbanks 99775- 1080
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