Theoretical note: tests of synergy in sweetener mixtures.
ABSTRACT Some methods for examining the additivity of sweeteners, and their synergy in mixtures depend upon setting component concentrations on the basis of sweetness equivalence, usually to a sucrose reference. These methods may under- or over-predict the sweetness of a mixture, leading to spurious claims of synergy or mixture suppression. This paper points out one problem with one such popular method, in that the method can lead to a conclusion that a substance would synergize with itself. To the extent that self-synergy is an illogical conclusion for a mixture comparison, such a method should be avoided in tests of synergy. The sweetness equivalence approach is contrasted with a simpler approach based on concentrations that does not lead to conclusions of self-synergy.
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ABSTRACT: High intensity sweeteners were evaluated for sweetness and bitterness intensity using time-intensity scaling. Mean intensities of 50:50 mixtures as well as the single sweeteners were used to compute predicted scores which were compared to the observed scores as a means of evaluating additivity in the mixtures. Concentration-dependent effects of subadditivity, additivity and hyperadditivity were observed within some sweetener pairs, but these did not follow any consistent pattern across sweeteners. Synergy, a special case of hyperadditivity evaluated by comparing predicted to observed scores, was seen in mixtures of aspartame and acesulfame-K at all concentrations. Aspartame/saccharin blends were synergistic only at the lowest concentration tested, despite the structural similarity between acesulfame-K and saccharin. Blends of sucrose/aspartame and acesulfame-K/saccharin did not exhibit synergy. Comparisons based on ratings of initial sweetness rather than the whole time-intensity curve, reflected previous findings of synergy in some sweetener pairs.01/1992;
- 7??e construction and prediction of psychophysical power functions for the sweetness of equiratio sugar mixtures A JND-scale/category scale convergence in taste Investigation of synergism in binary mixtures of sweeteners. 753-767..
Chem. Senses 23: 447-451, 1998
Theoretical Note: Tests of Synergy in Sweetener Mixtures
Harry T. Lawless
Department of Food Science, Stocking Hall, Cornell University, Ithaca, NY 14853, USA
Correspondence to be sent to: Harry Lawless, Department of Food Science, Stocking Hall, Cornell University, Ithaca, NY 14853, USA
Some methods for examining the additivity of sweeteners and their synergy in mixtures depend upon setting component
concentrations on the basis of sweetness equivalence, usually to a sucrose reference. These methods may under- or over-
predict the sweetness of a mixture, leading to spurious claims of synergy or mixture suppression. This paper points out one
problem with one such popular method, in that the method can lead to a conclusion that a substance would synergize with
itself. To the extent that self-synergy is an illogical conclusion for a mixture comparison, such a method should be avoided in
tests of synergy. The sweetness equivalence approach is contrasted with a simpler approach based on concentrations that does
not lead to conclusions of self-synergy.
The claim of mixture synergy implies that a combination of
two stimuli is perceived as more intense than a prediction of
the resulting intensity based on the properties of the
components of that mixture. This conclusion often has
commercial importance, insofar as synergistic results may
permit reductions in ingredients and thus cost savings in
food formulations. However, from the psychophysical side,
the demonstration of synergy is not straightforward, and
depends upon the model that one adopts for making the
critical comparison. Synergy is thus a controversial issue.
One critical view of this phenomenon is that if you find
synergy, you merely have failed to predict your result—in
other words, you have a bad model (D.A. Stevens, personal
Most researchers today agree that a model should take
into account the psychophysical functions of the compon-
ents. The psychophysical functions are usually non-linear,
and may follow mathematical relationships between
concentration and intensity that follow the power function
of Stevens or the semi-hyperbolic equation of Beidler,
depending in part on the scaling method employed and
the range of stimuli that are examined. Several years ago,
Bartoshuk and colleagues recognized the potential connec-
tion between empirical observations of mixture synergy
(or suppression) and the curvature of the psychophysical
function, proposing that substances with negatively acceler-
ated psychophysical functions (power function exponents
less than one) would tend to show suppression, while
substances with accelerating dose-response curves (power
function exponents greater than one) would synergize
(Bartoshuk, 1975; Bartoshuk and Cleveland, 1977). Later,
Frijters and co-workers demonstrated that with equiratio
mixtures, the psychophysical function would usually produce
an exponent between that of the components' individual
functions, a kind of compromise model (Frijters and Oude
Ophuis, 1983; De Graff and Frijters, 1987, 1988).
Frank et al. (1989) took this logic one step further, and
asked whether a claim of synergy was valid, unless the
mixture intensity was in fact higher than one would predict
based upon consideration of the psychophysical functions
of the components. Thus, the whole functions could be com-
pared, rather than combinations tested against individual
points. This approach had the appealing benefit of being
able to test and sometimes demonstrate synergy in the
response surface even though the individual component
functions were negatively accelerated.
However, the test for individual concentrations remains a
common phenomenon, since foods are formulated at
specific ingredient optima, and the entire psychophysical
function is rarely considered. A simple extension of the
equiratio approach with the consideration of psycho-
physical functions is to compare mixtures to components
based on a slice through the response surface, connecting
points of equal intensity. Thus, a concentration of each
component equisweet to 10% sucrose could be chosen, and
the intensity of the 50/50 mixture (or 75/25 or 25/75, etc.)
compared to the component intensities (or their average if
they are not quite matched).
Now, the question remains of what is to form the mixture
components. In the model shown in Figure 1, the slice
i Oxford University Press
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448 H.T. Lawless
component concentration-based comparison
(two dimensional plot)
I "unmixed" component B
N 50/50 Mixture
"unmixed" component A
Concentration, Component A
Three dimensional (response surface) plot
function, sweetener B C o n c e n t r a t i o n
Does mixture sweetness
y S lie above or below the intensity value
N connecting components?
function, sweetener A
Figure 1 Component concentration-based test of sweetener synergy. Mixtures are constructed along a constant sum (100% total) concentration line
(upper panel), generally connecting concentrations of the two components adjusted to be equally sweet. The lower panel shows the three-dimensional plot
for a response surface. The test of synergy asks whether the obtained sweetness of the 50/50 mixture lies on a response surface above the sweetness levels
of the unmixed components. In a more complete test, the psychophysical function on the response surface connecting all 50/50 mixtures can be compared
to the psychophysical functions of the unmixed components.
through the response surface uses the 50% concentration
points in constructing the mixtures. The mixture can readily
be made by combining equal volumes of the parent
(100% solutions). We will refer to this as the component
concentration comparison. This is a common approach (e.g.
Ayya and Lawless, 1992). It makes the sensible prediction
that a substance added to itself will show simple additivity.
However, the perceived intensities at the 50% concentration
levels may not represent one-half the intensity of the 100%
points, due to the curvature of the psychophysical function.
They may also be different in sweetness from the 50% level
of sucrose based on the equivalency match at the higher
Because perceived intensity of the 50% components is not
considered in the concentration-based comparison, others
have proposed that the comparison should be based on a
50% intensity level, rather than concentrations. The 50%
concentration level might be considerably off from the
50% intensity level or from the sucrose equivalent match to
one-half the unmixed component concentrations. Carr et al.
(1993) and Schiffman et al. (1995), in several extensive
studies of sweetener interactions, chose to work on the
intensity basis in choosing the 50% level for a binary
mixture. In this model, the comparison is based on the
concentrations that produce an intensity match to sucrose
at one-half the unmixed component concentration. For
example, in order to test the additivity of two sweeteners at
the 6% sucrose intensity level, the component concen-
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Tests of Sweetener Synergy 449
for hypothetical intensive sweetener
with positively accelerated sucrose matching function
showing illusory "synergy" in self-mixtures
c50% c10equiv c "self blend"
= 2 c50%
concentration of sweetener equisweet to 10% sucrose
J>50% = concentration of sucrose at one-half, i.e. 5%
C"50% = Concentration matching S5g<yo, to be used in "blend"
c "self blend" =t w i c e c50% ( = c50% + c 50%)
s "self blend" = sucrose equivalent in response to C »se|f b|e n d»
Since S "Seif biend"»
But this is an illusion due to the nonlinear sweetness matching function.
S1Oequiv • we conclude synergy.
Figure 2 The problem of illusory synergy arises when a substance has a non-linear matching function to sucrose, and the components concentrations are
based on intensities relative to sucrose equivalence. The concentration of the component is shown on the abscissa, and the sucrose concentration match
plotted on the ordinate. In the function shown here, the sweetener is positively accelerated relative to sucrose. Therefore, the concentration chosen as a 50%
point in the blend (based on the y-axis) produces a much greater than predicted sucrose match when doubled as a self-mixture. Thus, anchoring to the
sucrose equivalent intensity level would lead to a conclusion that the substance had synergized in a mixture with itself.
trations in the blend would be chosen such that they were
matched to 3% sucrose. This model tends to anchor to the
psychophysical function of sucrose, but does not choose
component concentrations in the blend that might be too
high or two low on their own psychophysical functions. It
also has the attractive property of producing simple
additivity when sucrose itself formed the components.
Obviously, adding 3% sucrose to 3% sucrose will evoke the
same response as 6% sucrose. This we will refer to as the
Carr et al. (1993, p. 226) formalized this test of synergy
with the following equation:
% synergy = 100 [SE(blend)/(SE(100% A) + SE(100% B)/2) - 1]
where SE(blend) is the sucrose equivalent concentration of
the blend obtained from the experiment, SE(100% A) is the
sucrose equivalent of unmixed component A and SE(100%
B) is the sucrose equivalent of the unmixed component B.
In this test, the components of the mixture, if equisweet,
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450 H.T. Lawless
would be the concentrations of A and B producing sucrose
equivalents equal to one-half the sucrose concentration
matching 100% A and that matching 100% B, respectively
(see Figure 2).
The problem with this comparison is that it can lead
to a demonstration of synergy when a substance is added
to itself. If we accept the premise that adding along a
substance's own psychophysical function is, by definition,
simple additivity, then the method of comparison must be
flawed. So, by definition, a compound cannot synergize with
itself (this is my premise) as mixing it with itself only follows
its own psychophysical function. Here is the problem: if the
substance has a non-linear concentration relationship in its
isointensity plot against sucrose, the self-blend can move
either too high or too low on its own psychophysical
function and produce the appearance of synergy or sup-
pression. The shape of the iso-intensity function against
sucrose has not been taken into account, and any change in
function shape from linearity can 'cause' illusory synergy or
The following example will help illustrate this point. Let
us take 50/50 mixture blends as an example. The author's
comparison is to find the concentration producing that level
of sweetness which is equal to the sucrose concentration at
50% of the parent concentrations (parent concentration
being equisweet to 10% w/v sucrose, a common benchmark).
So the location of the concentration to be present in the
blend requires finding the 50% sweetness level on the
response axis and then interpolating the appropriate con-
centration, but when the concentration-response function is
curved relative to sucrose and positively accelerated, the
curvature in the response function causes the self-mixture
blend 'to synergize' as the self-mixture concentration is
higher than the parent concentration. If we accept the
premise, then, that self-mixtures cannot synergize, this
model leads to a false conclusion and therefore must be
flawed. The opposite effect can be shown for psychophysical
functions that are negatively accelerated, i.e. that they will
show a false suppression effect in self-mixtures under this
In conclusion, a variety of models have been applied to
test the additivity of mixtures. One approach is simply
to add the component intensities, and compare that sum to
the intensity of a mixture which contains both components
at their original intensity level. However, this method of
adding together mean ratings assumes that the scale used
has interval properties and is unbounded. Frank et al. (1989)
recognized that a bounded scale would show hypoadditivity
at higher levels and thus a test of synergy must look beyond
simple additivity of responses. With bounded scales such as
category ratings or line-marking techniques, perceptual-
based additivity is bound to fail as the top of the scale
imposes an upper limit on response values. Also, as the
search for a true interval scale remains elusive, most
researchers avoid this simple test. Even unbounded scales
such as magnitude estimation have their detractors who
question whether such allegedly ratio scales have even
interval properties (Anderson, 1974; Birnbaum, 1982;
So some researchers in the area of mixtures have turned
to tests based on fractional concentrations, rather than
addition of intensities. One common approach has been
to choose equi-intense concentrations of two components,
and then blend them in various percentages of those
concentrations to produce a constant total of 100%. This
component concentration approach has good functional
value, as synergistic combinations (those producing higher
intensity than the components alone) logically entail the
possibility of reductions in concentrations to maintain
equal intensity and thus a cost savings in product de-
velopment. However, critics of this view point out that the
non-linear nature of the dose-response curve may result in
selection of component concentrations (e.g. 50% of each
component's starting concentration) which are much greater
than 50% of their parent concentration's intensities, so
'synergy' from such combinations should be in no way
surprising. The alternative proposed is to choose the
concentrations based on a 50% sucrose intensity match.
However, as shown above, this can lead to the questionable
outcome of a substance synergizing with itself, which many
would not accept as a true case of mixture synergy. The same
problem will occur if a simple 50% intensity level is chosen
as the basis for the component concentrations in the blend.
That is, the j-axis in Figure 2 can be changed to sweetness
intensity (rather than the sucrose match) and produce the
same demonstration of apparent synergy in a self-blend
when the psychophysical function is concave upward.
As previously demonstrated by Schiffman et al. (1995),
the component concentration comparison and the intensity
anchored comparison do not always produce the same
results when tests of synergy are applied to binary sweetener
mixtures. Claims of so-called taste enhancement may be
possible to substantiate by the choice of a more or less
conservative model, or one that is favored by the psycho-
physical intensity relationships of the components. It is
incumbent upon researchers in the fields of taste and
olfaction to question carefully what model and test was
applied in any 'demonstration' of synergy, and whether the
assumptions and implications of that model are in fact
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