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Antimicrobial Agents and Chemotherapy, December 2001, p. 3328-3333, Vol. 45, No. 12
0066-4804/01/$04.00+0 DOI: 10.1128/AAC.45.12.3328-3333.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
Fractional Maximal Effect Method for In Vitro
Synergy between Amoxicillin and Ceftriaxone and between Vancomycin
and Ceftriaxone against Enterococcus faecalis
and Penicillin-Resistant Streptococcus
pneumoniae
Norbert
Desbiolles,
Lionel
Piroth,
Catherine
Lequeu,
Catherine
Neuwirth,
Henri
Portier, and
Pascal
Chavanet*
Infectious Diseases Department and
EA562, University Hospital, Dijon, France
Received 25 September 2000/Returned for modification 29 April
2001/Accepted 12 July 2001
 |
ABSTRACT |
In the present study we assessed the use of a new in vitro testing
method and graphical representation of the results to
investigate the potential effectiveness of combinations of amoxicillin
(AMZ) plus ceftriaxone (CRO) and of CRO plus vancomycin (VAN)
against strains of Streptococcus pneumoniae highly
resistant to penicillin and cephalosporins (PRP strains). We
used the fractional maximal effect (FME) method of time-kill curves to
calculate adequate concentrations of the drugs to be tested rather than
relying on arbitrary choices. The concentrations obtained, each of
which corresponded to a fraction of the maximal effect, were tested alone and in combination with the bacterial strains in a broth medium.
Synergy was defined as a ratio of observed effect/theoretical effect,
called FME, of greater than 1, additivity was defined as an FME equal
to 1, and antagonism was defined as an observed effect lower than the
best effect of one of the antibiotics used alone. The area between
antagonism and additivity is the indifference zone. The well-known
synergy between amoxicillin and gentamicin against a reference strain
of Enterococcus faecalis was confirmed, with a best FME
equal to 1.07. Two strains of PRP, strains PRP-1 and PRP-2, were
studied. The MICs for PRP-1 and PRP-2 were as follows: penicillin, 4 and 16 µg/ml, respectively; AMZ, 2 and 8 µg/ml, respectively, CRO,
1 and 4 µg/ml, respectively; and VAN, 0.5 and 0.25 µg/ml,
respectively. For PRP-1 the best FME for the combination AMZ-CRO was
1.22 with drug concentrations of 1.68 mg/liter for AMZ and 0.17 mg/liter for CRO; the best FME for the combination VAN-CRO was 1.75 with VAN at 0.57 mg/liter and CRO at 0.17 mg/liter. For PRP-2 the best
FME obtained for the combination AMZ-CRO was 1.05 with drug
concentrations of 11.28 mg/liter for AMZ and 0.64 mg/liter for CRO; the
best FME obtained for the combination VAN-CRO was 1.35 with VAN at 0.25 mg/liter and CRO at 1.49 mg/liter. These results demonstrated the
synergy of both combinations, AMZ-CRO and VAN-CRO, against PRP strains
at drug concentrations achievable in humans. Consequently, either of
the combinations can be proposed for use for the treatment of PRP infections.
| |
INTRODUCTION |
The emergence of strains of
Streptococcus pneumoniae highly resistant to penicillin and
cephalosporins (PRP strains) (5, 10) and, often, to
other classes of antimicrobial agents (33) complicates
empirical treatment of pneumococcal infections. Therefore, all
potential modalities for the treatment of these infections must be
considered (6). Ceftriaxone or vancomycin is often one of
the drugs recommended for the treatment of severe infections due to PRP
such as meningitis. However, a combination of amoxicillin and
ceftriaxone could also be a candidate for the treatment of such infections.
In this context, our purpose was, first, to investigate the in
vitro interaction between amoxicillin and ceftriaxone and between vancomycin and ceftriaxone against PRP and, second, to identify the
range of concentrations that are of clinical interest.
The traditional methods used to test the in vitro interactions between
drugs are not very satisfactory, with difficulties in the
interpretation of the results (16). All these methods come
from two original models: the Loewe additivity model (24), illustrated by isobolograms, and the Bliss independence model (4), illustrated by dose-effect curves. The checkerboard
method, with fractional inhibitory concentration indices and
isobolograms, and the killing-curve method are used. Both methods have
their advantages and drawbacks (7, 8, 32, 36, 37).
There is also a great disparity in the definitions used to characterize
the interactions between drugs. For example, the limit value of
fractional inhibitory concentration indices used to define antagonism
varies from 1 to 8 according to previous studies. This disparity
also appears in the duration of the times of killing, which can
vary from 4 to 24 h and even longer (2).
The lack of standard definitions causes major problems, as it is
impossible to compare the results of different studies.
Several investigators have looked further into the interpretation of
the interactions between drugs (3) or the graphical representation of bacterial killing (34) or have
proposed the use of the area under the curve (AUC) of bacterial killing
as a criterion (1). Thus, additivity, synergy, antagonism,
and autonomy or indifference have been defined (17, 21,
35).
Methods based on mathematical models have been used as a general
approach to study the interactions between drugs (15). By
these methods, the characterization of the dose-effect curve of each
agent alone is critical; for this, the better-adapted structural model
is the Hill model applied to a Michaelis-Menten curve.
According to these principles, the use of the AUC obtained from killing
curves seems to be one of the better ways to evaluate in vitro the
interactions of drugs used together in comparison with the
theoretical AUC (26).
A further study has been carried out by using the fractional maximal
effect (FME) method (23). The main characteristic of this
method is that it tests calculated and not arbitrarily chosen concentrations of drugs. As a result, a maximal effect
(Emax) can be determined for each drug.
The theoretical effect of the combination is calculated by adding the
effects of each antibiotic used alone at the concentration tested in
the combination. This theoretical effect is then compared with the
effect obtained during the experiment.
The different interaction areas are defined as follows: additivity is
an observed effect equal to the theoretical effect, and the ratio
between them is equal to 1; synergy is an observed effect higher than
the theoretical effect, and the ratio between them is more than 1;
antagonism is an observed effect lower than the theoretical effect, and
the ratio between them is less than 1.
For the graphical representation, Li et al. chose the isobologram
method (23).
In the present study, we used the isobologram method with two
modifications: first, as proposed previously (17, 35), we introduced indifference as a fourth zone of interaction; second, the
graphical representation of the concentration-effect curve in two
dimensions was preferred, as it allows a global illustration of the
effects of each drug alone, drug-drug interactions, and theoretical addition.
| |
MATERIALS AND METHODS |
Drugs.
Ceftriaxone was obtained from Roche (Nutley, N.J.),
vancomycin was obtained from Lilly Laboratories (Indianapolis, Ind.), and amoxicillin was obtained from SmithKline Beecham (Brentford, United
Kingdom). The drugs were reconstituted as recommended by the manufacturers.
Strains.
Two strains of PRP (strains PRP-1 and PRP-2)
isolated from a clinical specimen were used. The penicillin MICs for
strains PRP-1 and PRP-2 were 4 and 16 mg/liter, respectively.
Strains were identified by common tests and were stored at 
70°C in
brain heart infusion (BHI) with 15% glycerol. Enterococcus
faecalis CIP 76117 was used as a reference strain and was provided
by the Institut Pasteur (Paris, France).
In vitro testing. (i) MIC.
MICs were determined by the agar
dilution method described by the National Committee for Clinical
Laboratory Standards (31).
(ii) Killing curves.
The organisms were grown in BHI for
4 h at 37°C and were then adjusted by dilution in BHI to obtain
a final inoculum of 5.5 × 106 organisms per
ml. The antibiotics were diluted in BHI to obtain the different
concentrations tested. To obtain a 1.9-ml final volume in 5-ml sterile
hemolysis tubes, 0.1 ml of the bacterial inoculum was finally added to
the tubes. They were then placed in an incubator at 37°C. A 100-µl
volume was then removed; and cultures were performed after serial
dilutions at 0, 3, 6, and 12 h for PRP strains and 24 h for
E. faecalis on Mueller-Hinton agar plates
supplemented with sheep blood at 37°C and in 5%
CO2 for S. pneumoniae. These counts
were then expressed as log number of CFU per milliliter and were used
to calculate the AUC by using the trapezoidal method.
This protocol was used with the concentrations of antibiotics in each
tube required to achieve bactericidal activity, as well as with the
antibiotics alone and in combination, to create the killing curves.
Criterion to achieve concentrations tested and
calculations.
We derived a method from the FME method of time-kill
curves in which the concentrations of the drugs to be tested are
calculated from the bactericidal activity curves and are chosen rather
arbitrarily. The AUC was the criterion chosen to construct the
bactericidal activity curves in triplicate for each antibiotic; the
effect (E) is equal to the ratio 1/AUC. A nonlinear
regression (the formula used was E = Emaxn × Cn/EC50n + Cn), performed with SPSS software (SPSS
Inc., Chicago, Ill.), was applied to each curve (for each concentration
C) to determine the following constants:
Emax (maximal effect),
EC50 (the concentration that produces one-half of
the Emax), and n (Hill's coefficient).
The FME is defined by the ratio observed effect/theoretical
effect.
Next, the two antibiotics (antibiotics A and B) are combined so that
the sum of FME is always equal to 1. The following pairs
were tested:
0.1FME
A + 0.9FME
B,
0.3FME
A + 0.7FME
B,
0.5FME
A + 0.5FME
B,
0.7FME
A + 0.3FME
B, and
0.9FME
A + 0.1FME
B.
The corresponding concentrations (
C) to be tested alone and
in combination were calculated by using the appropriate formula:
C = (FME × EC
50)/(1
FME).
Because the relation between the two antibiotics is not linear, the
theoretical effect of the combination had to be calculated
by using the
following formula (M. Katzper, personal communication):
These results (the FME for each test) were then plotted versus
the concentrations (antibiotics alone and in combination).
In this way,
different areas of interaction were defined as follows:
additivity was
defined as an effect equal to the theoretical sum
of the effects of
each antibiotic tested alone and was expressed
as an FME equal to 1;
synergy was defined as an effect superior
to additivity and was
expressed as an FME of greater than 1; antagonism
was defined as an
observed effect lower than the best effect of
an antibiotic used alone
and was expressed as an FME lower than
the best FME of the antibiotics
tested alone; and the area between
antagonism and additivity was the
indifference zone and was expressed
as an FME for the antibiotic
combination between the FME values
for antagonism and
additivity.
These theoretical interactions are represented graphically in Fig.
1.
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|
FIG. 1.
Theoretical graphical representation of the different
interactions between two antibiotics, antibiotics A and B. The
y axis represents the FME of each antibiotic alone (A,
B) and the antibiotic pair (A + B). The x axis
represents the concentration of either antibiotic A (increasing
concentrations from the left) or antibiotic B (increasing
concentrations from the right). The concentrations tested are those
corresponding to each fraction of maximal effect.  , effect of
antibiotic A; this effect is expressed as the FME of antibiotic A;  ,
effect of antibiotic B; this effect is expressed as the FME of
antibiotic B;  , the best effect of either antibiotic A or B ("best
alone" line); additivity line, theoretical addition of the effects of
A and B; this sum is always equal to 1; Synergy, area of synergy above
the additivity line; Indifferent, indifference zone between the
additivity line and the best alone line; antagonism, area of antagonism
below the best alone line.
|
|
| |
RESULTS |
MIC.
The MICs of the antibiotics tested are presented in Table
1. Both pneumococcal strains were
resistant to penicillin, while PRP-2 was also resistant to ceftriaxone.
E. faecalis.
Killing curve studies were
done over 24 h in triplicate at multiples of the MICs of
amoxicillin and gentamicin alone. The AUC was calculated for each
concentration tested, and the effect was defined as the inverse of the
AUC. The criteria for the nonlinear regression obtained from the
killing curve studies of each antibiotic are shown in Table
2. Figure
2A illustrates the FME for each antibiotic concentration tested and the FMEs for the antibiotic combinations tested. Synergy was observed when the concentration of amoxicillin was above 0.3 mg/liter. Below this concentration, the
effect of the combination was indifferent.
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FIG. 2.
In vitro FMEs of amoxicillin, gentamicin, ceftriaxone,
and vancomycin against a reference strain of E. faecalis
and two penicillin-resistant pneumococcal strains (strains PRP-1 and
PRP-2). (A) FME of the combination (open circle), amoxicillin
(increasing concentrations from the left;  ), or gentamicin
(increasing concentration from the right;  ) against E.
faecalis. (B) FME of the combination (open circle), amoxicillin
(increasing concentrations from the left; ), or ceftriaxone
(increasing concentration from the right; ) against strain PRP-1.
(C) FME of the combination (open circle), vancomycin (increasing
concentrations from the left; ), or ceftriaxone (increasing
concentration from the right; ) against strain PRP-1. (D) FME of the
combination (open circle), amoxicillin (increasing concentrations from
the left; ), or ceftriaxone (increasing concentration from the
right; ) against strain PRP-2. (E) FME of the combination (open
circle), vancomycin (increasing concentrations from the left; ), or
ceftriaxone (increasing concentration from the right; ) against
strain PRP-2.
|
|
S. pneumoniae.
For both PRP strains, the
criteria for the nonlinear regression obtained from the killing curve
studies with the range of antibiotic concentrations tested are
shown in Table 2. The FMEs of each antibiotic tested alone and the FMEs
of the different combinations are shown in Fig. 2B to E.
For strain PRP-1 and the combination amoxicillin-ceftriaxone, synergy
was observed with a concentration of amoxicillin of
0.3 mg/liter and
relatively low concentrations of ceftriaxone
(Fig.
2B). For this strain
and the combination of vancomycin and
ceftriaxone, synergy was obtained
with any concentration of each
antibiotic (Fig.
2C).
For strain PRP-2, the combination amoxicillin-ceftriaxone was found to
be synergistic for only one pair of concentrations.
With the other pair
of concentrations, the results were in the
indifference area (Fig.
2D).
A synergistic effect was obtained
for the vancomycin-ceftriaxone
combination, but it did not exist
for the lowest concentration of
ceftriaxone tested (Fig.
2E).
| |
DISCUSSION |
By the method used in the present study, we used the logarithmic
transformation of CFU to construct AUCs. Previous experiments were
performed with the metric results of CFU (data not shown), which
allows one to cope with very large variations in bacterial contents
that range from 0 to 1011 but with no
advantages for the graphical representation. Therefore, the method used to count the bacterial concentration in the
present work is commonly used and is easier to perform. This
logarithmic transformation of CFU probably minimizes the contrasts by
smoothing the graphical representation and so leads to a more cautious interpretation.
Our findings demonstrated synergy for amoxicillin and gentamicin
against E. faecalis (FME > 1) and thus confirmed
conclusions drawn from previous studies performed by different methods
(18, 19, 27, 30). The concentrations tested were very high
for gentamicin because the MIC was also very high; therefore, high concentrations were needed to obtain the
Emax. Despite this, synergy was
observed at concentrations achievable in humans. More precisely, synergy appears when the amoxicillin concentration is at least at 0.29 mg/liter, which is about the MIC of this antibiotic for this strain.
This is in accordance with previous data (25), in which
synergy was achieved if the penicillin concentration was at least equal
to the MIC for the strain, even for very resistant bacteria. Taken
together, these findings are in accordance with the known mechanism of
the interaction between beta-lactams and aminoglycosides
(29).
For penicillin-resistant (PRP-1) and broad-spectrum
cephalosporin-resistant pneumococci (PRP-2), the effect obtained with both combinations (amoxicillin-ceftriaxone and vancomycin-ceftriaxone) was not constant with the concentrations tested because this method was
very dynamic. However, in all cases there was always a section of the
curve that was in the area for synergism; the worst values were always
in the indifference zone, and antagonism was never found.
A closer analysis reveals that the vancomycin-ceftriaxone combination
seems to be slightly more effective than the amoxicillin-ceftriaxone combination, as it has higher FME values (the highest FMEs, 1.73 versus
1.21, respectively) and more extensive areas of synergy (the part of
the curve above the additivity line). For both combinations, the
synergy seems to be greater for strain PRP-1, which is the less
resistant strain, than for strain PRP-2, which is also reflected by
higher FME values (the highest FMEs for the two strains were 1.73 and
1.34, respectively) and more extensive areas of synergy.
However, the results that we obtained with the amoxicillin-ceftriaxone
combination are in accordance with those previously obtained with the
same strains (9). In the previous study, we demonstrated
by two different in vitro methods (the checkerboard method and
classical time-kill curve studies) that this antibiotic combination has
an improved antibacterial effect, but there were interpretation
difficulties; this improvement was also observed in an in vivo model of
pneumococcal infection. The method described here allows a simple
interpretation of results; notably, it provides a clearly defined
distinction between the different interaction areas and the range of
concentrations of interest.
Our results are also concordant with those of other studies that used
different in vivo or in vitro methods. When studying the interactions
between a broad-spectrum cephalosporin and amoxicillin against 25 PRP
strains, Johnson and Jones (20) have always observed favorable interactions: synergy, partial synergy, additivity, or
indifference. Friedland et al. (13, 14) have shown at
least an additive or a synergistic interaction between ceftriaxone and vancomycin against four PRP strains in vivo and in vitro. Marton and
Major (28) have also demonstrated the superiority of the vancomycin-broad-spectrum cephalosporin combination over
cephalosporins alone against two PRP strains. Other investigators
(22) have studied the bacterial activities of drug
combinations against cephalosporin-resistant S. pneumoniae
in the cerebrospinal fluid (CSF) of children with acute bacterial
meningitis. Their results showed that a combination of ceftriaxone and
vancomycin or a combination of ceftriaxone and rifampin had higher
levels of antibacterial activity in CSF than ceftriaxone alone.
Similarly, a French group (11) has shown that the
cefotaxime-vancomycin combination was at least additive against a
broad-spectrum cephalosporin-intermediate pneumococcal strain by
measuring bactericidal activity in the CSF of children with
acute bacterial meningitis. They also reported the results of in vitro
studies of different drug combinations against PRP strains that had
various levels of susceptibility to broad-spectrum
cephalosporins. The activities of trovafloxacin-vancomycin and
beta-lactam-vancomycin combinations were found to be additive or
indifferent even against broad-spectrum cephalosporin-resistant strains
(12).
Conclusion.
The new method for the testing of drug-drug
interactions described here permits a simple graphical representation
of the interaction and then an approach that uses the range of
concentrations of interest.
Our results confirm the results of previous in vitro and in vivo
studies in which amoxicillin-ceftriaxone and vancomycin-ceftriaxone
combinations appeared to be synergistic at some concentrations
against
penicillin- and/or broad-spectrum cephalosporin-resistant
pneumococcal
strains. Moreover, this synergy is present at drug
concentrations
achievable in humans. Therefore, the clinical interest
in these
combinations for the treatment of PRP infections seems
to be
confirmed.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Service des
Maladies Infectieuses, Hopital du Bocage, BP 1542, 21034 Dijon, France. Phone: 33 3 80 29 33 05. Fax: 33 3 80 29 36 38. E-mail:
p.chavanet{at}planetb.fr.
| |
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Antimicrobial Agents and Chemotherapy, December 2001, p. 3328-3333, Vol. 45, No. 12
0066-4804/01/$04.00+0 DOI: 10.1128/AAC.45.12.3328-3333.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
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Top
Abstract
Introduction
![<IT>E</IT><SUB><UP>A + B</UP></SUB><UP> = </UP>[(<IT>E</IT><SUB><UP>maxA</UP></SUB><UP> ×</UP><IT> C</IT><SUB><UP>A</UP></SUB><UP>/EC<SUB>50A</SUB></UP>)<UP> + </UP>(<IT>E</IT><SUB><UP>maxB</UP></SUB><UP> ×</UP><IT> C</IT><SUB><UP>B</UP></SUB><UP>/EC<SUB>50B</SUB></UP>)]<UP>/</UP>[<UP>1 + </UP>(<IT>C</IT><SUB><UP>A</UP></SUB><UP>/EC<SUB>50A</SUB></UP>)<UP> + </UP>(<IT>C</IT><SUB><UP>B</UP></SUB><UP>/EC<SUB>50B</SUB></UP>)]](/content/vol45/issue12/fulltext/3328/img001.gif)
