Naunyn-Schmiedeberg's Arch Pharmacol (2004) 370: 369–380DOI 10.1007/s00210-004-0983-9

ORIGINAL ARTICLE

Jarogniew J. Luszczki . Stanislaw J. Czuczwar

Three-dimensional isobolographic analysis of interactions

between lamotrigine and clonazepam in maximal

electroshock-induced seizures in mice

Received: 30 June 2004 / Accepted: 29 August 2004 / Published online: 23 October 2004# Springer-Verlag 2004

Abstract The anticonvulsant effects of lamotrigine (LTG)and clonazepam (CZP) and combinations thereof againstmaximal electroshock (MES)-induced seizures in micewere investigated using three-dimensional (3D) isobolo-graphic analysis. With this method, the doses of fixed-ratiocombinations of the drugs (1:3, 1:1 and 3:1) that elicited16, 50 and 84% of the maximum anticonvulsant effectwere determined. Additionally, to evaluate the character-istics of interactions observed with 3D isobolography, thebrain concentrations of both drugs were verified pharma-cokinetically. The 3D isobolographic analysis showed thatLTG and CZP combined at the fixed ratios of 3:1 and 1:1interacted synergistically in the MES test for all anticon-vulsant effects between 16% and 84% of maximum. Incontrast, the combination of LTG and CZP at the fixedratio of 1:3 showed only pure additivity for all estimatedeffects in 3D isobolography. Moreover, none of theexamined antiepileptic drugs altered the brain concentra-tions of the coadministered drug, so the observedinteractions in the MES test are of a pharmacodynamicnature. The 3D isobolographic findings suggest that inepilepsy therapy, increased efficacy of seizure control(synergistic interaction) might be achieved by using LTGand CZP in combination. In this study, some importantproblems and assumptions related to statistical analysis ofdata in 3D isobolography are discussed.

Keywords Three-dimensional isobolographic analysis .Lamotrigine . Clonazepam . Drug interactions

Introduction

Detailed evaluation of the characteristics of interactionsbetween antiepileptic drugs (AEDs) is of fundamentalimportance and clinical interest for epilepsy treatment.Progress in this field requires the meticulous examinationof type and degree (strength) of interactions in preclinicalstudies in animals. Combined therapy in epilepsy is acommon therapeutic issue in patients with refractoryseizures, for whom monotherapy with a current front-lineAED has proven inadequate. In such cases, clinicians areexpected to combine some AEDs to provide these patientswith a state of seizure freedom, devoid of any adverseeffects produced by the AEDs employed. Usually, thecombined therapy with AEDs is preselected rationally onthe basis of theoretical considerations concerning comple-mentary mechanisms of action of available AEDs and theobserved effects exerted by these AEDs in preclinicalstudies. There is no doubt that experiments on animalsprovide sufficient evidence about the characteristic ofinteractions occurring in vivo between AEDs (Deckers etal. 2000). From a pharmacological point of view, eachcombination of two fully active drugs always evokesinteractions of a pharmacodynamic, pharmacokinetic ormixed nature. Detailed characterization of the precisetypes of interactions between AEDs in preclinical studiesis thus of pivotal importance for their subsequent clinicalapplication. It is accepted that the AED combinationsexerting supra-additivity (synergy) with respect to theanticonvulsant activity and minimal or no side effects inanimals are recommended as favourable for clinicalpractice. Following a thorough review of the literaturerelating to patients on add-on therapy, a list of ten mosteffective two-drug combinations has been established(Stephen and Brodie 2002). Among these, combinations oflamotrigine (LTG) and valproate, LTG and topiramate andgabapentin and carbamazepine have provided patientswith intractable convulsive attacks freedom from seizuresfor over 1 year (Stephen and Brodie 2002). Similarly,isobolographic experiments on mice have revealed that thecombinations of LTG and valproate, LTG and topiramate

J. J. Luszczki (*) . S. J. CzuczwarDepartment of Pathophysiology, Skubiszewski MedicalUniversity of Lublin,Jaczewskiego 8,20-950 Lublin, Polande-mail: jarogniew@asklepios.am.lublin.plTel.: +48-81-7425837Fax: +48-81-7425828

S. J. CzuczwarIsotope Laboratory, Institute of Agricultural Medicine,Jaczewskiego 2,20-950 Lublin, Poland

and gabapentin and carbamazepine are synergistic in themaximal electroshock (MES) seizure test (Luszczki et al.2003a; Borowicz et al. 2002). Moreover, isobolographyhas also revealed antagonism for the combination of LTGand carbamazepine in the MES test in mice (Luszczki etal. 2003a). Indeed, this antagonism has been confirmed byclinical observations of aggravation of epilepsy (increasedseizure attacks) in patients given LTG plus carbamazepineas the adjunctive treatment (Jozwiak and Terczynski 2000;Besag et al. 1998). Undoubtedly, there is a goodcorrelation between the synergistic effects exerted bycombinations of some AEDs in isobolographic preclinicalstudies on animals and the state of seizure freedomreported in patients treated with the same two-drugcombinations. So, the combination studies with AEDs inrodents, as predictors of their anticonvulsant effects inclinical practice, are of considerable relevance forpreselecting the favourable combinations of AEDs.

Several methods of analysing the effects of combina-tions of two or more drugs are available (for review seeBerenbaum 1989; Pöch 1993; Greco et al. 1995). Of thesemethods, the most commonly used is the isobolographicanalysis proposed by Loewe (1953) and further adapted byTallarida (1992), who applied this method to the properevaluation of pharmacological interactions among drugs,co-administered in various fixed-ratio combinations. Thismethod has been accepted as the “gold standard” indetecting drug interactions in preclinical studies (Gebhart1992; Tallarida et al. 1999). Theoretically, isobolographicstudies can distinguish five most important types ofinteractions: pure additivity, supra-additivity (synergy),indifference, sub-additivity (relative antagonism), andinfra-additivity (absolute antagonism) (Loewe 1953;Berenbaum 1989; Gessner 1995; Tallarida et al. 1999).

A recent trend has been the evaluation of two-drugcombinations and their resultant interactions at variousestimated effect levels using 3D response-surface analysis(Prichard et al. 1991, 1993; Kanzawa et al. 1997; Tallaridaet al. 1999; Tallarida 2001). This modern approachprovides investigators with information about the exacttypes of interactions exerted by two-drug mixtures fordiverse estimated effects. Generally, when two drugs arecombined in preclinical studies, there are always threevariables: the doses of the two drugs and their resultantbiological effect. In 2D isobolographic analysis onevariable must be held constant so that 2D isobolographyis usually performed for the median (50%) effect(Berenbaum 1989; Greco et al. 1995). Since traditional2D isobolography cannot describe the subtle changes inobserved interactions precisely, 3D analysis is required fora complete description and clear identification of arelationship depending on the administered doses of twodrugs (Berenbaum 1989; Greco et al. 1995). For epilepsyresearch studies, this method of analysing interactions is ofconsiderable importance allowing the determination ofrelations existing between AEDs. Undoubtedly, 3Disobolography may contribute to the preselection ofAED combinations showing synergistic anticonvulsant

effects in animal experiments and that could be recom-mended for further rational duotherapy in humans.

Our previous isobolographic studies have shown thatclonazepam (CZP, a benzodiazepine receptor ligand)interacts synergistically with phenytoin and carbamaze-pine (both AEDs inhibit Na+ channels in neurons),exerting supra-additive (synergistic) interactions for allfixed-ratio combinations tested in the MES test in mice. Incontrast, mixtures of CZP with oxcarbazepine (a newerAED, also a Na+ channel blocker) show either supra-additive or sub-additive (antagonistic) interactions withrespect to the fixed-dose ratios employed (Luszczki et al.2003b; Luszczki and Czuczwar 2003).

In view of the foregoing, we sought to characterizeprecisely the interaction between LTG (a second genera-tion AED, the mechanism of action of which is also relatedto Na+ channel blockade in neurons) and CZP againstMES-induced seizures in mice using 3D isobolographicanalysis. The MES test in rodents is accepted widely as anexperimental model of generalized tonic-clonic seizuresand, to a certain extent, of partial convulsions with orwithout secondary generalization in humans (Fischer1989; Löscher and Schmidt 1988; Löscher et al. 1991;White et al. 2002). Finally, we measured total brain AEDconcentrations to ascertain whether the observed effectsresult from a pharmacodynamic and/or a pharmacokineticinteraction.

Materials and methods

Animals and experimental conditions

All experiments were performed on adult, male, albinoSwiss mice weighing 22–26 g. The mice were kept incolony cages with access to food and tap water ad libitum,under standardized housing conditions (natural light/darkcycle, 21±1°C). After 7 days adaptation to laboratoryconditions, the animals were assigned randomly toexperimental groups consisting of eight mice. Eachmouse was used only once. All tests were performedbetween 9.00 a.m. and 2.00 p.m. Procedures involvinganimals and their care were conducted in conformity withcurrent European Community and Polish legislation onanimal experimentation. Additionally, all efforts weremade to minimize animal suffering and to use only thenumber of animals necessary to produce reliable data. Theexperimental protocols and procedures employed wereapproved by the Local Ethics Committee at the MedicalUniversity of Lublin and confirmed with the Guide for theCare and Use of Laboratory Animals (License number:357/2002/377/02).

Drugs

In this study: LTG (Lamictal, Glaxo Wellcome, Kent, UK)and CZP (Polfa, Warsaw, Poland) were suspended in 1%solutions of Tween 80 (Sigma, St Louis, Mo., USA) in

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distilled water and administered i.p. as separate singleinjections in volumes of 5 ml/kg body weight. Drugsolutions were prepared freshly on each day of experi-mentation. LTG was given 60 min, and CZP 30 min beforeMES and brain sampling for the measurement of AEDconcentrations. The i.p. route of administration and pre-treatment times of the drugs were based on informationabout their biological activity from the literature (Gasior etal. 1999) and our previous experiments (Luszczki et al.2003a,b). The times to peak of maximum anticonvulsanteffects for the AEDs were used as the reference times inpharmacokinetic estimation of brain AED concentrations.

Electroconvulsions—maximal electroshock seizuretest

Electroconvulsions were induced by means of alternatingcurrent (0.2 s stimulus duration, 50 Hz) delivered to ear-clip electrodes from a generator (Rodent Shocker, Type221, Hugo Sachs, Freiburg, Germany). The criterion forthe occurrence of seizure activity was the tonic hindlimbextension (i.e. the outstretching of the hindlimbs 180° tothe plane of the body axis). The protective activities ofLTG and CZP were evaluated as their effective doses(ED16, ED50 and ED84 in mg/kg) against MES-inducedseizures (fixed current intensity 25 mA, maximum stim-ulation voltage of 500 V). The animals (at least fourgroups of mice with eight animals per group) wereadministered different drug doses yielding protectionagainst the MES-induced seizures in 10–30%, 30–50%,50–70%, and 70–90% of the animals. A dose/responsecurve for each AED administered alone was thenconstructed according to the log-probit method (Litchfieldand Wilcoxon 1949). Subsequently, the ED16, ED50 andED84 with their 95% confidence limits were calculated.These parameters represent the drug dose required toprotect 16, 50, and 84% of the animals tested againstelectroconvulsions, respectively. Similarly, the anticonvul-sant activity of a mixture of LTG and CZP was evaluatedand expressed as ED16,mix, ED50,mix and ED84,mix,respectively. The MES test has been described in moredetail elsewhere (Luszczki and Czuczwar 2003, 2004).

Measurement of total brain AED concentrations

Total brain concentrations of LTG and CZP, administeredat doses corresponding to the ED50,mix at the fixed ratio of1:1, were estimated using either HPLC (LTG) or afluorescence polarization immunoassay (FPIA) (CZP).Mice were killed by decapitation at times chosen tocoincide with that scheduled for the MES test. The wholebrains were removed from skulls, weighed and homo-genized in distilled water (2:1 v/w) in an Ultra-Turrax T8homogenizer (Staufen, Germany). The homogenates werecentrifuged at 10,000 g (MPW-360 centrifuge; MechanikaPrecyzyjna, Warsaw, Poland) for 10 min. The supernatantsamples (75 μl) containing CZP were analysed by FPIA

using a TDx analyser and reagent (“benzodiazepineserum”) as described by the manufacturer (AbbottLaboratories, North Chicago, Ill., USA). Total brain LTGconcentrations were determined using HPLC as describedelsewhere (Luszczki et al. 2003a). The total brain LTGconcentrations were expressed in microgram/millilitre;those of CZP in nanogram/millilitre brain supernatant asmeans±SD of at least eight determinations. The signifi-cance of differences between means was determined usingStudent’s t-test for unpaired samples.

Isobolographic analysis of interactions

The interactions between LTG and CZP were analysedisobolographically as detailed in our earlier studies, inwhich the theoretical background is described in detailwith the respective equations for isobolographic calcula-tions (Luszczki et al. 2003a,b; Luszczki and Czuczwar2003, 2004). In the present study, 3D isobolographicanalysis consisted of five basic stages as follows:

1. Evaluation of the anticonvulsant activity of individualAEDs followed by the determination of their dose/response relationships (DRRs) by means of log-probitlinear regression analysis (Litchfield and Wilcoxon1949). Generally, log-probit analysis yields a DRRwith parameter values for median effective dose(ED50), slope function (S), the equation to the DRRline and the coefficient of determination (r2). It shouldbe emphasized that the graphical presentation and thetest for parallelism of the examined DRR lines forAEDs administered alone are very important for 3Disobolographic analysis. The effective doses of AEDs(EDx with the 95% confidence limits or SEM) arecalculated directly from the respective DRR linesaccording to Litchfield and Wilcoxon (1949).

2. Theoretical choice of fixed drug-dose ratios forcombinations of examined AEDs associated with thecalculation of additive effective doses (EDx,add) withtheir SEM for each fixed-ratio combination. EDx,add

represents the total additive dose of the drugs inmixture, theoretically providing a x% protection ofanimals in the MES test; where x corresponds to anestimated effect exerted by the mixture of both AEDs(x=16, 50 or 84%). The additive doses in mixtures ofLTG and CZP (EDx,add) were calculated from thegeneral equation of additivity: a/A+b/B=1; where aand b are the doses of the first and the second drug co-administered in a mixture, exerting a desired effect (aninitially established reference point) and A and B arethe doses of the drugs which exert the same desiredeffect when administered separately (Loewe 1953).For 3D characterization of interactions only effectsranging between 16% and 84% (i.e. 4 and 6 probits)are evaluated, because the median-effect analysis isvery sensitive to slight changes at the extremes ofDRR, especially for effects greater than 84% or lowerthan 16% (e.g. ED90 or ED10) (Litchfield and

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Wilcoxon 1949). It should be stressed that the equi-effective drug doses and their fractions included in amixture are important for calculating the additive drugdoses (EDx,add) in 3D isobolography.

3. Experimental determination of effective doses (EDx,

mix) with their SEM for the previously chosen, fixed-ratio AED combinations (usually, 1:3, 1:1 and 3:1).EDx,mix is the experimentally determined total dose ofa mixture of two component drugs given in a fixed-ratio combination that is sufficient to elicit a protectionagainst MES-induced seizures in x% of tested animals(x=16, 50 or 84%). The experimentally derived EDx,

mix values (with 95% confidence limits) werecalculated from the respective DRR lines of combineddrug mixtures (Litchfield and Wilcoxon 1949). The95% confidence limits were transformed subsequentlyto SEM.

4. Statistical comparison of experimentally derived EDx,

mix with the corresponding theoretical additive EDx,add

using Student’s t-test for unpaired samples, accordingto Porreca et al. (1990) and Tallarida (2000), who haveproposed this test for analysing isobolographic data.This is the reason for transforming the experimentallydetermined 95% confidence limits of each EDx,mix intoSEM.

5. Graphical illustration of examined interactions as 2Dand 3D isobolograms, which are a simple form ofvisualization of interactions, facilitating their interpre-tation in preclinical studies.

The notation of fixed-ratio combinations in isobolo-graphy is based preferentially on natural numbers (1:5,1:3, 1:1, 3:1, 4:1, etc.) rather than on fractions of applieddrug doses or absolute drug dose ratios (for instance, theabsolute drug dose ratio, based on the mass quantity ofapplied drugs in mixture, for the fixed-ratio combinationof 1:1 for LTG and CZP in the MES test was 2.465:14.57,or alternatively, 1:5.911). To avoid misunderstanding andthe need for additional explanations, the notation of fixed-ratio combinations in form of natural numbers is widelyaccepted in isobolography (Berenbaum 1989; Gessner1995; Tallarida et al. 1999; Luszczki et al. 2003b). Forinstance, the description of a combination of two AEDs atthe fixed ratio of 1:3 means that two-drug mixturecomprises one-quarter of the EDx of the first drug andthree-quarters of the EDx of the second, resulting finally ina full EDx of this two-drug mixture; where x represents adesired effect (here, protection of 16, 50 or 84% of testedanimals against seizures), and EDx is the effective dose ofan individual drug achieving the desired effect. Analo-gously, a two-drug mixture at the fixed ratio of 7:1comprises seven-eighths of the EDx of the first drug andone-eighth of the EDx of the second. However, to obtainthe effective mixture dose (EDx,mix) protecting the animalsagainst MES-induced seizures, both drugs (at proportion-ally raised doses) were given to animals to determine aDRR line using the log-probit method. In other words, thedrug doses, at the accepted fixed-ratio combination,

increased proportionally until the median effective mixturedose was determined.

To visualize the types of interactions and determineapproximately the strength of obtained interactions, 2Disobolograms were drawn by plotting the points reflectingthe respective effective doses of LTG on the x-axis andthese of CZP on y-axis. The straight line connecting theEDx values for these drugs represents the theoreticalisobole for additive effects. If the experimental data lie onthis line, then the drugs in the two-drug mixture interact apurely additively (Loewe 1953). When the experimentaldata reflecting combinations of various fixed ratios liesignificantly below this line, the two component drugs actsynergistically. Conversely, antagonism may be recog-nized if these points lie above the additive isobole.

Moreover, an interaction index for all fixed-ratiocombinations was calculated as a quotient of the respectiveEDx,mix and EDx,add. This ratio describes the strength andmagnitude of interactions between two drugs in theisobolographic analysis (Berenbaum 1989; Tallarida etal. 1999; Tallarida 2002).

Software used

Microsoft’s Excel spreadsheet was used to perform thecalculations and to graph the results in form of 2Disobolograms. This spreadsheet was programmed tocompute all calculations automatically and determine theDRR lines of AEDs administered alone from log-probitlinear regression analysis (Litchfield and Wilcoxon 1949).The theoretically additive interactions at the fixed-ratiocombinations of 1:3, 1:1 and 3:1 for various effect levels(i.e. ED16, ED50 and ED84) were also calculated with thisprogram. The 3D isobolograms for the theoretical additiveand experimentally derived dose/response surfaces wereconstructed with the commercially available programStatistica.

Results

Anticonvulsant effects of LTG and CZP administeredsingly in the MES test in mice

In the present study, LTG and CZP showed clear-cutanticonvulsant activity against MES-induced seizures inmice (Fig. 1). The anticonvulsant effects of LTG werestudied at doses of 4, 5, 6 and 7 mg/kg, injected i.p. 60 minbefore the maximal electroconvulsions. Similarly, theantiseizure effects elicited by CZP were investigated atthe doses of 20, 25, 30, 35 and 40 mg/kg administered i.p.30 min prior to the MES test. The log-probit methodallowed the calculation of median effective doses (ED50)for LTG [4.93 (4.16–5.86) mg/kg] and CZP [29.14(25.25–33.63) mg/kg; Table 1]. The log-probit methodyielded the equations of the DRRs: y=7.599x−0.268 forLTG, and y=7.864x−6.517 for CZP; where y is a probit,and x is the decadian logarithm of the drug dose (Fig. 1).

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Log-probit linear regression analysis followed by χ2 (Chi-square) goodness-of-fit test revealed that the data generat-ing the lines of DRR for LTG and CZP were good-to-fit.As the experimentally determined value of χ2

E for CZP(0.231) was far lower than the critical value of χ2

T for 3 d.f. (7.815) at P<0.05 (Table 1), the DRR (log-probit) line isalso good-to-fit. Similarly, the experimentally calculatedvalue of χ2

E for LTG (0.015) was lower than the criticalvalue of χ2

T for 2 d.f. (5.991) at P<0.05 (Table 1), hence,the DRR (log-probit) line for LTG is also best-fit.Additionally, to detect any variance influencing thehomogeneity of data points of DRRs for LTG and CZP,the F-distribution test was performed according to Glantzand Slinker (2001). The calculated F value for CZP for 1(numerator) and 3 (denominator) d.f. was 180.895, anddiffered considerably from the critical F value of 34.12, atP<0.01 (Table 1). Likewise, the calculated F value forLTG for 1 (numerator) and 2 (denominator) d.f. was1,225.161, and drastically differed from the critical Fvalue of 98.50, at P<0.01 (Table 1). The F-distributionstatistic revealed also that the log-probit lines for LTG andCZP are good-to-fit (Fig. 1). Finally, the coefficient ofdetermination (r2) for both DRRs, i.e. for LTG and CZP,was determined. The value of r2 for the CZP DRR linewas 0.9837, indicating that 98.37% of the variance aroundthe straight DRR line (with the equation y=7.864x−6.517)can be attributed to the relationship between the CZP doseand observed anticonvulsant effect in the MES test (Table1; Fig 1). Similarly, r2 for the LTG DRR was 0.9984 sothat 99.84% of the variance around the linear regressionequation (y=7.599x−0.268) is attributable to the relation-ship between LTG dose and observed antiseizure effectagainst electroconvulsions in mice (Table 1, Fig. 1).Finally, linear regression analysis followed by the test for

parallelism indicated that the investigated DRR lines forLTG and CZP fulfilled the criterion of parallelism (Table1). The slope function ratio (SR) for LTG and CZP in theMES test was 1.010 and was lower than the factor ratio forslope function ratio (f ratio SR), which was 1.130 (Table1). The test for parallelism of two log-probit DRR lineswas performed according to Litchfield and Wilcoxon(1949); therefore, the original notation for SR and f-ratioSR is applied in the present study.

Anticonvulsant activity of combinations of LTG andCZP in the MES test in mice

For combined administration of LTG and CZP, LTG wasgiven i.p. into the right lower part of the abdomen and, 30min later, CZP was given i.p. into the left lower part of theabdomen. The animals were challenged with the MES test30 min after the second injection. This procedure of twoseparate, consecutive i.p. administrations allows theinvestigation of anticonvulsant effects exerted by thetwo-drug mixture at the time of the peak anticonvulsantactivity of each component (i.e. 60 min after LTG injectionand 30 min after CZP). The mixture of LTG and CZP atthe fixed ratio of 1:3 exerted a potent anticonvulsantactivity in the MES test. The DRR equation for thecombination of both AEDs was y=6.063x−3.262. Theexperimentally determined χ2

E for 1 d.f. was 0.019, and Ffor 1 (numerator) and 1 (denominator) d.f. was 425.43.The critical values for χ2

T (for 1 d.f. at P=0.05) and F (for1 and 1 d.f. at P<0.05) are 3.841, and 161, respectively(Glantz and Slinker 2001). Since, the calculated χ2

E valuewas considerably lower, and F greatly exceeded thecorresponding critical values (at P<0.05), the DRR for the

Fig. 1 Log-probit analysis of dose/response relationships (DRRs)for lamotrigine (LTG) and clonazepam (CZP) against maximalelectroshock (MES)-induced seizures in mice. Drug doses of LTGand CZP injected alone were transformed to logarithms and plottedon a log scale (abscissa, x), the corresponding protective effects weretransformed to probits and plotted on a probit scale (ordinate, y).

Log-probit linear regression analysis yielded y=7.599x−0.268(r2=0.9984) for LTG and y=7.864x−6.517 (r2=0.9837) for CZP.The χ2 (Chi-square) goodness-of-fit test and F-distribution statisticrevealed that the data are good-to-fit. The test for parallelism(Litchfield and Wilcoxon 1949) showed that the lines are parallel.For more details see also Table 1

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mixture of LTG and CZP at the fixed ratio of 1:3 wasgood-to-fit (Tallarida 2000; Glantz and Slinker 2001). r2

for this DRR was 0.9977 so that 99.77% of the varianceabout the linear regression is accounted for by the existingrelationship between the mixture doses and their resultantanticonvulsant effects in the MES test. The medianeffective dose for drug mixture (ED50,mix) at the fixedratio of 1:3 was 23.05 (17.72–29.99) mg/kg (Table 2, Fig.2).

Similarly, the DRR equation for the mixture of LTGwith CZP at the fixed ratio of 1:1 was y=4.759x+0.420.

χ2E for 1 d.f. was 0.011 and the F-distribution statistic for

1 and 1 d.f. at P<0.05 was 727.875. The tabular χ2T value

for 1 d.f. at P=0.05 was 3.841, and the critical value of F-distribution statistic for 1 and 1 d.f. at P<0.05 was 161.Since the experimentally determined χ2 and was con-siderably lower and the F-statistic higher than the tabularvalues (at P<0.05), the DRR for the mixture of LTG andCZP at the fixed ratio of 1:1 was good-to-fit. r2 for thisAED combination was 0.9986, indicating that 99.86% ofthe variance around the linear regression can be attributedto the relation between dose and response. ED50,mix for

Table 1 Anticonvulsant activity of lamotrigine(LTG) and clonaze-pam (CZP), each given alone, against maximal electroshock (MES)-induced seizures in mice. Raw data (for each AED administeredalone) allow the calculation of dose/response relationship (DRR)lines for the antiepileptic drugs (AEDs) required for isobolographicanalysis. As the DRR analysis was performed using the log-probitmethod, the original notation of DRR parameters was retained [Pnumber of animals protected against electroconvulsions, T totalnumber of animals challenged with the MES test, % percentage ofprotection against MES-induced seizures,ED50 median effectivedose of an AED protecting 50% of animals tested, calculated using

the log-probit method, S slope function of DRR line, f factor forED50, N total number of animals used between 4 and 6 probits ofexpected anticonvulsant effects, fS factor for slope function, y effectin probits, x decadian logarithm of drug dose, r2 coefficient ofdetermination for DRR line, d.f. degrees of freedom from DRRanalysis, i.e. number of analysed points−2, χ2

E value of Chi-squaregoodness-of-fit test determined experimentally, F value of F-distribution statistic determined experimentally, PR potency ratioi.e. quotient of experimentally determined ED50 for the two drugs,SR slope function ratio i.e. the quotient of calculated slope functionsfor the two DRR lines, f ratio SR factor ratio for slope function ratio]

Drug Dose (mg/kg) P/T % Log-probit parameters DRR analysis

LTG 3 0/8 0 ED50=4.93 (4.16−5.86)S=1.354f=1.187N=24SEM=0.431fS=1.107

y=7.599x−0.268r2=0.9984d.f.=2χ2

E=0.0148F=1225.161

4 2/8 255 4/8 506 6/8 757 7/8 87.58 8/8 100

CZP 20 1/8 12.5 ED50=29.14 (25.25−33.63)S=1.340f=1.154N=32SEM=2.130fS=1.069

y=7.864x−6.517r2=0.9837d.f.=3χ2

E=0.231F=180.895

25 2/8 2530 4/8 5035 6/8 7540 7/8 87.545 8/8 100

PR=5.905, Test for parallelism SR=1.010, f ratio SR=1.130. Since SR < f ratio SR the examined two DRR lines are parallel (Litchfield andWilcoxon 1949).

Table 2 Effect of fixed-ratio combinations of lamotrigine and clonazepam in MES-induced seizures in mice (FR fixed-ratio combination,ED50,mix median effective dose of the two-drug mixture protecting 50% of animals tested against MES-induced seizures)

FR LTG (mg/kg) CZP (mg/kg) Mixture (LTG + CZP, mg/kg) P/T % Log-probit parameters DRR analysis

1:3 0.6 10.6 11.2 0/8 0 ED50,mix=23.05 (17.72−29.99)S=1.462f=1.301N=16SEM=3.092

y=6.063x−3.262r2=0.9977d.f.=1χ2

E=0.019F=425.432

0.8 14.0 14.8 1/8 12.51.3 22.2 23.5 4/8 501.6 27.8 29.4 6/8 751.8 31.9 33.7 8/8 100

1:1 0.8 4.7 5.5 0/8 0 ED50,mix=9.17 (6.56−12.82)S=1.622f=1.398N=16SEM=1.567

y=4.759x+0.420r2=0.9986d.f.=1χ2

E=0.011F=727.875

1.0 5.7 6.7 2/8 251.3 7.7 9.0 4/8 502.3 13.8 16.1 7/8 752.8 16.5 19.3 8/8 100

3:1 1.4 2.8 4.2 0/8 0 ED50,mix=6.12 (4.71−7.95)S=1.460f=1.300N=16SEM=0.817

y=6.086x+0.214r2=0.9988d.f.=1χ2

E=0.009F=863.944

1.6 3.1 4.7 2/8 252.1 4.1 6.2 4/8 503.2 6.2 9.4 7/8 87.53.6 7.1 10.7 8/8 100

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this fixed-ratio combination of 1:1 was 9.17 (6.56–12.82)mg/kg (Table 2).

Log-probit linear regression analysis for the lastcombination tested in the present study, 3:1, yielded theDRR equation y=6.086x+0.214. χ2

E for 1 d.f. was 0.009and the F-distribution statistic for 1 and 1 d.f. 863.944. Asthe calculated χ2

E value was considerably lower, and F-distribution statistic greatly exceeded the correspondingcritical values (at P<0.05), the DRR for the mixture ofLTG and CZP at the fixed ratio of 3:1 was good-to-fit. r2

for this DRR was 0.9988, hence 99.88% of the varianceabout the regression line is attributable to the relationshipbetween the mixture doses and their resultant anticonvul-sant effects in the MES test. The ED50,mix for the fixedratio of 1:3 was 6.12 (4.71–7.95) mg/kg (Table 2).

Conventional (2D) isobolographic analysis ofinteractions

The mixture of both AEDs at the fixed ratio of 3:1 showedsupra-additivity (synergy) for all examined drug-doseeffects (ED16, ED50 and ED84). The experimentallyderived ED16,mix was 4.19±0.56 mg/kg and was consider-ably lower than the theoretically additive ED16,add (8.17±0.64 mg/kg) at P<0.001 (Table 3, Fig. 3a). Likewise, theexperimental ED50,mix (6.12±0.82 mg/kg) was signifi-cantly lower than the corresponding ED50,add (10.99±0.86mg/kg) at P<0.001 (Table 3, Fig. 3b) and the ED84,mix was8.93±1.19 mg/kg and substantially lower than thetheoretically additive ED84,add (14.77±1.15 mg/kg) atP<0.001 (Table 3, Fig. 3c).

Fig. 2 Log-probit analysis of DDRs for AEDs fixed-ratiocombinations of 1:3, 1:1 and 3:1. Doses of the two-drug mixturesat these fixed ratios were transformed to logarithms and plotted onthe abscissa. The corresponding protective effects (against electro-convulsions) were transformed into probits and plotted on theordinate. The equations of DRR lines for the fixed ratios of 1:3, 1:1

and 3:1 were y=6.086x+0.214 (r2=0.9988), y=4.759x+0.420(r2=0.9986), and y=6.063x−3.262 (r2=0.9977), respectively. Testsfor the homogeneity of DDR data (χ2 analysis) and the F-distribution statistic confirmed goodness of fit. For more detailssee also Table 2

Table 3 Isobolographic evaluation of interactions between lamo-trigine and clonazepam in the MES test in mice. Data are mean(±SEM) effective doses (EDx in mg/kg) protecting x=16, 50, or 84%of animals tested against electroconvulsions in the MES test. ED16,ED50 and ED84 values were determined either experimentally fromvarious mixtures of the two AEDs (EDmix) or theoretically from theequation of additivity (EDadd) (Nadd total number of animals

calculated for the additive mixture of the drugs examined, i.e.Nadd=N1+N2−4; where N1 and N2 are the total number of animalsused between 4 and 6 probits for drugs administered alone, Nmixtotal number of animals used between 4 and 6 probits for theexperimental mixture, t Student’s t-test statistic, P probability, Iinteraction index)

Effect FR ED mix Nmix ED add Nadd t d.f. P I

ED16 3:1 4.19±0.56*** 16 8.17±0.64 52 4.680 53 0.0001 0.511:1 5.65±0.97*** 16 12.69±0.95 52 5.185 45 0.0001 0.451:3 15.77±2.11 16 17.22±1.27 52 0.560 66 0.577 0.92

ED50 3:1 6.12±0.82*** 16 10.99±0.86 52 4.098 48 0.0002 0.561:1 9.17±1.57** 16 17.04±1.28 52 3.183 66 0.002 0.541:3 23.05±3.09 16 23.09±1.71 52 0.0113 66 0.991 1.00

ED84 3:1 8.93±1.19*** 16 14.77±1.15 52 3.529 44 0.001 0.601:1 14.88±2.54* 16 22.86±1.72 52 2.340 66 0.022 0.651:3 33.70±4.52 16 30.96±2.29 52 0.568 66 0.572 1.09

***P<0.001, **P<0.01, *P<0.05 vs. the respective ED add (Student’st-test for unpaired samples)

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Fig. 3a–c 2D isobolograms displaying the interactions observed forthe combination of LTG with CZP in the MES test in mice. Doses ofLTG and CZP for various effects (ED16, ED50 and ED84) are plottedon the graphs (a–c), on the x-axis and y-axis, respectively. Thesolidline on the axes represents the 95% confidence limits for the AEDsadministered alone. The straight diagonal line connecting these twoEDx values on each graph represents the theoretical line of additivityfor a continuum of different fixed-dose ratios. The open points (○)are the experimentally derived EDx,mix values for the total doseexpressed as the proportion of LTG and CZP that produced a desiredanticonvulsant effect (x=16, 50 and 84%) with accompanying 95%confidence limits (the line segments through the open points). Thedashed lines represent the theoretical additive 95% confidence limitsof the EDx add values, whereas the dotted line connecting the EDx,mixvalues represents the experimental isobole for the desired (x=16, 50or 84%) effect. a Interactions between LTG and CZP for the 16%anticonvulsant effect (ED16) in the MES test in mice. Theexperimentally derived ED16,mix values of the mixture of LTG andCZP, for the fixed ratios of 3:1 and 1:1 lie significantly below the

theoretical line of additivity, indicating supra-additive (synergistic)interactions (at ***P<0.001). The ED16,mix for the fixed ratio of 1:3is close to the line of additivity indicating pure additivity in the MEStest. b Interactions of LTG with CZP for the 50% antiseizure effect(ED50) against electroconvulsions in mice. Again, the experimentalED50,mix values of the mixture of LTG and CZP for the fixed ratiosof 3:1 and 1:1 lie significantly below the theoretical line ofadditivity, indicating supra-additive interactions (at ***P<0.001 and**P<0.01, respectively). The ED50,mix for the fixed ratio of 1:3 isnear to the line of additivity indicating a purely additive interactionin the MES test. c Interactions between LTG and CZP for the 84%anticonvulsant effect (ED84) in the MES test. The experimentalED84,mix values for the mixture of LTG and CZP at fixed ratios of3:1 and 1:1 lie significantly below the theoretical line of additivity,displaying supra-additive (synergistic) interactions (at ***P<0.001and *P<0.05, respectively). The ED50,mix for the fixed ratio of 1:3 isclose to the line of additivity indicating an almost purely additiveinteraction in the MES test

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The fixed-ratio combination of 1:1 for LTG and CZPdisplayed also supra-additive (synergistic) interactions forall drug dose-effects investigated. The experimentallydetermined ED16,mix (5.65±0.97 mg/kg) was considerablylower than the ED16,add (12.69±0.95) at P<0.001 (Table 3,Fig. 3a). Analogously, the ED50,mix (9.17±1.57 mg/kg)was drastically lower than the theoretically additiveED50,add (17.04±1.28) at P<0.01 (Table 3, Fig. 3b) andthe experimentally derived ED84,mix was 14.88±2.54 mg/kg, and significantly differed from the ED84,add (22.86±1.72 mg/kg) at P<0.05 (Table 3, Fig. 3c).

In contrast, the fixed-ratio combination of 1:3 exertedpurely additive interactions in the MES test for all drug-dose effects investigated. The experimentally derivedED16,mix, ED50,mix and ED84,mix for this fixed-ratiocombination were 15.77±2.11, 23.05±3.09, and 33.70±4.52 mg/kg, and the theoretically calculated ED16,add,ED50,add, and ED84,add were 17.22±1.27, 23.09±1.71, and30.96±2.29 mg/kg, respectively (Table 3, Fig. 3a–c).There were no significant differences between thecorresponding EDxs (x=16, 50 and 84) for the fixed-ratiocombination of 1:3 so the interactions were purelyadditive.

Three-dimensional isobolographic analysis ofinteractions

3D isobolographic analysis showed that the strength ofsupra-additivity (synergy) decreased with the increment ofobserved effects. In this study, the interaction index wasused as an indicator of the strength and magnitude ofexamined interactions between LTG and CZP. The inter-action index for the fixed-ratio combination of 3:1increased from 0.51 (ED16) to 0.60 (ED84). Thus, thesupra-additivity fell by 0.09 (9%) as the anticonvulsanteffects increased from 16% to 84% (Table 3). Similarly,the interaction index for the fixed ratio of 1:1 rose from0.45 (ED16) to 0.65 (ED84), i.e. a synergy reduction by 0.2(20%; Table 3). The interaction index for last fixed-ratiocombination tested (i.e. 1:3) also tended to increase withincreasing anticonvulsant effects. In this case, the interac-tion index ranged between 0.92 (ED16) and 1.09 (ED84),hence the additivity reduction was 0.18 (18%; Table 3).

Brain AED concentrations

Total brain concentrations of LTG and CZP wereestimated for the doses corresponding to the ED50,mix forthe fixed ratio of 1:1 (9.17 mg/kg), because at the fixedratio of 1:1, both AEDs are present at equi-effective doses.The total brain LTG concentration (for the drug appliedalone at 1.33 mg/kg) was 1.80±0.30 μg/ml and did notdiffer from that seen with the mixture of LTG (1.33 mg/kg)and CZP (7.84 mg/kg). In this case, the total brain LTGconcentration for the mixture of LTG and CZP was 1.83±0.41 μg/ml. Similarly, the total brain CZP level (for the

drug applied alone at 7.84 mg/kg) was 45.74±3.89 ng/mland 47.02±4.01 ng/ml when the mixture was given.

Discussion

The above results indicate clearly that LTG interactedsynergistically with CZP with respect to the anticonvulsantactivity against MES-induced seizures in mice. 3Disobolographic analysis showed that the drugs in thefixed-ratio combinations of 1:1 and 3:1 exerted supra-additive interactions, whereas at the fixed ratio of 1:3 theeffects were purely additive. The supra-additivity at thefixed ratios of 1:1 and 3:1 is consistent with the results ofour previous studies showing that some Na+ channelblockers, such as carbamazepine, phenytoin, and oxcarba-zepine, in combinations with CZP, show supra-additivityin the MES test (Luszczki et al. 2003b). The present studyalso indicates that LTG combined with CZP at the fixedratio of 1:3, showed pure additivity in the MES test,whereas phenytoin and carbamazepine combined withCZP at the fixed ratio of 1:3 show supra-additive(synergistic) interactions (Luszczki et al. 2003b). Incontrast, oxcarbazepine at the same fixed-ratio combina-tion of 1:3 displays sub-additivity (antagonism) in theMES test (Luszczki et al. 2003b).

It should be clearly stated that our results with respect tothe determination of the ED50 in the MES test aregenerally consistent with those of White et al. (2002), whohave reported an ED50 for LTG (injected i.p.) in the MEStest in mice of 7.47 (6.13–9.11) mg/kg, and 25.6 (9.12–65.9) mg/kg for i.p. CZP. In our study, the ED50 for LTGin the MES test was 4.93 (4.16–5.86) mg/kg and that forCZP was 29.14 (25.25–33.63) mg/kg (Table 1). The slightdifference between these ED50 values may reflect inter-laboratory variance in the determination of ED50 in theMES test. Moreover, LTG and CZP administered alone attheir ED50 did not impair motor coordination significantlyin the chimney test in mice (data not shown). The mediantoxic doses (TD50) for CZP and LTG, determinedpreviously in the chimney test are 48.8 (22.7–105.2) mg/kg (Luszczki et al. 2003b) and 28.7 (21.4–38.6) mg/kg(Luszczki et al. 2003a), respectively.

It should be emphasized that 3D isobolography requiresthe parallelism of DRR lines of AEDs administeredseparately. The test for parallelism confirms that theproportions of drugs in the mixture do not change duringthe evaluation of ED16,mix, ED50,mix and ED84,mix (Pöch1993; Sühnel 1998). In other words, if the DRRs areparallel the proportions of drugs in mixture are constantfor every effect level examined (see Table 4). Thismathematical certitude is a basic principle of 3Disobolography. If the DRRs for AEDs were not parallel,one would erroneously accept a high dose of one AED andcombine with a given dose of the second AED, possiblyresulting in false synergy, especially, when the effects forthe fixed ratios of 1:3 and 3:1 are examined. Conversely,one can accept a low dose of one AED and combine with agiven dose of the second AED, resulting finally in

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antagonistic interaction. In our opinion, the test forparallelism of DRR lines of tested AEDs should alwaysbe performed, even for 2D isobolographic analysis, toavoid methodological errors associated with a falsedetermination of AED proportions in mixture for variousfixed-ratio combinations. We maintain therefore that thetest for parallelism of two DRR lines should be a standardprocedure for 2D isobolography for the correct evaluationof the observed interactions between two fully activedrugs.

There is no doubt that combinations of two effectivedrugs may exert synergistic, antagonistic or additiveinteractions. To determine the strength, magnitude anddegree of such interactions, the interaction index iscalculated from the isobolar relation (Loewe 1953); (seeMaterials and methods). It is conceivable that as theinteraction index increases, the strength and degree ofsynergistic interaction decreases, leading to additivity oreven sub-additivity. In other words, the lower the dose ofthe experimental mixture that exerts a desired effect, themore supra-additive the observed interaction. In case ofsupra-additivity, the interaction index, as the quotient ofexperimental mixture dose (EDx,mix) and pure additive(theoretically calculated) mixture dose (EDx,add), should belowest. We have observed for the first time that theinteraction index increased proportionally with increasingestimated effect levels for all fixed-ratio combinationstested. In other words, the investigated combinations losttheir strength and power when the anticonvulsant effect of

Table 4 Proportions of tested AEDs in mixtures for various givendrug-dose effects (ED16, ED50, ED84). If the DRR lines of examinedAEDs are parallel, the theoretically calculated proportions of AEDsin mixture are constant for various estimated effects (i.e. 16%reflects ED16; 50%, ED50 and 84%, ED84). For instance: proportionsof AEDs in mixture at the fixed ratio of 1:3 for a 16% effect arecalculated as follows: 1/4 ED16,LTG + 3/4 ED16,CZP=ED16,mix; hence,the proportion of LTG in mixture (PLTG) is a quotient of LTG dose(1/4 ED16,LTG) and total dose of mixture (ED16,mix). Analogously,the proportion of CZP in mixture is calculated as follows: PCZP=3/4ED16,CZP/ED16,mix (PLTG and PCZP proportions of the respectiveAEDs in mixture)

Drug ED16 (mg/kg) ED50 (mg/kg) ED84 (mg/kg)

LTG 3.644 4.934 6.681CZP 21.741 29.137 39.049

FR Effect (%) PLTG PCZP

1:3 16 0.053 0.94750 0.053 0.94784 0.054 0.946

1:1 16 0.144 0.85650 0.145 0.85584 0.146 0.854

3:1 16 0.335 0.66550 0.337 0.66384 0.339 0.661

Fig. 4a–d 3D isobolographicsurface modelling for interac-tions between LTG and CZP inthe MES test in mice a,b The3D surface model consists of theexperimentally derived isobolo-grams for mixtures of LTG withCZP, constructed at various ef-fect levels between 16% and84%. To visualize the supra-additive interactions for themixture of LTG and CZP better,the left graph has been rotatedvertically, whereas the rightgraph represents the observedinteractions as a function ofAED dose/response effects. c,d3D surface model of purelyadditive interactions determinedfrom the equation of additivityfor mixtures of LTG with CZPconstructed at effect levels be-tween 16% and 84%

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individual AEDs increases (Table 3). The practicalimplications of this fact in experimental study are as yetunknown. The question of why the combinations of twoAEDs are more powerful at lower effect levels and,simultaneously, less powerful for higher estimated effectsneeds to be addressed in the future.

Another problem concerning the interaction indexshould be discussed here. In 3D isobolography, toillustrate synergy or antagonism between two drugssome authors plot the interaction index on the z-axis inthe Cartesian coordinates (Prichard et al. 1991, 1993;Sühnel 1992; Kanzawa et al. 1997). In such cases, asynergistic interaction, the interaction index of which islower than 1, appears in 3D graphs as a depression belowthe isobologram surface. In contrast, an antagonisticinteraction with interaction index higher than 1 appearsas a hill above the 3D surface. In our opinion, plotting theinteraction indices values on the z-axis is superfluous andleads finally to the absurdity of multiplication ofdimensions. It is clear that in our study, with thepresentation of the interaction indices values on the z-axis and various effect levels between 16% and 84% on Ω-axis, one can obtain a 4D isobolograms (obviously, x-axisand y-axis represent doses of LTG and CZP, respectively).Analogously, combinations of three AEDs may generate5D isobolograms, and so on. In such a situation, graphicalpresentation of 4D and 5D isobolograms may becomeproblematic. It is worth noting that, in our study, theobserved synergy between LTG and CZP is represented asa convex surface on the 3D isobologram (Fig. 4a,b). Wedo not recommend the presentation of the interactionindex as another variable in the Cartesian system becauseof the pragmatic fact that the less complicated theisobolograms, the more likely will readers understandand obtain useful information.

The observed synergistic interaction between LTG andCZP in the MES test in mice can be explained tentativelyon the basis of the molecular mechanisms of action of bothAEDs. In in vitro experiments LTG has been shown to acton voltage-dependent Na+ channels, binding to theirinactivated form and limiting the sustained repetitivefiring of neurons and to decrease the presynaptic release ofthe excitatory neurotransmitter glutamate (Cheung et al.1992). LTG also inhibits native high-voltage activatedCa2+ channels located presynaptically on nerve terminals(Leach et al. 1991; Calabresi et al. 1999). The inhibition ofthese P/Q- and N-types of Ca2+ channel probably accountsfor reduction of glutamate-mediated excitatory postsynap-tic potentials (Wang et al. 1996, 1998). With respect toCZP’s mechanisms of action, it is established thatbenzodiazepines (BDZs, including CZP) interact specifi-cally with a benzodiazepine receptor molecule to modulateallosterically the efficiency of the inhibitory neurotrans-mitter GABA at GABAA receptors (Haefely 1989;Macdonald et al. 2002). Moreover, BDZs at highconcentrations also block Na+ channels voltage-depen-dently, reducing high-frequency repetitive firing incultured mammalian neurons (McLean and Macdonald1988). Given these mechanisms of action of the two

AEDs, it is conceivable that the observed synergy in theMES test in mice resulted from a supplementarycooperation of both drugs in terms of reducing theseizures. So, the simultaneous Na+ channel blockade andGABAA-mediated neuronal inhibition contributed to thepotentiation of the anticonvulsant effects of the combinedtreatment with LTG and CZP.

To characterize the observed interactions between LTGand CZP in more detail, we evaluated and verified thepharmacokinetic correlates in the biophase (brain homo-genates of experimental animals). Measuring AED con-centrations in the biophase provides more relevantinformation and a greater insight into the characteristicsof the observed interactions than does the evaluation ofAED concentrations in the plasma of experimental animals(Cadart et al. 2002). Since distinct discrepancies can occurbetween plasma and brain concentrations of AEDs(Luszczki et al. 2003c), the pharmacokinetic verificationof AED concentrations was performed only in thebiophase. Moreover, brain AED concentrations wereanalysed bidirectionally, i.e. the concentrations of bothAEDs were estimated so as not to omit or neglect anyimportant pharmacokinetic interactions that may existbetween the AEDs and might lead to misinterpretation ofobserved interactions with isobolography. Pharmacokinet-ic data revealed that LTG did not affect the brain CZPconcentration, nor did CZP have a significant impact ontotal brain LTG concentration in experimental animals.Hence, in light of the above considerations, the observedsynergistic interaction between LTG and CZP for the fixedratio of 1:1 was of a pharmacodynamic nature.

In summary, this study aimed to acquaint andfamiliarise readers with 3D isobolography as the mostadequate and appropriate means of analysis of interactionsbetween two tested drugs in preclinical studies. Thesynergistic interaction observed for the combination ofLTG with CZP is worth considering in a clinical context,as there were no pharmacokinetic interactions detected inrelation to the examined combination of AEDs.

Acknowledgments This study was supported by a grant (PW447/2002-2004) from the Skubiszewski Medical University ofLublin. The authors thank Mr W. Zgrajka (Institute of AgriculturalMedicine, Lublin, Poland) for the skilful determination of the brainconcentrations of LTG. Dr J.J. Luszczki is a recipient of theFellowship for Young Researchers from the Foundation for PolishScience.

References

Berenbaum MC (1989) What is synergy? Pharmacol Rev 41:93–141[Erratum in Pharmacol Rev 41:422 (1990)]

Besag FM, Berry DJ, Pool F, Newbery JE, Subel B (1998)Carbamazepine toxicity with lamotrigine: pharmacokinetic orpharmacodynamic interaction? Epilepsia 39:183–187

Borowicz KK, Swiader M, Luszczki J, Czuczwar SJ (2002) Effectof gabapentin on the anticonvulsant activity of antiepilepticdrugs against electroconvulsions in mice—an isobolographicanalysis. Epilepsia 43:956–963

379

Cadart M, Marchand S, Pariat C, Bouquet S, Couet W (2002)Ignoring pharmacokinetics may lead to isoboles misinterpreta-tion: illustration with the norfloxacin-theophylline convulsantinteraction in rats. Pharm Res 19:209–214

Calabresi P, Centonze D, Marfia GA, Pisani A, Bernardi G (1999)An in vitro electrophysiological study on the effects ofphenytoin, lamotrigine and gabapentin on striatal neurons. BrJ Pharmacol 126:689–696

Cheung H, Kamp D, Harris E (1992) An in vitro investigation of theaction of lamotrigine on neuronal voltage-activated sodiumchannels. Epilepsy Res 13:107–112

Deckers CL, Czuczwar SJ, Hekster YA, Keyser A, Kubova H,Meinardi H, Patsalos PN, Renier WO, Van Rijn CM (2000)Selection of antiepileptic drug polytherapy based on mechan-isms of action: the evidence reviewed. Epilepsia 41:1364–1374

Fischer RS (1989) Animal models of the epilepsies. Brain Res Rev14:245–278

Gasior M, Ungard JT, Witkin JM (1999) Preclinical evaluation ofnewly approved and potential antiepileptic drugs againstcocaine-induced seizures. J Pharmacol Exp Ther 290:1148–1156

Gebhart GF (1992) Topical reviews: a new type of report in pain.Pain 49:1

Gessner PK (1995) Isobolographic analysis of interactions: anupdate on applications and utility. Toxicology 105:161–179

Glantz SA, Slinker BK (2001) Primer of applied regression andanalysis of variance, 2nd edn. MacGraw-Hill, New York

Greco WR, Bravo G, Parsons JC (1995) The search for synergy: acritical review from response surface perspective. PharmacolRev 47:331–385

Haefely W (1989) Benzodiazepines. Mechanisms of action. In: LevyR, Mattson R, Meldrum B, Penry JK, Dreifuss FE (eds)Antiepileptic drugs, 3rd edn. Raven, New York, pp 721–734

Jozwiak S, Terczynski A (2000) Open study evaluating lamotrigineefficacy and safety in add-on treatment and consecutivemonotherapy in patients with carbamazepine- or valproate-resistant epilepsy. Seizure 9:486–492

Kanzawa F, Nishio K, Fukuoka K, Fukuda M, Kunimoto T, Saijo N(1997) Evaluation of synergism by a novel three-dimensionalmodel for the combined action of cisplatin and etoposide on thegrowth of a human small-cell lung-cancer cell line, SBC-3. Int JCancer 71:311–319

Leach MJ, Baxter MG, Critchley MA (1991) Neurochemical andbehavioral aspects of lamotrigine. Epilepsia 32 (Suppl 2):S4–S8

Litchfield JT, Wilcoxon F (1949) A simplified method of evaluatingdose-effect experiments. J Pharmacol Exp Ther 96:99–113

Loewe S (1953) The problem of synergism and antagonism ofcombined drugs. Arzneimittelforschung 3:285–290

Löscher W, Schmidt D (1988) Which animal models should be usedin the search for new antiepileptic drugs? A proposal based onexperimental and clinical considerations. Epilepsy Res 2:145–181

Löscher W, Fassbender CP, Nolting B (1991) The role of technical,biological and pharmacological factors in the laboratoryevaluation of anticonvulsant drugs. II. Maximal electroshockseizure models. Epilepsy Res 8:79–94

Luszczki JJ, Czuczwar SJ (2003) Isobolographic and subthresholdmethods in the detection of interactions between oxcarbazepineand conventional antiepileptics-a comparative study. EpilepsyRes 56:27–42

Luszczki JJ, Czuczwar SJ (2004) Isobolographic profile ofinteractions between tiagabine and gabapentin: a preclinicalstudy. Naunyn-Schmiedeberg’s Arch Pharmacol 369:434–446

Luszczki JJ, Czuczwar M, Kis J, Krysa J, Pasztelan I, Swiader M,Czuczwar SJ (2003a) Interactions of lamotrigine with topir-amate and first-generation antiepileptic drugs in the maximalelectroshock test in mice: an isobolographic analysis. Epilepsia44:1003–1013

Luszczki JJ, Borowicz KK, Swiader M, Czuczwar SJ (2003b)Interactions between oxcarbazepine and conventional antiepi-leptic drugs in the maximal electroshock test in mice: anisobolographic analysis. Epilepsia 44:489–499

Luszczki JJ, Swiader M, Czuczwar M, Kis J, Czuczwar SJ (2003c)Interactions of tiagabine with some antiepileptics in themaximal electroshock in mice. Pharmacol Biochem Behav75:319–327

Macdonald RL (2002) Benzodiazepine. Mechanisms of action. In:Levy RH, Mattson RH, Meldrum BS, Perucca E (eds)Antiepileptic drugs, 5th edn. Lippincott, Philadelphia, pp179–186

McLean MJ, Macdonald RL (1988) Benzodiazepines, but not betacarbolines, limit high frequency repetitive firing of actionpotentials of spinal cord neurons in cell culture. J PharmacolExp Ther 244:789–795

Pöch G (1993) Combined effects of drugs and toxic agents. Modernevaluation in theory and practice. Springer, Wien

Porreca F, Jiang Q, Tallarida RJ (1990) Modulation of morphineantinociception by peripheral [Leu5]enkephalin: a synergisticinteraction. Eur J Pharmacol 179:463–468

Prichard MN, Prichard LE, Baguley WA, Nassiri MR, Shipman C(1991) Three-dimensional analysis of the synergistic cytotox-icity of gancyclovir and zidovudine. Antimicrob AgentsChemother 35:1060–1065

Prichard MN, Prichard LE, Shipman C (1993) Strategic design andtree-dimensional analysis of antiviral drug combinations.Antimicrob Agents Chemother 37:540–545

Stephen LJ, Brodie MJ (2002) Seizure freedom with more than oneantiepileptic drug. Seizure 11:349–351

Sühnel J (1992) Zero interaction response surfaces, interactionfunctions and difference response surfaces for combinations ofbiologically active agents. Arzneimittelforschung 42:1251–1258

Sühnel J (1998) Parallel dose-response curves in combinationexperiments. Bull Math Biol 60:197–213

Tallarida RJ (1992) Statistical analysis of drug combinations forsynergism. Pain 49:93–97

Tallarida RJ (2000) Drug synergism and dose-effect data analysis.Chapman & Hall/CRC, Boca Raton

Tallarida RJ (2001) Drug synergism: its detection and applications. JPharmcol Exp Ther 298:865–872

Tallarida RJ (2002) The interaction index: a measure of drugsynergism. Pain 98:163–168

Tallarida RJ, Stone DJ, McCary JD, Raffa RB (1999) Responsesurface analysis of synergism between morphine and clonidine.J Pharmcol Exp Ther 289:8–13

Wang SJ, Huang CC, Hsu KS, Tsai JJ, Gean PW (1996) Inhibitionof N-type calcium currents by lamotrigine in rat amygdalaneurones. Neuroreport 7:3037–3040

Wang SJ, Tsai JJ, Gean PW (1998) Lamotrigine inhibits depolar-ization-evoked Ca++ influx in dissociated amygdala neurons.Synapse 29:355–362

White HS, Woodhead JH, Wilcox KS, Stables JP, Kupferberg HJ,Wolf HH (2002) Discovery and preclinical development ofantiepileptic drugs. In: Levy RH, Mattson RH, Meldrum BS,Perucca E (eds) Antiepileptic drugs, 5th edn. Lippincott,Philadelphia, pp 36–48

380