Biphasic characteristic of interactions between stiripentol and carbamazepine in the mouse maximal electroshock-induced seizure model: a three-dimensional isobolographic analysis

Abstract

The anticonvulsant effects produced by stiripentol (STP), carbamazepine (CBZ), and their combination in the maximal electroshock (MES)-induced seizures in mice were investigated using three-dimensional (3D) isobolographic analysis. With 3D isobolography, the combinations of both drugs at the fixed-ratios of 1:3, 1:1, and 3:1 for 16%, 50% and 84% antiseizure effects, respectively, were examined in order to evaluate the preclinical characteristics of the interactions between STP and CBZ. Additionally, to characterize precisely the types of interactions observed in the MES test, free plasma and total brain CBZ concentrations were estimated for all fixed-ratios tested.

The 3D isobolographic analysis showed that STP and CBZ combined at the fixed-ratio of 1:3 produced supra-additive (synergistic) interactions in the MES test for the anticonvulsant effects ranging between 16% and 84%. In contrast, the combination of STP with CBZ at the fixed-ratio of 3:1 exerted sub-additive (antagonistic) interactions in 3D isobolography for all antiseizure effects examined in the MES test. Only the combination of STP and CBZ at the fixed-ratio of 1:1 was additive for the investigated effects (16%, 50% and 84%) in 3D isobolography. Pharmacokinetic evaluation of CBZ concentrations revealed that STP increased both free plasma and total brain CBZ concentrations for all fixed-ratio combinations tested (1:3, 1:1 and 3:1).

In conclusion, the 3D isobolographic findings suggest that the combination of STP with CBZ exerted biphasic characteristics of interactions in the MES test, despite the pharmacokinetic increase in CBZ content in plasma and brains of experimental animals.

Appendix

Test for parallelism of two DRR log-probit lines according to Litchfield and Wilcoxon (1949) comprises three calculations, as follows:

• 1. The determination of the slope ratio (SR), as a quotient of slope functions for the respective DRR lines. SR=S₁/S₂ where, S₁ and S₂ are the slopes of the DRR lines for the first and second drug. Generally, SR≥1.

• 2. The calculation of the f ratio for the slope ratio (f__{ratio_SR}), as follows: ${\text{f\_}}_{{{\text{ratio\_SR}}}} {\text{ = sqrt}}{\left\{ {{\left[ {{\text{log}}{\left( {{\text{f\_}}_{{{\text{ratio\_SR1}}}} } \right)}} \right]}^{2} + {\left[ {log{\left( {{\text{f\_}}_{{ratio{\text{\_}}SR{\text{2}}}} } \right)}} \right]}^{2} } \right\}}$

  where, f__{ratio_S1} and f__{ratio_S2} are the f ratios for the slope function for the first and second drug, respectively; sqrt is the square root of the expression in parentheses {}; log is the logarithm to the base 10.

  Noticeably, the f__{ratio_S1} is calculated, as follows: ${\text{f\_}}_{{{\text{ratio\_S1}}}} = {\text{A}}^{{{\text{2}}{\text{.77/sqrt}}{\left( {{\text{N}}} \right)}}}$

  where A=10^a

  a=1.1×(logS₁)²/logR

  R=(largest dose)/(smallest dose of a drug used).

  Hence, ${\text{A = 10}}^{{{\text{1}}{\text{.1}} \times {{\left[ {{\left( {\log {\text{S1}}} \right)}\hat{}2} \right]}} \mathord{\left/ {\vphantom {{{\left[ {{\left( {\log {\text{S1}}} \right)}\hat{}2} \right]}} {\log {\left( {{\text{largest/smallest dose}}} \right)}}}} \right. \kern-\nulldelimiterspace} {\log {\left( {{\text{largest/smallest dose}}} \right)}}}}$, where N’ is the total number of animals at those doses whose expected anticonvulsant effects ranged between 4 and 6 probits; ^2 is the power of 2. Transforming the above-mentioned equations, one can obtain: ${\text{f\_}}_{{{\text{ratio\_S1}}}} {\text{ = }}{\left\{ {{\text{10}}^{{{\text{1}}{\text{.1}} \times {{\left[ {{\left( {\log {\text{S1}}} \right)}\hat{}2} \right]}} \mathord{\left/ {\vphantom {{{\left[ {{\left( {\log {\text{S1}}} \right)}\hat{}2} \right]}} {\log {\left( {{\text{largest/smallest dose}}} \right)}}}} \right. \kern-\nulldelimiterspace} {\log {\left( {{\text{largest/smallest dose}}} \right)}}}} } \right\}}^{{2.77/{\text{sqrt}}{\left( {{\text{N}}{\text{1}}} \right)}}}$ and, analogously, ${\text{f\_}}_{{{\text{ratio\_S2}}}} {\text{ = }}{\left\{ {{\text{10}}^{{{\text{1}}{\text{.1}} \times {{\left[ {{\left( {\log {\text{S2}}} \right)}\hat{}2} \right]}} \mathord{\left/ {\vphantom {{{\left[ {{\left( {\log {\text{S2}}} \right)}\hat{}2} \right]}} {\log {\left( {{\text{largest/smallest dose}}} \right)}}}} \right. \kern-\nulldelimiterspace} {\log {\left( {{\text{largest/smallest dose}}} \right)}}}} } \right\}}^{{2.77/{\text{sqrt}}{\left( {{\text{N}}2} \right)}}}$

  Finally, one calculates f__{ratio_SR}, as presented above: ${\text{f\_}}_{{{\text{ratio\_SR = }}}} {\text{sqrt}}{\left\{ {{\left[ {{\text{log}}{\left( {{\text{f\_}}_{{{\text{ratio\_S1}}}} } \right)}} \right]}^{2} + {\left[ {\log {\left( {{\text{f\_}}_{{{\text{ratio\_S2}}}} } \right)}} \right]}^{2} } \right\}}$

• 3. The comparison of the SR with f__{ratio_SR}. Noticeably, two DRR lines are parallel if the calculated SR< f__{ratio_SR}, otherwise the two DRR lines are convergent.