Complex interactions of lovastatin with 10 chemotherapeutic drugs: a rigorous evaluation of synergism and antagonism.

BACKGROUND: Evidence bearing on the role of statins in the prevention and treatment of cancer is confounded by the diversity of statins, chemotherapeutic agents and cancer types included in the numerous published studies; consequently, the adjunctive value of statins with chemotherapy remains uncertain. METHODS: We assayed lovastatin in combination with each of ten commonly prescribed chemotherapy drugs in highly reproducible in vitro assays, using a neutral cellular substrate, Saccharomyces cerevisiae. Cell density (OD600) data were analyzed for synergism and antagonism using the Loewe additivity model implemented with the Combenefit software. RESULTS: Four of the ten chemotherapy drugs - tamoxifen, doxorubicin, methotrexate and rapamycin - exhibited net synergism with lovastatin. The remaining six agents (5-fluorouracil, gemcitabine, epothilone, cisplatin, cyclophosphamide and etoposide) compiled neutral or antagonistic scores. Distinctive patterns of synergism and antagonism, often coexisting within the same concentration space, were documented with the various combinations, including those with net synergism scores. Two drug pairs, lovastatin combined with tamoxifen or cisplatin, were also assayed in human cell lines as proof of principle. CONCLUSIONS: The synergistic interactions of tamoxifen, doxorubicin, methotrexate and rapamycin with lovastatin - because they suggest the possibility of clinical utility - merit further exploration and validation in cell lines and animal models. No less importantly, strong antagonistic interactions between certain agents and lovastatin argue for a cautious, data-driven approach before adding a statin to any chemotherapeutic regimen. We also urge awareness of adventitious statin usage by patients entering cancer treatment protocols.

Synergy evaluation of non-normalizable dose-response data: Generalization of combination index for the linear effect of drugs.

The study of drug synergy plays a prominent role in the search for drug combinations with beneficial interactions. Firstly, in this process, the drug-effect response of individual parts and the mixture needs to be derived. This function is usually well described by Hill (or other logistic or sigmoid) curve. Due to its boundedness, it allows the measured data to be normalized. The normalized data can then be processed by interaction analysis using the Loewe, Bliss, or other models to evaluate possible synergy or antagonism of two or more drugs. However, sometimes, the drug-effect responses observed in pharmaceutical research do not appear to be bounded. Theoretically, the drug-effect curve cannot grow to infinity, but it may be impossible to determine its upper bound within the observed region. In this case, standard models cannot be used, since they assume that data are normalized. The approach of this article bypasses the need to normalize the data, allowing its broader application and usefulness in finding potential synergies in pharmaceutical research.

A foundation for reference models for drug combinations with an application to Loewe's reference model.

BACKGROUND: Treating patients with combinations of drugs that have synergistic effects has become widespread practice in the clinic. Drugs work synergistically when the observed effect of a drug combination is larger than the effect predicted by the reference model. The reference model is a theoretical null model that returns the combined effect of given doses of drugs under the assumption that these drugs do not interact. There is ongoing debate on what it means for drugs to not interact. The controversy transcends mathematical punctuality, as different non-interaction principles result in different reference models. A famous reference model that has been in existence for already a long time is Loewe's reference model. Loewe's vision on non-interaction was purely intuitive: two drugs do not interact if all combinations of doses that result in a certain given effect lie on a straight line. RESULTS: We show that Loewe's reference model can be obtained from much more fundamental principles. First, we introduce the new notion of complementary dose. Secondly, we reformulate the existing concept of equivalent dose, whereby our formulation is more general than existing ones. Finally, a very general non-interaction principle is put forward. The proposed non-interaction principle represents a certain interplay between complementary and equivalent doses: drugs are non-interacting if complementarity is preserved under equivalence. It is then shown that Loewe's reference model naturally follows from these principles by an appropriate choice of complementarity. CONCLUSIONS: The presented work increases insight into Loewe's reference model for drug combinations, which is realized by the introduction of a very general non-interaction principle that does not refer to any specific dose-response curve, nor to any property of applicable dose-response curves.

Modeling dose-response functions for combination treatments with log-logistic or Weibull functions.

Dose-response curves of new substances in toxicology and related areas are commonly fitted using log-logistic functions. In more advanced studies, an additional interest is often how these substances will behave when applied in combination with a second substance. Here, an essential question for both design and analysis of these combination experiments is whether the resulting dose-response function will still be a member of the class of log-logistic functions, and, if so, what function parameters will result for the combined substances. Different scenarios might be considered in regard to whether a true interaction between the substances is expected, or whether the combination will simply be additive. In this paper, it is shown that the resulting function will in general not be a log-logistic function, but can be approximated very closely with one. Parameters for this approximation can be predicted from the parameters of both ingredients. Furthermore, some simple interaction structures can still be represented with a single log-logistic function. The approach can also be applied to Weibull-type dose-response functions, and similar results are obtained. Finally, the results were applied to a real data set obtained from cell culture experiments involving two cancer treatments, and the dose-response curve of a combination treatment was predicted from the properties of the singular substances.

Theory of synergistic effects: Hill-type response surfaces as 'null-interaction' models for mixtures.

BACKGROUND: The classification of effects caused by mixtures of agents as synergistic, antagonistic or additive depends critically on the reference model of 'null interaction'. Two main approaches are currently in use, the Additive Dose (ADM) or concentration addition (CA) and the Multiplicative Survival (MSM) or independent action (IA) models. We compare several response surface models to a newly developed Hill response surface, obtained by solving a logistic partial differential equation (PDE). Assuming that a mixture of chemicals with individual Hill-type dose-response curves can be described by an n-dimensional logistic function, Hill's differential equation for pure agents is replaced by a PDE for mixtures whose solution provides Hill surfaces as 'null-interaction' models and relies neither on Bliss independence or Loewe additivity nor uses Chou's unified general theory. METHODS: An n-dimensional logistic PDE decribing the Hill-type response of n-component mixtures is solved. Appropriate boundary conditions ensure the correct asymptotic behaviour. Mathematica 11 (Wolfram, Mathematica Version 11.0, 2016) is used for the mathematics and graphics presented in this article. RESULTS: The Hill response surface ansatz can be applied to mixtures of compounds with arbitrary Hill parameters. Restrictions which are required when deriving analytical expressions for response surfaces from other principles, are unnecessary. Many approaches based on Loewe additivity turn out be special cases of the Hill approach whose increased flexibility permits a better description of 'null-effect' responses. Missing sham-compliance of Bliss IA, known as Colby's model in agrochemistry, leads to incompatibility with the Hill surface ansatz. Examples of binary and ternary mixtures illustrate the differences between the approaches. For Hill-slopes close to one and doses below the half-maximum effect doses MSM (Colby, Bliss, Finney, Abbott) predicts synergistic effects where the Hill model indicates 'null-interaction'. These differences increase considerably with increasing steepness of the individual dose-response curves. CONCLUSION: The Hill response surface ansatz contains the Loewe additivity concept as a special case and is incompatible with Bliss independent action. Hence, when synergistic effects are claimed, those dose combinations deserve special attention where the differences between independent action approaches and Hill estimations are large.

Assessment of non-linear combination effect terms for drug-drug interactions.

Drugs interact with their targets in different ways. A diversity of modeling approaches exists to describe the combination effects of two drugs. We investigate several combination effect terms (CET) regarding their underlying mechanism based on drug-receptor binding kinetics, empirical and statistical summation principles and indirect response models. A list with properties is provided and the interrelationship of the CETs is analyzed. A method is presented to calculate the optimal drug concentration pair to produce the half-maximal combination effect. This work provides a comprehensive overview of typically applied CETs and should shed light into the question as to which CET is appropriate for application in pharmacokinetic/pharmacodynamic models to describe a specific drug-drug interaction mechanism.

Testing drug additivity based on monotherapies.

Under the Loewe additivity, constant relative potency between two drugs is a sufficient condition for the two drugs to be additive. Implicit in this condition is that one drug acts like a dilution of the other. Geometrically, it means that the dose-response curve of one drug is a copy of another that is shifted horizontally by a constant over the log-dose axis. Such phenomenon is often referred to as parallelism. Thus, testing drug additivity is equivalent to the demonstration of parallelism between two dose-response curves. Current methods used for testing parallelism are usually based on significance tests for differences between parameters in the dose-response curves of the monotherapies. A p-value of less than 0.05 is indicative of non-parallelism. The p-value-based methods, however, may be fundamentally flawed because an increase in either sample size or precision of the assay used to measure drug effect may result in more frequent rejection of parallel lines for a trivial difference. Moreover, similarity (difference) between model parameters does not necessarily translate into the similarity (difference) between the two response curves. As a result, a test may conclude that the model parameters are similar (different), yet there is little assurance on the similarity between the two dose-response curves. In this paper, we introduce a Bayesian approach to directly test the hypothesis that the two drugs have a constant relative potency. An important utility of our proposed method is in aiding go/no-go decisions concerning two drug combination studies. It is illustrated with both a simulated example and a real-life example.

Experimental designs for detecting synergy and antagonism between two drugs in a pre-clinical study.

The identification of synergistic interactions between combinations of drugs is an important area within drug discovery and development. Pre-clinically, large numbers of screening studies to identify synergistic pairs of compounds can often be ran, necessitating efficient and robust experimental designs. We consider experimental designs for detecting interaction between two drugs in a pre-clinical in vitro assay in the presence of uncertainty of the monotherapy response. The monotherapies are assumed to follow the Hill equation with common lower and upper asymptotes, and a common variance. The optimality criterion used is the variance of the interaction parameter. We focus on ray designs and investigate two algorithms for selecting the optimum set of dose combinations. The first is a forward algorithm in which design points are added sequentially. This is found to give useful solutions in simple cases but can lack robustness when knowledge about the monotherapy parameters is insufficient. The second algorithm is a more pragmatic approach where the design points are constrained to be distributed log-normally along the rays and monotherapy doses. We find that the pragmatic algorithm is more stable than the forward algorithm, and even when the forward algorithm has converged, the pragmatic algorithm can still out-perform it. Practically, we find that good designs for detecting an interaction have equal numbers of points on monotherapies and combination therapies, with those points typically placed in positions where a 50% response is expected. More uncertainty in monotherapy parameters leads to an optimal design with design points that are more spread out.

Effect of estrogenic binary mixtures in the yeast estrogen screen (YES).

Endocrine disrupting compounds (EDCs) of natural or synthetic origin can interfere with the balance of the hormonal system, either by altering hormone production, secretion, transport, or their binding and consequently lead to an adverse outcome in intact animals. An important aspect is the prediction of effects of combined exposure to two or more EDCs at the same time. The yeast estrogen assay (YES) is a broadly used method to assess estrogenic potential of chemicals. Besides exhibiting good predictivity to identify compounds which interfere with the estrogen receptor, it is easy to handle, rapid and therefore allows screening of a large number of single compounds and varying mixtures. Herein, we applied the YES assay to determine the potential combination effects of binary mixtures of two estrogenic compounds, bisphenol A and genistein, as well as one classical androgen that in vitro also exhibits estrogenic activity, trenbolone. In addition to generating data from combined exposure, we fitted these to a four-parametric logistic dose-response model. As all compounds tested share the same mode of action dose additivity was expected. To assess this, the Loewe model was utilized. Deviations between the Loewe additivity model and the observed responses were always small and global tests based on the whole dose-response data set indicated in general a good fit of the Loewe additivity model. At low concentrations concentration additivity was observed, while at high concentrations, the observed effect was lower than additivity, most likely reflecting receptor saturation. In conclusion, our results suggest that binary combinations of genistein, bisphenol A and trenbolone in the YES assay do not deviate from expected additivity.

Synergistic Effect of Venetoclax and Bendamustine in Early T-cell Precursor Acute Lymphoblastic Leukemia.

BACKGROUND/AIM: To date, therapeutic options for T-cell acute lymphoblastic leukemia (T-ALL) remain very limited. This study evaluated the efficacy of monotherapies and combination therapies including a selective BCL-2 inhibitor for T-ALL cell lines, namely Jurkat, CCRF-CEM, and Loucy. MATERIALS AND METHODS: Loucy is an early T-precursor ALL (ETP-ALL) cell line characterized by an immature phenotype, whereas Jurkat and CCRF-CEM are late T-cell progenitor ALL (LTP-ALL) cell lines. Monotherapy was conducted with venetoclax, cytarabine, bendamustine, or azacytidine, whereas combination therapy was performed with venetoclax plus cytarabine, venetoclax plus bendamustine, or venetoclax plus azacytidine. Cell viability assay was conducted after 48 h using Trypan blue and the 3-(4, 5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2H-tetrazolium (MTS). Statistical analysis for evaluating synergistic interactions between anticancer drugs was performed by using the SynergyFinder Plus and drc R package. RESULTS: Adding venetoclax to cytarabine, bendamustine, or azacitidine achieved an additive effect, with Loewe synergic scores ranging from -10 to 10 in Jurkat and CCRF-CEM. Conversely, the combination of venetoclax and cytarabine displayed an additive effect (Loewe synergic score: 8.45 and 5.82 with MTS and Trypan blue assays, respectively), whereas venetoclax plus bendamustine or azacitidine exhibited a synergistic effect (Loewe synergic score >10 with MTS assay) in Loucy. Remarkably, the Bliss/Loewe score revealed that the combination of venetoclax and bendamustine was the most synergistic, yielding a score of 13.832±0.55. CONCLUSION: The combination of venetoclax and bendamustine demonstrated the greatest synergistic effect in suppressing ETP-ALL cell proliferation. Further studies are warranted to determine the mechanisms for the synergism between venetoclax and bendamustine in high-risk T-ALL.

The many dimensions of combination therapy: How to combine antibiotics to limit resistance evolution.

In combination therapy, bacteria are challenged with two or more antibiotics simultaneously. Ideally, separate mutations are required to adapt to each of them, which is a priori expected to hinder the evolution of full resistance. Yet, the success of this strategy ultimately depends on how well the combination controls the growth of bacteria with and without resistance mutations. To design a combination treatment, we need to choose drugs and their doses and decide how many drugs get mixed. Which combinations are good? To answer this question, we set up a stochastic pharmacodynamic model and determine the probability to successfully eradicate a bacterial population. We consider bacteriostatic and two types of bactericidal drugs-those that kill independent of replication and those that kill during replication. To establish results for a null model, we consider non-interacting drugs and implement the two most common models for drug independence-Loewe additivity and Bliss independence. Our results show that combination therapy is almost always better in limiting the evolution of resistance than administering just one drug, even though we keep the total drug dose constant for a 'fair' comparison. Yet, exceptions exist for drugs with steep dose-response curves. Combining a bacteriostatic and a bactericidal drug which can kill non-replicating cells is particularly beneficial. Our results suggest that a 50:50 drug ratio-even if not always optimal-is usually a good and safe choice. Applying three or four drugs is beneficial for treatment of strains with large mutation rates but adding more drugs otherwise only provides a marginal benefit or even a disadvantage. By systematically addressing key elements of treatment design, our study provides a basis for future models which take further factors into account. It also highlights conceptual challenges with translating the traditional concepts of drug independence to the single-cell level.

A simple test for synergy for a small number of combinations.

A method for detecting deviations from the Loewe additive drug combination reference model for in vitro drug combination experimentation is described. It is often difficult to fit a response surface model to drug combination data, especially in situations where the experimental design contains a sparse set of combinations. The literature does contain good response surface modeling approaches, but they tend to be complex and can be difficult to execute. It is especially difficult to check model quality when fitting to more than two combined agents. A simple method based on sound statistical principles is proposed that examines the mean response deviation of each combination from the predicted response under Loewe additivity. The method can readily handle any number of combined agents, does not require sophisticated modeling, and can even be programmed into Microsoft Excel without the use of macros. Several potential extensions to the method are discussed in detail. Computer-generated simulations demonstrate the statistical capabilities of the approach, and a real-data example is given to illustrate the method.

Investigation of the robustness of two models for assessing synergy in pre-clinical drug combination studies.

Pre-clinical studies may be used to screen for synergistic combinations of drugs. The types of in vitro assays used for this purpose will depend upon the disease area of interest. In oncology, one frequently used study measures cell line viability: cells placed into wells on a plate are treated with doses of two compounds, and cell viability is assessed from an optical density measurement corrected for blank well values. These measurements are often transformed and analysed as cell survival relative to untreated wells. The monotherapies are assumed to follow the Hill equation with lower and upper asymptotes at 0 and 1, respectively. Additionally, a common variance about the dose-response curve may be assumed. In this paper, we consider two models for incorporating synergy parameters. We investigate the effect of different models of biological variation on the assessment of synergy from both of these models. We show that estimates of the synergy parameters appear to be robust, even when estimates of the other model parameters are biased. Using untransformed measurements provides better coverage of the 95% confidence intervals for the synergy parameters than using transformed measurements, and the requirement to fit the upper asymptote does not cause difficulties. Assuming homoscedastic variances appears to be robust. The added complexity of determining and fitting an appropriate heteroscedastic model does not seem to be justified.

Exploring synergy and its role in antimicrobial peptide biology.

Antimicrobial peptides will be an essential component in combating the escalating issue of antibiotic resistance. Identifying synergistic combinations of two or more substances will increase the value of these peptides further. Several potential pitfalls in conducting synergy testing with peptides are discussed in detail. As case studies, we describe observations of AMP synergy with peptides, antibiotics, and metal ions as well as some of the mechanistic details that have been uncovered. The Bliss and Loewe models for synergy are presented prior to recommending protocols for conducting checkerboard, minimal inhibitory concentration, and time-kill assays. Establishing mechanisms of action and exploring the potential for resistance will be crucial to translate these studies into the clinic.

Evaluation of synergism in drug combinations and reference models for future orientations in oncology.

Current cancer therapy includes a variety of strategies that can comprise only one type of treatment or a combination of multiple treatments. Chemotherapy is still the gold standard for cancer therapy, though sometimes associated with undesired side effects and the development of drug resistance. For this reason, drug combination is an approach that has been proposed to overcome the problems related to monotherapy and several studies have already demonstrated the superiority of combined therapies compared to monotherapy. The main goal when designing and evaluating drug combinations is to achieve synergistic effects by demonstrating that the combined effects are greatly superior to the expected from the additive effects of the single drugs, allowing for dosage reduction and therefore decreasing toxicity. Nevertheless, synergism quantification is not a simple task due to the different definitions of additivity and over the years several reference models have been proposed based on different assumptions and with different mathematical frameworks. In this review, we begin to cover the available treatment options for cancer therapy, with emphasis on the importance of drug combinations in cancer therapy. We next describe the classical reference models that have been proposed for synergism evaluation, usually classified as effect-based and dose-effect based methods, with a brief analysis of the current limitations of these models. We also describe here the novel methods for the accurate quantification of drug interactions in combined treatments. At the end of this manuscript, we covered some of the most recent preclinical and clinical combination studies that reflect the importance of the appropriate, accurate and precise application of the concepts and methodologies here described for the evaluation of synergism.

Multicenter Collaborative Study of the Interaction of Antifungal Combinations against Candida Spp. by Loewe Additivity and Bliss Independence-Based Response Surface Analysis.

Combination antifungal therapy is widely used but not well understood. We analyzed the spectrophotometric readings from a multicenter study conducted by the New York State Department of Health to further characterize the in vitro interactions of the major classes of antifungal agents against Candida spp. Loewe additivity-based fractional inhibitory concentration index (FICi) analysis and Bliss independence-based response surface (BIRS) analysis were used to analyze two-drug inter- and intraclass combinations of triazoles (AZO) (voriconazole, posaconazole), echinocandins (ECH) (caspofungin, micafungin, anidulafungin), and a polyene (amphotericin B) against Candida albicans, C. parapsilosis, and C. glabrata. Although mean FIC indices did not differ statistically significantly from the additivity range of 0.5−4, indicating no significant pharmacodynamic interactions for all of the strain−combinations tested, BIRS analysis showed that significant pharmacodynamic interactions with the sum of percentages of interactions determined with this analysis were strongly associated with the FIC indices (Χ2 646, p < 0.0001). Using a narrower additivity range of 1−2 FIC index analysis, statistically significant pharmacodynamic interactions were also found with FICi and were in agreement with those found with BIRS analysis. All ECH+AB combinations were found to be synergistic against all Candida strains except C. glabrata. For the AZO+AB combinations, synergy was found mostly with the POS+AB combination. All AZO+ECH combinations except POS+CAS were synergistic against all Candida strains although with variable magnitude; significant antagonism was found for the POS+MIF combination against C. albicans. The AZO+AZO combination was additive for all strains except for a C. parapsilosis strain for which antagonism was also observed. The ECH+ECH combinations were synergistic for all Candida strains except C. glabrata for which they were additive; no antagonism was found.

Mathematical Modelling of the Molecular Mechanisms of Interaction of Tenofovir with Emtricitabine against HIV.

The combination of the two nucleoside reverse transcriptase inhibitors (NRTI) tenofovir disoproxil fumarate (TDF) and emtricitabine (FTC) is used in most highly active antiretroviral therapies for treatment of HIV-1 infection, as well as in pre-exposure prophylaxis against HIV acquisition. Administered as prodrugs, these drugs are taken up by HIV-infected target cells, undergo intracellular phosphorylation and compete with natural deoxynucleoside triphosphates (dNTP) for incorporation into nascent viral DNA during reverse transcription. Once incorporated, they halt reverse transcription. In vitro studies have proposed that TDF and FTC act synergistically within an HIV-infected cell. However, it is unclear whether, and which, direct drug-drug interactions mediate the apparent synergy. The goal of this work was to refine a mechanistic model for the molecular mechanism of action (MMOA) of nucleoside analogues in order to analyse whether putative direct interactions may account for the in vitro observed synergistic effects. Our analysis suggests that depletion of dNTP pools can explain apparent synergy between TDF and FTC in HIV-infected cells at clinically relevant concentrations. Dead-end complex (DEC) formation does not seem to significantly contribute to the synergistic effect. However, in the presence of non-nucleoside reverse transcriptase inhibitors (NNRTIs), its role might be more relevant, as previously reported in experimental in vitro studies.

Solving the Problem of Assessing Synergy and Antagonism for Non-Traditional Dosing Curve Compounds Using the DE/ZI Method: Application to Nrf2 Activators.

Multi-drug combination therapy carries significant promise for pharmacological intervention, primarily better efficacy with less toxicity and fewer side effects. However, the field lacks methodology to assess synergistic or antagonistic interactions for drugs with non-traditional dose response curves. Specifically, our goal was to assess small-molecule modulators of antioxidant response element (ARE)-driven gene expression, which is largely regulated by the Nrf2 transcription factor. Known as Nrf2 activators, this class of compounds upregulates a battery of cytoprotective genes and shows significant promise for prevention of numerous chronic diseases. For example, sulforaphane sourced from broccoli sprouts is the subject of over 70 clinical trials. Nrf2 activators generally have non-traditional dose response curves that are hormetic, or U-shaped. We introduce a method based on the principles of Loewe Additivity to assess synergism and antagonism for two compounds in combination. This method, termed Dose-Equivalence/Zero Interaction (DE/ZI), can be used with traditional Hill-slope response curves, and it also can assess interactions for compounds with non-traditional curves, using a nearest-neighbor approach. Using a Monte-Carlo method, DE/ZI generates a measure of synergy or antagonism for each dosing pair with an associated error and p-value, resulting in a 3D response surface. For the assessed Nrf2 activators, sulforaphane and di-tert-butylhydroquinone, this approach revealed synergistic interactions at higher dosing concentrations consistently across data sets and potential antagonistic interactions at lower concentrations. DE/ZI eliminates the need to determine the best fit equation for a given data set and values experimentally-derived results over formulated fits.

Charting the Fragmented Landscape of Drug Synergy.

Even as the clinical impact of drug combinations continues to accelerate, no consensus on how to quantify drug synergy has emerged. Rather, surveying the landscape of drug synergy reveals the persistence of historical fissures regarding the appropriate domains of conflicting synergy models - fissures impacting all aspects of combination therapy discovery and deployment. Herein we chronicle the impact of these divisions on: (i) the design, interpretation, and reproducibility of high-throughput combination screens; (ii) the performance of algorithms to predict synergistic mixtures; and (iii) the search for higher-order synergistic interactions. Further progress in each of these subfields hinges on reaching a consensus regarding the long-standing rifts in the field.

Assessing the Effect of Mycotoxin Combinations: Which Mathematical Model Is (the Most) Appropriate?

In the past decades, many studies have examined the nature of the interaction between mycotoxins in biological models classifying interaction effects as antagonisms, additive effects, or synergisms based on a comparison of the observed effect with the expected effect of combination. Among several described mathematical models, the arithmetic definition of additivity and factorial analysis of variance were the most commonly used in mycotoxicology. These models are incorrectly based on the assumption that mycotoxin dose-effect curves are linear. More appropriate mathematical models for assessing mycotoxin interactions include Bliss independence, Loewe's additivity law, combination index, and isobologram analysis, Chou-Talalays median-effect approach, response surface, code for the identification of synergism numerically efficient (CISNE) and MixLow method. However, it seems that neither model is ideal. This review discusses the advantages and disadvantages of these mathematical models.