Statistical analysis of drug-drug and site-site interactions with isobolograms

The use of more than one drug to achieve a desired effect has been a common practice in pharmacologic testing and in clinical practice. For example, combinations of analgesics are frequently prescribed with a view to enhancing pain relief and reducing adverse effects. It is also well established that administration of more than one drug may give effects that are greater than, or less than, the additive effect of each drug given individually. A non-mechanistic method of characterizing the effect resulting from the administration of two compounds is the isobologram. It is relatively simple to draw and interpret isobolograms. However, this graphical technique, which employs equieffective concentrations of individual drugs and combinations of these, obtains the concentrations as random variables from concentration-effect data, usually transformed to a parallel line assay. Thus, statistical confidence limits from such assays, as well as from non-parallel designs, must be expressed on the isobologram if this diagram is to establish superadditive, subadditive, or merely additive effects. We now present a detailed statistical analysis of the isobolographic method illustrated with examples of the statistical procedures, a rational basis for selecting proportions of each drug in the combination, and a relatively novel application of the isobolographic concept, i.e., interactions involving different anatomical sites.     

Optimizing combination chemotherapy by controlling drug ratios

Cancer chemotherapy treatments typically employ drug combinations in which the dose of each agent is pushed to the brink of unacceptable toxicity; however, emerging evidence indicates that this approach may not be providing optimal efficacy due to the manner in which drugs interact. Specifically, whereas certain ratios of combined drugs can be synergistic, other ratios of the same agents may be antagonistic, implying that the most efficacious combinations may be those that utilize certain agents at reduced doses. Advances in nano-scale drug delivery vehicles now enable the translation of in vitro information on synergistic drug ratios into improved anticancer combination therapies in which the desired drug ratio can be controlled and maintained following administration in vivo, so that synergistic effects can be exploited. This "ratiometric" approach to combination chemotherapy opens new opportunities to enhance the effectiveness of existing and future treatment regimens across a spectrum of human diseases.     

Discovering Anti-platelet Drug Combinations with an Integrated Model of Activator-Inhibitor Relationships,Activator-Activator Synergies and Inhibitor-Inhibitor Synergies

Identifying effective therapeutic drug combinations that modulate complex signaling pathways in platelets is central to the advancement of effective anti-thrombotic therapies. However, there is no systems model of the platelet that predicts responses to different inhibitor combinations. We developed an approach which goes beyond current inhibitor-inhibitor combination screening to efficiently consider other signaling aspects that may give insights into the behaviour of the platelet as a system. We investigated combinations of platelet inhibitors and activators. We evaluated three distinct strands of information, namely: activator-inhibitor combination screens (testing a panel of inhibitors against a panel of activators); inhibitor-inhibitor synergy screens; and activator-activator synergy screens. We demonstrated how these analyses may be efficiently performed, both experimentally and computationally, to identify particular combinations of most interest. Robust tests of activator-activator synergy and of inhibitor-inhibitor synergy required combinations to show significant excesses over the double doses of each component. Modeling identified multiple effects of an inhibitor of the P2Y12 ADP receptor, and complementarity between inhibitor-inhibitor synergy effects and activator-inhibitor combination effects. This approach accelerates the mapping of combination effects of compounds to develop combinations that may be therapeutically beneficial. We integrated the three information sources into a unified model that predicted the benefits of a triple drug combination targeting ADP, thromboxane and thrombin signaling.     

Selective Targeting of CTNNB1-, KRAS- or MYC-Driven Cell Growth by Combinations of Existing Drugs

The aim of combination drug treatment in cancer therapy is to improve response rate and to decrease the probability of the development of drug resistance. Preferably, drug combinations are synergistic rather than additive, and, ideally, drug combinations work synergistically only in cancer cells and not in non-malignant cells. We have developed a workflow to identify such targeted synergies, and applied this approach to selectively inhibit the proliferation of cell lines with mutations in genes that are difficult to modulate with small molecules. The approach is based on curve shift analysis, which we demonstrate is a more robust method of determining synergy than combination matrix screening with Bliss-scoring. We show that the MEK inhibitor trametinib is more synergistic in combination with the BRAF inhibitor dabrafenib than with vemurafenib, another BRAF inhibitor. In addition, we show that the combination of MEK and BRAF inhibitors is synergistic in BRAF-mutant melanoma cells, and additive or antagonistic in, respectively, BRAF-wild type melanoma cells and non-malignant fibroblasts. This combination exemplifies that synergistic action of drugs can depend on cancer genotype. Next, we used curve shift analysis to identify new drug combinations that specifically inhibit cancer cell proliferation driven by difficult-to-drug cancer genes. Combination studies were performed with compounds that as single agents showed preference for inhibition of cancer cells with mutations in either the CTNNB1 gene (coding for β-catenin), KRAS, or cancer cells expressing increased copy numbers of MYC. We demonstrate that the Wnt-pathway inhibitor ICG-001 and trametinib acted synergistically in Wnt-pathway-mutant cell lines. The ERBB2 inhibitor TAK-165 was synergistic with trametinib in KRAS-mutant cell lines. The EGFR/ERBB2 inhibitor neratinib acted synergistically with the spindle poison docetaxel and with the Aurora kinase inhibitor GSK-1070916 in cell lines with MYC amplification. Our approach can therefore efficiently discover novel drug combinations that selectively target cancer genes.     

Benznidazole/Itraconazole Combination Treatment Enhances Anti-Trypanosoma cruzi Activity in Experimental Chagas Disease

The nitroheterocyclic drugs nifurtimox and benznidazole are first-line drugs available to treat Chagas disease; however, they have limitations, including long treatment courses and toxicity. Strategies to overcome these limitations include the identification of new drugs with specific target profiles, re-dosing regimens for the current drugs, drug repositioning and combination therapy. In this work, we evaluated combination therapy as an approach for optimization of the current therapeutic regimen for Chagas disease. The curative action of benznidazole/itraconazole combinations was explored in an established infection of the mice model with the T. cruzi Y strain. The activities of the benznidazole/itraconazole combinations were compared with the results from those receiving the same dosage of each individual drug. The administration of benznidazole/itraconazole in combination eliminated parasites from the blood more efficiently than each drug alone. Here, there was a significant reduction of the number of treatment days (number of doses) necessary to induce parasitemia suppression with the benznidazole/itraconazole combination, as compared to each compound administered alone. These results clearly indicate the enhanced effects of these drugs in combination, particularly at the dose of 75 mg/kg, as the effects observed with the drug combinations were four times more effective than those of each drug used alone. Moreover, benznidazole/itraconazole treatment was shown to prevent or decrease the typical lesions associated with chronic experimental Chagas disease, as illustrated by similar levels of inflammatory cells and fibrosis in the cardiac muscle tissue of healthy and treated mice. These results emphasize the importance of exploring the potential of combination treatments with currently available compounds to specifically treat Chagas disease.     

A semiparametric response surface model for assessing drug interaction

Summary .   When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Existing response surface models are not adequate to capture the complex patterns of drug interactions. We propose a two-component semiparametric response surface model with a parametric function to describe the additive effect of a combination dose and a nonparametric function to capture the departure from the additive effect. The nonparametric function is estimated using the technique developed in thin plate splines, and the pointwise bootstrap confidence interval for this function is constructed. The proposed semiparametric model offers an effective way of formulating the additive effect while allowing the flexibility of modeling a departure from additivity. Example and simulations are given to illustrate that the proposed model provides an excellent estimation for different patterns of interactions between two drugs.     

Interactions of Mexiletine with Novel Antiepileptic Drugs in the Maximal Electroshock Test in Mice: An Isobolographic Analysis

The aim of the study was to evaluate precisely the type of interactions between mexiletine (an antiarrhythmic drug) and four new generation antiepileptic drugs: lamotrigine, oxcarbazepine, topiramate and pregabalin in the maximal electroshock test in mice (MES). The isobolographic analysis was used to assess the nature of interactions between the tested drugs. Total brain concentrations of antiepileptics were also measured to detect possible pharmacokinetic interactions. The results obtained indicated that the mixture of mexiletine and pregabalin at the fixed ratios of 1:1 and 3:1 led to supra-additive interaction in terms of seizure suppression, while the proportion of 1:3 occurred additive. Synergism was also demonstrated for the combination of mexiletine and topiramate in all three proportions. Combinations of mexiletine with lamotrigine and mexiletine with oxcarbazepine were found to be additive. Adverse-effect profiles of mexiletine, antiepileptics and drug combinations were evaluated in the chimney test (motor coordination) and step-through passive-avoidance task (long-term memory). Mexiletine and drug combinations did not impair long-term memory. Moreover, all combinations of mexiletine with lamotrigine, oxcarbazepine and topiramate had no significant effect on motor coordination. However, the results from the chimney test indicated that pregabalin, administered alone at its ED₅₀ dose from the MES-test, significantly impaired motor performance. Similar adverse effects were observed when mexiletine was co-administered with pregabalin at the fixed-dose ratio combinations of 1:1 and 1:3. However, reduction of pregabalin dose at the fixed ratio of 3:1 seems to prevent significant motor impairment. The results may indicate that mexiletine can be considered as an adjunctive drug in antiepileptic treatment, particularly in patients with concomitant cardiac arrhythmia.     

Two-drug combinations of memory enhancers: effect of dose ratio upon potency and therapeutic window, in mice

Two-drug combinations have been reported to enhance retention more effectively than when either drug was administered alone at the same dose. Some combinations of cholinergic drugs enhance retention even though the total drug dosage is reduced by as much as 97% compared to the dose needed to improve retention when the same drugs are administered singly. The choice of dose ratio is usually arbitrary or based on empirical results. The present study systematically varied the ratio of two drugs in a combination and at the same time varied the dosage of each drug. The drug combinations were administered to mice immediately after training on T-maze footshock avoidance task. Retention was tested one week later. Three two-drug combinations were selected for presentation because they differed considerably as to (a) the lowest effective total dose that improved memory-retention, (b) the optimal ratio that improved retention and (c) the width of the therapeutic window. The effect of a drug combination on retention was found to be dependent on the particular drugs in the combination, the ratio and the dose administered.     

Unprecedented Therapeutic Potential with a Combination of A2A/NR2B Receptor Antagonists as Observed in the 6-OHDA Lesioned Rat Model of Parkinson's Disease

In Parkinson''s disease, the long-term use of dopamine replacing agents is associated with the development of motor complications; therefore, there is a need for non-dopaminergic drugs. This study evaluated the potential therapeutic impact of six different NR2B and A_2A receptor antagonists given either alone or in combination in unilateral 6-OHDA-lesioned rats without (monotherapy) or with (add-on therapy) the co-administration of L-Dopa: Sch-58261+ Merck 22; Sch-58261+Co-101244; Preladenant + Merck 22; Preladenant + Radiprodil; Tozadenant + Radiprodil; Istradefylline + Co-101244. Animals given monotherapy were assessed on distance traveled and rearing, whereas those given add-on therapy were assessed on contralateral rotations. Three-way mixed ANOVA were conducted to assess the main effect of each drug separately and to determine whether any interaction between two drugs was additive or synergistic. Additional post hoc analyses were conducted to compare the effect of the combination with the effect of the drugs alone. Motor activity improved significantly and was sustained for longer when the drugs were given in combination than when administered separately at the same dose. Similarly, when tested as add-on treatment to L-Dopa, the combinations resulted in higher levels of contralateral rotation in comparison to the single drugs. Of special interest, the activity observed with some combinations could not be described by a simplistic additive effect and involved more subtle synergistic pharmacological interactions. The combined administration of A_2A/NR2B-receptor antagonists improved motor behaviour in 6-OHDA rats. Given the proven translatability of this model such a combination may be expected to be effective in improving motor symptoms in patients.     

Efficient improvement of silage additives by using genetic algorithms

The enormous variety of substances which may be added to forage in order to manipulate and improve the ensilage process presents an empirical, combinatorial optimization problem of great complexity. To investigate the utility of genetic algorithms for designing effective silage additive combinations, a series of small-scale proof of principle silage experiments were performed with fresh ryegrass. Having established that significant biochemical changes occur over an ensilage period as short as 2 days, we performed a series of experiments in which we used 50 silage additive combinations (prepared by using eight bacterial and other additives, each of which was added at six different levels, including zero [i.e. , no additive]). The decrease in pH, the increase in lactate concentration, and the free amino acid concentration were measured after 2 days and used to calculate a "fitness" value that indicated the quality of the silage (compared to a control silage made without additives). This analysis also included a "cost" element to account for different total additive levels. In the initial experiment additive levels were selected randomly, but subsequently a genetic algorithm program was used to suggest new additive combinations based on the fitness values determined in the preceding experiments. The result was very efficient selection for silages in which large decreases in pH and high levels of lactate occurred along with low levels of free amino acids. During the series of five experiments, each of which comprised 50 treatments, there was a steady increase in the amount of lactate that accumulated; the best treatment combination was that used in the last experiment, which produced 4.6 times more lactate than the untreated silage. The additive combinations that were found to yield the highest fitness values in the final (fifth) experiment were assessed to determine a range of biochemical and microbiological quality parameters during full-term silage fermentation. We found that these combinations compared favorably both with uninoculated silage and with a commercial silage additive. The evolutionary computing methods described here are a convenient and efficient approach for designing silage additives.     

Hierarchical Bayes model for predicting effectiveness of HIV combination therapies

HIV patients are treated by administration of combinations of antiretroviral drugs. The very large number of such combinations makes the manual search for an effective therapy practically impossible, especially in advanced stages of the disease. Therapy selection can be supported by statistical methods that predict the outcomes of candidate therapies. However, these methods are based on clinical data sets that have highly unbalanced therapy representation. This paper presents a novel approach that considers each drug belonging to a target combination therapy as a separate task in a multi-task hierarchical Bayes setting. The drug-specific models take into account information on all therapies containing the drug, not just the target therapy. In this way, we can circumvent the problem of data sparseness pertaining to some target therapies. The computational validation shows that compared to the most commonly used approach that provides therapy information in the form of input features, our model has significantly higher predictive power for therapies with very few training samples and is at least as powerful for abundant therapies.     

Reconstructing gene regulatory networks: from random to scale-free connectivity

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.     

Efficient Improvement of Silage Additives by Using Genetic Algorithms

The enormous variety of substances which may be added to forage in order to manipulate and improve the ensilage process presents an empirical, combinatorial optimization problem of great complexity. To investigate the utility of genetic algorithms for designing effective silage additive combinations, a series of small-scale proof of principle silage experiments were performed with fresh ryegrass. Having established that significant biochemical changes occur over an ensilage period as short as 2 days, we performed a series of experiments in which we used 50 silage additive combinations (prepared by using eight bacterial and other additives, each of which was added at six different levels, including zero [i.e., no additive]). The decrease in pH, the increase in lactate concentration, and the free amino acid concentration were measured after 2 days and used to calculate a “fitness” value that indicated the quality of the silage (compared to a control silage made without additives). This analysis also included a “cost” element to account for different total additive levels. In the initial experiment additive levels were selected randomly, but subsequently a genetic algorithm program was used to suggest new additive combinations based on the fitness values determined in the preceding experiments. The result was very efficient selection for silages in which large decreases in pH and high levels of lactate occurred along with low levels of free amino acids. During the series of five experiments, each of which comprised 50 treatments, there was a steady increase in the amount of lactate that accumulated; the best treatment combination was that used in the last experiment, which produced 4.6 times more lactate than the untreated silage. The additive combinations that were found to yield the highest fitness values in the final (fifth) experiment were assessed to determine a range of biochemical and microbiological quality parameters during full-term silage fermentation. We found that these combinations compared favorably both with uninoculated silage and with a commercial silage additive. The evolutionary computing methods described here are a convenient and efficient approach for designing silage additives.     

Conversion of 1-alkyl-2-acetyl-sn-glycerols to platelet activating factor and related phospholipids by rabbit platelets

Bleomycin is an anti-tumor agent whose cytotoxicity is related to the introduction of both single-stranded and double-stranded breaks in cellular DNA. In an assay using isolated nuclei, low levels of ethidium bromide substantially increased bleomycin induced release of nuclear chromatin. Treatment of mouse L1210 leukemia cells in vitro with low levels of ethidium bromide followed 1 hr later by bleomycin produced a synergistic effect that was 8 fold greater than that expected from the additive cytotoxicity of each drug alone. Interestingly, when the order of drug addition was reversed the drug synergism was much reduced (2 fold). The combination of DNA unwinding and strand scission agents may represent a novel and rational approach to the chemotherapy of cancer.     

Evaluation of a DNA pooled-sampling strategy for estimating the RFLP diversity of maize populations

Molecular characterization by means of RFLPs of large sets of populations is presently limited by experimental costs. In order to reduce costs, we have evaluated a method based on the RFLP analysis of balanced bulks of DNA from several individuals. The precision of this approach for estimating allele frequencies within each population was investigated using (i) DNA extracted from controlled bulks of leaf tissues of maize inbred lines, (ii) data obtained from individual analyses of 10 maize populations. Both approaches showed that allele frequencies can generally be estimated with a high precision (coefficients of determination up to 0.99 for some probe-enzyme combinations assayed), relative to the variation in allele frequencies observed among maize populations. Although further efforts are needed to define a set of probe-enzyme combinations that can be routinely image processed, these results, and preliminary results from a 65 maize populations project, suggest that this approach could provide highly informative data for large sets of populations, and at relatively low costs.     

Simultaneous analysis of multiple data types in pharmacogenomic studies using weighted sparse canonical correlation analysis

Variation in drug response results from a combination of factors that include differences in gender, ethnicity, and environment, as well as genetic variation that may result in differences in mRNA and protein expression. This article presents two integrative analytic approaches that make use of both genome-wide SNP and mRNA expression data available on the same set of subjects: a step-wise integrative approach and a comprehensive analysis using sparse canonical correlation analysis (SCCA). In addition to applying standard SCCA, we present a novel modification of SCCA which allows different weighting for the various pair-wise relationships in the SCCA. These integrative approaches are illustrated with both simulated data and data from a pharmacogenomic study of the drug gemcitabine. Results from these analyses found little overlap in terms of genes detected, possibly detecting different biological mechanisms. In addition, we found the proposed weighted SCCA to outperform its unweighted counterpart in detecting associations between the genomic features and phenotype. Further research is needed to develop and assess new integrative methods for pharmacogenomic studies, as these types of analyses may uncover novel insights into the relationship between genomic variation and drug response.     

Error bands for the linear-quadratic dose-effect relation

Least square or maximum likelihood fits to the linear-quadratic dose-effect relation are common in experimental radiobiology and in radio-epidemiology. The fit procedure provides the estimates of the linear and the quadratic dose coefficients, a and b, as well as their standard errors, s(a) and s(b). The magnitude of the standard errors s(a) and s(b) is partly determined by the fact that-for a given data set-different parameter combinations (a, b) can produce rather similar fits, i.e. larger values of a can be roughly compensated by smaller values of b. The values s(a) and s(b) are, because of this interrelation, unsuitable to determine error bands of the dose-effect relation. The exact analysis accounts for the co-variance of the parameters, but it is rarely employed. To avoid the consideration of co-variances a simple parameter change is introduced here that replaces the dose-squared coefficient, b, by a+ bDelta. This term is the effect-to-dose ratio at the reference dose Delta, and can thus be termed reference slope. With the proper value of Delta-which is readily determined for a data set, and is 2 Gy for the dicentric chromosome data which are used as example-the two parameters initial slope, a, and reference slope are then orthogonal, i.e. there is no inter-dependence of the parameter values, and their uncertainties can be treated as independent. In the case of three-model parameters, e.g. the linear-quadratic model with an intercept term, c, the same type of parameter change can be applied to make both the first and the third parameter orthogonal to a. The curve fit is then performed conveniently with the standard computer routines, and parameter uncertainties are obtained that provide by simple error propagation the equations for the standard error or confidence bands of the dose-effect relation. Appendix A gives the numerical scheme.     

The drug cocktail network

Background

Combination of different agents is widely used in clinic to combat complex diseases with improved therapy and reduced side effects. However, the identification of effective drug combinations remains a challenging task due to the huge number of possible combinations among candidate drugs that makes it impractical to screen putative combinations.

Results

In this work, we construct a 'drug cocktail network' using all the known effective drug combinations extracted from the Drug Combination Database (DCDB), and propose a network-based approach to investigate drug combinations. Our results show that the agents in an effective combination tend to have more similar therapeutic effects and share more interaction partners. Based on our observations, we further develop a statistical approach termed as DCPred (D rug C ombination Pred ictor) to predict possible drug combinations by exploiting the topological features of the drug cocktail network. Validating on the known drug combinations, DCPred achieves the overall AUC (Area Under the receiver operating characteristic Curve) score of 0.92, indicating the predictive power of our proposed approach.

Conclusions

The drug cocktail network constructed in this work provides useful insights into the underlying rules of effective drug combinations and offer important clues to accelerate the future discovery of new drug combinations.