Nonlinear Blending: A Useful General Concept for the Assessment of Combination Drug Synergy

Human diseases may involve cellular signaling networks that contain redundant pathways, so that blocking a single pathway in the system cannot achieve the desired effect. As such, the use of drugs in combination are particularly effective interventions in networked systems. However, common synergy measures are often inadequate to quantify the effect of two different drugs in complex cellular systems. This article proposes a general approach to quantifying the synergy of two drugs in combination. This approach is called strong nonlinear blending. Drugs with different relative potencies, different effect maxima, or situations of potentiation or coalism pose no problem for strong nonlinear blending as a way to assess the increased response benefit to be gained by combining two drugs. This is important as testing drug combinations in complex biological systems are likely to produce a wide variety of possible response surfaces. It is also shown that for monotone increasing (or decreasing) dose response surfaces that strong nonlinear blending is equivalent to improved potency along a ray of constant dose ratio. This is important because fixed dose ratios form the basis for many preclinical and clinical combination drug experiments. Two examples are given involving HIV and cancer chemotherapy combination drug experiments.     

A Bayesian Approach to Dose–Response Assessment and Synergy and Its Application to In Vitro Dose–Response Studies

Summary In this article, we propose a Bayesian approach to dose–response assessment and the assessment of synergy between two combined agents. We consider the case of an in vitro ovarian cancer research study aimed at investigating the antiproliferative activities of four agents, alone and paired, in two human ovarian cancer cell lines. In this article, independent dose–response experiments were repeated three times. Each experiment included replicates at investigated dose levels including control (no drug). We have developed a Bayesian hierarchical nonlinear regression model that accounts for variability between experiments, variability within experiments (i.e., replicates), and variability in the observed responses of the controls. We use Markov chain Monte Carlo to fit the model to the data and carry out posterior inference on quantities of interest (e.g., median inhibitory concentration IC ₅₀ ). In addition, we have developed a method, based on Loewe additivity, that allows one to assess the presence of synergy with honest accounting of uncertainty. Extensive simulation studies show that our proposed approach is more reliable in declaring synergy compared to current standard analyses such as the median‐effect principle/combination index method ( Chou and Talalay, 1984 , Advances in Enzyme Regulation 22, 27–55), which ignore important sources of variability and uncertainty.     

Inhibitory effect of cinnamoyl compounds against human malignant cell line

In the present study, anti-proliferative effects of dietary polyphenolic compounds have been observed and demonstrated the strong anticancer efficacy of curcumin (CMN), an active constituent of dietary spice (turmeric) using human leukemia cancer cell line. CMN inhibited the proliferation of K562 leukemic cells by induction of apoptosis. The current study demonstrated synergy with combination of drug therapy, and suggested that combination of ferulic acid and cisplatin synergistically inhibited cellular proliferation. Cytotoxic synergy was observed independent of the sequence of addition of two drugs to cultured cells. The synergized growth inhibitory effect with cisplatin was probably associated with G2-M arrest in cell cycle progression. These findings suggested that among the cinnamoyl compounds, CMN was most potent and FER appeared to be a better modulating agent on human malignant cell line.     

HSP90 Inhibition Enhances Antimitotic Drug-Induced Mitotic Arrest and Cell Death in Preclinical Models of Non-Small Cell Lung Cancer

HSP90 inhibitors are currently undergoing clinical evaluation in combination with antimitotic drugs in non-small cell lung cancer (NSCLC), but little is known about the cellular effects of this novel drug combination. Therefore, we investigated the molecular mechanism of action of IPI-504 (retaspimycin HCl), a potent and selective inhibitor of HSP90, in combination with the microtubule targeting agent (MTA) docetaxel, in preclinical models of NSCLC. We identified a subset of NSCLC cell lines in which these drugs act in synergy to enhance cell death. Xenograft models of NSCLC demonstrated tumor growth inhibition, and in some cases, regression in response to combination treatment. Treatment with IPI-504 enhanced the antimitotic effects of docetaxel leading to the hypothesis that the mitotic checkpoint is required for the response to drug combination. Supporting this hypothesis, overriding the checkpoint with an Aurora kinase inhibitor diminished the cell death synergy of IPI-504 and docetaxel. To investigate the molecular basis of synergy, an unbiased stable isotope labeling by amino acids in cell culture (SILAC) proteomic approach was employed. Several mitotic regulators, including components of the ubiquitin ligase, anaphase promoting complex (APC/C), were specifically down-regulated in response to combination treatment. Loss of APC/C by RNAi sensitized cells to docetaxel and enhanced its antimitotic effects. Treatment with a PLK1 inhibitor (BI2536) also sensitized cells to IPI-504, indicating that combination effects may be broadly applicable to other classes of mitotic inhibitors. Our data provide a preclinical rationale for testing the combination of IPI-504 and docetaxel in NSCLC.     

Nonlinear response surface in the study of interaction analysis of three combination drugs

Few articles have been written on analyzing three‐way interactions between drugs. It may seem to be quite straightforward to extend a statistical method from two‐drugs to three‐drugs. However, there may exist more complex nonlinear response surface of the interaction index () with more complex local synergy and/or local antagonism interspersed in different regions of drug combinations in a three‐drug study, compared in a two‐drug study. In addition, it is not possible to obtain a four‐dimensional (4D) response surface plot for a three‐drug study. We propose an analysis procedure to construct the dose combination regions of interest (say, the synergistic areas with ). First, use the model robust regression method (MRR), a semiparametric method, to fit the entire response surface of the , which allows to fit a complex response surface with local synergy/antagonism. Second, we run a modified genetic algorithm (MGA), a stochastic optimization method, many times with different random seeds, to allow to collect as many feasible points as possible that satisfy the estimated values of . Last, all these feasible points are used to construct the approximate dose regions of interest in a 3D. A case study with three anti‐cancer drugs in an in vitro experiment is employed to illustrate how to find the dose regions of interest.     

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.     

Quantitative comparison of cardiac ventricular myocyte electrophysiology and response to drugs in human and nonhuman species

Explanations for arrhythmia mechanisms at the cellular level are usually based on experiments in nonhuman myocytes. However, subtle electrophysiological differences between species may lead to different rhythmic or arrhythmic cellular behaviors and drug response given the nonlinear and highly interactive cellular system. Using detailed and quantitatively accurate mathematical models for human, dog, and guinea pig ventricular action potentials (APs), we simulated and compared cell electrophysiology mechanisms and response to drugs. Under basal conditions (absence of β-adrenergic stimulation), Na(+)/K(+)-ATPase changes secondary to Na(+) accumulation determined AP rate dependence for human and dog but not for guinea pig where slow delayed rectifier current (I(Ks)) was the major rate-dependent current. AP prolongation with reduction of rapid delayed rectifier current (I(Kr)) and I(Ks) (due to mutations or drugs) showed strong species dependence in simulations, as in experiments. For humans, AP prolongation was 80% following I(Kr) block. It was 30% for dog and 20% for guinea pig. Under basal conditions, I(Ks) block was of no consequence for human and dog, but for guinea pig, AP prolongation after I(Ks) block was severe. However, with β-adrenergic stimulation, I(Ks) played an important role in all species, particularly in AP shortening at fast rate. Quantitative comparison of AP repolarization, rate-dependence mechanisms, and drug response in human, dog, and guinea pig revealed major species differences (e.g., susceptibility to arrhythmogenic early afterdepolarizations). Extrapolation from animal to human electrophysiology and drug response requires great caution.     

When the Most Potent Combination of Antibiotics Selects for the Greatest Bacterial Load: The Smile-Frown Transition

Conventional wisdom holds that the best way to treat infection with antibiotics is to ‘hit early and hit hard’. A favoured strategy is to deploy two antibiotics that produce a stronger effect in combination than if either drug were used alone. But are such synergistic combinations necessarily optimal? We combine mathematical modelling, evolution experiments, whole genome sequencing and genetic manipulation of a resistance mechanism to demonstrate that deploying synergistic antibiotics can, in practice, be the worst strategy if bacterial clearance is not achieved after the first treatment phase. As treatment proceeds, it is only to be expected that the strength of antibiotic synergy will diminish as the frequency of drug-resistant bacteria increases. Indeed, antibiotic efficacy decays exponentially in our five-day evolution experiments. However, as the theory of competitive release predicts, drug-resistant bacteria replicate fastest when their drug-susceptible competitors are eliminated by overly-aggressive treatment. Here, synergy exerts such strong selection for resistance that an antagonism consistently emerges by day 1 and the initially most aggressive treatment produces the greatest bacterial load, a fortiori greater than if just one drug were given. Whole genome sequencing reveals that such rapid evolution is the result of the amplification of a genomic region containing four drug-resistance mechanisms, including the acrAB efflux operon. When this operon is deleted in genetically manipulated mutants and the evolution experiment repeated, antagonism fails to emerge in five days and antibiotic synergy is maintained for longer. We therefore conclude that unless super-inhibitory doses are achieved and maintained until the pathogen is successfully cleared, synergistic antibiotics can have the opposite effect to that intended by helping to increase pathogen load where, and when, the drugs are found at sub-inhibitory concentrations.     

In silico drug combination discovery for personalized cancer therapy

Background

Drug combination therapy, which is considered as an alternative to single drug therapy, can potentially reduce resistance and toxicity, and have synergistic efficacy. As drug combination therapies are widely used in the clinic for hypertension, asthma, and AIDS, they have also been proposed for the treatment of cancer. However, it is difficult to select and experimentally evaluate effective combinations because not only is the number of cancer drug combinations extremely large but also the effectiveness of drug combinations varies depending on the genetic variation of cancer patients. A computational approach that prioritizes the best drug combinations considering the genetic information of a cancer patient is necessary to reduce the search space.

Results

We propose an in-silico method for personalized drug combination therapy discovery. We predict the synergy between two drugs and a cell line using genomic information, targets of drugs, and pharmacological information. We calculate and predict the synergy scores of 583 drug combinations for 31 cancer cell lines. For feature dimension reduction, we select the mutations or expression levels of the genes in cancer-related pathways. We also used various machine learning models. Extremely Randomized Trees (ERT), a tree-based ensemble model, achieved the best performance in the synergy score prediction regression task. The correlation coefficient between the synergy scores predicted by ERT and the actual observations is 0.738. To compare with an existing drug combination synergy classification model, we reformulate the problem as a binary classification problem by thresholding the synergy scores. ERT achieved an F1 score of 0.954 when synergy scores of 20 and -20 were used as the threshold, which is 8.7% higher than that obtained by the state-of-the-art baseline model. Moreover, the model correctly predicts the most synergistic combination, from approximately 100 candidate drug combinations, as the top choice for 15 out of the 31 cell lines. For 28 out of the 31 cell lines, the model predicts the most synergistic combination in the top 10 of approximately 100 candidate drug combinations. Finally, we analyze the results, generate synergistic rules using the features, and validate the rules through the literature survey.

Conclusion

Using various types of genomic information of cancer cell lines, targets of drugs, and pharmacological information, a drug combination synergy prediction pipeline is proposed. The pipeline regresses the synergy level between two drugs and a cell line as well as classifies if there exists synergy or antagonism between them. Discovering new drug combinations by our pipeline may improve personalized cancer therapy.

     

Analysis of Compound Synergy in High-Throughput Cellular Screens by Population-Based Lifetime Modeling

Despite the successful introduction of potent anti-cancer therapeutics, most of these drugs lead to only modest tumor-shrinkage or transient responses, followed by re-growth of tumors. Combining different compounds has resulted in enhanced tumor control and prolonged survival. However, methods querying the efficacy of such combinations have been hampered by limited scalability, analytical resolution, statistical feasibility, or a combination thereof. We have developed a theoretical framework modeling cellular viability as a stochastic lifetime process to determine synergistic compound combinations from high-throughput cellular screens. We apply our method to data derived from chemical perturbations of 65 cancer cell lines with two inhibitors. Our analysis revealed synergy for the combination of both compounds in subsets of cell lines. By contrast, in cell lines in which inhibition of one of both targets was sufficient to induce cell death, no synergy was detected, compatible with the topology of the oncogenically activated signaling network. In summary, we provide a tool for the measurement of synergy strength for combination perturbation experiments that might help define pathway topologies and direct clinical trials.     

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.     

A generalized response surface model with varying relative potency for assessing drug interaction

When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Based on the Loewe additivity reference model, many existing response surface models require constant relative potency and some of them use a single parameter to capture synergy, additivity, or antagonism. However, the assumption of constant relative potency is too restrictive, and these models using a single parameter to capture drug interaction are inadequate to describe the phenomenon when synergy, additivity, and antagonism are interspersed in different regions of drug combinations. We propose a generalized response surface model with a function of doses instead of one single parameter to identify and quantify departure from additivity. The proposed model can incorporate varying relative potencies among multiple drugs as well. Examples and simulations are given to demonstrate that the proposed model is effective in capturing different patterns of drug interaction.     

Landscape of Targeted Anti-Cancer Drug Synergies in Melanoma Identifies a Novel BRAF-VEGFR/PDGFR Combination Treatment

A newer generation of anti-cancer drugs targeting underlying somatic genetic driver events have resulted in high single-agent or single-pathway response rates in selected patients, but few patients achieve complete responses and a sizeable fraction of patients relapse within a year. Thus, there is a pressing need for identification of combinations of targeted agents which induce more complete responses and prevent disease progression. We describe the results of a combination screen of an unprecedented scale in mammalian cells performed using a collection of targeted, clinically tractable agents across a large panel of melanoma cell lines. We find that even the most synergistic drug pairs are effective only in a discrete number of cell lines, underlying a strong context dependency for synergy, with strong, widespread synergies often corresponding to non-specific or off-target drug effects such as multidrug resistance protein 1 (MDR1) transporter inhibition. We identified drugs sensitizing cell lines that are BRAF^V600E mutant but intrinsically resistant to BRAF inhibitor PLX4720, including the vascular endothelial growth factor receptor/kinase insert domain receptor (VEGFR/KDR) and platelet derived growth factor receptor (PDGFR) family inhibitor cediranib. The combination of cediranib and PLX4720 induced apoptosis in vitro and tumor regression in animal models. This synergistic interaction is likely due to engagement of multiple receptor tyrosine kinases (RTKs), demonstrating the potential of drug- rather than gene-specific combination discovery approaches. Patients with elevated biopsy KDR expression showed decreased progression free survival in trials of mitogen-activated protein kinase (MAPK) kinase pathway inhibitors. Thus, high-throughput unbiased screening of targeted drug combinations, with appropriate library selection and mechanistic follow-up, can yield clinically-actionable drug combinations.     

Insulin induces epidermal growth factor (EGF) receptor clustering and potentiates EGF-stimulated DNA synthesis in swiss 3T3 cells: a mechanism for costimulation in mitogenic synergy

In many cellular systems, activation with more than one ligand can produce a cellular response that is greater than the sum of the individual responses to the ligands. This synergy is sometimes referred to as coactivation. In Swiss 3T3 fibroblasts, activation of the epidermal growth factor (EGF) receptor produces a weak induction of DNA synthesis. Insulin has no stimulatory effect on this response. However, in combination, EGF and insulin synergize to cause a large induction of S phase. The underlying cellular biochemistry of this effect has been examined. The data indicate that phospholipase C activation is a major component of agonist-induced DNA synthesis. In contrast, activation of p70 S6 kinase by single agonists was inversely related to their ability to stimulate DNA synthesis. Therefore, it was examined whether stimulation of Swiss 3T3 cells with insulin causes changes in the subcellular distribution of EGF receptors and phospholipase Cgamma1 that could potentially explain the observed synergy or costimulation. It was found that insulin effectively induced the accumulation of EGF receptors on the actin arc of cells without activation of the EGF receptor. In contrast, EGF, when added for several hours, did not cause accumulation of the EGF receptor at this site. However, both EGF and insulin stimulated the accumulation of phospholipase Cgamma1 at the actin arc, which was coincident with the EGF receptor in the case of insulin- stimulated cells. Therefore, it is suggested that the insulin-induced coclustering of the EGF receptor with phospholipase Cgamma1 at the actin arc may allow for greater efficiency of signal transduction, resulting in the synergy observed for these two hormones in stimulation of DNA synthesis.     

Permeation of Therapeutic Drugs in Different Formulations across the Airway Epithelium In Vitro

Background

Pulmonary drug delivery is characterized by short onset times of the effects and an increased therapeutic ratio compared to oral drug delivery. This delivery route can be used for local as well as for systemic absorption applying drugs as single substance or as a fixed dose combination. Drugs can be delivered as nebulized aerosols or as dry powders. A screening system able to mimic delivery by the different devices might help to assess the drug effect in the different formulations and to identify potential interference between drugs in fixed dose combinations. The present study evaluates manual devices used in animal studies for their suitability for cellular studies.

Methods

Calu-3 cells were cultured submersed and in air-liquid interface culture and characterized regarding mucus production and transepithelial electrical resistance. The influence of pore size and material of the transwell membranes and of the duration of air-liquid interface culture was assessed. Compounds were applied in solution and as aerosols generated by MicroSprayer IA-1C Aerosolizer or by DP-4 Dry Powder Insufflator using fluorescein and rhodamine 123 as model compounds. Budesonide and formoterol, singly and in combination, served as examples for drugs relevant in pulmonary delivery.

Results and Conclusions

Membrane material and duration of air-liquid interface culture had no marked effect on mucus production and tightness of the cell monolayer. Co-application of budesonide and formoterol, applied in solution or as aerosol, increased permeation of formoterol across cells in air-liquid interface culture. Problems with the DP-4 Dry Powder Insufflator included compound-specific delivery rates and influence on the tightness of the cell monolayer. These problems were not encountered with the MicroSprayer IA-1C Aerosolizer. The combination of Calu-3 cells and manual aerosol generation devices appears suitable to identify interactions of drugs in fixed drug combination products on permeation.     

Synergy research: Approaching a new generation of phytopharmaceuticals

The longstanding, successful use of herbal drug combinations in traditional medicine makes it necessary to find a rationale for the pharmacological and therapeutic superiority of many of them in comparison to isolated single constituents. This review describes many examples of how modern molecular–biological methods (including new genomic technologies) can enable us to understand the various synergistic mechanisms underlying these effects. Synergistic effects can be produced if the constituents of an extract affect different targets or interact with one another in order to improve the solubility and thereby enhance the bioavailability of one or several substances of an extract. A special synergy effect can occur when antibiotics are combined with an agent that antagonizes bacterial resistance mechanisms. The verification of real synergy effects can be achieved through detailed pharmacological investigations and by means of controlled clinical studies performed in comparison with synthetic reference drugs. All the new ongoing projects aim at the development of a new generation of phytopharmaceuticals which can be used alone or in combination with synthetic drugs or antibiotics. This new generation of phytopharmaceuticals could lend phytotherapy a new legitimacy and enable their use to treat diseases which have hitherto been treated using synthetic drugs alone.     

A systems biology approach to identify effective cocktail drugs

Background

Complex diseases, such as Type 2 Diabetes, are generally caused by multiple factors, which hamper effective drug discovery. To combat these diseases, combination regimens or combination drugs provide an alternative way, and are becoming the standard of treatment for complex diseases. However, most of existing combination drugs are developed based on clinical experience or test-and-trial strategy, which are not only time consuming but also expensive.

Results

In this paper, we presented a novel network-based systems biology approach to identify effective drug combinations by exploiting high throughput data. We assumed that a subnetwork or pathway will be affected in the networked cellular system after a drug is administrated. Therefore, the affected subnetwork can be used to assess the drug's overall effect, and thereby help to identify effective drug combinations by comparing the subnetworks affected by individual drugs with that by the combination drug. In this work, we first constructed a molecular interaction network by integrating protein interactions, protein-DNA interactions, and signaling pathways. A new model was then developed to detect subnetworks affected by drugs. Furthermore, we proposed a new score to evaluate the overall effect of one drug by taking into account both efficacy and side-effects. As a pilot study we applied the proposed method to identify effective combinations of drugs used to treat Type 2 Diabetes. Our method detected the combination of Metformin and Rosiglitazone, which is actually Avandamet, a drug that has been successfully used to treat Type 2 Diabetes.

Conclusions

The results on real biological data demonstrate the effectiveness and efficiency of the proposed method, which can not only detect effective cocktail combination of drugs in an accurate manner but also significantly reduce expensive and tedious trial-and-error experiments.

     

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.     

SynergyFinder Plus: Toward Better Interpretation and Annotation of Drug Combination Screening Datasets

Combinatorial therapies have been recently proposed to improve the efficacy of anticancer treatment. The Synergy Finder R package is a software used to analyze pre-clinical drug combination datasets. Here, we report the major updates to the Synergy Finder R package for improved interpretation and annotation of drug combination screening results. Unlike the existing implementations, the updated Synergy Finder R package includes five main innovations. 1) We extend the mathematical models to higher...