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.     

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.     

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.     

Chemogenomics and orthology‐based design of antibiotic combination therapies

Combination antibiotic therapies are being increasingly used in the clinic to enhance potency and counter drug resistance. However, the large search space of candidate drugs and dosage regimes makes the identification of effective combinations highly challenging. Here, we present a computational approach called INDIGO, which uses chemogenomics data to predict antibiotic combinations that interact synergistically or antagonistically in inhibiting bacterial growth. INDIGO quantifies the influence of individual chemical–genetic interactions on synergy and antagonism and significantly outperforms existing approaches based on experimental evaluation of novel predictions in Escherichia coli. Our analysis revealed a core set of genes and pathways (e.g. central metabolism) that are predictive of antibiotic interactions. By identifying the interactions that are associated with orthologous genes, we successfully estimated drug‐interaction outcomes in the bacterial pathogens Mycobacterium tuberculosis and Staphylococcus aureus, using the E. coli INDIGO model. INDIGO thus enables the discovery of effective combination therapies in less‐studied pathogens by leveraging chemogenomics data in model organisms.     

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.

     

Mathematical modeling of multi-drugs therapy: a challenge for determining the optimal combinations of antiviral drugs

In the current era of antiviral drug therapy, combining multiple drugs is a primary approach for improving antiviral effects, reducing the doses of individual drugs, relieving the side effects of strong antiviral drugs, and preventing the emergence of drug-resistant viruses. Although a variety of new drugs have been developed for HIV, HCV and influenza virus, the optimal combinations of multiple drugs are incompletely understood. To optimize the benefits of multi-drugs combinations, we must investigate the interactions between the combined drugs and their target viruses. Mathematical models of viral infection dynamics provide an ideal tool for this purpose. Additionally, whether drug combinations computed by these models are synergistic can be assessed by two prominent drug combination theories, Loewe additivity and Bliss independence. By combining the mathematical modeling of virus dynamics with drug combination theories, we could show the principles by which drug combinations yield a synergistic effect. Here, we describe the theoretical aspects of multi-drugs therapy and discuss their application to antiviral research.     

In Vitro Chemotherapeutic Combinations Against Isoniazid-Resistant Mycobacterium tuberculosis and Mycobacterium fortuitum

It is an acceptable medical practice to use second-line antimycobacterial drugs in combination with isoniazid in treatment of isoniazid-resistant tuberculosis. Recent investigations have demonstrated the importance of determining chemotherapeutic interaction in instances of multiple antibiotic use. We studied the inhibitory effect of combinations of isoniazid with ethambutol, rifampin, ethionamide, cycloserine, viomycin, and kanamycin against three isoniazid-resistant strains of Mycobacterium tuberculosis and three strains of M. fortuitum. The isobologram technique with drug concentrations of 0.4 to 100 mug/ml was used. With the exception of single instances in which kanamycin plus isoniazid (M. tuberculosis strain 9999) and ethionamide plus isoniazid (M. fortuitum strain 2080) seemed to have a synergistic effect, neither synergy nor antagonism was noted for any of the combinations. These studies show that the combined use of isoniazid and a second line antimycobacterial agent results in vitro in indifferent inhibitory activity.     

Using a newly introduced framework to measure ecological stressor interactions

Understanding how stressors combine to affect population abundances and trajectories is a fundamental ecological problem with increasingly important implications worldwide. Generalisations about interactions among stressors are challenging due to different categorisation methods and how stressors vary across species and systems. Here, we propose using a newly introduced framework to analyse data from the last 25 years on ecological stressor interactions, for example combined effects of temperature, salinity and nutrients on population survival and growth. We contrast our results with the most commonly used existing method – analysis of variance (ANOVA) – and show that ANOVA assumptions are often violated and have inherent limitations for detecting interactions. Moreover, we argue that rescaling – examining relative rather than absolute responses – is critical for ensuring that any interaction measure is independent of the strength of single‐stressor effects. In contrast, non‐rescaled measures – like ANOVA – find fewer interactions when single‐stressor effects are weak. After re‐examining 840 two‐stressor combinations, we conclude that antagonism and additivity are the most frequent interaction types, in strong contrast to previous reports that synergy dominates yet supportive of more recent studies that find more antagonism. Consequently, measuring and re‐assessing the frequency of stressor interaction types is imperative for a better understanding of how stressors affect populations.     

Data-Driven Analysis in Drug Discovery

In the process of drug discovery for new chemical entities, application of appropriate pharmacological models often is not possible because the molecular mechanism of the compound is not yet elucidated. Therefore, a data-driven approach using generic tools designed to quantify characteristic patterns of concentration-response curves is required. This article outlines the options available for quantifying agonist and antagonist activity. Specifically, for agonists, the use of the Operational model for the determination of functional effects (equimolar potency ratios for full agonists, calculation of relative efficacy) is described. For antagonists, the measurement of pK_B (-log of the equilibrium dissociation constant of the antagonist-receptor complex) for orthosteric antagonists that do not alter basal response (simple competitive antagonists), increase basal response (partial agonists), and decrease basal response (in constitutively active systems; inverse agonists) is discussed. In addition, this article considers methods to discern orthosteric receptor antagonism from allosteric antagonism whereby the agonist and antagonist bind to separate sites and interact through a conformational change in the receptor. Methods for the measurement of the pK_B for allosteric modulators as well as co-operativity constants for these modulators is described.     

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.     

The Concept of Additivity of Drug Combinations in the Case of Quantal Response

The concept of additivity of drug combinations is widely accepted in pharmacology and toxicology. Up to now, no general statistical methods to test that property are available. The present paper gives a mathematical formulation of additivity, a method to fit dose response surfaces under additivity assumption and a statistical test.     

Systematic exploration of synergistic drug pairs

Drug synergy allows a therapeutic effect to be achieved with lower doses of component drugs. Drug synergy can result when drugs target the products of genes that act in parallel pathways (‘specific synergy’). Such cases of drug synergy should tend to correspond to synergistic genetic interaction between the corresponding target genes. Alternatively, ‘promiscuous synergy’ can arise when one drug non‐specifically increases the effects of many other drugs, for example, by increased bioavailability. To assess the relative abundance of these drug synergy types, we examined 200 pairs of antifungal drugs in S. cerevisiae. We found 38 antifungal synergies, 37 of which were novel. While 14 cases of drug synergy corresponded to genetic interaction, 92% of the synergies we discovered involved only six frequently synergistic drugs. Although promiscuity of four drugs can be explained under the bioavailability model, the promiscuity of Tacrolimus and Pentamidine was completely unexpected. While many drug synergies correspond to genetic interactions, the majority of drug synergies appear to result from non‐specific promiscuous synergy.     

Minocycline Synergizes with N-Acetylcysteine and Improves Cognition and Memory Following Traumatic Brain Injury in Rats

Background

There are no drugs presently available to treat traumatic brain injury (TBI). A variety of single drugs have failed clinical trials suggesting a role for drug combinations. Drug combinations acting synergistically often provide the greatest combination of potency and safety. The drugs examined (minocycline (MINO), N-acetylcysteine (NAC), simvastatin, cyclosporine A, and progesterone) had FDA-approval for uses other than TBI and limited brain injury in experimental TBI models.

Methodology/Principal Findings

Drugs were dosed one hour after injury using the controlled cortical impact (CCI) TBI model in adult rats. One week later, drugs were tested for efficacy and drug combinations tested for synergy on a hierarchy of behavioral tests that included active place avoidance testing. As monotherapy, only MINO improved acquisition of the massed version of active place avoidance that required memory lasting less than two hours. MINO-treated animals, however, were impaired during the spaced version of the same avoidance task that required 24-hour memory retention. Co-administration of NAC with MINO synergistically improved spaced learning. Examination of brain histology 2 weeks after injury suggested that MINO plus NAC preserved white, but not grey matter, since lesion volume was unaffected, yet myelin loss was attenuated. When dosed 3 hours before injury, MINO plus NAC as single drugs had no effect on interleukin-1 formation; together they synergistically lowered interleukin-1 levels. This effect on interleukin-1 was not observed when the drugs were dosed one hour after injury.

Conclusions/Significance

These observations suggest a potentially valuable role for MINO plus NAC to treat TBI.     

The Pharmaco –, Population and Evolutionary Dynamics of Multi-drug Therapy: Experiments with S. aureus and E. coli and Computer Simulations

There are both pharmacodynamic and evolutionary reasons to use multiple rather than single antibiotics to treat bacterial infections; in combination antibiotics can be more effective in killing target bacteria as well as in preventing the emergence of resistance. Nevertheless, with few exceptions like tuberculosis, combination therapy is rarely used for bacterial infections. One reason for this is a relative dearth of the pharmaco-, population- and evolutionary dynamic information needed for the rational design of multi-drug treatment protocols. Here, we use in vitro pharmacodynamic experiments, mathematical models and computer simulations to explore the relative efficacies of different two-drug regimens in clearing bacterial infections and the conditions under which multi-drug therapy will prevent the ascent of resistance. We estimate the parameters and explore the fit of Hill functions to compare the pharmacodynamics of antibiotics of four different classes individually and in pairs during cidal experiments with pathogenic strains of Staphylococcus aureus and Escherichia coli. We also consider the relative efficacy of these antibiotics and antibiotic pairs in reducing the level of phenotypically resistant but genetically susceptible, persister, subpopulations. Our results provide compelling support for the proposition that the nature and form of the interactions between drugs of different classes, synergy, antagonism, suppression and additivity, has to be determined empirically and cannot be inferred from what is known about the pharmacodynamics or mode of action of these drugs individually. Monte Carlo simulations of within-host treatment incorporating these pharmacodynamic results and clinically relevant refuge subpopulations of bacteria indicate that: (i) the form of drug-drug interactions can profoundly affect the rate at which infections are cleared, (ii) two-drug therapy can prevent treatment failure even when bacteria resistant to single drugs are present at the onset of therapy, and (iii) this evolutionary virtue of two-drug therapy is manifest even when the antibiotics suppress each other''s activity.     

Multivariate slope ratio assay with repeated measurements

A method is given for analyzing a slope ratio assay in which a test drug is compared with a standard drug, two or more response variates being measured on each subject at each of several successively increased drug doses. The method requires all subjects to receive the same number of doses, all subjects on the same drug to receive the same doses, the ratio of corresponding doses of the two drugs to be constant over the successive increases, and response variables to be measured only once on each subject at each dose with no missing data allowed. The technique is also applicable when doses are randomly assigned, provided there is no carry-over effect between doses. For each of the J response variates, the relative potency of the test drug with respect to the standard is defined and estimated in the usual way; a 100(1-alpha)% confidence region is then obtained for the vector of the J relative potencies. A procedure is given for testing the equality of some or all of the J relative potencies; an estimator of a common relative potency is obtained by a standard multivariate least squares method. A common relative potency is of interest because the multiple outcome variables are often different indicators of a general physiologic response. The procedures in the paper are illustrated by a simple example concerning the effects of two anesthetics on children.     

In vitro activity of antibiotic combinations against multidrug-resistant strains of Acinetobacter baumannii and the effects of their antibiotic resistance determinants

Various combinations of antibiotics are reported to show synergy in treating nosocomial infections with multidrug-resistant (MDR) Acinetobacter baumannii (A. baumannii). Here, we studied hospital-acquired outbreak strains of MDR A. baumannii to evaluate optimal combinations of antibiotics. One hundred and twenty-one strains were grouped into one major and one minor clonal group based on repetitive PCR amplification. Twenty representative strains were tested for antibiotic synergy using Etest(?). Five strains were further analyzed by analytical isoelectric focusing and PCR to identify β-lactamase genes or other antibiotic resistance determinants. Our investigation showed that the outbreak strains of MDR A. baumannii belonged to two dominant clones. A combination of colistin and doxycycline showed the best result, being additive or synergistic against 70% of tested strains. Antibiotic additivity was observed more frequently than synergy. Strains possessing the same clonality did not necessarily demonstrate the same response to antibiotic combinations in vitro. We conclude that the effect of antibiotic combinations on our outbreak strains of MDR A. baumannii seemed strain-specific. The bacterial response to antibiotic combinations is probably a result of complex interactions between multiple concomitant antibiotic resistance determinants in each strain.     

Stimulus amplification, efficacy, and the operational model. Part I--binary complex occupancy mechanisms.

A simple function, developed to represent the stimulus produced at the n -th step of a multistep signaling sequence, is applied to the classic model of agonist-receptor interaction. The model indicates that the relative efficacy of two agonists can be easily estimated from three experimental measures: maximal response, EC50, and apparent dissociation constant. Efficacy ratios obtained in this manner appear statistically and mathematically equivalent to those estimated with null-based methods. Enhancement of both maximal response (vertical amplification) and potency (horizontal amplification) are demonstrated to result from the interaction between highly efficacious agonists and signal transduction mechanisms. Both properties, not just relative maxima, must therefore be examined when comparing relative efficacy. Three additional generalized stimulus-response models are developed and shown to be functionally equivalent. Increasing the complexity of the function used to represent stimulus amplification does not appear to alter the conclusions derived based on the simple model of stimulus amplification. Analysis of the results also reveals a close relationship between mechanistic and operational modes of drug action, and allows operational parameters to be given mechanistic interpretation.     

Data-driven analysis in drug discovery

In the process of drug discovery for new chemical entities, application of appropriate pharmacological models often is not possible because the molecular mechanism of the compound is not yet elucidated. Therefore, a data-driven approach using generic tools designed to quantify characteristic patterns of concentration-response curves is required. This article outlines the options available for quantifying agonist and antagonist activity. Specifically, for agonists, the use of the Operational model for the determination of functional effects (equimolar potency ratios for full agonists, calculation of relative efficacy) is described. For antagonists, the measurement of pKB (-log of the equilibrium dissociation constant of the antagonist-receptor complex) for orthosteric antagonists that do not alter basal response (simple competitive antagonists), increase basal response (partial agonists), and decrease basal response (in constitutively active systems; inverse agonists) is discussed. In addition, this article considers methods to discern orthosteric receptor antagonism from allosteric antagonism whereby the agonist and antagonist bind to separate sites and interact through a conformational change in the receptor. Methods for the measurement of the pKB for allosteric modulators as well as co-operativity constants for these modulators is described.     

Baclofen and NOS inhibitors interact to evoke synergistic hypothermia in rats

Our laboratory recently demonstrated that a drug combination of baclofen and L-NAME, a nonspecific nitric oxide synthase (NOS) inhibitor, evokes synergistic hypothermia in rats. These data are the first demonstration of synergy between a GABA agonist and NOS inhibitor. While the hypothermic synergy suggests a role for NOS in baclofen pharmacology, it is unclear whether the super-additive hypothermia is specific for baclofen and L-NAME or extends to drug combinations of baclofen and other NOS inhibitors. The site of action (central or peripheral) and isoforms of NOS that mediate the synergy are also unknown. Here, we confirm the hypothermic synergy with additional data and discuss potential mechanisms of the drug interaction. Baclofen (2.5, 3.5, 5 and 7.5 mg/kg, i.p.) was administered to rats by itself or with 7-nitroindazole (7-NI), a neuronal NOS inhibitor. 7-NI (10 mg/kg, i.p.) did not affect body temperature. For combined administration, 7-NI (10 mg/kg, i.p.) increased the relative potency of baclofen (F=18.9, P<0.05). The present data validate the hypothermic synergy caused by the drug combination of baclofen and L-NAME and implicate nNOS in the synergy. In a context broader than thermoregulation, NO production and transmission may play an important role in baclofen pharmacology.     

Minimal biophysical model of combined antibiotic action

Phenomenological relations such as Ohm’s or Fourier’s law have a venerable history in physics but are still scarce in biology. This situation restrains predictive theory. Here, we build on bacterial “growth laws,” which capture physiological feedback between translation and cell growth, to construct a minimal biophysical model for the combined action of ribosome-targeting antibiotics. Our model predicts drug interactions like antagonism or synergy solely from responses to individual drugs. We provide analytical results for limiting cases, which agree well with numerical results. We systematically refine the model by including direct physical interactions of different antibiotics on the ribosome. In a limiting case, our model provides a mechanistic underpinning for recent predictions of higher-order interactions that were derived using entropy maximization. We further refine the model to include the effects of antibiotics that mimic starvation and the presence of resistance genes. We describe the impact of a starvation-mimicking antibiotic on drug interactions analytically and verify it experimentally. Our extended model suggests a change in the type of drug interaction that depends on the strength of resistance, which challenges established rescaling paradigms. We experimentally show that the presence of unregulated resistance genes can lead to altered drug interaction, which agrees with the prediction of the model. While minimal, the model is readily adaptable and opens the door to predicting interactions of second and higher-order in a broad range of biological systems.