Uncovering emergent interactions in three-way combinations of stressors

Interactions within higher-order antibiotic combinations do not influence the rate of adaptation in bacteria

The prevalence and strength of antibiotic resistance has led to an ongoing battle between the development of new treatments and the evolution of resistance. Combining multiple drugs simultaneously is a potential solution for combating antibiotic resistance. However, this approach introduces new factors that must be considered, including the influence of drug interactions on the rate of resistance evolution. When antibiotics are used in combination, their effects can be additive, synergistic, or antagonistic. In this study, we investigated the effect of higher-order interactions involving 3 drugs on resistance evolution in Staphylococcus epidermidis. Previous studies have shown that synergistic interactions can increase the adaptation rate. However, the effects of higher-order interactions on rates of adaptation are unclear. We investigated the adaptation of Staphylococcus epidermidis to single-, 2-, and 3-drug environments to assess how interactions within drug combinations influence the rate of adaptation. We analyzed both the overall interaction and emergent interaction, the latter being a unique interaction that occurs in 3-drug combinations due to the presence of all three drugs, rather than simply strong pairwise interactions. Our results show that neither the overall interactions nor the emergent interactions affect adaptation rates.

Ibuprofen as an adjuvant to conventional antimicrobials and essential oil compounds against skin pathogens

AIMS

Antimicrobial resistance continues to be a growing concern, resulting in increased use of drug combinations. Antibiotic adjuvants are an emerging strategy that may potentiate an antibiotics efficacy. Ibuprofen's polypharmacological properties have been investigated for their antimicrobial and host-modulating potential. This study aimed to investigate the potential of a novel multidrug combination involving ibuprofen, essential oil compounds (EOCs), and conventional antimicrobials against skin pathogens.

METHODS AND RESULTS

The minimum inhibitory concentrations of ibuprofen, conventional antimicrobials, and EOCs were determined and then combined and tested against 14 (reference and clinical) skin pathogens. The cytotoxicity was analysed using the MTT assay, whilst the anti-inflammatory effects were evaluated using lipopolysaccharide activated RAW264.7 murine macrophages. Four pairwise (Ibuprofen and antibiotic) (ΣFIC 0.33-0.50) and three triple (Ibuprofen and antibiotic with EOC) (ΣFIC 0.44-0.47) synergistic antimicrobial interactions were identified. These combinations demonstrated cell viability of 77.59%-100%. No combination significantly reduced nitric oxide production.

CONCLUSION

The results from this study provide insight into the potential of a multidrug combination involving ibuprofen with conventional antimicrobials and EOCs against common skin pathogens.

Quantifying higher-order epistasis: beware the chimera

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.

Evolutionary druggability for low-dimensional fitness landscapes toward new metrics for antimicrobial applications

The term 'druggability' describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and 7 β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ('variant vulnerability'), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ('drug applicability'). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G x G x E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

High-throughput characterization of bacterial responses to complex mixtures of chemical pollutants

Our understanding of how microbes respond to micropollutants, such as pesticides, is almost wholly based on single-species responses to individual chemicals. However, in natural environments, microbes experience multiple pollutants simultaneously. Here we perform a matrix of multi-stressor experiments by assaying the growth of model and non-model strains of bacteria in all 255 combinations of 8 chemical stressors (antibiotics, herbicides, fungicides and pesticides). We found that bacterial strains responded in different ways to stressor mixtures, which could not be predicted simply from their phylogenetic relatedness. Increasingly complex chemical mixtures were both more likely to negatively impact bacterial growth in monoculture and more likely to reveal net interactive effects. A mixed co-culture of strains proved more resilient to increasingly complex mixtures and revealed fewer interactions in the growth response. These results show predictability in microbial population responses to chemical stressors and could increase the utility of next-generation eco-toxicological assays.

The evolution of resistance to synergistic multi-drug combinations is more complex than evolving resistance to each individual drug component

Multidrug antibiotic resistance is an urgent public health concern. Multiple strategies have been suggested to alleviate this problem, including the use of antibiotic combinations and cyclic therapies. We examine how adaptation to (1) combinations of drugs affects resistance to individual drugs, and to (2) individual drugs alters responses to drug combinations. To evaluate this, we evolved multiple strains of drug resistant Staphylococcus epidermidis in the lab. We show that evolving resistance to four highly synergistic combinations does not result in cross-resistance to all of their components. Likewise, prior resistance to one antibiotic in a combination does not guarantee survival when exposed to the combination. We also identify four 3-step and four 2-step treatments that inhibit bacterial growth and confer collateral sensitivity with each step, impeding the development of multidrug resistance. This study highlights the importance of considering higher-order drug combinations in sequential therapies and how antibiotic interactions can influence the evolutionary trajectory of bacterial populations.

Evolutionary druggability: leveraging low-dimensional fitness landscapes towards new metrics for antimicrobial applications

The term "druggability" describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and seven β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ("variant vulnerability"), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ("drug applicability"). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G × G × E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns-ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Meta-analysis of three-stressor combinations on population-level fitness reveal substantial higher-order interactions

Although natural populations are typically subjected to multiple stressors, most past research has focused on single-stressor and two-stressor interactions, with little attention paid to higher-order interactions among three or more stressors. However, higher-order interactions increasingly appear to be widespread. Consequently, we used a recently introduced and improved framework to re-analyze higher-order ecological interactions. We conducted a literature review of the last 100 years (1920-2020) and reanalyzed 142 ecological three-stressor interactions on species' populations from 38 published papers; the vast majority of these studies were from the past 10 years. We found that 95.8 % (n = 136) of the three-stressor combinations had either not been categorized before or resulted in different interactions than previously reported. We also found substantial levels of emergent properties-interactions that are not due to strong pairwise interactions within the combination but rather uniquely due to all three stressors being combined. Calculating net interactions-the overall accounting for all possible interactions within a combination including the emergent and all pairwise interactions-we found that the most prevalent interaction type is antagonism, corresponding to a smaller than expected effect based on single stressor effects. In contrast, for emergent interactions, the most prevalent interaction type is synergistic, resulting in a larger than expected effect based on single stressor effects. Additionally, we found that hidden suppressive interactions-where a pairwise interaction is suppressed by a third stressor-are found in the majority of combinations (74 %). Collectively, understanding multiple stressor interactions through applying an appropriate framework is crucial for answering fundamental questions in ecology and has implications for conservation biology and population management. Crucially, identifying emergent properties can reveal hidden suppressive interactions that could be particularly important for the ecological management of at-risk populations.

The community-function landscape of microbial consortia

Quantitatively linking the composition and function of microbial communities is a major aspiration of microbial ecology. Microbial community functions emerge from a complex web of molecular interactions between cells, which give rise to population-level interactions among strains and species. Incorporating this complexity into predictive models is highly challenging. Inspired by a similar problem in genetics of predicting quantitative phenotypes from genotypes, an ecological community-function (or structure-function) landscape could be defined that maps community composition and function. In this piece, we present an overview of our current understanding of these community landscapes, their uses, limitations, and open questions. We argue that exploiting the parallels between both landscapes could bring powerful predictive methodologies from evolution and genetics into ecology, providing a boost to our ability to engineer and optimize microbial consortia.

Sample-efficient identification of high-dimensional antibiotic synergy with a normalized diagonal sampling design

Antibiotic resistance is an important public health problem. One potential solution is the development of synergistic antibiotic combinations, in which the combination is more effective than the component drugs. However, experimental progress in this direction is severely limited by the number of samples required to exhaustively test for synergy, which grows exponentially with the number of drugs combined. We introduce a new metric for antibiotic synergy, motivated by the popular Fractional Inhibitory Concentration Index and the Highest Single Agent model. We also propose a new experimental design that samples along all appropriately normalized diagonals in concentration space, and prove that this design identifies all synergies among a set of drugs while only sampling a small fraction of the possible combinations. We applied our method to screen two- through eight-way combinations of eight antibiotics at 10 concentrations each, which requires sampling only 2,560 unique combinations of antibiotic concentrations.

Antibiotic resistance is a growing public health concern, and there is an increasing need for methods to combat it. One potential approach is the development of synergistic antibiotic combinations, in which a mixture of drugs is more effective than any individual component. Unfortunately, the search for clinically beneficial drug combinations is severely restricted by the pace at which drugs can be screened. To date, most studies of combination therapies have been limited to testing only pairs or triples of drugs. These studies have identified primarily antagonistic drug interactions, in which the combination is less effective than the individual components. There is an acute need for methodologies that enable screening of higher-order drug combinations, both to identify synergies among many drugs and to understand the behavior of higher-order combinations. In this work we introduce a new paradigm for combination testing, the normalized diagonal sampling design, that makes identifying interactions among eight or more drugs feasible for the first time. Screening d drugs at m different combinations requires m ⋅ 2^d samples under our design as opposed to m^d under exhaustive screening, while provably identifying all synergies under mild assumptions about antibiotic behavior. Scientists can use our design to quickly screen for antibiotic interactions, accelerating the pace of combination therapy development.

Systematic measurement of combination-drug landscapes to predict in vivo treatment outcomes for tuberculosis

Lengthy multidrug chemotherapy is required to achieve a durable cure in tuberculosis. However, we lack well-validated, high-throughput in vitro models that predict animal outcomes. Here, we provide an extensible approach to rationally prioritize combination therapies for testing in in vivo mouse models of tuberculosis. We systematically measured Mycobacterium tuberculosis response to all two- and three-drug combinations among ten antibiotics in eight conditions that reproduce lesion microenvironments, resulting in >500,000 measurements. Using these in vitro data, we developed classifiers predictive of multidrug treatment outcome in a mouse model of disease relapse and identified ensembles of in vitro models that best describe in vivo treatment outcomes. We identified signatures of potencies and drug interactions in specific in vitro models that distinguish whether drug combinations are better than the standard of care in two important preclinical mouse models. Our framework is generalizable to other difficult-to-treat diseases requiring combination therapies. A record of this paper's transparent peer review process is included in the supplemental information.

Hidden suppressive interactions are common in higher-order drug combinations

The rapid increase of multi-drug resistant bacteria has led to a greater emphasis on multi-drug combination treatments. However, some combinations can be suppressive—that is, bacteria grow faster in some drug combinations than when treated with a single drug. Typically, when studying interactions, the overall effect of the combination is only compared with the single-drug effects. However, doing so could miss “hidden” cases of suppression, which occur when the highest order is suppressive compared with a lower-order combination but not to a single drug. We examined an extensive dataset of 5-drug combinations and all lower-order—single, 2-, 3-, and 4-drug—combinations. We found that a majority of all combinations—54%—contain hidden suppression. Examining hidden interactions is critical to understanding the architecture of higher-order interactions and can substantially affect our understanding and predictions of the evolution of antibiotic resistance under multi-drug treatments.

•

Most instances of suppressive interactions are missed by standard methods

•

A majority (54%) of all antibiotic combinations tested contain hidden suppression

•

Identifying hidden suppression can affect what combinations should be used

Guided screen for synergistic three-drug combinations

Combinations of three or more drugs are routinely used in various medical fields such as clinical oncology and infectious diseases to prevent resistance or to achieve synergistic therapeutic benefits. The very large number of possible high-order drug combinations presents a formidable challenge for discovering synergistic drug combinations. Here, we establish a guided screen to discover synergistic three-drug combinations. Using traditional checkerboard and recently developed diagonal methods, we experimentally measured all pairwise interactions among eight compounds in Erwinia amylovora, the causative agent of fire blight. Showing that synergy measurements of these two methods agree, we predicted synergy/antagonism scores for all possible three-drug combinations by averaging the synergy scores of pairwise interactions. We validated these predictions by experimentally measuring 35 three-drug interactions. Therefore, our guided screen for discovering three-drug synergies is (i) experimental screen of all pairwise interactions using diagonal method, (ii) averaging pairwise scores among components to predict three-drug interaction scores, (iii) experimental testing of top predictions. In our study, this strategy resulted in a five-fold reduction in screen size to find the most synergistic three-drug combinations.

COMBSecretomics: A pragmatic methodological framework for higher-order drug combination analysis using secretomics

Multi drug treatments are increasingly used in the clinic to combat complex and co-occurring diseases. However, most drug combination discovery efforts today are mainly focused on anticancer therapy and rarely examine the potential of using more than two drugs simultaneously. Moreover, there is currently no reported methodology for performing second- and higher-order drug combination analysis of secretomic patterns, meaning protein concentration profiles released by the cells. Here, we introduce COMBSecretomics (https://github.com/EffieChantzi/COMBSecretomics.git), the first pragmatic methodological framework designed to search exhaustively for second- and higher-order mixtures of candidate treatments that can modify, or even reverse malfunctioning secretomic patterns of human cells. This framework comes with two novel model-free combination analysis methods; a tailor-made generalization of the highest single agent principle and a data mining approach based on top-down hierarchical clustering. Quality control procedures to eliminate outliers and non-parametric statistics to quantify uncertainty in the results obtained are also included. COMBSecretomics is based on a standardized reproducible format and could be employed with any experimental platform that provides the required protein release data. Its practical use and functionality are demonstrated by means of a proof-of-principle pharmacological study related to cartilage degradation. COMBSecretomics is the first methodological framework reported to enable secretome-related second- and higher-order drug combination analysis. It could be used in drug discovery and development projects, clinical practice, as well as basic biological understanding of the largely unexplored changes in cell-cell communication that occurs due to disease and/or associated pharmacological treatment conditions.

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.

Mining and visualizing high-order directional drug interaction effects using the FAERS database

Background

Adverse drug events (ADEs) often occur as a result of drug-drug interactions (DDIs). The use of data mining for detecting effects of drug combinations on ADE has attracted growing attention and interest, however, most studies focused on analyzing pairwise DDIs. Recent efforts have been made to explore the directional relationships among high-dimensional drug combinations and have shown effectiveness on prediction of ADE risk. However, the existing approaches become inefficient from both computational and illustrative perspectives when considering more than three drugs.

Methods

We proposed an efficient approach to estimate the directional effects of high-order DDIs through frequent itemset mining, and further developed a novel visualization method to organize and present the high-order directional DDI effects involving more than three drugs in an interactive, concise and comprehensive manner. We demonstrated its performance by mining the directional DDIs associated with myopathy using a publicly available FAERS dataset.

Results

Directional effects of DDIs involving up to seven drugs were reported. Our analysis confirmed previously reported myopathy associated DDIs including interactions between fusidic acid with simvastatin and atorvastatin. Furthermore, we uncovered a number of novel DDIs leading to increased risk for myopathy, such as the co-administration of zoledronate with different types of drugs including antibiotics (ciprofloxacin, levofloxacin) and analgesics (acetaminophen, fentanyl, gabapentin, oxycodone). Finally, we visualized directional DDI findings via the proposed tool, which allows one to interactively select any drug combination as the baseline and zoom in/out to obtain both detailed and overall picture of interested drugs.

Conclusions

We developed a more efficient data mining strategy to identify high-order directional DDIs, and designed a scalable tool to visualize high-order DDI findings. The proposed method and tool have the potential to contribute to the drug interaction research and ultimately impact patient health care.

Availability and implementation

http://lishenlab.com/d3i/explorer.html

Effect of drug combinations on the kinetics of antibiotic resistance emergence in Escherichia coli CFT073 using an in vitro hollow-fibre infection model

Antibiotic resistance is one of the major threats to public health today. To address this problem requires an urgent comprehensive approach. Strategic and multitargeted combination therapy has been increasingly used clinically to treat bacterial infections. The hollow-fibre infection model (HFIM) is a well-controlled in vitro bioreactor system that is increasingly being used in the assessment of resistance emergence with monotherapies and combination antibiotic therapies. In this study, the HFIM was evaluated as a reliable in vitro method to quantitatively and reproducibly analyse the emergence of antibiotic resistance using ampicillin, fosfomycin and ciprofloxacin and their simultaneous combinations against Escherichia coli CFT073, a clinical uropathogenic strain. Bacteria were exposed to clinically relevant pharmacokinetic (PK) concentrations of the drugs for 10 days. Drug and bacterial samples were collected at different time points for PK analysis and to enumerate total and resistant bacterial populations, respectively. The results demonstrated that double or triple combinations significantly delayed the emergence of resistant E. coli CFT073 subpopulations. These findings suggest that strategic combinations of antimicrobials may play a role in controlling the emergence of resistance during treatment. Further animal and human trials will be needed to confirm this and to ensure that there is no adverse impact on the host microbiome or unexpected toxicity. The HFIM system could potentially be used to identify clinically relevant combination dosing regimens for use in a clinical trial evaluating the appearance of resistance to antibacterial drugs.

High-order interactions distort the functional landscape of microbial consortia

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

High-order interactions distort the functional landscape of microbial consortia

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

COMBImage2: a parallel computational framework for higher-order drug combination analysis that includes automated plate design, matched filter based object counting and temporal data mining

BACKGROUND

Pharmacological treatment of complex diseases using more than two drugs is commonplace in the clinic due to better efficacy, decreased toxicity and reduced risk for developing resistance. However, many of these higher-order treatments have not undergone any detailed preceding in vitro evaluation that could support their therapeutic potential and reveal disease related insights. Despite the increased medical need for discovery and development of higher-order drug combinations, very few reports from systematic large-scale studies along this direction exist. A major reason is lack of computational tools that enable automated design and analysis of exhaustive drug combination experiments, where all possible subsets among a panel of pre-selected drugs have to be evaluated.

RESULTS

Motivated by this, we developed COMBImage2, a parallel computational framework for higher-order drug combination analysis. COMBImage2 goes far beyond its predecessor COMBImage in many different ways. In particular, it offers automated 384-well plate design, as well as quality control that involves resampling statistics and inter-plate analyses. Moreover, it is equipped with a generic matched filter based object counting method that is currently designed for apoptotic-like cells. Furthermore, apart from higher-order synergy analyses, COMBImage2 introduces a novel data mining approach for identifying interesting temporal response patterns and disentangling higher- from lower- and single-drug effects. COMBImage2 was employed in the context of a small pilot study focused on the CUSP9v4 protocol, which is currently used in the clinic for treatment of recurrent glioblastoma. For the first time, all 246 possible combinations of order 4 or lower of the 9 single drugs consisting the CUSP9v4 cocktail, were evaluated on an in vitro clonal culture of glioma initiating cells.

CONCLUSIONS

COMBImage2 is able to automatically design and robustly analyze exhaustive and in general higher-order drug combination experiments. Such a versatile video microscopy oriented framework is likely to enable, guide and accelerate systematic large-scale drug combination studies not only for cancer but also other diseases.

Noise-precision tradeoff in predicting combinations of mutations and drugs

Many biological problems involve the response to multiple perturbations. Examples include response to combinations of many drugs, and the effects of combinations of many mutations. Such problems have an exponentially large space of combinations, which makes it infeasible to cover the entire space experimentally. To overcome this problem, several formulae that predict the effect of drug combinations or fitness landscape values have been proposed. These formulae use the effects of single perturbations and pairs of perturbations to predict triplets and higher order combinations. Interestingly, different formulae perform best on different datasets. Here we use Pareto optimality theory to quantitatively explain why no formula is optimal for all datasets, due to an inherent bias-variance (noise-precision) tradeoff. We calculate the Pareto front of log-linear formulae and find that the optimal formula depends on properties of the dataset: the typical interaction strength and the experimental noise. This study provides an approach to choose a suitable prediction formula for a given dataset, in order to best overcome the combinatorial explosion problem.

Sometimes a combination of drugs works much better than each drug alone. Finding such drug cocktails is a pressing challenge in order to combat drug resistance and to improve drug effects. However, it is impossible to test all combinations of multiple drug experimentally. Therefore, researchers are looking for computational rather than experimental approaches to overcome this problem. One approach is to measure the effect of few drugs and plug it into a formula that predicts the effect of many drugs together. Existing prediction formulae typically perform best on the dataset that they were developed on, but less well on other datasets. Here we explain this observation and give a guide for the choice of an optimal prediction formula for a given dataset. The optimal formula depends on two main properties of the dataset: 1) The interaction strength between the drugs and 2) The experimental noise in the data. This study may help researchers discover effective combinations of multiple drugs and multiple perturbations in general.

Prediction of ultra-high-order antibiotic combinations based on pairwise interactions

Drug combinations are a promising approach to achieve high efficacy at low doses and to overcome resistance. Drug combinations are especially useful when drugs cannot achieve effectiveness at tolerable doses, as occurs in cancer and tuberculosis (TB). However, discovery of effective drug combinations faces the challenge of combinatorial explosion, in which the number of possible combinations increases exponentially with the number of drugs and doses. A recent advance, called the dose model, uses a mathematical formula to overcome combinatorial explosion by reducing the problem to a feasible quadratic one: using data on drug pairs at a few doses, the dose model accurately predicts the effect of combinations of three and four drugs at all doses. The dose model has not yet been tested on higher-order combinations beyond four drugs. To address this, we measured the effect of combinations of up to ten antibiotics on E. coli growth, and of up to five tuberculosis (TB) drugs on the growth of M. tuberculosis. We find that the dose model accurately predicts the effect of these higher-order combinations, including cases of strong synergy and antagonism. This study supports the view that the interactions between drug pairs carries key information that largely determines higher-order interactions. Therefore, systematic study of pairwise drug interactions is a compelling strategy to prioritize drug regimens in high-dimensional spaces.

Prevalence and patterns of higher-order drug interactions in Escherichia coli

Interactions and emergent processes are essential for research on complex systems involving many components. Most studies focus solely on pairwise interactions and ignore higher-order interactions among three or more components. To gain deeper insights into higher-order interactions and complex environments, we study antibiotic combinations applied to pathogenic Escherichia coli and obtain unprecedented amounts of detailed data (251 two-drug combinations, 1512 three-drug combinations, 5670 four-drug combinations, and 13608 five-drug combinations). Directly opposite to previous assumptions and reports, we find higher-order interactions increase in frequency with the number of drugs in the bacteria’s environment. Specifically, as more drugs are added, we observe an elevated frequency of net synergy (effect greater than expected based on independent individual effects) and also increased instances of emergent antagonism (effect less than expected based on lower-order interaction effects). These findings have implications for the potential efficacy of drug combinations and are crucial for better navigating problems associated with the combinatorial complexity of multi-component systems.

Interactions play an important role in determining the dynamics of complex systems yet higher-order interactions that involve more than two components are poorly understood. A research team from University of California, Los Angeles led by Pamela Yeh, use a bacteria system to show that higher-order interactions among antibiotics are prevalent and also that there are systematic patterns in how they occur: the frequency of higher-order interactions increases with the number of components, net interactions tend to be more synergistic, and emergent interactions—arising at specific higher-order levels—tend toward antagonism. By detecting patterns in interactions as the number of drugs increases, they provide a method to handle the combinatorial complexity that results from higher-order interactions, yielding a solid foundation for exploring the patterns and consequences of emergent phenomena in other research areas.

Diagonal Method to Measure Synergy Among Any Number of Drugs

A synergistic drug combination has a higher efficacy compared to the effects of individual drugs. Checkerboard assays, where drugs are combined in many doses, allow sensitive measurement of drug interactions. However, these assays are costly and do not scale well for measuring interaction among many drugs. Several recent studies have reported drug interaction measurements using a diagonal sampling of the traditional checkerboard assay. This alternative methodology greatly decreases the cost of drug interaction experiments and allows interaction measurement for combinations with many drugs. Here, we describe a protocol to measure the three pairwise interactions and one three-way interaction among three antibiotics in duplicate, in five days, using only three 96-well microplates and standard laboratory equipment. We present representative results showing that the three-antibiotic combination of Levofloxacin + Nalidixic Acid + Penicillin G is synergistic. Our protocol scales up to measure interactions among many drugs and in other biological contexts, allowing for efficient screens for multi-drug synergies against pathogens and tumors.

A general pharmacodynamic interaction model identifies perpetrators and victims in drug interactions

Assessment of pharmacodynamic (PD) drug interactions is a cornerstone of the development of combination drug therapies. To guide this venture, we derive a general pharmacodynamic interaction (GPDI) model for ≥2 interacting drugs that is compatible with common additivity criteria. We propose a PD interaction to be quantifiable as multidirectional shifts in drug efficacy or potency and explicate the drugs’ role as victim, perpetrator or even both at the same time. We evaluate the GPDI model against conventional approaches in a data set of 200 combination experiments in Saccharomyces cerevisiae: 22% interact additively, a minority of the interactions (11%) are bidirectional antagonistic or synergistic, whereas the majority (67%) are monodirectional, i.e., asymmetric with distinct perpetrators and victims, which is not classifiable by conventional methods. The GPDI model excellently reflects the observed interaction data, and hence represents an attractive approach for quantitative assessment of novel combination therapies along the drug development process.

Assessment of pharmacodynamic interactions is at the heart of combination therapy development. Here the authors introduce a general drug interaction scoring model that enables quantification of synergistic and antagonistic interactions and determination of the directionality of the interactions.

Enhanced identification of synergistic and antagonistic emergent interactions among three or more drugs

Interactions among drugs play a critical role in the killing efficacy of multi-drug treatments. Recent advances in theory and experiment for three-drug interactions enable the search for emergent interactions-ones not predictable from pairwise interactions. Previous work has shown it is easier to detect synergies and antagonisms among pairwise interactions when a rescaling method is applied to the interaction metric. However, no study has carefully examined whether new types of normalization might be needed for emergence. Here, we propose several rescaling methods for enhancing the classification of the higher order drug interactions based on our conceptual framework. To choose the rescaling that best separates synergism, antagonism and additivity, we conducted bacterial growth experiments in the presence of single, pairwise and triple-drug combinations among 14 antibiotics. We found one of our rescaling methods is far better at distinguishing synergistic and antagonistic emergent interactions than any of the other methods. Using our new method, we find around 50% of emergent interactions are additive, much less than previous reports of greater than 90% additivity. We conclude that higher order emergent interactions are much more common than previously believed, and we argue these findings for drugs suggest that appropriate rescaling is crucial to infer higher order interactions.

Efficient measurement and factorization of high-order drug interactions in Mycobacterium tuberculosis

Combinations of three or more drugs are used to treat many diseases, including tuberculosis. Thus, it is important to understand how synergistic or antagonistic drug interactions affect the efficacy of combination therapies. However, our understanding of high-order drug interactions is limited because of the lack of both efficient measurement methods and theoretical framework for analysis and interpretation. We developed an efficient experimental sampling and scoring method [diagonal measurement of n-way drug interactions (DiaMOND)] to measure drug interactions for combinations of any number of drugs. DiaMOND provides an efficient alternative to checkerboard assays, which are commonly used to measure drug interactions. We established a geometric framework to factorize high-order drug interactions into lower-order components, thereby establishing a road map of how to use lower-order measurements to predict high-order interactions. Our framework is a generalized Loewe additivity model for high-order drug interactions. Using DiaMOND, we identified and analyzed synergistic and antagonistic antibiotic combinations against Mycobacteriumtuberculosis. Efficient measurement and factorization of high-order drug interactions by DiaMOND are broadly applicable to other cell types and disease models.

Suppressive drug combinations and their potential to combat antibiotic resistance

Antibiotic effectiveness often changes when two or more such drugs are administered simultaneously and unearthing antibiotic combinations with enhanced efficacy (synergy) has been a longstanding clinical goal. However, antibiotic resistance, which undermines individual drugs, threatens such combined treatments. Remarkably, it has emerged that antibiotic combinations whose combined effect is lower than that of at least one of the individual drugs can slow or even reverse the evolution of resistance. We synthesize and review studies of such so-called 'suppressive interactions' in the literature. We examine why these interactions have been largely disregarded in the past, the strategies used to identify them, their mechanistic basis, demonstrations of their potential to reverse the evolution of resistance and arguments for and against using them in clinical treatment. We suggest future directions for research on these interactions, aiming to expand the basic body of knowledge on suppression and to determine the applicability of suppressive interactions in the clinic.

When more is less: Emergent suppressive interactions in three-drug combinations

BACKGROUND

In drug-drug interactions, there are surprising cases in which the growth inhibition of bacteria by a single antibiotic decreases when a second antibiotic is added. These interactions are termed suppressive and have been argued to have the potential to limit the evolution of resistance. Nevertheless, little attention has been given to suppressive interactions because clinical studies typically search for increases in killing efficiency and because suppressive interactions are believed to be rare based on pairwise studies.

RESULTS

Here, we quantify the effects of single-, double-, and triple-drug combinations from a set of 14 antibiotics and 3 bacteria strains, totaling 364 unique three-drug combinations per bacteria strain. We find that increasing the number of drugs can increase the prevalence of suppressive interactions: 17% of three-drug combinations are suppressive compared to 5% of two-drug combinations in this study. Most cases of suppression we find (97%) are "hidden" cases for which the triple-drug bacterial growth is less than the single-drug treatments but exceeds that of a pairwise combination.

CONCLUSIONS

We find a surprising number of suppressive interactions in higher-order drug combinations. Without examining lower-order (pairwise) bacterial growth, emergent suppressive effects would be missed, potentially affecting our understanding of evolution of resistance and treatment strategies for resistant pathogens. These findings suggest that careful examination of the full factorial of drug combinations is needed to uncover suppressive interactions in higher-order combinations.