Pairwise interactions and the battle against combinatorics in multidrug therapies

Automated and miniaturized screening of antibiotic combinations via robotic-printed combinatorial droplet platform

Antimicrobial resistance (AMR) has become a global health crisis in need of novel solutions. To this end, antibiotic combination therapies, which combine multiple antibiotics for treatment, have attracted significant attention as a potential approach for combating AMR. To facilitate advances in antibiotic combination therapies, most notably in investigating antibiotic interactions and identifying synergistic antibiotic combinations however, there remains a need for automated high-throughput platforms that can create and examine antibiotic combinations on-demand, at scale, and with minimal reagent consumption. To address these challenges, we have developed a Robotic-Printed Combinatorial Droplet (RoboDrop) platform by integrating a programmable droplet microfluidic device that generates antibiotic combinations in nanoliter droplets in automation, a robotic arm that arranges the droplets in an array, and a camera that images the array of thousands of droplets in parallel. We further implement a resazurin-based bacterial viability assay to accelerate our antibiotic combination testing. As a demonstration, we use RoboDrop to corroborate two pairs of antibiotics with known interactions and subsequently identify a new synergistic combination of cefsulodin, penicillin, and oxacillin against a model E. coli strain. We therefore envision RoboDrop becoming a useful tool to efficiently identify new synergistic antibiotic combinations toward combating AMR.

Mutators can drive the evolution of multi-resistance to antibiotics

Antibiotic combination therapies are an approach used to counter the evolution of resistance; their purported benefit is they can stop the successive emergence of independent resistance mutations in the same genome. Here, we show that bacterial populations with 'mutators', organisms with defects in DNA repair, readily evolve resistance to combination antibiotic treatment when there is a delay in reaching inhibitory concentrations of antibiotic-under conditions where purely wild-type populations cannot. In populations of Escherichia coli subjected to combination treatment, we detected a diverse array of acquired mutations, including multiple alleles in the canonical targets of resistance for the two drugs, as well as mutations in multi-drug efflux pumps and genes involved in DNA replication and repair. Unexpectedly, mutators not only allowed multi-resistance to evolve under combination treatment where it was favoured, but also under single-drug treatments. Using simulations, we show that the increase in mutation rate of the two canonical resistance targets is sufficient to permit multi-resistance evolution in both single-drug and combination treatments. Under both conditions, the mutator allele swept to fixation through hitch-hiking with single-drug resistance, enabling subsequent resistance mutations to emerge. Ultimately, our results suggest that mutators may hinder the utility of combination therapy when mutators are present. Additionally, by raising the rates of genetic mutation, selection for multi-resistance may have the unwanted side-effect of increasing the potential to evolve resistance to future antibiotic treatments.

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.

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.

Uncovering Key Metabolic Determinants of the Drug Interactions Between Trimethoprim and Erythromycin in Escherichia coli

Understanding interactions between antibiotics used in combination is an important theme in microbiology. Using the interactions between the antifolate drug trimethoprim and the ribosome-targeting antibiotic erythromycin in Escherichia coli as a model, we applied a transcriptomic approach for dissecting interactions between two antibiotics with different modes of action. When trimethoprim and erythromycin were combined, the transcriptional response of genes from the sulfate reduction pathway deviated from the dominant effect of trimethoprim on the transcriptome. We successfully altered the drug interaction from additivity to suppression by increasing the sulfate level in the growth environment and identified sulfate reduction as an important metabolic determinant that shapes the interaction between the two drugs. Our work highlights the potential of using prioritization of gene expression patterns as a tool for identifying key metabolic determinants that shape drug-drug interactions. We further demonstrated that the sigma factor-binding protein gene crl shapes the interactions between the two antibiotics, which provides a rare example of how naturally occurring variations between strains of the same bacterial species can sometimes generate very different drug interactions.

Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

Multiobjective optimization identifies cancer-selective combination therapies

Combinatorial therapies are required to treat patients with advanced cancers that have become resistant to monotherapies through rewiring of redundant pathways. Due to a massive number of potential drug combinations, there is a need for systematic approaches to identify safe and effective combinations for each patient, using cost-effective methods. Here, we developed an exact multiobjective optimization method for identifying pairwise or higher-order combinations that show maximal cancer-selectivity. The prioritization of patient-specific combinations is based on Pareto-optimization in the search space spanned by the therapeutic and nonselective effects of combinations. We demonstrate the performance of the method in the context of BRAF-V600E melanoma treatment, where the optimal solutions predicted a number of co-inhibition partners for vemurafenib, a selective BRAF-V600E inhibitor, approved for advanced melanoma. We experimentally validated many of the predictions in BRAF-V600E melanoma cell line, and the results suggest that one can improve selective inhibition of BRAF-V600E melanoma cells by combinatorial targeting of MAPK/ERK and other compensatory pathways using pairwise and third-order drug combinations. Our mechanism-agnostic optimization method is widely applicable to various cancer types, and it takes as input only measurements of a subset of pairwise drug combinations, without requiring target information or genomic profiles. Such data-driven approaches may become useful for functional precision oncology applications that go beyond the cancer genetic dependency paradigm to optimize cancer-selective combinatorial treatments.

Allosteric inhibition explained through conformational ensembles sampling distinct "mixed" states

Allosteric modulation provides an effective avenue for selective and potent enzyme inhibition. Here, we summarize and critically discuss recent advances on the mechanisms of allosteric partial agonists for three representative signalling enzymes activated by cyclic nucleotides: the cAMP-dependent protein kinase (PKA), the cGMP-dependent protein kinase (PKG), and the exchange protein activated by cAMP (EPAC). The comparative analysis of partial agonism in PKA, PKG and EPAC reveals a common emerging theme, i.e. the sampling of distinct “mixed” conformational states, either within a single domain or between distinct domains. Here, we show how such “mixed” states play a crucial role in explaining the observed functional response, i.e. partial agonism and allosteric pluripotency, as well as in maximizing inhibition while minimizing potency losses. In addition, by combining Nuclear Magnetic Resonance (NMR), Molecular Dynamics (MD) simulations and Ensemble Allosteric Modeling (EAM), we also show how to map the free-energy landscape of conformational ensembles containing “mixed” states. By discussing selected case studies, we illustrate how MD simulations and EAM complement NMR to quantitatively relate protein dynamics to function. The resulting NMR- and MD-based EAMs are anticipated to inform not only the design of new generations of highly selective allosteric inhibitors, but also the choice of multidrug combinations.

Moonshots for aging

 As the global population ages, there is increased interest in living longer and improving one’s quality of life in later years. However, studying aging – the decline in body function – is expensive and time-consuming. And despite research success to make model organisms live longer, there still aren’t really any feasible solutions for delaying aging in humans. With space travel, scientists and engineers couldn’t know what it would take to get to the moon. They had to extrapolate from theory and shorter-range tests. Perhaps with aging, we need a similar moonshot philosophy. And though “shot” might imply medicine, perhaps we need to think beyond medical interventions. Like the moon once was, we seem a long way away from provable therapies to increase human healthspan (the healthy period of one’s life) or lifespan (how long one lives). This review therefore focuses on radical proposals. We hope it might stimulate discussion on what we might consider doing significantly differently than ongoing aging research.

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.

Design of high-order antibiotic combinations against M. tuberculosis by ranking and exclusion

Combinations of more than two drugs are routinely used for the treatment of pathogens and tumors. High-order combinations may be chosen due to their non-overlapping resistance mechanisms or for favorable drug interactions. Synergistic/antagonistic interactions occur when the combination has a higher/lower effect than the sum of individual drug effects. The standard treatment of Mycobacterium tuberculosis (Mtb) is an additive cocktail of three drugs which have different targets. Herein, we experimentally measured all 190 pairwise interactions among 20 antibiotics against Mtb growth. We used the pairwise interaction data to rank all possible high-order combinations by strength of synergy/antagonism. We used drug interaction profile correlation as a proxy for drug similarity to establish exclusion criteria for ideal combination therapies. Using this ranking and exclusion design (R/ED) framework, we modeled ways to improve the standard 3-drug combination with the addition of new drugs. We applied this framework to find the best 4-drug combinations against drug-resistant Mtb by adding new exclusion criteria to R/ED. Finally, we modeled alternating 2-order combinations as a cycling treatment and found optimized regimens significantly reduced the overall effective dose. R/ED provides an adaptable framework for the design of high-order drug combinations against any pathogen or tumor.

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.

Prediction of drug cocktail effects when the number of measurements is limited

Cocktails of drugs can be more effective than single drugs, because they can potentially work at lower doses and avoid resistance. However, it is impossible to test all drug cocktails drawn from a large set of drugs because of the huge number of combinations. To overcome this combinatorial explosion problem, one can sample a relatively small number of combinations and use a model to predict the rest. Recently, Zimmer and Katzir et al. presented a model that accurately predicted the effects of cocktails at all doses based on measuring pairs of drugs. This model requires measuring each pair at several different doses and uses interpolation to reduce experimental noise. However, often, it is not possible to measure each pair at multiple doses (for example, in scarce patient-derived tumor material or in large screens). Here, we ask whether measurements at only a single dose can also predict high-order drug cocktails. To address this, we present a fully factorial experimental dataset on all drug cocktails built of 6 chemotherapy drugs on 2 cancer cell lines. We develop a formula that uses only pair measurements at a single dose to predict much of the variation up to 6-drug cocktails in the present data, outperforming commonly used Bliss independence and regression approaches. This model, called the pairs model, is an extension of the Bliss independence model to pairs: For M drugs, it equals the product of all pair effects to the power 1/(M−1). The pairs model also shows good agreement with previously published data on antibiotic triplets and quadruplets. The present model can only predict combinations at the same doses in which the pairs were measured and is not able to predict effects at other doses. This study indicates that pair-based approaches might be able to usefully predict and prioritize high-order combinations, even in large screens or when material for testing is limited.

Drug cocktails are a promising strategy for diseases such as cancer and infections, because cocktails can be more effective than individual drugs and can overcome problems of drug resistance. However, finding the best cocktail comprising a given set of drugs is challenging because the number of experiments needed is huge and grows exponentially with the number of drugs. This problem is exacerbated when the experiments are expensive and the material for testing is rare. Here, we present a way to address this challenge using a mathematical formula, called the pairs model, that requires relatively few experimental tests in order to estimate the effects of cocktails and to predict which cocktail is most effective. The formula does well on experimental data generated in this study using combinations of between 3 and 6 anticancer drugs, as well as on existing data that use combinations of antibiotics.

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.