Finding potent multidrug combinations against cancer and infections is a pressing therapeutic challenge; however, screening all combinations is difficult because the number of experiments grows exponentially with the number of drugs and doses. To address this, we present a mathematical model that predicts the effects of three or more antibiotics or anticancer drugs at all doses based only on measurements of drug pairs at a few doses, without need for mechanistic information. The model provides accurate predictions on available data for antibiotic combinations, and on experiments presented here on the response matrix of three cancer drugs at eight doses per drug. This approach offers a way to search for effective multidrug combinations using a small number of experiments.drug combinations | drug cocktails | cancer treatment | mechanism-free formula | predictive formula T o kill cancer cells or bacteria, combination therapy can be more effective than individual drugs (1-6). Combination therapy is thought to allow increased efficacy at low doses, thus reducing side effects and toxicity; it is also believed to minimize the chances of resistance (7-9), a pressing problem in treating cancer and infectious diseases.Much work has been devoted to classifying how pairs of drugs interact (10)(11)(12)(13)(14). Across systems, a good first approximation is the Bliss independence model (15,16), in which the pair effect is the product of the individual drug effects: If the effect of the drugs are g 1 and g 2 , the effect of the combination is g 12 = g 1 · g 2 . The Bliss model ignores interactions in which drugs enhance each other effectssynergism-or inhibit each other's effects-antagonism. Some drugs even inhibit each other so much that the combined effect is lower than either drug alone, an effect called hyperantagonism (17)(18)(19)(20)(21).Going beyond drug pairs has been difficult. Experimentally testing high-order combinations beyond pairs in a systematic way is challenging because it requires an exponentially large number of experiments (22-25): For N drugs at D doses, one needs D N experiments. For N = 10 drugs and D = 8 doses, this means ∼10 9 measurements. The combinatorial explosion makes exhaustive testing of drug dose combinations unfeasible. This problem is especially acute in cases where material is scarce, such as testing of patient-derived samples (26)(27)(28)(29). Hence, models for predicting high-order effects are essential.Apart from detailed simulations of particular systems (22,30,31), there has been little study of general mechanism-independent models for multiple drugs. An exception is the elegant study by Wood et al. (32) that showed that combinations of antibiotics can be predicted by an Iserliss-like formula that uses pair effects to predict the effects of higher-order mixtures. For example, the effect of a drug triplet is modeled as g 123 = g 12 g 3 + g 13 g 2 + g 23 g 1 − 2g 1 g 2 g 3 . This formula has not been tested on cancer drug mixtures, to the best of our knowledge.Another line of research u...

Many countries have applied lockdown that helped suppress COVID-19, but with devastating economic consequences. Here we propose exit strategies from lockdown that provide sustainable, albeit reduced, economic activity. We use mathematical models to show that a cyclic schedule of 4-day work and 10-day lockdown, or similar variants, can, in certain conditions, suppress the epidemic while providing part-time employment. The cycle reduces the reproduction number R by a combination of reduced exposure time and an anti-phasing effect in which those infected during work days reach peak infectiousness during lockdown days. The number of work days can be adapted in response to observations. Throughout, full epidemiological measures need to continue including hygiene, physical distancing, compartmentalization and extensive testing and contact tracing. We do not call for immediate adoption of this policy, but rather to consider it as a conceptual framework, which, when combined with other interventions to control the epidemic, can offer the beginnings of predictability to many economic sectors.Current non-pharmaceutical interventions (NPI) to suppress COVID-19 use testing, contact tracing, physical distancing, mask use, identification of regional outbreaks, compartmentalization down to the neighborhood and company level, and population-level quarantine at home known as lockdown ( 1 -4 ) . The aim is to flatten the infection curve and prevent overload of the medical system until a vaccine becomes available.Lockdown is currently in place in many countries. It has a large economic and social cost, including unemployment on a massive scale. Once a lockdown has reduced the number of critical cases to a desired goal, a decision must be reached on how to exit it responsibly. The main concern is the risk of resurgence of the epidemic. One strategy proposes reinstating lockdown when a threshold number of critical cases is exceeded in a resurgence, and stopping lockdown again once cases drop below a low threshold ( 2 , 5 ) ( Fig 1A,S1). While such an "adaptive triggering" strategy can prevent healthcare services from becoming overloaded, it leads to economic uncertainty and continues to accumulate cases with each resurgence.

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.

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.

Age‐related diseases such as cancer, cardiovascular disease, kidney failure, and osteoarthritis have universal features: Their incidence rises exponentially with age with a slope of 6–8% per year and decreases at very old ages. There is no conceptual model which explains these features in so many diverse diseases in terms of a single shared biological factor. Here, we develop such a model, and test it using a nationwide medical record dataset on the incidence of nearly 1000 diseases over 50 million life‐years, which we provide as a resource. The model explains incidence using the accumulation of senescent cells, damaged cells that cause inflammation and reduce regeneration, whose level rise stochastically with age. The exponential rise and late drop in incidence are captured by two parameters for each disease: the susceptible fraction of the population and the threshold concentration of senescent cells that causes disease onset. We propose a physiological mechanism for the threshold concentration for several disease classes, including an etiology for diseases of unknown origin such as idiopathic pulmonary fibrosis and osteoarthritis. The model can be used to design optimal treatments that remove senescent cells, suggeting that treatment starting at old age can sharply reduce the incidence of all age‐related diseases, and thus increase the healthspan.

In the last decades, growing evidence showed the therapeutic capabilities of Cannabis plants. These capabilities were attributed to the specialized secondary metabolites stored in the glandular trichomes of female inflorescences, mainly phytocannabinoids and terpenoids. The accumulation of the metabolites in the flower is versatile and influenced by a largely unknown regulation system, attributed to genetic, developmental and environmental factors. As Cannabis is a dioecious plant, one main factor is fertilization after successful pollination. Fertilized flowers are considerably less potent, likely due to changes in the contents of phytocannabinoids and terpenoids; therefore, this study examined the effect of fertilization on metabolite composition by crossbreeding (-)-Δ9-trans-tetrahydrocannabinol (THC)- or cannabidiol (CBD)-rich female plants with different male plants: THC-rich, CBD-rich, or the original female plant induced to develop male pollen sacs. We used advanced analytical methods to assess the phytocannabinoids and terpenoids content, including a newly developed semi-quantitative analysis for terpenoids without analytical standards. We found that fertilization significantly decreased phytocannabinoids content. For terpenoids, the subgroup of monoterpenoids had similar trends to the phytocannabinoids, proposing both are commonly regulated in the plant. The sesquiterpenoids remained unchanged in the THC-rich female and had a trend of decrease in the CBD-rich female. Additionally, specific phytocannabinoids and terpenoids showed an uncommon increase in concentration followed by fertilization with particular male plants. Our results demonstrate that although the profile of phytocannabinoids and their relative ratios were kept, fertilization substantially decreased the concentration of nearly all phytocannabinoids in the plant regardless of the type of fertilizing male. Our findings may point to the functional roles of secondary metabolites in Cannabis.

We suggest a scheme to manipulate paraxial diffraction by utilizing the dependency of a four-wave mixing process on the relative angle between the light fields. A microscopic model for four-wave mixing in a Λ-type level structure is introduced and compared to recent experimental data. We show that images with feature size as low as 10 μm can propagate with very little or even negative diffraction. The mechanism is completely different from that conserving the shape of spatial solitons in nonlinear media, as here diffraction is suppressed for arbitrary spatial profiles. At the same time, the gain inherent to the nonlinear process prevents loss and allows for operating at high optical depths. Our scheme does not rely on atomic motion and is thus applicable to both gaseous and solid media.