Bliss independence and Loewe additivity , as well as the median effect equation for multiple drugs are commonly used as reference models for the combined action of two independent inhibitors [11,27]. In this paper, we concentrated on Bliss independence and Loewe additivity because, unlike the median effect equation, these two reference models. dence and Loewe additivity. Bliss independence is based on probabilistic arguments: the combined effect of two inhibitors on the survival is defined as the probability of being affecte An advantage of Bliss independence over Loewe additivity, and the related CI, is that drug interaction can be applied to clinical data when the outcome of treatment is survival, e.g. recurrence-free survival, time to recurrence/progression, progression-free survival, or overall survival The Bliss independence-based model has fewer restrictions than Loewe additivity-based models. First, Loewe additivity models rely on accurately estimated dose-response curves to support the calculation of the effective dose for a given response Loewe additivity-based models work well only when monotherapy dose-response curves are well characterized through parametric models such as four-parameter logistic (4PL) nonlinear regression curves. When dose-response curves are nonstandard or not available, we find that the Bliss independence-based model provides a viable alterna-tive
Current methods based on Loewe additivity and Bliss independence are associated with implicit assumptions of the interacting system. We reviewed the hyperplane theorem that used a generalized equation for defining the isobols (surfaces of equal effect) for 2 noninteracting drugs. We showed that under certain conditions, the original equation. In this paper, we will exclusively focus on Loewe Additivity, which tends to lead to better predictions of synergy than Bliss Independence (Cokol et al., 2011). Loewe argued that, if two individual doses x 1 * and x 2 * give rise to the same response, say y , then, in case of no interaction between the compounds, all dose combinations on the. Loewe (1928) Pharmacological additivity Definitions of independence, synergy, antagonism are argued, but Loewe's additivity is undisputed. Fig. 65, Gaddum (1942) Pharmacology Gaddumcalled additivity a special case of synergy Despite these limitations, Loewe Additivity has still been one of the major reference models used and the foundation for many synergy methods. Bliss Independence. A commonly used alternative to Loewe Additivity is the Bliss Independence model A mathematical approach to study combined effects of toxicants in vitro: evaluation of the Bliss independence criterion and the Loewe additivity model. Toxicol. In Vitro 21 , 759-769 (2007)
(B) Plot comparing Bliss independence and Loewe additivity between two drugs with higher Hill slopes of 2. (C) Percentage of simulated Bliss screens in which each asymptotically additive. It is shown that LOEWE additivity leads to good predictions of mixture toxicities for most combinations, whereas BLISS independence tends to underestimate mixture toxicities. By this it is reaffirmed that there is a solid basis for forthcoming regulatory activities on mixtures of chemicals
The Loewe additivity model defines the expected effect as if a drug was combined with itself, while the Bliss independence model utilizes probabilistic theory to model the effects of individual drugs in a combination as independent yet competing events Two main different approaches, the Bliss independence criterion and the Loewe additivity model, have been generally used in co-exposure experiments. In some cases, they can present dramatically different results, depending on the slope of the pure dose-response curves of single substances The Hill response surface ansatz contains the Loewe additivity concept as a special case and is incompatible with Bliss independent action. Hence, when synergistic effects are claimed, those dose combinations deserve special attention where the differences between independent action approaches and H Commonly-utilized reference models include the Highest single agent (HSA) model (Berenbaum, 1989), the Loewe additivity model (Loewe, 1953), the Bliss independence model (Bliss, 1939), and more recently, the Zero interaction potency (ZIP) model (Yadav et al., 2015). The assumptions being made in these reference models are different from each.
Bliss independence Bliss independence is based on probability theory and assumes the two inhibitors are working through inde-pendent mechanisms [15]. The inhibitors do not inter-fere with each other, but contribute to a common result. Unlike Loewe additivity, calculating Bliss independence does not require determination of dose-response curve multiple diverse drugs, favoring the Bliss effect-additivity and motivating a simple model of dosage-orthogonality. In contrast to Loewe additivity, which predicts that the total dosag
Bliss independence, Loewe additivity: Data from wet-lab experimental: Data from wet-lab experimental platforms can be directly used: MacSynergyII : Free software: Bliss independence: Dose-response data: MacSynergy II is essentially an Excel file and it scales the input data to %inhibition using positive and negative controls: Combenefit : Free. Enjoy speedy delivery. Next day or express delivery available, plus free returns globally. New arrivals every week. Explore the new season collections or shop bestsellers Unlike Loewe additivity, calculating Bliss independence does not require determination of dose-response curves for the individual compounds to determine the theoretical results, making it easier to compute . Bliss independence models the combined effect (E T) as the product of the individual effects with drugs A (E A) and B (E B) for the Bliss Independence model, for the Loewe Additivity. Note that when the combination counts three drugs, the equation CI = 1 corresponds to the plane passing through A, B, and C when doses of drugs A, B, and C are, respectively, presented by three coordinate axes, instead of a line when combining two drugs Loewe additivity and Bliss independence models are being widely Computational and Structural Biotechnology Journal 13 (2015) 504-513 E-mail address: jing.tang@helsinki.ﬁ (J. Tang)
The simulated data using the Loewe Additivity-based or Bliss Independence-based GPDI model were re-estimated using the MTP model linked to the GPDI model (based on Bliss Independence or Loewe Additivity), the Empiric Bliss Independence-based model, or the Greco model based on Loewe Additivity, in order to compare the estimated PD interactions. Two reference models Loewe additivity and Bliss independence are used for synergy evaluation. A new index based on Bliss independence is introduced, comparable to the interaction index based on Loewe Additivity. An example data set is used to demonstrate the implementation of these analysis methods. In the final discussion, we point out some. It is clear that the adherents of Loewe additivity and Bliss independence have heard all the most compelling arguments for and against each model, and cannot be persuaded to switch allegiances. Thuswe propose that both models be tentatively acceptedThis recommendation is made even though predictions o Four well-known reference models are used to compute the synergy of drug combinations. These are loewe additivity, bliss independence, highest single agent, and zero interaction potency (see Fig. 1). The brief description of these model are given in the succeeding subsections The degree of independence (DI) (52, 53) which is (experimental IIP minus Loewe additivity IIP) divided by (Bliss independence IIP minus Loewe additivity IIP), was calculated (SI Appendix, Fig. S13 and Note S2). In general, the DI value becomes close to 1 when the drug combination shows independent inhibition (e.g., experimental IIP close to.
drugs. Two classic models for combined drug effects, Loewe additivity (18) and Bliss independence (19), predict the expected efficacies of drug combinations given the experimentally determined efficacies of individual component drugs. Loewe additivity assumes that drugs act through the same target; Bliss Loewe additivity (Equation 2) [27,28], Highest Single Agent (HSA) (Equation 3) [29], and Zero Interaction Potency (ZIP) (Equation 4) [30]. = 1+ 2− 1 2 (1) Equation 1. Bliss independence model. yBliss - Bliss response; y1 - drug1 response; y2 - drug2 response. = + ( 1+ 2 ) 1+( 1+ 2 ) (2) Equation. - Loewe additivity - Bliss Independence • Comparison to Greco model 14 200x Mono A B D) Time (h) Ind. Prediction of Loewe Additivity 15 Observation Prediction Ax Bx (fold MIC) Individual predictions using Greco (left) or GPDI model (right) 16 Observation Prediction Ax Bx (fold MIC) INT values at EC50 1 The main difference between Bliss independence and Loewe additivity for evaluating PD interactions is based on the definition of additivity and 'no interaction' between the two agents when used in combination. The terms independence and additivity are often used interchangeably, which is inappropriate Bliss independence Bliss independence predicts effects to be sequential, i.e., the effects are probabilistically independent. Using the Emax model, the effect can be calculated from: where φ is a parameter describing any synergism (if φ<1) or antagonism (φ>1). Loewe additivity and Bliss independence give similar bu
on the Loewe additivity (LA) theory and the Bliss independence (BI) theory. RWPE-1 cells were treated with NP (0.01-100 µM) and BPA (1-5000 µM) in either a single or a combined format. A cell viability assay and lactate dehydrogenase (LDH) leakage rate assay were employed as endpoints. As predicted by the two models and based on the cel Drug combinations may have additive, antagonistic, synergistic, or potentiation effects as determined by mathematical models including Loewe additivity, Bliss independence, or Chou-Talalay models. Animal models of cutaneous malignancy may be utilized for in vivo toxicity and effectiveness preclinical evaluation of promising combination regimens Among these works, the Loewe additivity 49, 50 and Bliss independence 46, 51 models are two of the most useful frameworks of synergy. The Loewe additivity model assumes that two drugs act through similar mechanisms. Equipotent dose ratios determine the effects of each drug and their combination Among existing methods, under the assumption that two drugs acting by independent mechanisms, Bliss independence model is used to define combined effect of two drugs ; given that two similar drugs competitively acting on a target, Loewe additivity model is used to predict the combined effect of two drugs The Loewe additivity and Bliss independence form the basis of sophisticated protocols for assessing drug combinations, especially in cancer-targeted chemotherapy[33, 34]. Research on biological network systems, as well as the biochemical characteristics of drugs, has also unraveled the mechanisms by which drug combinations produce synergistic.
conventionally analyzed by Loewe additivity or Bliss independence (Bliss, 1939; Lehar et al., 2009; Loewe, 1953; Loewe and Muischnek, 1926; Whitehead et al., 2013). However, the Loewe model assumes a linear dose-effect relationship, whereas biological responses to kinase inhibitors typically display a logistic curve shape The Bliss independence model, for example, assumes that each sample has independent, yet competing effects, while the Loewe additivity model defines the expected effect as a sample combined with itself. 47 Recently, an additional reference model, the zero interaction potency (ZIP) model, was developed that takes advantage of both Loewe and. these authors is Loewe additivity for dose-additivity and Bliss independence for the independence criterion. The cases for which the combination effects deviate from the zero interaction effect are called Loewe/Bliss synergism/antagonism. This terminology avoids the difficulties which usually arise when the terms synergism or antagonism are. Synergy or antagonism between NAbs can be defined relative to either the Loewe additivity model (29, 30), which assumes that two inhibitors have similar mechanisms or compete for the same binding site, or the Bliss independence model , which assumes that inhibitors have independent binding sites and independent mechanisms
Bridging Bliss Independence and Loewe Additivity models at low drug concentrations The starting point for Loewe's model is proportionality between drug effect and drug concentration, which is reasonable to assume at low drug concentrations. In this condition, the Bliss model can be adapted as Equation S12 can be simplified The traditional one is to detect deviations from additivity as suggested by Loewe and Muischnek or from independence as outlined by Bliss . The second dominating strategy evaluates synergy in terms of the estimate of at least one interaction parameter in a response surface model, essentially according to that introduced by Box ( 11 ), estimated. Drug-drug interaction data were analyzed by the Loewe additivity and Bliss independence drug interaction models. Results: ITMN-191 and R1479 displayed a moderate level of synergistic antiviral activity against an HCV replicon by isobologram analysis. Combination index (CI) values for IC50, IC75 and IC90 effect levels at multiple drug ratios. Loewe additivity is suggested to be a suitable concept for zero-interaction when noninteracting drugs have similar modes of action, however, when the drugs are believed to act independently, Bliss independence is more appropriate (37, 38)
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 thei Loewe additivity model [Loewe, 1953] defines the expected effect yLOEW E as if a drug was combined with itself. Unlike the HSA and the Bliss independence models giving a point estimate using different assumptions, the Loewe additivity model considers the dose-response curves of individual drugs
Y at Y.(B) Loewe additivity (Loewe, 1928) is the drug-with-itself reference for synergy, where I Loewe at X,Y yields additive doses relative to the components' effective concentrations X I,Y I at I Loewe.(C) Bliss boosting describes combinations with a variable boost babove E max (the greater of the single agent limiting efﬁcacies E X, Drug-drug interaction data were analyzed by the Loewe additivity model and the Bliss independence drug-interaction model. Results: The combination of ITMN-191 and Peg-IFN-_-2a inhibited HCV RNA replication synergistically in Huh7 cells Bliss independence-based drug-interaction modeling showed significant antagonism in vitro and in vivo, with the observed drug effects being 20%-69% lower than would be expected if the drugs were acting independently. These in vitro and in vivo findings of antagonism were consistent with the findings from Loewe additivity-based drug-interaction. The Loewe additivity (engl. Loewe additivity) is a model describing the dependence of the effects of two agents from one another. Other models are e.g. B. Bliss independence (in German 'Independence according to Bliss'). properties. Loewe additivity describes the additive effect of two active ingredients with the same mode of action
alyzed using the Loewe additivity and Bliss independence drug interaction models [12, 13]. CalcuSynTM (Biosoft) was used to quantify differences between observed effects and predict-ed ones. Drugs were mixed at ﬁxed molar ratios that matched their equipotent concentrations, which were maintained dur-ing serial dilutions [12-14] Because Bliss independence model was not a final proof for synergistic interaction, we wanted to apply another universal reference model used for evaluating the effects of drug interaction, namely Loewe additivity model, which is regarded as gold standard in pharmacology to further confirm our observation. 29 To perform Loewe model.
Loewe additivity model focuses on dose reduction and the Bliss independence model focuses on treatment effect enhancement. The two reference models handle the same question from two different perspectives. The Bliss independence model has been criticized for its potential to incorrectly claim synergy when two identical drugs ar by jürgen sühnel - 1 a selection of experimental data e(exp) shown in figures 1 and 2, loewe additivity and bliss indepencence expected effects e(la) and e(bi), any differences between them and index of interaction i according to eq. [3]. the table was automatically generat, 199 tivity: Bliss Independence and Loewe Additivity. Bliss Independence states that additivity occurs when two agents act independently of the other. Loewe Additivity defines the effects seen with a second drug present are the same as that seen when a drug is added to itself; in other words, when a drug is tested in combination with itself The nature and the intensity of the interactions were assessed using the Loewe additivity model [fractional inhibitory concentration (FIC) index] and the Bliss independence (BI) model. Results: Significant synergy was found between each of the three antifungal agents and farnesol, while antagonism was not observed for any of the combinations.
according to both Bliss (independence) and Loewe (additivity). (3) Offers robustness against outliers. (4) Takes heteroscedasticity (survival level dependent experimental variability) into account by selecting a relevant subset of residuals for resampling statistics. (5 Note that Bliss masking is similar to both HSA and Loewe additivity for very high or very low concentrations where the single agent effects are almost flat. References. Bliss (1939), Ann. Appl. Biol. 26:585-615. Greco, Bravo, Parsons (1995), Pharmacol Rev 47:331-85. Mani et al. (2008), PNAS 105:3461-6 The copula model unites both the dose addition (DA, Loewe additivity) and dose independence (DI, Bliss independence) hypotheses of combinations into a single explicit equation and returns both hypotheses as special cases. The model predicts the linear isoboles from sham (like against like) experiments and the linear, concave, convex and mixed.
(ZIP), Bliss independence, Loewe additivity, and Highest single agent (HSA). < 10 > 28 Synergy Score A A. H358 xenograft-bearing mice were treated with MRTX1257 @ 30mg/kg for a single dose or QD x 3 days. Tumors were harvested at 6, 24, and 48hrs post last dose (n=3) and biomarkers were assessed by immunoblot.. The most commonly used reference models for calculating combination drug response include the Highest single agent (HSA) model, Loewe additivity model, Bliss independence model, and the Zero interaction potency (ZIP) model [133,134,135,136]. Combination therapy and drug synergism for targeted heterogeneous tumors and the interacting tumor. relative potency), then CrownSyn uses the Loewe Additivity model. Otherwise, CrownSyn uses the Bliss Independence model2. The Loewe Additivity model rests on both the dose equivalence principle and the sham combination principle, which cannot be satisfied if the two dose-response curves are not available or difficult to estimate
traced back to two distinct origins: Loewe additivity and Bliss independence (Loewe and Muischnek, 1926; Bliss, 1939). Loewe additivity considers that each component in a mixture has an identical molecular mechanism and hence behaves in the same way and reaches the same biological target. Alternatively, Bliss independence is based on th 'Bliss Independence' and 'Loewe Additivity'. Bliss Independence asserts that each drug in a combination exerts its killing action PLoS Pathogens | www.plospathogens.org 1 January 2012 | Volume 8 | Issue 1 | e100248 The Bliss independence model employs a probabilistic perspective and allows the expected combination response to be computed as the multiplicative product of individual drug response; whereas other models such as the Zero Interaction Potential (ZIP) model combines the Bliss model and the Loewe's additivity model. The Loewe's additivity model. Loewe additivity. Bliss independence and MacSynergyII Data were analysed using the software MacSynergyII [23]. From experimental individual drug effects, the program calculates a theoretically expected 'additive' combined-drug effect if the drugs act independently COMBIA offers considerable improvements over established software for synergy analysis such as MacSynergy (TM) II as it includes both Bliss (independence) and Loewe (additivity) analyses, together with a tailored non-parametric statistical analysis employing heteroscedasticity, controlled resampling, and global (omnibus) testing
or Independence Action (IA) models. The CA and IA models were defined as follows. CA model (Loewe additivity; 4, 5): IA model (Bliss independence; 4, 5): where LC x,A and LC x,B are the lethal concentrations of compound A and B for x% mortality in a single exposure to A and B, respectively; C A and C B are the concentrations for A and B in a. Loewe [5] and Bliss [3]. Bliss developed the model of response additivity which is also called the criterion of Bliss independence. These definitions are not only formal thoughts but do have some practical implications [8] which are especially important in the field of radiation oncology. Response additivity means that we assume sta range of IIP values that would be predicted for each combination by the Loewe additivity (bottom of red bar) and Bliss independence (top of red bar) models of drug interaction, given the individual eﬀicacies of the component drugs. A black dash indicates the empirical IIP, which was calculated using th Independence (Bliss, 1939). Loewe Additivity assumes that one compound can be substituted for another, which makes sense when the two compounds have the same mechanism of action. In Bliss Independence, on the other hand, the underlying assumption is that the two compounds have a diﬀerent mechanism of action, leading to an addition of the. have realised that the definition of additivity is most important. Synergism and antagonism are referred to as a 'more than expected' or 'less than expected' additive effect, respectively [9]. The majority of interaction methods are based on two definitions of additivity, namely, Bliss independence and Loewe additivity
We used both the Loewe Additivity model and the Bliss Independence model to determine drug interaction (synergistic, independent, or antagonistic). In general, we observed synergy with all the combinations in the tumor derived cell lines. In the transformed epithelial cell line, synergy was observed only in the olaparib combination Key words: Loewe additivity - Bliss independence - Loewe synergism - Locwe antagonism - Bliss synergism - Bliss antagonism - Inertism - Synergism - Antagonism - Coalism Introduction A group of six scientists with strong interests in the assessment of the joint effects of combinations of agents, met together for the Fifth Internationa The most commonly used null expectation models are Loewe additivity and Bliss independence , whereby effects can be categorized as additive, synergistic, or antagonistic. For this study, we measured synergy by the Loewe additivity-based combination index (CI) score, which can handle cases where two drugs act on targets regulating a common. 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.
We propose tests for the two most common forms of interaction, Bliss independence and Loewe additivity. To test for Bliss independence we use a two stage approach. We first choose a best model using model selection and then use the best model to construct a likelihood ratio test for interaction Bliss independence model. Bliss independence implies that two agents do not cooperate, i.e. act independently of each other. Additionally, the assumption is that a decreasing monotherapy curves express the fractions of unaffected control populations, while increasing curves express the fractions of affected control populations.. Bliss independence model is formulated for the fractional. The HSA model describes a simple superposition of the single agent curves. Loewe additivity (Loewe, 1928) is the drug-with-itself reference to represent dose-additive pairings. The 'Bliss boosting' model extends Bliss Independence (Bliss, 1939) to allow variable boosts in effect at hig SynToxProfiler allows users to estimate synergy between drugs using either the highest single-agent (HSA) model (Berenbaum M.C,1989), Bliss independence (Bliss C.I.,1939), or Loewe additivity model (Loewe S,1953), and zero interaction efficacy (ZIP) model (Yadav, B, 2015) as implemented in the SynergyFinder R-package (Ianevski et al, 2017) from. alyzed using the Loewe additivity and Bliss independence drug interaction models [12, 13]. CalcuSynTM (Biosoft) was used to quantify differences between observed effects and predict ed ones. Drugs were mixed at fixed molar ratios that matched their equipotent concentrations, which were maintained dur ing serial dilutions [12-14]
Loewe additivity36 and Bliss independence37. Loewe additivity assumes that two inhibitors act on a target through a similar mechanism, as shown by Chou and Talalay for mutually exclusive enzyme inhibitors38. Bliss independence assumes that inhibitors can bind mutually nonexclusively through distinct mechanisms. Th Data were analyzed using Loewe additivity and Bliss independence models for synergy, and resistance studies were performed using HCV colony formation assays.Clemizole's antiviral effect was highly synergistic with the HCV protease inhibitors SCH503034 and VX950, without toxicity
Bliss CI. The toxicity of poisons applied jointly. Annals of Applied Biology. 1939;26(3):585-615. View Article Google Scholar 17. Baeder DY, Yu G N Hozé, Rolff J, Regoes RR. Antimicrobial combinations: Bliss independence and Loewe additivity derived from mechanistic multi-hit models Bliss independence-based drug-interaction modeling showed significant antagonism in vitro and in vivo, with the observed drug effects being 20%-69% lower than would be expected if the drugs were acting independently. These in vitro and in vivo findings of antagonism were consistent with the findings from Loewe additivity-based drug. (O) Interaction of eribulin with siCHEK1 #2 in H358 cells, evaluated by Bliss independence (figure) and Loewe additivity (table). Article Snippet: Two siRNAs designed against CHEK1 were purchased from Sigma-Aldrich : SASI_Hs02_00326304 targeting CTGAAAGAGACTTGTGAGAA, and SASI_Hs02_00326305 targeting TAGATATGAAGCGTGCCGT