Theoretical Basis, Experimental Design, and Computerized Simulation of Synergism and Antagonism in Drug Combination Studies
Abstract
The median-effect equation derived from the mass-action law principle at equilibrium-steady state via mathematical induction and deduction for different reaction sequences and mechanisms and different types of inhibition has been shown to be the unified theory for the Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, and Scatchard equation. It is shown that dose and effect are interchangeable via defined parameters. This general equation for the single drug effect has been extended to the multiple drug effect equation for n drugs. These equations provide the theoretical basis for the combination index (CI)-isobologram equation that allows quantitative determination of drug interactions, where CI < 1, = 1, and > 1 indicate synergism, additive effect, and antagonism, respectively. Based on these algorithms, computer software has been developed to allow automated simulation of synergism and antagonism at all dose or effect levels. It displays the dose-effect curve, median-effect plot, combination index plot, isobologram, dose-reduction index plot, and polygonogram for in vitro or in vivo studies. This theoretical development, experimental design, and computerized data analysis have facilitated dose-effect analysis for single drug evaluation or carcinogen and radiation risk assessment, as well as for drug or other entity combinations in a vast field of disciplines of biomedical sciences. In this review, selected examples of applications are given, and step-by-step examples of experimental designs and real data analysis are also illustrated. The merging of the mass-action law principle with mathematical induction-deduction has been proven to be a unique and effective scientific method for general theory development. The median-effect principle and its mass-action law based computer software are gaining increased applications in biomedical sciences, from how to effectively evaluate a single compound or entity to how to beneficially use multiple drugs or modalities in combination therapies.
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The Chou-Talalay method requires multiple dose levels for each drug when applied to in vivo studies.
“For example, when the Chou-Talalay method is applied to in vivo studies (9, 36), it requires multiple dose levels for each drug, so there will be may groups (for an example, see ref. 37), while in practice, we normally have only four groups, not only to save cost but to focus on the selected drug dose levels.”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [36]
For breast cancer cells (MDA-MB-231), the combination index for doxorubicin is very close to 1, indicating additivity.
“Table 2 demonstrates that for breast cancer cells the CI for Doxorubicin is very close to 1, indicating additivity [10,11].”
From Chemotherapeutic treatment efficacy and sensitivity are increased by adjuvant alternating electric fields (TTFields) (2009) · cites this paper as [11]
The dose reduction index for TTFields-DTIC interaction after 72 hours of combined treatment in U-118 glioma cells is 175.
“The DRIs for TTFields-drug interaction after 72 hours of combined treatment was 1316 for paclitaxel, 23 for doxorubicin, 152 for cyclophosphamide and 175 for DTIC (in U-118 glioma cells).”
From Chemotherapeutic treatment efficacy and sensitivity are increased by adjuvant alternating electric fields (TTFields) (2009) · cites this paper as [11]
The dose reduction index for TTFields-paclitaxel interaction after 72 hours of combined treatment is 1316.
“The DRIs for TTFields-drug interaction after 72 hours of combined treatment was 1316 for paclitaxel, 23 for doxorubicin, 152 for cyclophosphamide and 175 for DTIC (in U-118 glioma cells).”
From Chemotherapeutic treatment efficacy and sensitivity are increased by adjuvant alternating electric fields (TTFields) (2009) · cites this paper as [11]
The dose reduction index for TTFields-cyclophosphamide interaction after 72 hours of combined treatment is 152.
“The DRIs for TTFields-drug interaction after 72 hours of combined treatment was 1316 for paclitaxel, 23 for doxorubicin, 152 for cyclophosphamide and 175 for DTIC (in U-118 glioma cells).”
From Chemotherapeutic treatment efficacy and sensitivity are increased by adjuvant alternating electric fields (TTFields) (2009) · cites this paper as [11]
The dose reduction index for TTFields-doxorubicin interaction after 72 hours of combined treatment is 23.
“The DRIs for TTFields-drug interaction after 72 hours of combined treatment was 1316 for paclitaxel, 23 for doxorubicin, 152 for cyclophosphamide and 175 for DTIC (in U-118 glioma cells).”
From Chemotherapeutic treatment efficacy and sensitivity are increased by adjuvant alternating electric fields (TTFields) (2009) · cites this paper as [11]
All tested derivatives showed strong synergism (0.1< CIavg <0.3) with doxorubicin on P-gp expressing L5178 MDR cells, similarly to parental compound 1.
“All tested derivatives showed strong synergism (0.1< CI avg < 0.3) [25] with doxorubicin on the P-gp expressing L5178 MDR cells, similarly to their parental compound (1).”
From Nitrogen-containing ecdysteroid derivatives vs. multi-drug resistance in cancer: Preparation and antitumor activity of oximes, oxime ethers and a lactam (2018) · cites this paper as [25]
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- Authors
- Chou, T.-C.
- Affiliations
- Memorial Sloan Kettering Cancer Center (US)
- Corresponding author
- Chou, Ting-Chao
- ORCID
- Chou, Ting-Chao
- Venue
- Pharmacological Reviews
- Publisher
- Elsevier BV
- Published
- 2006-09
- Volume
- 58
- Issue
- 3
- Pages
- 621-681
- ISSN
- 0031-6997 (ISSN-L)
- OpenAlex
- W2103562758
- Cited by
- 5,163
- References
- 1
- Citations by year
- 2026: 206 · 2025: 300 · 2024: 324 · 2023: 390 · 2022: 379 · 2021: 445 · 2020: 413 · 2019: 408 · 2018: 362 · 2017: 352 · 2016: 310 · 2015: 283 · 2014: 254 · 2013: 179 · 2012: 158
- FWCI
- 4.57
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Pharmacological Reviews (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › thermodynamics and calorimetric analyses
- Keywords
- drug synergy, drug antagonism, mass action law, combination index, isobologram, Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, experimental design, carcinogen risk assessment, radiation risk assessment, combination therapy
- MeSH terms
- Algorithms, Animals, Electronic Data Processing, Computer Simulation, Dose-Response Relationship, Drug, Drug Antagonism, Drug Combinations, Drug Synergism, Humans, Medical Informatics, Models, Biological, Models, Theoretical, Research Design, Software, Statistics as Topic
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