Friday, September 24, 2010

The M-Theory vs. The Median-Effect Theory

Stephen Hawking’s “M-theory” (in The Grand Design, with Leonard Mlodinow, Bantam, New York, 2010) has been considered the fundamental law of Nature and our universe followed inevitably from this law. The experimental evidence for this theory remains to be seen but it has already elicited the debate on science and religion regarding who or what created the universe. If the M-theory is, indeed, universally true, I wonder if it is consistent with the “Unified Theory” of the median-effect principle of the mass-action law which is explicitly “derived” from the physico-chemical dynamics via mathematical induction and deduction (see Pharmacological Reviews 58: 621-681,20061; free PDF access at This proposition is feasible due to the fact that sometimes different approaches (e.g., physical and biological models) can ultimately converge to the same conclusion and share the same implications. There is no telling what “M” in the M-theory means. Speculations in public media include "Mother", “Master”, “Main”, “Magic”, “Miracle”, “Mystery”, “Muffin” and “Membrane”. My proposition is that the “M” in the M-theory stands for “Median” with the evidences given below.
I published the median-effect equation (MEE, the Median-Effect Theory) in the Journal of Theoretical Biology (59: 253-276)2 in 1976 and its related studies3-6 recently proposed the Median-based GPS-concept for bio-informatics in Nature Precedings (npre.2008.2064.2)7 which is available free at The rearrangement of MEE yields the mathematical form of the Michaelis-Menten, Hill, Henderson-Hasselbalch, and Scatchard equations and thus, these basic equations in biochemistry and biophysics are the special cases of MEE which described the quantitative relativity between the fraction “affected” vs. the fraction “unaffected” in all cases1,8,9. It is not surprising that half-affected (Dm) is equivalent to half-saturated (K), half occupied (K), half-ionized (pKa) and half-bound and half-free (Kd) in biochemistry and biophysics. Thus, a cup half-full is a cup half-empty, and the MEE described the dynamic relationship between fullness and emptiness. This is why the median-effect equation and its principle and its median-effect plot is the Unified Theory that explicitly defined the interchangeable relationship between the dose and effect (or cause and consequence, matter and property, material and function), like two sides of the same coin, at the equilibrium dynamic state1,7. The general validity is assured by the derivation via “mathematical induction and deduction” through over three hundred mechanism specific equations2,6. It is shown that the “Median” is the common link and common reference point from the first-order to higher order dynamics and from single entity to the combination of multiple entities10,11. The extension for MEE yields the combination index (CI) theorem of Chou-Talalay in 198312,13. The MEE2 and CI1,14-20 have been widely applied in biomedical literature, especially in drug-combination studies for in vitro1,9,17, in animals15,18,19, and in clinical trials15,20. One article on CI by Chou and Talalay alone (Advances in Enzyme Regulation 22: 27-55, 1984)13 has been cited 2,142 times in over 453 different biomedical journals internationally in over 40 different disciplines of biomedical sciences (based on the Thompson Reuters ISI Web of Knowledge) indicating that it is a well tested and widely applied theory. In other words, the unified theory of MEE and its CI theorem have been widely tested and extensively confirmed by tens of thousands of experimental data sets.  Instead of looking at “universal” constitutions and events at quantum physics level, we might as well look at the fundamental biophysics/biochemistry mass-action law level, which is closer to the real life and the life-less-ness.
The MEE was originally derived from enzyme kinetics/dynamics molecular systems and has been successfully applied experimentally to the cellular system in vitro and in vivo, in animal and in human clinical trials using the computer software for automated simulations21-26. Recently, MEE has been applied to interpret the Chinese ancient philosophy such as Confucian Doctrine of the Mean27,28, Harmony in Daoism29, Chou Dun-Yi’s Wuji er Taiji30 and over 4,000 year old Fu-Si Ba Gua30,31.  This theory has interpreted the ancient philosophy in terms of time, space, order, vector and dynamic equilibrium to establish the median-based quantitative philosophy. It is proven that the “Median” is the harmonic mean of the kinetic constants in the Lineweaver-Burk plot (Kii and Kis) which has concluded that pure non-competitiveness is pure “Harmony7,29. All these entities have different phenotypes, different constitutive elements or different degrees of complexicity are governed by the fundamental physico-chemical natural law by the “median” mediated dynamics. The relationship between the dose of an entity (or multiple entities) and the effect of its (their) functions is underlined by Nature’s basic rule (equation) of the “Median” based mass-action law principle, not random points, nor random trends1,16.
Thereby, the universal materials and functions or events are dictated by the  Nature’s physico-chemical law based on the “Median”1,7.
It is logical and scientifically valid to expect that the mathematically derived equation from subatomic particles and the quantum mechanics that has the real generality, and is feasible to be applicable to all entitles and events, as long as the “derivation” of the M-theory per se is valid. This would rely on the expert physicists/mathematicians to verify it, and it is beyond the scope of my comments. Further support to the M-theory will be its real life applications.
Recent comment on the M-theory by Joseph Silk of the Astronomer Department at University of Oxford and Johns Hopkins University, on October 8, 201032 discussed the attempts to unify gravity with quantum theory in conjunction with the string theory. Although there is still no final conclusion, one statement indicates "On large enough scales, once one counts all the black holes, stars, and empty space, the overall energy of the universe is close to zero (as measured)". I consider this statement consistent with the equilibrium state unified theory of the "median-effect" principle of the MEE.
As Hawking said, “If we do discover a complete theory, it should be in time understandable in broad principle by everyone. Then we shall all, philosophers, scientists, and just ordinary people be able to take part in the discussion of why we and the universe exist”. In this regard, however, it is particularly difficult to apprehend for the 10th dimension universe used by the Hawking’s rationale. On the other hand, the Unified Theory of Chou derived from the mass-action law1,8,16, all terms of the equations of the MEE and its CI theorem are simple ratios1 (i.e., all units canceled out), and thus the theory is dimensionless2,10,11,13.


1.   Chou, T. C. Theoretical basis, experimental design, and computerized simulation of synergism and antagonism in drug combination studies. Pharmacol. Rev. 58, 621-681 (2006). (Free web link:
2.   Chou, T. C. Derivation and properties of Michaelis-Menten type and Hill type equations for reference ligands. J. Theor. Biol. 59, 253-276 (1976).
3.   Chou, T. C. Combinatorial analysis of multiple substrate-multiple product enzyme reactions. J. Theor. Biol. 35, 285-297 (1972).
4.   Chou, T. C. On the determination of availability of ligand binding sites in steady-state systems. J. Theor. Biol. 65, 345-356 (1977).
5.   Chou, T. C. & Chou, J. H. Determination of availability of ligand binding site at steady state for topological assessment of receptors with the aid of microcomputers. Eur. J. Pharmacol. 183, 921 (1990).
6.   Chou, T. C. Relationships between inhibition constants and fractional inhibition in enzyme-catalyzed reactions with different numbers of reactants, different reaction mechanisms, and different types and mechanisms of inhibition. Mol. Pharmacol. 10, 235-247 (1974).
7.   Chou, T. C. The mass-action law based GPS concept for bio-informatics. Nature Precedings (npre.2008.2064-2); July 22, 2008. Available free at
8.   Chou, T. C. The median-effect principle and the combination index for quantitation of synergism and antagonism. In: Chou, T. C. & Rideout, D. C., editors. Synergism and Antagonism in Chemotherapy. San Diego: Academic Press; pp 61-102 (1991).
9.   Chou, T. C., Rideout, D., Chou, J. & Bertino, J. R. Chemotherapeutic synergism, potentiation, and antagonism, in Encyclopedia of Human Biology, vol 2, 2nd ed (Dulbecco, R. ed) pp 675-683, Academic Press, New York (1997).
10. Chou, T. C. & Talalay, P. A simple generalized equation for the analysis of multiple inhibitions of Michaelis-Menten kinetic systems. J. Biol. Chem. 252, 6438-6442 (1977).
11. Chou, T. C. & Talalay, P. Generalized equations for the analysis of inhibitions of Michaelis-Menten and higher-order kinetic systems with two or more mutually exclusive and nonexclusive inhibitors. Eur. J. Biochem. 115, 207-216 (1981).
12. Chou, T. C. & Talalay, P. Analysis of combined drug effects: a new look at a very old problem. Trends Pharmacol. Sci. 4, 450-454 (1983).
13. Chou, T. C. & Talalay, P. Quantitative analysis of dose-effect relationships: the combined effects of multiple drugs or enzyme inhibitors. Adv. Enz. Regul. 22, 27-55 (1984).
14. Chou, T. C. What is synergy? Scientist 21, 15 (2007).
15. Chou, T. C. Preclinical versus clinical drug combination studies. Leuk. Lymphoma 49, 2059-2080 (2008).
16. Chou, T. C. Drug combination studies and their synergy quantification using the Chou-Talalay method. Cancer Res. 70, 440-446 (2010).
17. Chou, T. C., Motzer, R. J., Tong, Y. & Bosl, G. J. Computerized quantitation of synergism and antagonism of taxol, topotecan, and cisplatin against human teratocarcinoma cell growth: a rational approach to clinical protocol design. J. Natl. Cancer Inst. 86, 1517-1524 (1994).
18. Chou, T. C., Dong, H. J. & Timmermans, P. B. M. W. M. Design, experimentation and computerized automated data analysis of synergistic drug combinations against xenograft tumors by Taxotere and T-900607. Proc. Am. Assoc. Cancer Res. 46, 1167 (2005).
19. Chou, T. C. Drug combination against xenograft tumors in nude mice: Experimental design, execution, and computerized simulation of synergism and antagonism (An abstract for the mini-symposium). Proc. Am. Assoc. Cancer Res. 49, 997 (2008).
20. Mildvan, D. et al. Synergy, activity and tolerability of zidovudine and interferon-alpha in patients with symptomatic HIV-1 infection: AIDS Clinical Trial Group 068. Antivir. Ther. 1, 77-88 (1996).
21. Chou, J. H. & Chou, T. C. Dose-Effect Analysis with Microcomputers: Quantitation of ED50, ID50, Synergism, Antagonism, Low-Dose Risk, Receptor Ligand Binding and Enzyme Kinetics: Computer Software for the IBM PC Series. Cambridge (UK): Elsevier-Biosoft (1989).
22. Chou, T. C. & Hayball, M. P. CalcuSyn for Windows: Multiple-Drug Dose-Effect Analyzer and Manual. Cambridge (UK): Biosoft (1997).
23. Chou, T. C. & Martin, N. CompuSyn for Drug Combinations: PC Software and User’s Guide: A Computer Program for Quantitation of Synergism and Antagonism in Drug Combinations, and the Determination of IC50 and ED50 and LD50 Values. Paramus (NJ): ComboSyn (2005).
24. Chou, J. H. & Chou, T. C. Computerized simulation of dose-reduction index (DRI) in synergistic drug combinations. Pharmacologist 30, A231 (1988).
25. Chou, T. C. & Chou, J. Computerized indexing of drug combinations: prediction of synergism and antagonism of more than two drugs by polygonogram (abstract). FASEB J. 12, A832 (1998).
26. Chou, T. C. Assessment of synergistic and antagonistic effect of chemotherapeutic agents in vitro, in Chemosensitivity Testing in Gynecologic Malignancies and Breast Cancer, Vol 19 (Koechli, O. R., Sevin, B. U. & Haller, U. eds) pp 91-107, Karger-Verlag, Basel (1994).
27. Chou, T. C. On the Revelation of the Confucian Doctrine of the Mean in Modern Science Principle. Am. Philosophical Assoc East Annual Meeting, Baltimore, Maryland, 12/27-30/2007.
28. Chou, T. C. The Ancient Chinese Philosophy and the Algorithm of Modern Science Principle. Peking University Invited Seminar, co-sponsored by the Department of Philosophy and College of Life Sciences, Beijing China 10/24/2008.
29. Chou, T. C. A New Look at the Ancient Asian Philosophy through Modern Mathematical and Topological Analysis”. World Congress of Philosophy, Seoul National University, Seoul, Korea 07/30-08/05/2008 (Electronic publication, in press)
30. Chou, T. C. On the Complement between Ancient Chinese Philosophy and Modern Science Algorithms. 16th International Conference of Chinese Philosophy, Taipei 07/08-11/2009 (Made available by the Conference Organizer in electronic CD, No. D-16)
31. Chou, T. C. Yijing concept in contemporary mathematics, topology, and sciences. The 13th I-Ching World Conference, Wuxi, China. June 14-17, 2010; p. 642-653.
32. Silk, J. One theory to rule them all. Science 330, 179-180 (2010).