Mass-Action Law Dynamics Theory and Algorithm for Translational and Precision Medicine Informatics

By Ting-Chao Chou

“Mass-Action Law Dynamics Theory and Algorithm for Translational and Precision Medicine Informatics provides a comprehensive overview and update of the mass-action law-based unified dose-effect biodynamics, pharmacodynamics, bioinformatics, and the combination index theorem for synergy definition (MAL-BD/PD/BI/CI). Contents advocate the fundamental MAL-PD/BI/CI/BI principle for biomedical R&D, clinical trials protocol design computerized data analysis, illustrates the MAL-dynamics theory with sample analysis, and includes data entry and automated computer report print-outs. In 11 sections “Mass-Action Law Dynamics Theory and Algorithm for Translational and Precision Medicine Informatics leads the reader from an introduction and overview, to trial protocols and MAL-PD/CI approach for biomedical R&D in vitro and in animals. It describes the current Landscape of International FDA Drug Evaluation, Clinical Pharmacology, and Clinical Trials Guidance. This is a valuable resource for biomedical researchers, healthcare professionals, and students seeking to harness the power of data informatics in precision medicine.

• gives insight into that index equation (DRIE) that digitally determines how many folds of dose-reduction is needed for each drug in synergistic combinations • provides a comprehensive overview and update of mass-action law-based unified bioinformatics, dose effect biodynamics, pharmacodynamics, and the combination index theorem for synergy definition (MAL-BD/PD/BI/CI) • describes how the MAL theory/algorithm-based “Top-Down digital approach is the opposite and yet is a complementary alternative to the observation/statistics-based “Bottom-Up traditional approach in R&D

• Language: English
• Publisher: Academic Press
• Release date: Apr 9, 2024
• ISBN: 9780443288753

Ting-Chao Chou

Born in Taiwan, Ting-Chao (David) Chou received his Ph.D. in Pharmacology from Yale University and completed his Post-Doctoral Fellowship at Johns Hopkins University School of Medicine. He joined Memorial Sloan-Kettering Cancer Center (MSKCC) in New York and became a Member and Professor of Pharmacology at Cornell University Graduate School of Medical Sciences in 1988. He retired from MSKCC in 2013 and founded PD Science LLC. Professor Chou was elected to the Membership of The Johns Hopkins Society of Scholars, induced by the President of JHU on April 8, 2019, among 16 national and international inductees. Dr. Chou’s published 375 papers have garnered over forty thousand hundred citations with an h-index of 75 and i10-index of 290. He is the inventor/co-inventor of 40 U.S. patents. Currently, he advocates for MAL-based digital biomedical R&D for translational medicine bioinformatics (BI) to provide a complementary alternative basic framework to the traditional statistics-based R&D

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Chapter I A new alternative concept for cost-effective R&D: The MAL-dynamics/algorithms/digital informatics⊛

Abstract

This chapter provides a comprehensive overview, illustrations, and updates of the mass-action law (MAL) based on unified general dose-effect pharmacodynamics, biodynamics, bioinformatics, and the combination index theorem for synergy definition and quantification (MAL-PD/BD/BI/CI). The general system analysis was developed with pattern analysis, combinatory analysis, and mathematical induction and deduction on the MAL principle, which resulted in (i) The general median-effect equation (MEE) for each entity with two basic dynamic parameters of potency (Dm) and dynamics-order (m), for the potency and the shape of dose-effect curves; (ii) the combination index equation (CIE) theorem/algorithm, determines the drugs or entities interaction, where CI < 1, =1, and >1 indicate synergism, additive-effect, and antagonism, respectively; (iii) the dose-reduction index equation (DRIE) that digitally determines the outcomes of how many folds of dose-reduction for each drug in synergistic combinations. Since all terms of MAL-general-equations (MEE, CIE, and DRIE) are dimensionless-relativity ratios, they are equally applicable in vitro, in animals, and in clinical trials. They are also valid regardless of drug entities, units, mechanisms, or physical states. To date, this MAL-PD/BD/BI/CI theory-based "Top-Down" approach and quantitative method has received multidisciplinary research popularity globally, with citations in over 1500 journals and 1268 citing patents, encompassing nearly all disciplines of biomedical sciences and beyond, the subjects including material, agricultural, marine, environmental and food sciences. Original applications were mainly in vitro; however, in vivo PD applications are on the rise. The MAL-BD/PD unified theory/method has the features of simplicity, efficiency, and cost-effectiveness, allows automated computer simulation with only a few dose-data points, and shares the same basic MAL principle. In vitro, in vivo, or other physical states in animal studies and clinical trial protocol design, automated computerized data analysis and simulation to single drug and drug combinations. With the same MAL-PD principle, thus enabling comparisons and rankings. This book illustrates the MAL-dynamics theory to update the increasing applications in recent years and to provide specific real sample analysis, including data entries and automated computer report print-outs in Appendixes and Supplementary Materials in PDF slides illustrations. The MAL-theory-based Top Down approach (traditional biomedical R&D) is an observation and statistics-based "Bottom-Up approach with specific aims, proposals, and methods to reach feasible hypotheses or conclusions. This open approach is usually accomplished with multiple experimental evidence and results, using unbiased statistics or other methods to reach a hypothesis, mechanism, or interpretive conclusion. However, the best curve fitting for dose-effect relationship data is frequently empirical and requires many dose-data points. The primary purpose of this book is to indicate that the MAL theory/algorithm-based Top-Down digital approach is the opposite and yet a complementary alternative to the observation/statistics-based Bottom-Up" traditional approach in R&D.

Keywords

Mass-action law dynamics; Bioinformatics algorithms; Biodynamics simulation; Pharmacodynamics; Median-effect equation; Median-effect plot and simulation; Doctrine of the median; Combination index equation; Combination index computer simulation; CompuSyn software; CalcuSyn software; Dose-reduction index equation; Dose-reduction index computer simulation; Definition of synergism; Definition of pharmacodynamics

This book discusses two fundamentally different functional dynamic concepts and informatics for dose-dependent biomedical R&D for in vitro in animal studies and design and data analysis in clinical trials. Traditional biomedical R&D is an observation-based Bottom Up approach with specific aims, proposals, methods, and feasible conclusions. This open approach is usually accomplished with multiple experimental evidence and results, using unbiased statistics or other methods to reach a hypothesis, mechanism, or conclusion. However, the best curve fitting for dose-effect data is frequently empirical and requires many dose-data points. Here, a nontraditional general unified theory-based Top Down approach is based on the biophysical biochemical fundamental principle of the mass-action law (MAL), which provides features of efficiency, cost-effectiveness, and quantitative digital simulation of informatics (Table 1). This Top Down approach used an unprecedented system analysis such as pattern analysis, combinatorial analysis, and mathematical induction and deduction, involving the derivation of over 300 reaction-rate equations, and using a reverse process of thinking [1,2,6–8]. The MAL-based concept, reducing the statistical dependence in nature's ecosystem, provides a complementary alternative that will mark the beginning of a new avenue of accelerated progress toward sustainable development goals with algorithm-based digital guidance on transformative and accelerated actions leading up to the Econo-Green scientific R&D in biomedical sciences and beyond.

Table 1

a These two approaches are fundamentally opposite concepts. Yet, they are complementary alternatives to each other for the functional pharmacodynamics, biodynamics, and informatics in R&D. They are like two sides of the same coin, or front and rear views of the same entity. This book focuses on MAL-PD-based Top-Down unified general dose-effect dynamics theory/method for efficient, cost-effective, and digital simulation for translational bioinformatics and for the algorithm-based digital, indexed conclusions. The preliminary reports of this table contents have been described in Refs. [1–5]. See Figs. 3, 5b, 11a, and Tables 3, 4c, 5, 6, 7a, 8 for further comparisons and discussions. Chapter IX Section E of this book provides mathematical derivations and concepts.

This MAL approach led to the discovery of the median-effect equation (MEE) as the unified biodynamics, pharmacodynamics, and bioinformatics general principle (BD/PD/BI). The parameter m is dynamic order signifying the shape of the dose-effect curve, and Dm, the median-effect dose signifying potency, and the universal reference point and the dynamic orders common link. In the MAL-general theory, Dm serves as the normalization factor for all doses (Figs. 1a, 1b, and 2). The Dm (i.e., half affected/half unaffected) [1,6,7] is the unified form for Km in the Michaelis-Menten equation for enzyme kinetics, the Ka in the Henderson-Hasselbalch equation for pH-ionization, the Kad in the Langmuir equation for adsorption isotherm, the K in the Hill equation for higher-order ligand occupancy, and the Kd in the Scatchard equation for receptor binding. All these specific theoretical equations are derived from specific subjects or specific models, and thus cannot be the general unified and integrated theory for multidisciplinary sciences (for more details, see Chapters IX and X).

Fig. 1a

Fig. 1a The unified PD/BD/BI general theory of the Mass-Action Law (MAL) derivation of major specific biochemical and biophysical equations from the Median-Effect Equation (MEE). Source: Chou TC. Theoretical basis, experimental design, and computerized simulation of synergism and antagonism in drug combination studies. Pharmacol Rev 2006;58(3):621–81. https://doi.org/10.1124/pr.58.3.10 [figure 4].

Fig. 1b

Fig. 1b The median-effect equation (MEE) and median-effect plot (MEP). It is the unified general theory for pharmacodynamics of the mass-action law (MAL-PD), equation/algorithm, and plot. For general discussions, see Ref. [1]. It is important to note two facts: one is fa + fu = 1, another is when fa = fu, then, D is equal to Dm. It is also important to note that both the left and right sides of MEE are dimensionless relativity ratios. Therefore, MEE is independent of the unit, mechanism, physical state, in vitro, in cells, organs, diseases, animals, humans, or in environments. Source: Chou TC. Derivation and properties of Michaelis-Menten type and Hill type equations for reference ligands. J Theor Biol 1976;59(2):253–76. https://doi.org/10.1016/0022-5193(76)90169-7 [equation 35].

Fig. 2

Fig. 2 The median dose ( D m ) is the universal biodynamics reference point and the dynamic-order common link. It normalized the dose-effect curves into a general simple form. Source: Chou TC. Derivation and properties of Michaelis-Menten type and Hill type equations for reference ligands. J Theor Biol 1976;59(2):253–76. https://doi.org/10.1016/0022-5193(76)90169-7 [figures 1 and 2].

The system analysis, similar to MEE derivation, on the MAL-dynamics principle—multiple-entities interactions resulted in the unified general combination index equation (CIE), algorithm, and computer simulation, which quantitatively determine Synergism (CI < 1), additive-effect (CI = 1) and antagonism (CI > 1) automatically [1,2,3,7,8,9] with computer simulation [10,11,12]. The MAL-MEE CI theory has been cited in over 1515 scientific journals covering biochemistry, molecular, cell biology, genetics, pharmacology, agricultural, marine, environmental, and food sciences. All terms of MEE and CIE are dimensionless relativity ratios (i.e., dose divided by the Dm dose and effect divided by the designated effect level; whereas DRIE is dose divided by the designed dose), and thus can generally be applicable in vitro, in vivo, and all physical states (in nanoparticles, cells, tissues, organs, animals, humans, diseases, clinical trials, and in environments); in actions or interactions of drugs, biologics, radiation, ultraviolet, microwave, thermo-dynamics, and photo-dynamics effects [13–15].

This monograph has four main schemes: (i) It provides the MAL-based theory/algorithm approach as the complementary alternative to the observation and statistics-based approach in research and development; It clearly defines the important issues of biomedical sciences, Pharmacodynamics (PD) and Synergism (defines as CI < 1) in mathematical terms. Furthermore, it advocates the importance of efficiency, cost-effectiveness, and digital computer simulation and automation in R&D, as presented in this chapter. (ii) It compares the Top-Down MAL-Based approach with the Bottom-Up Empirical observation-based approach, in clinical trials protocol design and data analysis of anti-HIV agents in AIDS patients (Chapter II), in real example implementations, advantages vs limitations, success, and failures, as well as lesions learned from the failures using specific examples, as described in Chapters II–IV. (iii) It reviews the current status of international FDAs, including the US FDA, in the fundamental principle of drug-evaluations regulations and guidelines. It also points out the apparent deficiency, the needed modernization, and a consensus. In addition, it illustrates why the unified general MAL-PD theory, algorithm, and computer software can solve many practical issues, and save time, effort, and resources in translational medicine and precision medicine, as demonstrated in Chapters V–VIII. Finally, (iv) it exemplifies that the MAL-PD/BD/BI and CI theory/method has citations in over 1493 scientific journals internationally, encompassing broad disciplines of biomedical, agricultural, marine, toxicological, environmental, and food sciences, as indicated in Chapters IX and X. Among 607 references in this book, about 60% of them are those published from January 2021 to October 2023.

As indicated in Chapters IX and X of this book, the MAL integrated unified Top Down theory/method is unlikely obtainable from the traditional specific aimed approach. The theory/algorithm-based Top-Down digital approach is the opposite yet complementary alternative to the traditional observation/statistics-based Bottom-Up approach. Interestingly, the Top Down and Bottom Up concepts also appear in 4-of-6 Quarks (top, down, bottom, up, charm, and strange) in the standard model of elementary particle physics and in Fu-Xi Ba Gua and Yin-Yang of ancient philosophy (in figure 13 of Ref. [1] 2006), and see Figs. 30 and 31, and in Refs. [4, 5, 35–39, 66] of Chapter IX, that are interacting in pair and complementary to each other. These two opposite approaches share the same ultimate goal of R&D in diversified sciences for unified R&D informatics, in unity, just like the two sides of the same coin, or the front and the rear views for the same entity. We cannot have both sides or views simultaneously the subject is rotating or, the observer is circulating (see Chapter IX, Sections C–E). We can see both at the same time with mirror and mirror images, but the sizes and directions seem not the same on the same subject.

The unique coincidences of the ancient and modern philosophy in Nature's equilibrium ecosystem dynamics and common interdisciplinary principles are illustrated in Chapter IX, Section C.

Like classical biomedical sciences for observation/statistics-based approach, the contemporary computer artificial intelligence (AI), including cloud computing, computer learning, Open AI, Generative AI, and ChatGPT, all belong to the Bottom-Up approach. An example conversation between a biologist with MAL-PD/BD/CI/BI background with ChatGPT on five Synergism Issues are given in Chapter IX, Section E. These resulted in interesting revelations of the remarkably surprising power of utilities, deficiencies, and risks of ChatGPT. The Bottom-Up and Top-down approaches are expected to finally converge as complementary alternatives.

The early thinking of this author on Nature's system analysis, pattern analysis, combinatory analysis, and mathematical derivation, in conceptual, philosophical, and mathematical terms, evolved into the flowchart (Figs. 5a and 5b), are described in the PhD thesis at Yale University, 1970 (see Chapter IX, Section F [17] and Appendix VI) Surprisingly, this concept led to the discovery of the second degree Pascal Triangle for binomial expansion theorem, where all elements of the triangle are squared (Chapter IX, Section F). In addition, it is possible to develop a general mathematical algorism for the author rank-weighted triangle for citation attribution in n-authored papers (Chapter IX, Section G).

For efficiency, cost-effective, quantitative, and digital simulation reasons, I strongly recommend the MAL-BD/MEE-based doctrine of the median (DOM or The Way of Median) and the concept of the unity of the bio-R&D informatics be utilized for integrated translational medicine, precision medicine, and digital biology.

A Challenges from complexity and diversity and the MAL-solutions

Many scientific disciplines encounter complexity and diversity that slow down progress, ramify investigation into distinct disciplines, enlarge sample size, or spend more time, effort, and resources in research and development (R&D). This phenomenon is particularly apparent in biomedical sciences and pharmaceutical drug developments. The development of sound fundamental unified general principles for biological and biomedical science will facilitate concise guidance, defined priority, and regulatory policy; consolidate multidisciplinary interrelations; improve efficiency and cost-effectiveness; and also integrate the in vitro, in animal, inhuman, and in environmental sciences, under the same domain. This will reduce ambiguity and uncertainty, thus avoiding excessive expansion of R&D expenditure and excessive reliance on statistical means for plausible conclusions and indications. In recent decades, the rapid progress of electronic tools and intelligent technology greatly improved speed, volume, and accuracy in broad scientific fields, including algorithm-based digital precision medicine, translational medicine, as well as medical and pharmaceutical research, development, and regulations. The ideological-divide, especially in social sciences such as politics, economy, religion, and arts, is expected to create complexity and ramifications in AI regulations, depending on different people's constituents, geological locations, and time periods in history. Despite of generative AI's tremendous capability and speed, such as NVDIA's physical GPU and CPU and its Omniverse/Generative AI combinations, however, creativity, innovation, and mathematical inference is not yet the strength in AI overall.

The mountains of big-size data approaches such as cloud computing, artificial intelligence (AI) including computer learning, and generative AI, with the collection of millions or billions of pieces of data for electronic analysis, generate big success in e-commerce and e-ecology, open-AI, and ChatGPT, that transform humanity. This basic concept, like classical biomedical research and development, is a Bottom-Up approach. Although the AI concept is rapidly growing with utilities and risks to be determined and regulated. However, here the eminent issue is how to handle and analyze the small size data (e.g., in vivo animal studies and clinical trials) rigorously, efficiently, and quantitatively in animal studies and in clinical trials in real-world for this digital electronic era, which is extremely important and likely will transform the R&D and regulatory landscape and greatly impact biomedical R&D. So far, the rapid progress of structural and mechanistic sciences are short of fundamental functional dynamics principle to bridge them. Although chemical structures, biochemical and metabolic pathways, and protein, DNA, and RNA component sequencing and their steric structures are extremely important in knowledge inquiry, however, they need the general dynamics of action and interaction fundamental digital principles to unify them. The Mass-Action Law-unified general theory and algorithms of dose-dependent dynamics of Mass and Action is hereby proposed to integrate them, that is, the structure/mechanical entity and the functional activity of effect.

The biochemical and biophysical equations for specific purposes are derived from the mass-action law (MAL), such as the Michaelis-Menten equation of enzyme kinetics, the Hill equation for higher order ligand occupancy, the Henderson-Hasselbalch equation for pH-ionization, the Scatchard equation for receptor binding, and the Langmuir equation for adsorption isotherm. The MAL-based unified general functional dynamics theory/equations/algorithms/methods in this book are mathematically derived with only dose (mass) as the variable for the corresponding effects; and kept constant for all other variables, for example, temperature (isothermal), volume (isochoric) and pressure (isobaric).

Recently, there have been great advances in entity structural and mechanistic studies for DNA, RNA, protein, and biological/chemical molecules; in primary, secondary, and tertiary structural terms, including exact sequences, pathways, assembling, and networks. Although, accurate and reliable, these observational findings still need a functional dynamic unified-basic principle to integrate them [1,2]. A single dose of effect cannot provide basic dynamics parameters for allowing dynamics analysis. It requires two or more doses and their effects for MAL dynamics analysis to acquire the underlining MAL digital/indexed general, integrated informatics for conclusions. The unified MAL-dynamics theory, basically a Top-Down approach, can provide defined digital algorithms, definitions, fundamental entity characteristics, and digital action and interaction informatics (see Figs. 1a, 1b, 2–4).

Fig. 3

Fig. 3 Dose-effect curves and the median-effect plot (MEP). (A) Dose-effect curves (DEC) for ED 50 , TD 50 , and LD 50 in vitro and in vivo. (B) The corresponding median-effect plot (MEP). (C) Different shapes of DEC linearization with MEP resulted in (D) with a different slope; (E) different potency of DEC linearized MEP resulted in (F) with different x -intercepts. This linearization is the basis for the minimum two data points theory (MTDPT) theory for small-size experimentation for the Econo-Green bio-R&D.

Fig. 4

Fig. 4 Three unified general equations, that is, MEE, CIE, and DRIE of the Mass-Action Law PD/BD/BI (MAL-PD) theory and equations with new paradigm revelations. Note that all terms in MEE, CIE, and DRIE are dimensionless relativity ratios, thus regardless of the unit, mechanism, in vitro, in animals, or in humans, etc. This whole book will repeatedly refer to these three unified general equations of the mass-action law. Source: Chou TC. Theoretical basis, experimental design, and computerized simulation of synergism and antagonism in drug combination studies. Pharmacol Rev 2006;58(3):621–81. https://doi.org/10.1124/pr.58.3.10 [equations 7–9, 16, 19, 20, and