About the book

This book is a survey of new and old ways of analyzing data from ligand-receptor interactions obtained from dose-response experiments at equilibrium, and demonstrates how theoretical mechanistic schemes can be adopted to these data. The aim is to show how best to simulate physically what happens when two drugs are given simultaneously, as in combinational drug therapy, by introducing a so called four-pane two-state model (FP-TSM). With simple mathematics, this book contributes on a small scale to Systems Biology.

Abstract PART I

Part I is on one-state models. The various concepts of ligand-receptor interaction were
first developed during a so-called classic era ending in 1945, and then during a post-classic era, starting in 1965, with what could be called a transition period between 1945 and 1965. Concepts from the classic era were mostly concerned with occupancy or function as a two-step and one-state mechanism, while the post-classic era was and is preoccupied with states of conformational changes for un-liganded receptive units, a two-state mechanism. To have a single-word indicator for dose-response effects at equilibrium, the term "synagics" is introduced.

Abstract Chapter 1

Basic reaction schemes and their formulations are derived and equations are referred to as ‘law of . . .' because of their axiomatic nature. The chapter begins with a derivation of equations for the interaction between a ligand and a one-state receptive unit: so called simple agonism. Formulations are derived for both function and binding reaction schemes. The chapter looks at potency, partial agonism, receptor reserve, intrinsic activity, efficacy, and intrinsic efficacy from the transition period. It also introduces the concepts of ‘allostery', spontaneous activity, and inverse agonism, all of which are discussed more thoroughly in other chapters of the book.

Abstract Chapter 2

Effects by secondary ligands on agonism are examined and a secondary binding site in receptive units is introduced. Secondary ligands in one-state models are termed interventors. When they inhibit they are either inhibitors or ant-agonists. The chapter deals with several aspects of a second ligand interfering with the binding of a primary ligand and/or with the function induced by a primary ligand. Inhibitory processes may be competitive or non-competitive ant-agonism. Competitive ant-agonism is obtained through one or two binding sites, whereas non-competitive ant-agonism requires at least two binding sites. Un-competitive ant-agonism is a special case of the non-competitive reaction scheme. Meanwhile, interaction of two ligands within a receptive unit may also involve graded activation between sites as exemplified in a so-called ‘intervention' model. For the intervention model, a third parameter, the co-lateral coefficient, and the term ‘co-lateral binding' are defined.

Abstract Chapter 3

This chapter is split into four divisions. The first division comprises formulations for the modeling of ligand-dependent auto-inhibition as well as for a so-called ‘low-dose hook-effect'; all related to simple auto-intervention in one-state models. The second division is a general introduction to biological auto-regulation and control, and also includes reflections on the meaning of ‘self'. Several separate issues relate to biological self-regulation. In the field of ligand-receptor interactions, auto-regulation may relate to either ligand-induced alteration of a receptive unit or to control induced within receptive units per se before further down-stream feedback regulations. The third division deals with concentration-dependent auto-inhibition and time-dependent phenomena, such as ligand-induced desensitization, both types eliciting auto-regulatory inhibition in receptive systems with only one type of ligand. The chapter also treats various aspects of desensitization including homologous and heterologous desensitization with examples of intrinsic (receptor-dependent) and extrinsic (phosphorylation-dependent) desensitization. The fourth division includes additional examples of models related to ligand-dependent auto-inhibition and desensitization.

Abstract Chapter 4

This chapter deals with methods to determine dissociation constants for ant-agonists and interventors. The focus is on the analysis of present theoretical tools based on one-state models used for synagic evaluation of the mentioned constants. Methods cover the Cheng-Prusoff formulation and its functional equivalent. Schild's method is briefly mentioned. The chapter also introduces novel concepts from the experimental fields that point to future implementation of two-state models as presented in Part II.

Abstract PART II

Still at the receptor level, Part II deals with the word ‘complex' as a reference to reaction schemes involving two-state receptor models. Molecules that modify the behavior of primary ligands in two-state reaction schemes are referred to as modulators. With a realization of un-liganded receptors existing in two- and multi-conformations, the two-state model, developed for ion-channels and enzymes during the 1950s, has recently undergone a dramatic re-emergence in pharmacology.

Abstract Chapter 5

Receptive units are mostly thought of as quiescent until the moment they are stimulated by an agonist, which affects and alters the effector activity. This is clearly seen in enzymology and transport physiology since substrates or transported molecules in many types of experiments must be present in order to allow measurement of function. However, the above dogmatism about receptor units seems to have vanished with the recent realization that even in the absence of agonists, many systems - including systems of over-expressed receptors - display spontaneous activity, which also explains the behavior of inverse agonists. Two reaction schemes, the delCastillo-Katz model (dC&K) and the cyclic two-state model (cTSM), are formulated and analyzed in detail. The dC&K model is compared with Stephenson's scheme and with the operational model by Black and Leff. Based on the cTSM, an age-old enigma of conformational induction versus conformational selection is discussed - and solved.

Abstract Chapter 6

This chapter deals with classical reaction schemes as the random, the ordered, and the ping-pong mechanisms of one-state models. Furthermore, the derivation of ordered and random reaction schemes for both function and binding is generalized using Pascal's triangle. Ping-pong and pump models are combined.

Abstract Chapter 7

This chapter considers several two-state cubic models. Hall's allosteric two-state model (ATSM) is formulated, applied, and analyzed in some detail. The same is done for Bindslev's homotropic two-state model (HOTSM). These two models are further compared and other cubic models are introduced, including a hybrid model of the ATSM and the HOTSM, which is the four-pane two-state model (FP-TSM). This chapter presents mechanistic models while Chapter 10 on Hill-exponentiation and Chapter 12 on synergy present non-mechanistic models.

Abstract PART III

Part III deals with various aspects of data manipulation and analysis. With current computing capabilities, non-linear fitting routines for analysis of plots without reciprocal scales are a must. Only as an aside should information be given about when, for example, to use reciprocal Eadie-Scatchard plots or the null-method of a Schild plot. And the Lineweaver-Burk (reciprocal) plot should only be mentioned as a historic curiosity. The Eadie-Scatchard plot for agonist action is restricted to analysis of simple agonism while the Schild plot is restricted to analysis of simple competitive ant-agonist action. Nonetheless, these two plots are the methods that are used the most in certain fields of life sciences for analysis of the interaction between ligands and receptive units.

Abstract Chapter 8

This chapter concludes that there is a general relationship between responses and their concentrations presented as the factor-squared rule, which goes beyond the so-called 80-% rule. In addition it is concluded that Hill plots are also logit plots, and a plot of data employing a ‘logistic' Hill equation is simply the same as a semi-log plot of data. The chapter also provides a tutorial on how to implement an analysis of one's own synagic data. The chapter ends with a presentation of out-dated plots.

Abstract Chapter 9

Dose-response relations at equilibrium, synagics, are analyzed using the SigmaPlot software version 9, though other software packages may also be used. Further, the chapter describes how the software may be used to present data plotting, parameter fitting, and curve generation. The SigmaPlot software allows for analysis in one and the same graph of user-defined theories, presentation of 3-D plots of theories with two independent variables, including contour plots, and even plots of multiple 3-D plots. The chapter is divided into four brief tutorials on how to use the software as an analytical tool for dose-response relationships; with plots of experimental data, fitting theories to curves, and generating 2-D and 3-D plots of theoretical reaction schemes for comparison with experimental curves. The last tutorial is on the use of the factor-squared rule for an estimate on theory deviation from reality, and finally the testing of one theory on another.

Abstract Chapter 10

Chapter 10 begins with an account of how and why the Hill equation was introduced. The purpose of ‘the Hill' was to get an empirical description of the aberrant behavior of dose-response relations and ease calculations. The chapter illustrates and discusses a frequently observed failure of linearity for experimental data in the so-called Hill plot. Further, there is an analysis and critique of what has been termed the ‘logistic' Hill equation. The ‘logistic' Hill is given perspective vis-a-vis the original logistic equation. An explanation is given of how the ‘logistic' Hill equation is a mere semilog presentation-possibility of data. The chapter concludes with a list of facts about the use of the Hill formulation. Finally, the reader is taken on a brief tour through the history and use of the term logistic in data analyses, summarized in an Appendix. The purpose is to illustrate in a superior way the terms logistic and ‘logistic', and thus maybe even resolve some of the obfuscation of their use. This chapter presents non-mechanistic models. Mechanistic models are detailed in Chapter 7.

Abstract Chapter 11

The chapter reviews some of the features of null-methods and, in particular, the null- method of Schild plots, popular in pharmacology. Less use of the Schild method for synagic analysis of ant-agonists is recommended, in favour of other strategies.

Abstract Chapter 12

‘Synergy' covers the effects over and above those expected for a simple additive effect of drug combinations. Describing and understanding the effects of combining two or more drugs, two or more substrates, and in general two or more ligands, has challenged a broad segment of scientists in a number of research fields. A list is presented of drug  combinations from the human disease field, covering therapies for cancer, AIDS, and auto-immunological diseases such as asthma, diabetes, inflammatory bowl diseases, and  rheumatoid arthritis, as well as many others. For instance, although combinatorial cancer therapy is increasingly being improved, models predicting the correct combination of drugs and their mutual concentration and timing are still in great demand. Future approaches for synergy analyses are suggested.

Abstract PART IV

In Part IV, biological regulation and allostery are described in more detail. Molecular and dynamic forces operating at equilibrium and at steady-state in a nano-world. At a nano-scale, equilibrium conditions are not static. This is also illustrated by observing the physics of and around the cell membrane.

Abstract Chapter 13

Chapter 13 deals with models for regulation at the receptor level, focusing on allostery. It briefly presents three aspects related to process control, in order to put allosteric regulation in perspective. The three aspects are (i) network control, (ii) morphogen signaling with pattern formation, and (iii) evolution of bio-logical regulation. All three aspects operate within cells, at cells, between cells, and beyond - that is, at and above the receptor level. Recent aspects of the state of affaires for allostery are presented.

Abstract Chapter 14

What is the difference between the two terms ‘co-operativity' and ‘allostery'? The chapter defines the two terms allostery and co-operativity in a strict sense for modeling dose-response relations at equilibrium, i.e., synagics. It also presents other understandings of the two terms and suggests new allosteric models to explain complex synagics such as reverse bell-shaped dose-response relationships.

Abstract Chapter 15

The Monod-Wyman-Changeux model is described and reviewed. In particular, the chapter scrutinizes the use of the so-called state-of-function R derived from the MWC theory and suggests another function-of-state for use on systems without spontaneous activity. The chapter ends with a recommendation to use genuine two-state models such as the allosteric two-state model (ATSM) and the homotropic two-state model (HOTSM) for dose-response data obtained at equilibrium. For future analysis of synagic data the reader is encouraged to develop and implement the hybrid model combined of these two models, that is, the so called four-pane two-state model (FP-TSM), to its full potential.