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 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.

http://www.protocol-online.org/forums/uploads/monthly_09_2010/post-8165-008503000%201284677034.ipb

Theoretical Basis, Experimental Design, and Computerized Simulation of Synergism and Antagonism in Drug Combination Studies

Photosensitizers of the porphyrin and phthalocyanine series for photodynamic therapy

In recent years several review articles and books have been published on the use of porphyrin-based compounds in photodynamic therapy (PDT). This critical review is focused on (i) the basic concept of PDT, (ii) advantages of long-wavelength absorbing photosensitizers (PS), (iii) a brief discussion on recent advances in developing PDT agents, and (iv) the various synthetic strategies designed at the Roswell Park Cancer Institute, Buffalo, for developing highly effective long-wavelength PDT agents and their utility in constructing the conjugates with tumor-imaging and therapeutic potential (Theranostics). The clinical status of certain selected PDT agents is also summarized (205 references).

The role of porphyrin chemistry in tumor imaging and photodynamic therapy

HLA-Haploidentical Bone Marrow Transplantation for Hematologic Malignancies Using Nonmyeloablative Conditioning and High-Dose, Posttransplantation Cyclophosphamide

http://www.informaticsjournals.com/index.php/jnr/article/download/232/232

Synergy research: approaching a new generation of phytopharmaceuticals.

The standard checkerboard titration for detecting synergy between antibiotics is practicable for combinations of two antibiotics, laborious for combinations of three, and not feasible for combinations of four or more. Nevertheless, methods for testing of combinations of several antibiotics are urgently needed because some combinations might be superior to those in use and enable the successful treatment of infections resistant to current therapy. A simple method for measurement of synergy (or antagonism) with combinations of any number of agents has been developed which requires less effort than the standard checkerboard titration of two agents. With this method, the concentrations of each of n agents producing some specified effect (such as minimal inhibitory concentration or minimal bactericidal concentration) are determined. A reference combination made up of 1/n of each of these concentrations is titrated to find a dilution that produces the specified effect. The degree of dilution required is equal to the sum of the fractional inhibitory concentrations (concentration of each agent in combination/concentration of each agent alone) as conventionally determined by checkerboard titrations; sums of less than 1, 1, and greater than 1 indicate synergy, additivity, and antagonism, respectively.

A Method for Testing for Synergy with Any Number of Agents

The expected effect of a combination of agents: the general solution.

Publisher Summary The existence of any substantial interaction between different agents that are used clinically or to which man is exposed environmentally is potentially of great importance. One agent may affect another's absorption, metabolism, or excretion. It may alter tissue sensitivity to another agent, and may react with it physically or chemically. A variety of different criteria have been devised for deciding whether the agents in a combination interact pharmacologically. The purpose of this chapter is to examine these criteria critically for the progress in this field. To summarize, the effect–summation criterion may be used when the effects of all the agents in a combination are directly proportional to dose. The key to any criterion for examining interactions between different agents lies in the definition of zero interaction. The interactions that can be analyzed by constructing isoboles or calculating interaction indices are not restricted to cases in which all agents in a combination produce the effect under consideration. The therapeutic significance of interactions between agents requires careful consideration.

Criteria for Analyzing Interactions between Biologically Active Agents

The in vivo biological activity of various fractions and components of haematoporphyrin derivative (HpD) have been determined by measuring the depth of necrosis of implanted tumours in mice exposed to light after the administration of standard doses of porphyrins dissolved in alkali. In this assay, haematoporphyrin, hydroxyethylvinyldeuteroporphyrin and protoporphyrin are inactive, but the mono- and di-acetates of haematoporphyrin (which are major components of HpD) and acetoxyethylvinyldeuteroporphyrin are active. However, the situation appears to be more complex than this. The normal method for preparing HpD for injection involves an alkali treatment which causes hydrolysis and elimination of the acetoxy functions, and the only recognized products (haematoporphyrin, hydroxyethylvinyldeuteroporphyrin and protoporphyrin) are inactive in the in vivo assay. It is concluded that the active component here is a porphyrin, possibly a dimer or oligomer, which is retained on the column during the normal separation by HPLC. This conclusion is supported by the observations that (i) the crude material obtained from the spent column is active without further alkali treatment, and (ii) activity develops over 30 min, when HpD or the mono- or diacetates of haematoporphyrin are treated with sodium bicarbonate in aqueous DMSO. The advantages of working with a pure substance (e.g. haematoporphyrin diacetate) rather than a mixture (HpD) are stressed.

In vivo biological activity of the components of haematoporphyrin derivative.

IT is customary, in prolonging the survival of homografts with a chemical agent, to give frequent doses of the agent over a prolonged period. Effective agents are generally toxic, and their use is attended by considerable mortality, in both laboratory animals and man. The immune response is not uniformly susceptible to inhibition by these agents throughout its course1, nor is it uniformly active. It is likely, therefore, that dose-schedules not closely adapted to this changing sensitivity and activity of the immune response may, on one hand, subject the recipient to unnecessary toxicity and, on the other, fail to attack the immune response sufficiently during its most vulnerable period. It is therefore of some importance to establish the principles on which optimum dose-schedules may be based.

M. C. Berenbaum

Papers

A Method for Testing for Synergy with Any Number of Agents

The expected effect of a combination of agents: the general solution.

Criteria for Analyzing Interactions between Biologically Active Agents

In vivo biological activity of the components of haematoporphyrin derivative.

Prolongation of homograft survival in mice with single doses of cyclophosphamide.