The Pharmaceutical Scientist Guide to Solution Kinetic Models Mathematical Description and Applications

Introduction Chemical reactions are processes in which reactants are transformed into products in the presence of a solvent. Many complex chemical reactions and biological processes that occur in solution can be described by using a series of simple stepwise chemical reactions. Thus, the mechanism of complex chemical reactions and biological process can be defined as contributions from all these stepwise chemical reactions. Thermodynamic and kinetic concepts deal with the physical and chemical relationships between reactants and products. In particular, chemical thermodynamic deals with relationships between energy properties of reactants and products at equilibrium and with energy differences in these properties between various equilibrium states while chemical kinetic deals with rates of reactions (i.e., how fast reactants are converted to products) and how these rates depend upon experimental factors such as, concentration, solvent, and temperature. Therefore, thermodynamic and kinetic concepts are important in providing essential mechanistic evidence in support of any chemical or biological process....

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Introduction

Consider the following second-order homogenous dimerization reaction (III.1)....

Introduction

Consider the following second-order heterogenous reaction that contains two different reagents (V.1)....

Introduction

Since real samples contain many substrates, competitive reactions among these substrates for the same or different binding sites on proteins, receptors and so on is a common occurrence in biological samples. For example, several substrates could competitively bind to an enzyme with a single binding site. Utilizing strictly a kinetic approach to model these types of competitive reactions is not possible since the mathematical models either cannot be integrated or the solutions are too complex to be of practical value. To derive equations for a competitive model, we will assume that all the binding reactions are at equilibrium. This assumption places restrictions on the experimental conditions and thus, it is imperative that the model be understood before experimental data is collected. We will first review reversible binding reactions for a single substrate binding to a single binding site. We will expand this model to two different substrates binding to a single binding site and to multiple binding sites....

Introduction

A large variety of naturally occurring as well as synthetic molecules (i.e., substrates) have been shown to cause specific enzyme inactivation by covalently binding at the catalytic site of the enzyme. These types of suicide substrates can be broadly categorized as reactive derivatization reagents and as latent derivatization reagents. Reactive derivatization reagents are typically substrates that are structural analogs of naturally occurring molecules for the target enzyme that contains a built-in reactive group, such as a haloketone, or an epoxide group. These suicide substrates take advantage of the binding specificity at the active site of the enzyme to set up a displacement reaction between the substrate and the enzyme such that a covalent modification of the protein occurs. These types of substrates can be thought of as protein derivatization regents (i.e., affinity labels). Latent derivatization reagents require that the enzyme begin catalysis such that the process creates the reactive group within the substrate. In many cases, an electrophilic species is generated from the substrate that ultimately reacts with a nucleophilic side chain of the protein. In this chapter, we will focus only on reactive derivatization mechanisms. Latent derivatization mechanisms will be covered in Chapter 7.

Introduction

Living cells have a unique ability to couple exergonic (energy yielding) and endergonic (energy requiring) reactions to produce proteins that are used by the cell to grow and reproduce. Proteins have highly specific three-dimensional structures and activity. Three-dimensional structural changes in these proteins result in loss of proteins activity and can occur as a result of relatively small changes in temperature and pH. Therefore, many proteins are so fragile that these proteins must be continually synthesized just to maintain the integrity of the cell. At 37°C few, if any, of the exergonic and endergonic reactions of intermediary metabolism would occur at a rate sufficient to permit cell maintenance and growth. Thus, the energy for this biosynthesis is derived from exergonic reactions and not from large temperature changes. To prevent exergonic and endergonic reactions from taking place randomly in different parts of the cell, specialized proteins whose sole function is to catalyze biochemical reactions are used to couple these reactions (i.e., enzymes). Thus, enzymes have a high degree of specificity and stereochemical specificity for their substrate. Therefore, living cells can operate under relatively mild conditions because they utilize enzymes, which selectively lower the energies of activation of the vital biochemical reactions. Enzymes, then, are catalysts that speed up the rate of chemical reactions without themselves being consumed....

Introduction

Inhibition of normal enzyme activity represents a major strategy in drug design as noted by the fact that many of the top drugs by sales are enzyme inhibitors. The inhibition of an enzyme-catalyzed reaction can enable the selective modulation of a variety of biochemical processes such as cell growth, division, and viability untenable, or interrupting major metabolic pathways by blocking the formation of an essential or undesirable metabolite. Enzyme inhibition is complementary to receptor modulation via antagonists and is some cases can be used to potentate the activity of a desirable species by inhibiting its degradation. An antagonist is a drug that produces no response of a receptor but completely prevents the natural substrate from producing its effect. Drugs producing the same maximal response as the natural substrate are known as agonists. Enzyme inhibition is illustrated in the following scheme where biological activity of specie P can be attenuated via inhibition of the enzyme involved in its biosynthesis....

Inhibition by Multiple Substrates Binding to the Enzyme

In cases where a high concentration of substrate is used, the substrate itself may cause inhibition. This type of inhibition can be identified when the rate declines instead of approaching the maximum velocity. The form of the rate equations will depend on the type of inhibition. Consider the reversible binding reaction (XVII.1) where two substrate molecules bind to the enzyme....

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