**10. Kinetics of drug disposition process**

Drug disposition process most of the times follows the 1st order kinetics in which disposition is proportional to the concentration of the drug at any given time. Therefore, the concentration of a drug in plasma will decrease at a rate that is proportional at all times to the concentration itself. Therefore;

$$\frac{\text{vol}[\mathbb{C}]}{d} = \mathbb{K}[\mathbb{C}]$$

$$\mathbb{J}\frac{\text{vol}[\mathbb{C}]}{\mathbb{C}[\mathbb{C}]} = \mathbb{J}\mathbf{K}dt$$

**9. Dosage and effect**

484 Drug Discovery

A particular dose of an administered drug is subject to the biochemical processes in the body as shown in Figure 5. The desired effect of a drug is proportional to the concentration of the drug at its site of action which is described by the following kinetic parameters: (i) The apparent volume of distribution (Vd) which is the volume of the hydrophilic and hydrophobic spaces in the body that the drug is distributed in. It is obtained by dividing the injected dose (Do) by the initial concentration (Co) in blood plasma. Drugs that bind to tissues extensively exhibit low concentrations in the plasma and therefore, have higher a Vd compared to those that are mainly bound by blood plasma proteins. An average 70kg person has a total body water

Plasma

Free drug

Excretion Absorption

The apparent volume of distribution cannot tell us where in the body the drug really is. The (Ctox) is the maximum drug concentration beyond which there would be toxic effects in the body, while the (Cther) is the plasma concentration of a drug that would achieve a therapeutic effect or effective clinical response. The steady state concentration (Css) is that concentration that should be maintained between any two drug administration intervals. These pharmaco‐ kinetic data are important in that they characterize the fate of drugs in the body and are required by pharmacologists to calculate doses and frequencies of drug administration. However, in some clinical responses, the intensity of pharmacological action correlates better with the concentration of free drug in plasma, while in other responses there is no direct relationship between drug concentration and clinical response. The main variations of the drug

**i.** Drugs which combine with their receptors as quickly as they dissociate from them;

for this category of drugs, the pharmacological effect increases or reduces in tandem

Metabolites

Biotransformation

volume of ~ 50L of which ~ 10L occupy extra-cellular space.

Free drug

Free drug

**Figure 5.** Drug disposition routes from absorption to excretion

with the plasma drug concentration.

Locus of action Receptor

Tissue deposits

Bound drug

Bound drug

response effects include;

$$\begin{aligned} \left[\text{In[C]}\right]\_{\mathfrak{C}\_{\phi}}^{\text{ct}} &= & \mathbf{Kt} \\\\ \left[\text{In[C]}\right]\_{\mathfrak{t}} &= & \mathbf{In[C]}\_{\mathfrak{t}} = \text{ Kt} \text{ or } \text{InC} = \text{ InC}\_{\mathfrak{o}} \text{ 'Kt} \\\\ \mathbf{e}^{\text{ln}} \quad \frac{\left[\mathbf{C}\right]\_{\mathfrak{t}}}{\left[\text{C}\right]\_{\mathfrak{o}}} &= & \mathbf{e}^{\text{-Kt}} \\\\ \left[\text{C}\_{\mathfrak{t}}\right] &= & \left[\text{C}\_{\mathfrak{o}}\right] \text{e}^{-\text{Kt}} \end{aligned}$$

A more convenient form of this equation is obtained by taking log10

Since

$$1\,\text{ln}\,\text{x} = 2.303\log\_{10}\text{x} \tag{1}$$

It follows that;

$$2.303\log\_{10}\text{C} = 2.30.3\log\_{10}\text{C}\_0\text{-Kt}$$

and log10 C=log10 C0 - *Kt* 2.303

A linear relationship is obtained when the logarithm of concentrations (log10C) is plotted against (t), times of observation (Figure 6).

to form the active triphosphates which functions to inhibit the enzyme reverse transcriptase, while L– dopa (inactive), which is used in the treatment of parkinsons disease, is converted into dopamine (active) in the basal ganglia. Futamide, a drug used in the treatment of prostate cancer, undergoes hydroxylation at the alkyl side chain to form hydroxyflutamide, a metab‐ olite that is more active and has a longer duration of action compared to the parent drug.

Introduction to Biochemical Pharmacology and Drug Discovery

http://dx.doi.org/10.5772/52014

487

An active drug is converted into another form which is also active, for instance diazepam, a

An active drug is converted to inactive products, for example, pentobarbital is hydroxylated

These include oxidation, reduction and hydrolytic reactions and such reactions generally introduce or unmask a functional group (hydroxyl, amine, sulfhydryl etc) that make the drug

Consist of synthetic/conjugation reactions in which an endogenous substance such as glucur‐ onic acid or glutathione combines with the functional group derived from phase I reactions to produce a highly polar drug conjugate. All tissues have some ability to carry out drug biotransformation reactions but the most important organs of biotransformation include; the liver, GIT, lungs, skin, and kidneys in that order and most phase II reactions result in a decrease in the pharmacological activity of the drug. The fact that the GIT and liver are the major sites of drug biotransformation means that drugs which are administered orally will be extensively bio-transformed before they eventually reach systemic circulation. This first-pass effect can severely limit the oral bio- availability of some drugs. In addition, intestinal micro-organisms are capable of catalyzing drug biotransformation reactions e.g. a glucuronide conjugate of a drug may be excreted through the intestine via the bile where gut bacteria may convert the conjugate back into free drug. The free drug is then reabsorbed and re-enters the liver via the portal vein where the conjugation process is repeated. This leads to a phenomenon known as

At sub-cellular level, enzymes of drug biotransformation are located in the endoplasmic reticulum, mitochondria, cytosol and lysosome. The major site of drug biotransformation within the hepatocytes and other cells is the membrane of the smooth endoplasmic reticulum. The smooth endoplasmic reticulum constitutes the microsome fraction during differential centrifugation of whole blood. The microsome fraction can be used to carry out many drug

sedative hypnotic, is metabolized to an equally active metabolite, oxazepam.

**11.2. Maintenance of activity**

to forminactive metabolites.

**11.4. Phase I reactions**

**11.5. Phase II reactions**

entero-hepaticcirculation.

biotransformation reactions *in vitro.*

more polar.

**11.3. Inactivation**

**Figure 6.** Logarithmic time course of drug concentration

Half-life (t1/2) of a drug: this is the time period during which the concentration decreases to one- half of its previous value. T 1/2 can be evaluated from the elimination rate constant.

$$\text{When } \mathbf{t} = t\_{1/2}, \mathbf{C}\_{\mathbf{t}} = \frac{\mathbf{C}\_0}{2}$$

therefore,

$$\begin{array}{ll} \frac{\mathbf{C}\_{0}}{2} = \mathbf{C}\_{0}e^{-K \operatorname{tr}\_{1/2}} \\\\ \frac{1}{2} = e^{-K \operatorname{tr}\_{1/2}} \quad \text{but} \quad \mathbf{K}t\_{1/2} = \log\_{e} 2 \\\\ t\_{1/2} = \log\_{e} \frac{2}{K} = \frac{0.693}{K} \end{array}$$
