Pharmacokinetics with Calculations from A to Z for Pharmacy

Drug absorption

• Refers to the route or method by which the drug reaches the blood supply, this depends on how the drug is administered.
• The most common and preferred method of administration is the oral route.
• It depends on hydrophilic/hydrophobic properties, polarity and ionization of the drug.

I-Stability:   ”Oral drugs have to be chemically stable to survive the stomach HCl and metabolically stable to survive the digestive enzymes in GIT and metabolic enzymes in liver (mainly cytochrome P450 ).  -Insulin, local anaesthetics and first penicillins are acid labile , so they can't be taken orally but are given parentrally.  

Drug absorption

Pharmacokinetics & related topics  Drug absorption 

• II-Solubility
• The drug should have the correct balance of water versus fat solubility
• Oral drugs should be sufficiently polar to dissolve in the GIT and blood supply, but sufficiently fatty to pass through the cell membranes (optimum hydrophophobic/hydrophilic balance).
• Most oral drugs obey Lipinski’s rule of five, i.e.

1-A molecular weight less than 500

2-No more than 5 hydrogen bond donor groups                                                               

3-No more than 10 hydrogen bond acceptor groups

4-A calculated log P value less than + 5

Pharmacokinetics & related topics  Drug absorption 

• II-Solubility

  A- Polarity:

• Some polar drugs break these rules are usually poorly absorbed and have to be administered by injection.
• Highly polar drugs will dissolve in GIT but they will fail to be absorbed through the lipid cell membrane of the gut wall while nonpolar drugs will be poorly soluble in the GIT instead they will dissolve in the fat globules leading to poor surface contact with cell membranes resulting in poor absorption , too.

 Pharmacokinetics & related topics              Drug absorption   B-Ionization:  The presence of the weak ionizable -NH- group in many drug structure would have three advantages:  A- good solubility due to =NH2+ cation in stomach acid  B- good absorption due to conversion to non ionized form in intestine in slightly alkaline pH  C-good target interactions  due to participation   of ammonium ion in   them 

Drug absorption  -Henderson-Hasselbalch equation   pH= pKa + log [A-]/[HA]  C-Size :  Large molecular weight drugs generally have poor absorption because they mostly have a large number of polar groups which will lead to poor absorption of these drugs. 

Pharmacokinetics & related topics   Drug absorption mechanisms: 

• Most drugs with  proper solubility in both water and lipid will be absorbed through the lipid cell membrane of the gut wall cells .
• Carrier proteins are essential to a cell’s survival as they transport highly polar building blocks required for various biosynthetic pathways.

Pharmacokinetics & related topics   Drug absorption mechanisms: 

• Some  polar drugs, are absorbed by special carrier proteins such as levodopa  fluorouracil, lisinopril, methotrexate and erythromycin, which are similar in structure to (or bear a structural resemblance to) one of the building blocks (such as amino acid) then it too may be smuggled into the cell
• Other polar drugs with high molecular weight are absorbed by pinocytosis (without passing through the membrane).

Pharmacokinetics & related topics   Drug absorption mechanisms: 

•   Some polar drugs with low molecular weight (<200) are absorbed by passing through the pores between cells lining the gut wall.
• Thus polar drugs are orally active if they are small enough to pass between the cells of the gut wall or are recognized by carrier proteins or are taken across the gut wall by pinocytosis.
• N.B: sometimes drugs are designed to be highly polar to be retained in the gut and not absorbed to treat gut infections as some antibacterial agents for gut infections. 

Drug distribution 

• Once the drug is absorbed, it is rapidly distributed around the blood supply, then slowly distributed to the various tissues and organs.
• Distribution to the interstitial fluid surrounding tissues and organs is rapid if the drug is not bound to plasma proteins .
• Some drugs have to enter cells in order to reach their target.
• A certain percentage of a drug may be absorbed into fatty tissue (e.g. Barbiturates) and/or bound to macromolecules

Drug distribution 

• Drugs entering the CNS have to cross the blood-brain barrier. Polar drugs (e.g. Penicillin) are unable to cross this barrier unless they make use of carrier proteins or are taken across by pinocytosis (e.g. insulin).
• Some drugs cross the placental barrier into the fetus and may harm development or prove toxic in newborn babies (e.g. alcohol, nicotine, cocaine, barbiturates)

Drug distribution may be affected:

• Altered organ perfusion due to hemodynamic changes
  • May effect delivery to site of action, site of metabolism and site of elimination
  • Inflammation and changes in capillary permeability may enhance delivery of drug to a site
• Hypoxemia affecting organ function
• Altered hepatic function and drug metabolism

VOLUME OF DISTRIBUTION

Volume of distribution (VD) is a calculation of the apparent volume in which a drug is dissolved.

This definition assumes that the drug is evenly distributed and that metabolism or elimination has not taken place. In reality, it does not correspond to any real volume:

This equation is very easy to remember. Suppose you take 1000 mg of sugar and dissolve it into a beaker of water. After it has dissolved, you take a sample of water (let’s say, 10 mL) and determine the concentration of sugar in that sample (for example, 1 mg/mL). From this finding you can calculate the volume of water in which the sugar was dissolved, as follows:

1 mg/mL = 1000 mg/volume of water

Thus,

In this case the volume was 1000 mL or 1 L. If you keep the units straight, the equation does not need to be memorized.

Try another one. Suppose 500 mg of “Newdrug” is administered to a medical student. The plasma concentration is 0.01 mg/mL. What is the volume of distribution?*

The volume of distribution is rather large. Your selected medical student is not, however, a huge water balloon. The only explanation is that the drug is hiding at some place in the body where it is not recorded by the measurement of plasma concentration. The drug could be lipid soluble and stored in fat, or it could be bound to plasma proteins. As this example shows, the volume of distribution is a hypothetical volume and not a real volume.

The volume of distribution gives a rough accounting of where a drug goes in the body, especially if you have a feel for the various body fluid compartments and their sizes. In addition, it can be used to calculate the dose of a drug needed to achieve a desired plasma concentration.

The various body fluid compartments for a standard 70-kg man are illustrated in this figure.

HALF-LIFE

The elimination half-life (t1/2) is the time required for the Cp of the drug to decrease to 50% of an earlier value. The units for half-life are expressed as time (minutes, hours).

The half-life of a drug can also be used to determine the time required for an infused drug to reach steady state.

The t1/2, total clearance, and Vd are related by the following equation: t1/2=0.693×VdCL

Changes in total clearance or Vd alter the t1/2. For example, reduced renal clearance resulting from renal disease or toxicity decreases total clearance and increases t1/2.

Linear Pharmacokinetics 

• Linear = rate of elimination is proportional to amount of drug present
• Dosage increases result in proportional increase in plasma drug levels

Nonlinear Pharmacokinetics 

• Nonlinear = rate of elimination is constant regardless of amount of drug present
• Dosage increases saturate binding sites and result in non- proportional increase/decrease in drug levels

One-Compartment Open Model: Intravenous Bolus Administration

The most common and the most desirable route of drug administration is the oral route in which dosage forms (drug products) such as tablets, capsules, or oral solutions are generally used. In order to develop pharmacokinetic models to describe and predict drug disposition kinetically, the model must account for both the route of administration and the pharmacokinetic behavior of the drug in the body. Once drug disposition can be predicted by a pharmacokinetic model, then dosing regimens for individuals or groups of patients can be calculated.

The one-compartment open model is the simplest way to describe the process of drug distribution and elimination in the body. This model assumes that the drug can enter or leave the body (ie, the model is “open”), and the entire body acts like a single, uniform compartment. The simplest route of drug administration from a modeling perspective is a rapid intravenous injection (IV bolus). The simplest pharmacokinetic model that describes drug disposition in the body is the IV bolus model where the drug is injected all at once into a box (the human body) or compartment, and the drug distributes/equilibrates instantaneously and rapidly throughout the compartment. Drug elimination from the compartment also begins to occur immediately after the IV bolus injection.

Of course, this model is a simplistic view of drug disposition in the body, which in reality is infinitely more complex than a single compartment. In the body, when a drug is given in the form of an IV bolus, the entire dose of drug enters the bloodstream immediately, and the drug “absorption process” into the plasma is considered to be instantaneous. In most cases, the drug quickly distributes via the circulatory system to potentially all the tissues in the body. Uptake of drugs by various tissue organs will occur at varying rates and extents, depending on the blood flow to the tissue, the lipophilicity of the drug, the molecular weight of the drug, and the binding affinity of the drug for the tissue mass. Most drugs are eliminated from the body either through the kidney and/or by being metabolized in the liver. Because of rapid drug equilibration between the blood and tissues, drug distribution and elimination occur as if the dose is all dissolved in a tank of uniform fluid (a single compartment) from which the drug is eliminated. The volume in which the drug seems to be distributed is termed the apparent volume of distribution, VD. The apparent volume of distribution assumes that the drug is theoretically rapidly and uniformly distributed in the body throughout the apparent volume. The VD is determined from the injected amount or the dose and the plasma drug concentration Cp0 immediately after injection. For simplicity, it is assumed that the injected dose disperses and distributes instantly. This model is also termed a well-stirred one-compartment model.

Metabolism 

• Drugs and toxins are seen as foreign to patients bodies
• Drugs can undergo metabolism in the lungs, blood, and liver
• Body works to convert drugs to less active forms and increase water solubility to enhance elimination
• Liver - primary route of drug metabolism
• Liver may be used to convert pro-drugs (inactive) to an active state
• Types of reactions
• Phase I (Cytochrome P450 system)
• Phase II

 What is CYP?

'CYP' is a host of enzymes that use iron to oxidise things, often as part of the body's strategy to dispose of potentially harmful substances by making them more water-soluble. Bertz and Granneman (Clin Pharmacokinet 1997 32 210-58) found that 56% of 315 drugs were primarily cleared by CYP! Adding something like a hydroxyl group to a xenobiotic is just part of the body's strategy to get rid of the 'drug' - this is often followed by conjugugation to groups such as glucuronide to increase the solubility even further. To try and thoroughly confuse you, the initial P450-mediated oxidation is often referred to as "Phase I metabolism" and the subsequent conjugation (which has nothing to do with P450) as "Phase II".

What does CYP do?

CYP catalyses a variety of reactions including epoxidation, N-dealkylation, O-dealkylation, S-oxidation and hydroxylation. A typical cytochrome P450 catalysed reaction is:

Where is it found?

It is not surprising that much of the CYP in man is found in the liver, the main organ involved in drug and toxin removal, but a remarkable amount is also found in the small intestine. CYP usually sits around in the 'microsomal' part of the cytoplasm (endoplasmic reticulum). Metabolic clearance of drugs is not the only function of CYP - recently, it has been found that CYP is intimately involved in vascular ###i, particularly in the brain. CYP is vital to the formation of cholesterol, steroids and arachidonic acid metabolites. Other functions surely remain to be uncovered.

How many different CYPs are there?

There are over a thousand different CYPs, although the number in man is only about fifty (49 genes and 15 pseudo genes have been sequenced). It is likely that most of the human CYPs have already been discovered. Why are there so many varieties of CYP? The massive hetereogeneity of these oxidases is thought to reflect the complex interdependence {read: 'ongoing battle'} between plants and animals. Plants develop new alkaloids to limit their consumption by animals - the animals develop new enzymes to metabolise the plant toxins, and so it goes. It is possible to peer back in evolution by looking at similarities between CYP isoenzymes. When we do so, it appears that the number of CYP genes exploded at about the time when organisms moved from the oceans to dry land - around 400 million years ago!

What's in a name?

First-time readers may wish to skip the following section, as it may well confuse them.

Why cytochrome P 450? There's a story attached to this. Initially, when researchers realised how important cytochromes were in metabolism, they needed a way of identifying them unequivocally. We know that most CYP is anchored to membranes of the microsomal portion of the cell. This attachment is unfortunate for investigators, as grinding up cells and extracting the microsomal portion results in a rather opaque suspension. Special tricks are needed to identify the CYP component - the microsome-containing solution is divided into two (after adding an agent that reduces any haem that might be present), and one part is exposed to carbon monoxide. If the solution exposed to CO strongly absorbs light at a wavelength of 450nm compared with the original solution, it must contain CYP. This is called "difference spectroscopy", and we are finding the "reduced CO difference spectrum". (The P in P450 stands for "pigment").

{Fine Print: When we said that absorption at 450nm on exposure to CO uniquely identifies P450, we lied just a little. The reason why absorption occurs at this wavelength is related to one of the six 'ligands' associated with the iron atom contained in the haem. The haem ring itself provides four ligands (nitrogens), but in P450 the fifth is an unusual, negatively charged sulphur atom. This is known to its few friends as a "thiolate anion", and proteins containing this unusual moiety are called "haem-thiolate proteins". There are other haem-thiolate proteins apart from P450 - they include cystathionine beta-synthetase (EC 4.2.1.22), haem chloroperoxidase (1.11.1.10) and nitric oxide synthetase (1.14.13.39).

Cytochrome P450 chemistry is fascinating and challenging. Note that the bond between the two atoms in an oxygen molecule is rather strong. This implies that a substantial amount of energy is required to break the bond - energy that is supplied by addition of electrons to the iron atom of heme. These electrons in turn come from the last protein in an "electron transfer chain". There are two such chains in cells that end up at P450. The first is in the endoplasmic reticulum (ER), and the protein involved is called NADPH cytochrome P450 reductase - electrons pass from NADPH to FAD to FMN and thence to heme. The second chain lurks within mitochondria. A complex bucket brigade of proteins hands the electrons down to heme. NADPH passes electrons to ferredoxin reductase, thence to ferredoxin (which itself has an iron-sulphur cluster), and from there to CYP. }

CYP Isoforms

This section looks at how we classify CYP, polymorphis and its importance, and enzyme inductions as well as other controversial issues such as the importance of CYP to drug design, the relationship between CYP and P-glycoprotein, and how CYP has been implicated in causing cancer and other diseases.

How do we classify CYP?

There are numerous isoforms of cytochrome P450. (An isoform is a CYP enzyme variant that derives from one particular gene). They are classified according to the similarities of their amino-acid sequences. Such classification allows division of CYP isoforms into:

• families - CYP families contain genes that have at least a 40% sequence homology. There are at least 74 CYP families, but only about seventeen of these have been described in man.
• subfamilies - Members of a subfamily must have at least a 55% identity. About thirty subfamilies are well characterised in man
• individual genes - There are fifty or so genes important in man.

Families are numbered - for example CYP2, CYP21.  Subfamilies are identified by a letter, and thus we get CYP3A, CYP2D.  Individual genes are identified by a number, for example CYP2D6.

• CYP3A4 (by far the most important)
• CYP2D6
• CYP2C9
• CYP2C19

On exposure to appropriate substrates, enzyme induction occurs with all of these CYPs, apart from CYP2D6. In addition, those in italics above are polymorphic.

What is polymorphism?

In different people and different populations, activity of CYP oxidases differs. Genetic variation in a population is termed 'polymorphism' when both gene variants exist with a frequency of at least one percent. Such differences in activity may have profound clinical consequences, especially when multiple drugs are given to a patient. There are profound racial differences in the distribution of various alleles - data on a drug that works in one way in one population group cannot necessarily be extrapolated to another group.

Why does polymorphism occur, and why is it important?

The explanations for the various polymorphisms are thought to be complex, but perhaps the most interesting is the high expression of CYP2D6 in many persons of Ethiopian and Saudi Arabian origin. 2D6 is not inducible, so these people have developed a different strategy to cope with the (presumed) high load of toxic alkaloids in their diet - multiple copies of the gene. These CYPs therefore chew up a variety of drugs, making them ineffective - many antidepressants and neuroleptics are an important example. Conversely, prodrugs will be extensively activated - codeine will be turned in vast amounts into morphine!

In contrast, many individuals lack functional 2D6. These subjects will be predisposed to drug toxicity caused by antidepressants or neuroleptics, but will find codeine (and indeed, tramadol) to be inefficacious due to lack of activation! Other drugs that have caused problems in those lacking 2D6 include dexfenfluramine, propafenone, mexiletine, and perhexiline. Perhexiline was in fact withdrawn from the market due to the neuropathy it caused in those 2D6 inactive patients unfortunate enough to be treated with it. Even beta-blocker removal may be impaired (for example, propranolol) in 2D6-deficient people.

Another potentially disastrous polymorphism is deficient activity of CYP2C9. This is because patients possessing this enzyme variant are ineffective in clearing (S)-warfarin - so much so that they may be fully anticoagulated on just 0.5mg of warfarin a day! As if this isn't enough, the same CYP is important in removal of phenytoin and tolbutamide, both potentially very toxic drugs in excess. The flip-side is that the prodrug losartan will be poorly activated and inefficacious with 2C9 deficiency. Azole antifungals, sulphinpyrazone, and even amiodarone may cause a similar effect by inhibiting the enzyme.

Occasionally one derives benefit from an unusual CYP phenotype. For example, cure rates for peptic ulcer treated with omeprazole are substantially greater in individuals with defective CYP2C19, owing to the sustained, high plasma levels achieved.

Is enzyme induction of CYP important?

Yes. Although most of the CYPs can be induced (the notable exception being 2D6), perhaps the most important in this regard is CYP3A4. 3A4 is the most prevalent CYP in the body, and metabolises many substrates. The most important inducers of 3A4 are antimicrobials such as rifampicin, and anticonvulsants like carbamazepine and phenytoin, but potent steroids such as dexamethasone may also induce 3A4. The long list of agents metabolised by the enzyme include opioids, benzodiazepines and local anaesthetics, as well as erythromycin, cyclosporine, haloperidol, calcium channel blockers, cisapride and pimozide. Oral contraceptives are also metabolised, and their efficacy may be impaired when an inducer such as rifampicin is taken.

Even more important than the inducers of 3A4 are the inhibitors. There is a long list - azole antifungals, HIV protease inhibitors, calcium channel blockers, some macrolides like troleandromycin and erythromycin, and the commonly used 'SSRI' antidepressants. Lethal clinical consequences can result from combining 3A4 inhibitors with drugs that are metabolised by this cytochrome. Non-sedating antihistamines have resulted in fatal arrhythmias, as has occurred with cisapride administration in combination with an inhibitor. Erythromycin in combination with theophylline may cause toxicity due to the latter.

Where does P-Glycoprotein come in?

There is an interesting association between some CYPs and the important transmembrane pump protein, P-glycoprotein (the product of the MDR1 gene). Generally, if P-glycoprotein is there, then CYP3A4 is not far behind. This seems to be part of a concerted strategy by the body to eliminate xenobiotics - the P-glycoprotein pumps out what it can, and CYP3A zaps the rest! This association makes for even more interesting drug interactions, for example calcium-channel blockers interact with the membrane pump and the CYP! The same holds for drugs as diverse as azole antifungals, immunosuppressants and macrolides.

Does CYP have something to tell us about drug design?

Designing and ultimately marketing a drug costs a bomb. The interaction between CYP and freshly minted drugs is therefore rather important to pharmaceutical companies, so much so that predominant degradation of a drug by one of the polymorphic CYPs is often enough to stop further research on that drug in its tracks!

Is CYP important in cancer?

There has been much speculation about the role of the various CYP proteins and polymorphisms as causes of cancer. Some CYPs may activate pro-carcinogens to carcinogens; many are probably involved in the removal of carcinogens from the body. In addition, several cancers are hormone sensitive, and those CYPs involved in, for example, steroid or retinoic acid metabolism may play a crucial role in suppression or promotion of malignancies through such metabolism.

There has been much speculation (but little production of hard evidence) that some CYPs found in the lung promote lung cancer, especially in cigarette smokers.

Which CYPs localise in specific tissues?

Some isoforms are found throughout the body, for example CYP51, while others are limited to one specific tissue (take CYP11B2, found mainly if not exclusively in the glomerulosa zone of the adrenal gland)!

Differential expression of some CYPs in different organs may also have clinical consequences, especially where the unfortunate side-effect of 'degradation' of a drug is to make a more toxic product. The degradation of paracetamol by 2E1 results in a highly active intermediate product which in sufficient quantities can result in fulminant liver failure. Anti-oxidants protect against this catastrophe; in contrast, chronic ethanol consumption induces 2E1 and may increase the likelihood of toxicity.

Does CYP change with age?

Variable expression of CYP has substantial clinical consequences, not only in different people and different race groups, but also in individuals as they progress from infancy to old age. For example: CYP1A2 is not expressed in neonates, making them particularly susceptible to toxicity from drugs such as caffeine.

• Principles of Xenobiotic Biotransformation

• Hydrolysis, Reduction, and Oxidation

  • Hydrolysis

    • Carboxylesterases

    • Cholinesterases (AChE and BChE)

    • Paraoxonases (Lactonases)

    • Prodrugs and Alkaline Phosphatase

    • Peptidases

    • β-Glucuronidase

    • Epoxide Hydrolases

  • Reduction

    • Azo- and Nitro-Reduction

    • Carbonyl Reduction—AKRs and SDRs

    • Disulfide Reduction

    • Sulfoxide and N-Oxide Reduction

    • Quinone Reduction—NQO1 and NQO2

    • Dihydropyrimidine Dehydrogenase

    • Dehalogenation

    • Dehydroxylation—mARC, Cytochrome b5, ###i/i###5 Reductase, and Aldehyde Oxidase

    • Aldehyde Oxidase—Reductive Reactions

  • Oxidation

    • Alcohol, Aldehyde, Ketone Oxidation–Reduction Systems

    • Alcohol Dehydrogenase

    • Aldehyde Dehydrogenase

    • Dimeric Dihydrodiol Dehydrogenase

    • Molybdenum Hydroxylases (Molybdoenzymes)

    • Xanthine Oxidoreductase

    • Aldehyde Oxidase

    • Amine Oxidases

    • Aromatization

    • Peroxidase-Dependent Cooxidation

    • Flavin Monooxygenases

    • Cytochrome P450

    • Activation of Xenobiotics by

    • Cytochrome P450

    • Inhibition of Cytochrome P450

    • Induction of Cytochrome P450—Xenosensors

Metabolism via Oxidation of Aromatic Compounds

Oxidation of aromatic compound results in the formation of arenol metabolites by hydroxylation. This process for most of the aromatic compounds takes place through the formation of an epoxide intermediate ‘arene oxide’ by the cytochrome P450 enzymes, followed by the NIH shift or 1,2-hydride shift. Alternatively the reactive arene oxide can undergo other reactions to produce trans-dihydrodiol metabolites, as well as macromolecular adducts with proteins, DNA or RNA which can result in high toxicity.

Mechanism of the NIH shift or 1,2-hydride shift

The 1,2-hydride shift is also called the NIH shift because it was discovered in the National Institutes of Health (NIH) laboratory in Bethesda, Maryland, USA. To explain the mechanism of the NIH shift, the classic example of 4-Deuterioanisole can be taken as in the figure below, in which the deuterium atom moves from the 4-position to the 3-position.

1. The first step involves the epoxidation of the aromatic ring to form the arene oxide by the cytochrome P450 enzymes.
2. The arene oxide can form a zwitterionic species
3. A 1,2-hydride (or in this case deuteride) shift or NIH shift occurs in which a hydride (or in this case deuteride) attacks the positively (+) charged 3-position carbon atom resulting in the formation of a dienone intermediate.
4. The dienone quickly tautomerizes to form the 3-deuterio-4-hydroxyanisole metabolite in order to restore aromaticity and completes the 1,2-hydride or NIH shift.

What controls position for aromatic oxidation and some examples of aromatic oxidation?

Rule of Thumb- In general, the position which is electron rich and has the least steric hindrance gets oxidized on the aromatic ring to form the metabolite. Hence it is important to brush up upon basic organic chemistry and effects of aromatic substituents before tackling metabolism problems.

1. For mono-substituted benzene rings, oxidation occurs majorly at the para position with minor oxidation at the ortho position. These hydroxylated metabolites then further undergo glucuronide or sulfate conjugation becoming hydrophilic and thus easily excreted out of the body. Examples of drugs undergoing this metabolic oxidation are Phenytoin(anticonvulsant), Warfarin (anticoagulant), Propranolol (antihypertensive), Atorvastatin(lowers cholesterol), Phenobarbital (sedative hypnotic) etc.
2. The presence of substituents on the aromatic ring also influence the process of hydroxylation. Electron withdrawing groups such as Cl, COOH, SO₂NHR, -N⁺R₃ slow downthe process whereas electron donating groups accelerate the process of oxidation. Examples of aromatic compounds with electron withdrawing groups are Clonidine-antihypertensive agent (-Cl groups) and Probenecid-uricosuric agent (-SO₂NHR and -COOH). Probenecid has been reported to not undergo hydroxylation at all.
3. If there are two or more phenyl rings, hydroxylation proceeds in the electron rich ring. For example, Diazepam (anti-anxiety) has two phenyl rings in its structure, but hydroxylation occurs primarily in the electron rich ring as the other ring has an electron withdrawing group (-Cl) attached. Other examples of such oxidation are Chlorpromazine (antipsychotic agent), p-Chlorobiphenyl etc.
4. There are certain compounds which are resistant to aromatic hydroxylation despite of the aromatic rings. This is because of the presence of multi electronegative chlorine atoms attached to the rings. Thus these compounds escape metabolism and are present in the body for a longer time due to their lipophilic property. Examples are Polychlorinated biphenyls (PCBs) and 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). These compounds are present as pollutants and are toxic thus increasing the risks of health hazards.

   2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD)

Importance for understanding aromatic oxidation in xenobiotic metabolism

Certain xenobiotics on metabolism in the body turn to active metabolites (bioactivation) which can be toxic to the body. They can be carcinogenic or cause hepatic necrosis or can induce mutagenesis.  The toxicity of these bioactive metabolites can be explained by the fact that the proteins and nucleic acids in the body are nucleophilic in nature and can react with the arene oxides forming covalent bonds. A couple of the examples is of the polychlorinated biphenyls (PCBs) and 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) mentioned above. These molecules are environmental pollutants. PCBs were widely used as a dielectric and in coolant fluids in transformers, capacitors and motors. TCDD was a contaminant in a herbicide called “Agent Orange” which was later used as a chemical warfare agent.

Another important example for xenobiotic metabolism is that of polycyclic aromatic hydrocarbons. These polycyclic aromatic hydrocarbons such as Benzo[a]pyrene are formed in auto emission, refuse burning, and even in cigarette smoke and are ubiquitous to the environment. The possibility of aromatic oxidation in such structures is present at a number of positions. While not all metabolites are toxic, certain oxidation products lead to highly reactive carcinogenic molecules.

Importance of Glutathione Conjugation (GSH-conjugation) – The body’s defense against arene oxides

Glutathione (GSH) is a tripeptide molecule which is present throughout the body and has a reactive sulfhydryl group as a part of a cysteine amino acid. Glutathione is the body’s defense mechanism against reactive arene oxides. Reactive arene oxides can conjugate with the sulfhydryl group of the glutathione in the presence of enzyme GSH S-transferase to form the glutathione adduct, which can then be processed to form a premercapturic acid and mercapturic acid derivatives for excretion. This prevents the reactive arene oxides from reacting with the body’s macromolecular proteins, DNA and RNA and thus acts as a anti-carcinogenic molecule. However, GSH levels in the body are limited and can be depleted. Once depleted, these arene oxides can cause permanent damage to tissues and generally attack the liver first resulting in necrosis.

Conjugation

• Glucuronidation and Formation

• of Acyl-CoA Thioesters

• Sulfonation

• Methylation

• Acetylation

• Amino Acid Conjugation

• Glutathione Conjugation

• Thiosulfate Sulfurtransferase (Rhodanese)

• Unusual Conjugation Reactions

• Phosphorylation

DRUG ELIMINATION
The kidney is the most important organ for the excretion of drugs and/or their
metabolites. Some compounds are also excreted via bile, sweat, saliva, exhaled air, or
milk, the latter a possible source of unwanted exposure in nursing infants. Drug
excretion may involve one or more of the following processes.

A. Renal Glomerular Filtration
Glomeruli permit the passage of most drug molecules, but restrict the passage of
protein-bound drugs. Changes in glomerular filtration rate affect the rate of
elimination of drugs which are primarily eliminated by filtration (e.g., digoxin,
kanamycin).

B. Renal Tubular Secretion
The kidney can actively transport some drugs (e.g., dicloxacillin) against a
concentration gradient, even if the drugs are protein-bound. (Actually, only free
drug is transported, but the protein-drug complex rapidly dissociates.) A drug
called probenecid competitively inhibits the tubular secretion of the penicillins,
and may be used clinically to prolong the duration of effect of the penicillins.

C. Renal Tubular Reabsorption
Many drugs are passively reabsorbed in the distal renal tubules. Reabsorption is
influenced by the same physicochemical factors that influence gastrointestinal
absorption: nonionized, lipid-soluble drugs are extensively reabsorbed into 

plasma, while ionized and polar molecules will remain in the renal filtrate and be
excreted via urine. Thus, as in the gut, urine pH plays an important role, as does
urine volume. Urine pH may vary widely from 4.5 to 8.0, may be influenced by
diet, exercise, or disease, and tends to be lower during the day than at night. It is
sometimes clinically useful, particularly in drug overdose cases, to alter the pH of
the urine (of the patient). For drugs which are weak acids, urine alkalinization
favors the ionized form and promotes excretion. Alternatively, acidification
promotes the renal clearance of weak bases.

D.Biliary Excretion
Comparatively little is known about hepatic drug elimination. Many drugs and
metabolites are passed into the small intestine via bile and may undergo
enterohepatic cycling. Recent studies have attempted to interrupt enterohepatic
cycling of drugs, pesticides and heavy metals through the oral administration of
non-absorbable, nonspecific adsorbents such as charcoal or cholestyramine. The
results, generally a decrease in drug half-life, have been surprising in that they
suggest that many more drugs undergo enterohepatic cycling than previously
suspected.

Reminder: When the pH is higher than the pK, the unprotonated forms (A− and B) predominate. When the pH is less than the pK, the protonated forms (HA and BH+) predominate.

ORDER OF REACTION
This is the number of concentration terms that determine the rate. Consider the reaction:
A + B ---------> C + D
The rate of the reaction is proportional to the concentration of A to the power of x, [A]x and also
the rate may be proportional to the concentration of B to the power of y, [B]y.
The overall equation is, Rate = k [A]x [B]y
The overall order of reaction is x+y

RATE CONSTANT
A rate constant is a proportionality constant that appears in a rate law. For example, k is the rate
constant in the rate law d [A]/dt = k [A].
Rate constants are independent of concentration but depend on other factors, most notably
temperature.

First order and zero order processes
The rate of absorption or elimination can be expressed either in terms of a half- time (t1/2, the time required for 50% to be absorbed or eliminated, or a rate constant (k), the fraction absorbed or eliminated per unit time. For absorption we usually use the symbols ka and t1/2a, and for elimination ke and t1/2e.
If either value is known, the other can be calculated from the relationships:
k = 0.693/t1/2          OR               t1/2 = 0.693/k
For most sites of administration drug absorption follows first order kinetics and
for most routes of elimination the process also is first order or exponential.

1. First order kinetics
A first order process is one by which a constant fraction of the drug present will be absorbed or eliminated in a unit of time. For a drug eliminated by a first order process, a plot of plasma
concentration after the last dose as a function of time will give a straight line on semilog paper. 

2. Zero order kinetics
Zero order kinetics describe processes in which a constant amount of drug is absorbed or eliminated per unit time. A constant rate intravenous infusion is one example of a zero order process.
For most drugs, absorption and elimination follow first order kinetics because the drug concentration is not sufficient to saturate the mechanism for absorption or elimination. If the process saturates, then zero order kinetics apply. For some drugs, elimination kinetics are dose-dependent (or more correctly, concentration-
dependent). As the plasma level increases, the value of t1/2e increases; the plasma concentration increases disproportionately with increases in dose, and finally, elimination rate becomes independent of plasma concentration.

The time course of change in plasma concentration
When a drug is administered in a single dose, and when absorption and elimination are first order processes, it is reasonable to have some idea of the effects of three variables (t1/2a, dose and t1/2e) on the time-course of change in plasma concentration,
1. More rapid absorption will increase the peak plasma concentration,
decrease the latency (time required to attain drug effect) and decrease the
duration of effect.
2. An increase in dose will also decrease latency and increase peak plasma
concentration and increase duration of effect.
3. More rapid elimination will decrease peak plasma concentration and
duration of effect.

The Plateau Effect
When repeated doses of a drug are given at sufficiently short intervals, and elimination is a first order process, the plasma concentration (and total body store) will increase to a steady value or plateau. The same thing will happen if a drug is administered as a constant rate intravenous infusion (zero order in) and eliminated
by a first order process. The latter case may be simpler to consider first.
During constant IV infusion, the total body store increases exponentially to a steady value. The half-time for the change in plasma concentration is equal to t1/2e. This means that 50% of the final concentration is attained in one t1/2e, 75% in two and 87.5% in three. 90% of the final value is attained in 3.3t1/2e; this is a
useful fact to remember.
With intermittent dosing, unless the dose interval is quite long compared to t1/2e, accumulation and the increase in plasma concentration will follow a similar time- course, but there will be fluctuations in plasma level between doses. The shorter the dose interval and the smaller the dose, the smaller will be the fluctuations

Elimination rate (Er) and elimination rate constant (ke)
These parameters describe, in mathematical terms, the elimination of a
drug by all processes (i.e., renal + hepatic + all other).
a. Zero order elimination
Implies that a fixed number of drug molecules are eliminated per
unit time. Ethanol is a good example. In this case, Er = ke.
b. First order elimination
Implies that a constant fraction of the drug molecules are
eliminated per unit time. This is the case for most drugs. In this
case, ke is simply defined as the slope of decline in plasma drug
concentration, i.e.,
ke = delta y/delta x = ln (2) = 0.693
                                   t1/2e    t1/2e

OBJECTIVES

• Describe the differences between linear pharmacokinetics and nonlinear pharmacokinetics.

• Illustrate nonlinear pharmaco­kinetics with drug disposition examples.

• Discuss some potential risks in dosing drugs that follow nonlinear kinetics.

• Describe the use of the Michaelis–Menten equation to simulate the elimination of a drug by a saturable enzymatic process.

• Estimate the dose for a nonlinear drug such as phenytoin in multiple-dose regimens.

Linear pharmacokinetics

• Change in plasma concentration due to ADME process is proportional to dose of drug administered (single or multiple)
• Follow First order kinetics
• Semilog plot for concentration vs time is super imposable (Principle of superimposition)
• No change in F, Ka, Ke, Vd, Clearance etc.

Nonlinear Pharmacokinetics
• Rate process of ADME are dependent on carrier or enzymes having definite capacity and subjected to saturation.
• Change in concentration is no more proportional to dose administered during the total process of ADME.
•  Nonlinear pharmacokinetics can be best described by Michaelis Menten Equation. (Follow First order + Zero order kinetics)

• Change in different pharmacokinetic parameters.

Detection of non linearity
• Determination of steady state plasma concentration at different doses If:
Css α Xo (Linear)
Css α Xo (Non linear)
• Determination of some important pharmacokinetic parameters
Bio-availability (F) , t 1/2, Cl etc. are constant, any change show non-linearity.

Stages at which Nonlinearity occur Non linearity can occur at any of the following
stage during the fate of drug in body:
• Absorption
• Distribution
• Biotransformation/Metabolism
• Excretion

Causes of Nonlinearity During absorption
• Absorption is solubility or dissolution rate limited eg. Griseofulvine
• Absorption involve carrier mediated transportation eg. Riboflavin, ascorbic acid
• Hepatic metabolism attain saturation eg. Propranolol, hydralazine

Causes of Nonlinearity During Distribution
• Saturation of binding sites on plasma proteins eg. Phenylbutazone, naproxen.
• Saturation of tissue binding sites eg. Thiopental, fentanyl.

Causes of Nonlinearity During Metabolism
• Capacity limited metabolism due to enzyme or cofactor saturation eg. Alcohol, Phenytoin.
• Enzyme induction eg. Carbamazepine

Causes of Nonlinearity During Excretion
• Active tubular secretion eg. Penicillin G
• Active tubular re-absorption eg. Glucose, water soluble vitamins.
• Other sources: Forced Diuresis, change in urine pH, nephrotoxicity etc.

OBJECTIVES:

Clearance (Cl)
Clearance refers to the volume of plasma cleared of drug (by all processes) per unit time, i.e., Cl = ke x Vd

Loading Dose 

Maintenance Dose

Kinetics following a single drug dose
1. Intravenous
The curve is triphasic, with a rapid peak, decline (the distribution phase) and a slow elimination phase from which ke can be calculated.
2. Subcutaneous or intramuscular
The drug takes a finite time to reach the circulation. The levels of drug in blood continue to rise until the number of drug molecules being eliminated per unit time exceeds that being absorbed per unit time. In general, the entire dose will reach the circulation, i.e., bioavailability (F) = 1.
3. Oral
The pattern is similar to that of SC or IM, but usually bmax is lower, and tmax occurs later.

Steady State Kinetics
The administration of a drug at intervals shorter than about 4 elimination half- times will result in accumulation of the drug in the body. The accumulation will continue until the amount of drug absorbed per unit time equals the amount of drug eliminated per unit time, at which time a plateau, or steady state concentration (Css) will be reached.
1. Constant IV infusions
For constant IV infusions, zero order absorption, and first order elimination apply. 

At equilibrium, input = output. i.e., ka = Cl x Css = Vd x ke x Css thus, Css = ka/(Vd x ke)
The important principle here is that Css is regulated only by Ka and ke.
Therefore, to double Css, simply double the drug infusion rate (which is usually in units of mg/hr)

Note: There are important exceptions where doubling the dose does not
result in a doubling of Css. In these cases, "dose-dependent kinetics"
apply; in this course, we will not cover the mathematics of dose-dependent
kinetics. Most dose-dependent situations occur because one or more of
the processes involved in drug absorption, distribution, metabolism, or
excretion show saturability, a condition in which the rate of a given
process increases or decreases with the drug concentration. For example,
the active tubular secretion of penicillin is saturable; thus, as the dose is
increased, ke will decrease. As another example, the first pass hepatic
metabolism of propranolol is saturable; thus, as the oral dose is increased,
the effective ka will increase.

2. Repeated oral doses
In this case, ka is influenced by the bioavailability (F) of the drug, the interval between drug doses, and the dose itself. Thus, ka = F x Dm/T,
where Dm = maintenance dose (e.g., in mg)
T = dose interval (e.g., in hours)
F = bioavailability (the fraction absorbed)
Note that the units of ka are mg/hr, just as in the case of the IV situation described above.
At steady state, input = output, i.e., ka = F x Dm/T = Css x Vd x ke
Rearranging this equation, we obtain:
Css = Dm F/(Vd x ke x T) = (1.44 x Dm x F x t1/2e) /(T x Vd)

(Note: 1.44 is simply the reciprocal of .693, i.e. 1/0.693)

This last equation is one which you must know in order to calculate maintenance doses and dose intervals. Once you have decided what the target Css should be, this equation will permit you to calculate dose and

dose interval. Note, however, that there is no unique dose (Dm) and dose interval (T), since these are two variables in the same equation. Thus, it is possible that different combination of Dm and T could be used to achieve the same Css.

3. Initial oral loading dose
When a prompt drug response is needed, e.g., with the use of theophylline to treat an acute asthma episode, it is often useful to initiate treatment with a single "loading dose" which is larger than the typical maintenance dose of the drug. The loading dose allows one to achieve plasma drug concentrations above the minimum effective concentration (MEC) quickly.

Second loading dose
In practice, one often administers an initial loading dose, allows some time
to pass, and then obtains a measurement of the plasma drug concentration.
Sometimes (hopefully) the measured value will fall in the desired range, in
which case no additional loading dose is required and one can proceed
with "maintenance" therapy. Other times, however, the measured serum
drug concentration will be found to be too low, in which case a second
loading dose may need to be administered. How does one calculate this
second, smaller loading dose?
The only parameter which needs to be altered in the original loading dose
equation is Css, from which one must subtract the actual measured value.
In other words:
D2 = (Vd) (Css - Cact)
                     F
where D2 = the second loading dose
Css = the desired steady state concentration
F = bioavailability
Cact= the actual measured serum drug concentration 
Thus, D2 equals the dose of drug required to alter the serum drug concentration from the observed value to the desired value.

INTRODUCTION FOR ALL PHARMACOKINETICS CALCULATIONS AS GENERAL VIEW

EXPLAIN ABOUT CALCULATION FOR POTENCY UNIT WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR BIOAVAILABILITY WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR T1/2 OF 1ST ORDER KINETICS WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR Vd  WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR ZERO ORDER KINETICS WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR 1ST ORDER KINETIC WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR DOSE FRACTION ELIMINATION  WITH EXAMPLE

EXPLAIN ABOUT CALCULATION FOR Controlled release & Loading Dose WITH EXAMPLE