# Structural Biochemistry/Pharmacokinetics
## Introduction

Pharmacokinetics, abbreviated as "PK", (from Ancient Greek pharmakon "drug" and kinetikos "to do with motion") is a subdivision of pharmacology focused on effects of a biological system on chemical substances. It deals with three main stages of drug’s life span in our body such as absorption, distribution, and excretion. This area mainly applies to chemical drugs but it also goes into substances ingested or delivered externally to an organism, such as nutrients, metabolites, hormones, toxins, etc.
Pharmacokinetics is often studied with respect to pharmacodynamics. The two should not be confused; pharmacokinetics is described as what the body does to the drug whereas pharmacodynamics is described as what the drug does to the body. Pharmacokinetics extends to the mechanisms of absorption and distribution of drug, the rate in which a drug effect begins along with the duration of the effect, the chemical transformation of the drug in the body (most likely by enzymes), and the effects and routes of excretion of the drug.

## Timing

All drugs, no matter how they are delivered, share some common features when we consider their effects over time. There is initially an interval, the latency period, during which the concentration of the drug is increasing in the blood but is not yet high enough for a drug effect to be detected. How long this latency period will last is related generally to the absorption time of the drug. As the concentration of the drug continues to rise, the effect will become stronger.

## Cross-Tolerance and Cross-Dependence

It is possible that a tolerance effect for one drug might automatically induce a tolerance for another. This effect is called cross tolerance, which is commonly observed in the physiological and psychological effects of alcohol, barbiturates and a class of antianxiety medications. As a result of cross tolerance, an alcoholic generally develops a tolerance for a barbiturate, which can be a risk factor when undergoing surgery with an anesthetic. On the other hand, if we can relive the withdrawal symptoms of one drug by administering another drug, then the two drugs show cross-dependence. In effect, one drug can substitute for whatever physiological effects have been produced by a second drug that has been discontinued.

# Compartment Model

Pharmacokinetics and its role in drug dosage: Pharmacokinetics is a primary systematic regulation that supports applied therapeutics. It is the mathematical basis to test the duration of a drug in the body, and the effects it has on the body. When patients are in need of medicine, doctors issue prescriptions with the appropriate medicines and dosages for the specific condition. This dosage is monitored under the drug use process (DUP). Doctors and pharmacists always make sure that the patient is not suffering from a drug related problem. Once this claim is confirmed, a clinical diagnosis can be made and the pharmacist can apply the DUP to guarantee that the dosage and procedure is appropriate for the patient. The regimen is made according to the patient’s ability to process the drugs. Drugs have four stages in the body: absorption, distribution, metabolism, and excretion. The drug concentration is prescribed on the basis of this fundament. When the patient understands these stages, the medicine can be distributed to the patient. The pharmacist must confirm that the drug, dosage, and regime are suitable, and that the patient leaves with a clear understanding and acceptance. Clinical pharmacokinetics is a crucial foundation that pharmacists must be familiar with and master, and is a quality that pharmacists need to have in order to successfully practice pharmaceutical care. Ideally, the intensity of a drug is calculated at the activation site, the receptor. But since that is not possible, the drug level is measured in the blood, saliva, urine, and/or the cerebrospinal fluid.
Reaction Rates: To accurately apply the methods of ADME, the rates of these steps must be taken into consideration. The rate of reaction, the velocity that the reaction continues at, can either be of zero order, or first order. Volume of Distribution: The volume of distribution is not a real quantitative volume value, but more of a apparent volume. It is a measure in which the concentration of the drug can be determined. It is the volume of the plasma that is required to dissolve the drug in the body. Since the body is not a homogeneous entity, it can be difficult to precisely measure the concentration. The concentration of the drug may be different in various parts of the body. However, it is important to note that the concentration will be proportional throughout the body, and the values can be rationalized accordingly. The formula Vd= X/Cp is used to convert a drug amount to its concentration. Vd is the Volume of distribution, X is the amount of drugs in the tissues, and Cp is the amount of drug in the specific part of the body. Using the formula, if the drug has a large volume of distribution, and it does not match to the accurate volume reading, then the drug is said to be highly dispersed in the tissues. If the drug has a matching volume of distribution to the accurate volume reading, then the drug is unsuccessfully dispersed and is strictly contained in the plasma. Drug Clearance: Drug Clearance (CL) is the volume of plasma in the vascular section absent of drugs per unit time through the functions of metabolism and excretion. The clearance for a specific drug remains the same throughout if it is confirmed and removed from the first order kinetics. CL=k X Vd, where k is the first order elimination rate constant, and Vd is the volume of distribution. Multiple Doses: Many patients need to take medication more than once for it to be effective. When drugs are consumed by the body, the drug accumulate in the body and the concentration will rise until it reaches a steady state condition. A steady state happens when the concentration of drug consumed equals the concentration of drug eliminated within the same time frame. At the steady state, the plasma concentration of the drug and the high and lows are constant throughout. The amount of time required to arrive at the steady state depends on the half life of the drug. The larger value the dose is, the larger the steady state levels are. When the dosing interval is lower than the half life value, the higher the accumulation is, and a higher steady state level. In situations where the dosing interval is greatly higher when compared with the half life of the drug, there will be zero accumulation. Many drugs have a dosing interval that is proportional to the half life of the drug, but independent with the amount of doses recommended, or the time required to reach the steady state.

## Pharmacokinetics of Drug Dispersion

Compartment Model is a mathematical representation that is introduced in the pharmacokinetics of drug dispersion in the body. It is a simulation of the pharmacokinetic possess of drug that has been introduced to the body. Scientists usually study one- or two- compartment model [1].

### One Compartment Model without Absorption

One Compartment Model is a closed homogeneous system that the administered drug is released and diffused in a single unit of the body organ without absorption, which is an ideal condition [1]. The one-compartment model follows the idea that once the drug has entered the body, it instantly distributes itself equally throughout the body into equilibrium. This is because the model depicts the body as a kinetically homogeneous unit. The concentration of drug in plasma, which also quantitatively indicates changes in the tissue, is then graphed linearly thus representing a one-compartment model. An example of One-Compartment Model is intravenous injection with no absorption. The kinetic characteristics of this model are determined by the total mass of drug (M), concentration of drug (C), volume of the body fluid (V), first order elimination constant (k) and diffusion time (t).[2]
The three variables mean:
V: volume of the body fluid C: concentration of drug
Mass Balance of One Compartment Model:
The variables mean:
k: first order elimination constant C0 : initial concentration of administered drug t: drug diffusion time C/C0: rate constant with respect to time
When t = 0, we can obtain the maximum concentration of drug, which is also the initial concentration: Cmax = C0
From which we can also tell: Mmax = M0
Circulation half-life (t1/2) Calculation in One-Compartment Model:
therefore,

### One Compartment Model with Absorption

One Compartment Model with Absorption is closed system that the administered drug diffuses from a transdermal patch into the blood stream.
The variables are same as Figure 1-1 except that:
D: total amount of initial drug absorption compartment ka: absorption constant
Mass Balance of One Compartment with Absorption:
dM/dt = kaD-kM dD/dt = -kaD D=D0 at t=0
Therefore,
Finally, M =D_0 k_a/(k-k_a )(e^(-k_a t)-e^(-kt))
This model can be related to therapeutic window:

### Two Compartment Model

The two-compartment model separates the body into two compartments: a central compartment and a peripheral compartment. The central compartment consists of blood and well perfused organs such as the liver, kidney, heart, brain, etc. The peripheral compartment consists of poorly perfused tissue such as muscle, lean tissue, fats, etc. The model follows the idea that once the drug has entered the body, it distributes itself between the central and peripheral compartment. However, equilibrium is not achieved between the two compartments.

## ADME

Pharmacokinetics is the basis for which the time course of drugs in body systems and their corresponding effects can be quantified. The four processes culminating the time span of drugs in the body can be described as follows:
    Absorption - the process of the intake of the drug into the body
    Distribution - the process of the dispersion of the drug into the blood stream and tissues
    Metabolism - the process of the parent compounding into daughter metabolites
    Excretion - the process of eliminating the drug from the body
These processes, often known as ADME, are responsible for the various concentrations of the drug in the blood stream at difference points in the development of the administration of medicine. Often, the effectiveness of a drug is dependent upon its concentration in the body. Other factors such as the site of administration and the dosage can affect the pharmacokinetic properties of the drug.
Alternatively, LADME may be used in place of ADME. The L adds to the ADME scheme the process of Liberation, or the release of the drug from its carrier (usually its protective coating or similar material).

## How do scientists study pharmacokinetics?

Since researchers in pharmacokinetics field are following drug action in the body, perfect timing is a significant demand for the researchers. Scientists must determine when and where a drug should target inside bodies. However, it is not easy to keep track of the drugs. Even though scientists have known the strategy how medicines pass thought the body, the scientists cannot actually see where a drug is going. Therefore, the scientists use the tools of mathematics and chemistry in their researches.
Mathematical tools: Mathematics supplies models and precise methods to measure body fluids which help researchers determine their interest goal. Measurements of blood and urine lead to the answers such as where the drug is and how much of the drug broke down at a given time. Meanwhile, blood levels of liver enzymes can help predict how much of a drug is going to be absorbed.
Chemistry’s usage: The interaction between a drug and an organism is actually a series of chemical reaction between the drug molecule and molecules inside the organism. Hence, knowledge of how drugs react in biological environments is necessary to predict the amount of drugs a body requires or the maximum amount of drugs a body can withstand.

## Advances Using Pharmacokinetics

By using the model of cocaine pharmacokinetics, scientists have seen promising effects of using enzyme therapy in treating drug abuse. Studying the cocainemetabolizing enzyme to see if it can keep the drug from entering the brain and causing producing the physiological effects can lead to advancements in production of an anti-cocaine medication. The model of this could be easily translated into therapy for other physiological effective drugs.

## Kinetics

In order to properly understand the pharmacokinetic process of ADME, the rates of these process must be examined. The rate, or velocity, at which each of these processes proceed follows either zero-order or first-order kinetics.
Zero-order kinetics
In a zero order reaction, the rate of reaction is independent of the concentration of the reactant(s); the rate is constant. The rate law for a zero order reaction is:
    r = k
If drug A, for example, is being excreted out of the body at a constant rate, according the zero order kinetics, the rate of excretion can be described as:
    dA/dt = k
First-order kinetics
In a first order reaction, the rate of reaction is dependent upon the concentration of only one reactant, even if more than one reactant is present. The rate law for a first order reaction is:
    -r = k[A]
where [A] is the concentration of reactant A. If the same drug A is being excreted out of the body through first order kinetics, the rate law would be written as:
    dA/dt = -k[A]
Most drugs proceed through first order kinetics, and the process of ADME in a biological system usually follows first order kinetics as well.

## References

U.S. department of Health and Human Services - Medicines by Design
Zheng F, Zhan C-G (2012) Modeling of Pharmacokinetics of Cocaine in Human Reveals the Feasibility for Development of Enzyme Therapies for Drugs of Abuse. PLoS Comput Biol 8(7): e1002610. doi:10.1371/journal.pcbi.1002610
Levinthal, Charles, "Drugs, Behavior, and Modern Society", Pearson Education, Inc., 2008
* ↑ Zheng F, Zhan C-G (2012) Modeling of Pharmacokinetics of Cocaine in Human Reveals the Feasibility for Development of Enzyme Therapies for Drugs of Abuse. PLoS Comput Biol 8(7): e1002610. doi:10.1371/journal.pcbi.1002610