[Cology] How to calculate PA2 value easily.

Dose-response curves in the presence of antagonists

Competitive antagonists

The term antagonist refers to any drug that will block, or partially block, a response. When investigating an antagonist the first thing to check is whether the antagonism is surmountable by increasing the concentration of agonist. The next thing to ask is whether the antagonism is reversible. After washing away antagonist, does agonist regain response? If an antagonist is surmountable and reversible, it is likely to be competitive (see next paragraph). Investigations of antagonists that are not surmountable or reversible are beyond the scope of this manual.

A competitive antagonist binds reversibly to the same receptor as the agonist. A dose-response curve performed in the presence of a fixedconcentration of antagonist will be shifted to the right, with the same maximum response and (generally) the same shape.

Gaddum derived the equation that describes receptor occupancy by agonist in the presence of a competitive antagonist. The agonist isdrug A. Its concentration is [A] and its dissociation constant is Ka. The antagonist is called drug B, so its concentration is [B] and dissociation constant is Kb. If the two drugs compete for the same receptors, fractional occupancy by agonist (f) equals:

The presence of antagonist increases the EC50 by a factor equal to 1+[B]/Kb. This is called the dose-ratio. You don't have to know the relationship between agonist occupancy and response for the equation above to be useful in analyzing dose response curves.

You don't have to know what fraction of the receptors is occupied at the EC50 (and it doesn't have to be 50%). Whatever that occupancy, you'll get the same occupancy (and thus the same response) in the presence of antagonist when the agonist concentration is multiplied by the dose-ratio.

The graph below illustrates this point. If concentration A of agonist gives a certain response in the absence of antagonist, butconcentration A' is needed to achieve the same response in the presence of a certain concentration of antagonist, then the dose-ratio equals A'/A. You'll get a different dose ratio if you use a different concentration of antagonist.

If the two curves are parallel, you can assess the dose-ratio at any point. However, you'll get the most accurate results by calculating the dose-ratio as the EC50 in the presence of antagonist divided by the EC50 in the absence of antagonist. The figure below shows the calculation of dose ratio.

Schild plot

If the antagonist is competitive, the dose ratio equals one plus the ratio of the concentration of antagonist divided by its Kd for thereceptor. (The dissociation constant of the antagonist is sometimes called Kb and sometimes called Kd)

A simple rearrangement gives:

If you perform experiments with several concentrations of antagonist, you can create a graph with log(antagonist) on the X-axis and log(dose ratio -1 ) on the Y-axis. If the antagonist is competitive, you expect a slope of 1.0 and the X-intercept and Y-intercept will both equal the Kd of the antagonist.

If the agonist and antagonist are competitive, the Schild plot will have a slope of 1.0 and the X intercept will equal the logarithm of the Kd of the antagonist. If the X-axis of a Schild plot is plotted as log(molar), then minus one times the intercept is called the pA2 (p for logarithm, like pH; A for antagonist; 2 for the dose ratio when the concentration of antagonist equals the pA2). The pA2 (derived from functional experiments) will equal the Kd from binding experiments if antagonist and agonist compete for binding to a single class ofreceptor sites.

Creating and analyzing Schild plots with Prism

Enter your dose-response data with X as log of the agonist concentration, and Y as response. (If you enter your data with X asconcentration, do a transform to create a table where X is log of agonist concentration). Label each Y column with a heading (title) that is the log of antagonist concentration. The first column should be the control, with agonist only (no antagonist). Label this column "control".

Use nonlinear regression to fit a sigmoid dose-response curve. Choose a standard slope or variable slope, depending on your data. From the nonlinear regression dialog, check the option to calculate dose-ratios for Schild plots.

The values of the dose ratio can only be interpreted if all the dose-response curves are parallel. If you selected the sigmoid curve with a standard slope, this will be true by definition. If you let Prism determine the slope factor for each curve, look at these (and their standard errors) to see if they differ significantly. If the slope factors differ, then the interaction is probably not strictly competitive, and Schild analysis won't be useful. If the slope factors are indistinguishable, consider holding all the slope factors constant to a single value.

The curve fit results include a results view called Summary table which tabulates the log(DR-1) for each data set (except the first, which is the control). To graph these data, go to the graph section and click the button New graph. Choose a new graph from the summary table of the nonlinear regression results.

First fit to linear regression to determine slope and intercept. If the antagonist is competitive, the Schild plot ought to have a slope that is indistinguishable from 1.0. You can check this assumption by seeing whether the confidence interval for the slope includes 1.0.

If the confidence interval for the slope does not include 1.0, your antagonist is probably not a simple competitive antagonist. For suggestions of further analyses, see T. Kenakin, Pharmacologic Analysis of Drug-Receptor Interaction, 3rd Ed. Lippincott-Raven Press, 1997.

If the confidence interval does include 1.0, refit the line constraining the slope to equal 1.0. You cannot do this with Prism's linearregression analysis. However, you can use Prism's nonlinear regression to fit a line with a constant slope. Use this equation:

Y = X - pA2

When X=pA2, Y=0. As X increases above pA2, Y increases as well the same amount. Fit this equation to determine the pA2 of the antagonist.

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Carbon NanoTubes : Emerging Carrier in Nanotechnology

Recently Carbon nanotubes have been designed to be used as a drug delivery

vector. It has shown potential in tissue engineering, nuclear targeting, and

drug, protein and peptide drug delivery also. The small nanoscale dimension

and astonishing properties make them a distinctive carrier with a wide range

of promising applications. This review briefly outlines some of the important

biomedical application of carbon nanotubes.

Introduction

In the last few decades

various micro and nanoscale drug carrier systems have been developed in order to

find well-organized and proficient carrier systems for drugs, genes, and antigen

which will assist the targeting and delivering of bioactives into specific and

precise organ, tissues and cells. These diverse drug delivery systems include

microemulsion, multiple emulsions, liposomes, niosomes, nanoemulsion,

microspheres, nanoparticle, resealed erythrocyte and dendrimers.

In recent times carbon nanotubes (CNTs) have been designed to be used as a drug delivery carrier.

Carbon nanotubes were discovered by Bacon in the late 1950s. But they were not

fully appreciated at that time. In 1991 Iijima discovered CNTs and proposed it

as an interesting material due to their structural properties1. CNTs

consist of graphite sheets rolled up in to tubular form. These new nanomaterials

belonging to the family of fullerene are the third allotropes of

carbon2. Recently, scientists have also accounted that CNTs hold

potential of a drug delivery systems. The studies have shown that CNTs loaded

with peptides3, proteins4, nucleic acids5 and

drugs6 comprise effective targeting into the cells. Depending upon

the number of graphene sheets, CNTs can be classified as single-wall carbon

nanotubes and multi-wall carbon nanotubes.

1. Single-wall carbon nanotubes

Single-wall carbon

nanotubes (SWNTs) are made of a single graphene sheet. These are seamless

cylinders, were first reported in 19931. Their diameters range from

about 1 to 2 nm, and their length is usually in order of the micrometers. SWNTs

typically team up to form bundles. These bundles consists hexagonally arranged

SWNTs to form a crystal-like structure (figure 1 A).

2. Multi-wall carbon nanotubes

The multi-wall carbon nanotubes (MWNTs) are made up of collection of several

graphene cylinders. MWNTs have a diameter of about 1-100nm and length of about

1-50 micrometers. The distance between each layer of MWNTs is about 0.36nm1

(figure 1 B)

Single-wall carbon nanotubes

Figure 1: (A) Single-wall carbon nanotubes (B) Multi-wall carbon nanotubes

Carbon nano horns and

fullerenes are some structurally related compound to carbon nanotubes. Carbon

nano horns are composed of graphite carbon atom structurally similar to CNTs.

The difference between CNTs and carbon nano horns is that, the latter have an

irregular horn like shape. Fullerene molecules are almost round cages of 60

carbon atoms arranged in interlocking hexagons and pentagons, like the patches

on a soccer ball.

Physicochemical properties

of CNTs include ultra light weight, ordered structure with high aspect ratio,

high mechanical strength and metallic or semi-metallic behavior with high

surface area. There are some limitations of CNTs also, which includes lack of

solubility in most solvents and aggregation. Both these limitations can be

overcome by functionalization or modification of their surface1.

Biomedical application of carbon nanotubes

Owing to the large inner

volume, CNTs proffer attractive advantages for biomedical applications. These

large inner volumes can be filled with desired bioactives of small size as well

as of large size such as proteins and peptides. The targeting and

biocompatibility aspects of bioactive loaded CNTs can also be enhanced by

effective surface functionalization.

Carbon nanotubes mediated drug delivery

In general drug delivery

system is designed to improve the pharmacological and therapeutic profile of a

drug molecule. The large inner volume of CNTs allows encapsulation of both low

as well as high molecular weight drugs. It also permits encapsulation of both

hydrophilic and lipophilic drugs. More than one drug can also be loaded in CNTs

in the case of multi-drug therapy. Ligands and diagnostic moieties can also be

conjugated to surface of CNTs by functionalization to target the drugs to

specific site of action. The CNTs can act as controlled release system for drug

by releasing the loaded drugs for a long period of time. In this way CNTs can be

used multifunctionally for drug delivery and targeting.

Cellular and nuclear targeting

The endeavor behind targeted drug delivery is to enhance

the efficiency and diminishing the noxious effects. The CNTs can be chemically

surface modified such that ligands can be attached to their surface functional

groups. These ligands which are specific to certain receptors can carry the CNTs

directly to the specific site without affecting on non-target site. On the other

hand diagnostic moieties like fluoroisothiocyanate (FITC) can also be attached

to the CNTs for probing their way to the nucleus.

Carbon nanotubes in peptide delivery

The use CNTs in peptide

delivery has also been done by scientist. Application of CNT as a template for

presenting bioactive peptides to the immune system has been done. For this

purpose, by using a bifunctional linker epitope of virus and amine group of CNT

can be covalently link and immunization can be done. Subsequently the

immunogenic features of peptide–CNT conjugates can be assessed in vivo. In this

way CNTs can achieve high value in peptide delivery also7.

Carbon nanotubes in tissue engineering

The main objective of

tissue engineering is to restore unhealthy or damaged tissue with biologic

alternative which can reinstate and preserve regular tasks. The carbon nanotubes

can be used for tissue engineering by visualizing and enhancing cellular

performance and by tracking and labeling of cells8.

Conclusion

It can be concluded that

functionalization of CNTs will open new era in the potential of CNTs in

biomedical field. Some CNT are highly toxic, mostly due to their insolubility,

which is of great concerned in using CNTs. This problem can also be overcome by

functionalization. This offers the possibility of introducing more than one

function on the same CNT molecule to target bioactives, imaging agents, drugs

and ligand moieties at once. Further investigations must be done by the

scientists in the field of CNTs to establish them for their biomedical

applications.

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