Qualitative aspect of drug action – Schild plot
Schild plot: Schild plot is defined as pharmacological method of receptor classification. By using schild plot dose-effect curve for an agonist is determined in the presence of various concentrations of a competitive antagonist for its receptor in the presence of agonist i.e. equilibrium dissociation constant is calculated. The experiment is carried out for series of dose ratios for a given effect. For example the ratio of the dose of agonist (A’) to produce a specific effect (e.g.,half maximal effect) in the presence of the antagonist (B) to the dose required in the absence of the antagonist (A) is calculated. This is determined for several doses of antagonist and then log ((A’/A) -1) versus the negative log B is plotted. If the regression of log ((A’/A) -1) on -log B is linear with a slope of -1, then this indicates that the antagonism is competitive and by definition the agonist and antagonist act at the same recognition sites. If the slope of the regression is not -1, then by definition the antagonist is not competitive or some other condition is in effect. This might include multiple binding sites or pharmacokinetic interactions.
Agonist: Agonist is a drug which has both affinity and efficacy.
Antagonist: Antagonist is a drug which has affinity and zero efficacy.
Affinity:Affinity is a property of a drug; it measures how tight a drug binds to a receptor. To bind to a receptor a functional group of the drug should bind to the complementary receptor. The binding capacity of the drug defines the action of the drug.
Efficacy: Efficacy of a drug can be defined as ability of drug which activates the receptor to produce desired effect after binding.
Affinity and efficacy are explained in the equation as:
A + R AR* Response
B + R BR No Response
Where A is agonist, B is antagonist, K+1 is association rate constant for binding, K-1is dissociation rate constant for binding
α- Association rate constant for activation
β- Dissociation rate constant for activation
By using law of mass action affinity is explained as
B + R BR
Drug free receptor drug-receptor complex
At equilibrium KB = [R] [B] KB = Equilibrium dissociation constant
Hill-Langmuir equation: this equation explains drug occupancy
[RT] = [R] + [BR]
If [RT] = Total number of receptors then by substituting this in law of mass action equation
[RB] = [B]
[RT] KB + [B]
By this equation it is determined that drug occupancy (affinity) depends on drug concentration and equilibrium dissociation constant.
Equilibrium dissosciation constant: EQUILIBRIUM DISSOCIATION CONSTANT (Kd) :
It is the characteristic property of the drug and the receptors. It is defined as the concentration of the drug required to occupy 50 % of the receptors. The higher the affinity of the drug for the receptors lower is the Kd value. Mathematically Kd is k2/k1 where k2 is the rate of dissociation of the drug from the receptor and k1 is the rate of association of the drug for the receptor.
Receptor (R) and Drug (D) interact in a reversible manner to form a drug-receptor (RD) complex.
Where R = Receptor
D = Drug (L for ligand is sometimes used in these equations)
k1 = the association rate constant and has the units of M-1min-1
k2 = the dissociation rate constant and has the units of min-1.
k2 is sometimes written as k-1.
If an agonist binds to the receptor, then the interaction of the agonist (D) and the receptor (R) results in a conformational change in the receptor leading to a response.
If an antagonist binds to the receptor, then the interaction of antagonist (D) and receptor (R) does not result in the appropriate conformation change in the receptor and a response does not occur.
For drugs that follow the law of simple mass action the rate of formation of the complex can be defined by the following equation
d[RD]/dt refers to the change in the concentration of [RD] with time (t).
Note: the square brackets refer to concentration.
This equation indicates that the rate at which the drug receptor complex (RD) is formed is proportional to the concentration of both free receptor (R) and free drug (D). The proportionality constant is k1.
The rate of dissociation can be defined by the following equation
-d[RD]/dt is the decrease in drug-receptor complex with time
This equation indicates that the rate at which the drug-receptor complex (RD) dissociates back to free drug and free receptor is proportional to the concentration of the drug receptor complex. The proportionality constant is k2.
When the drug and the receptor are initially mixed together, the amount of drug-receptor complex formed will exceed the dissociation of the drug-receptor complex. If the reaction is allowed to go for a long enough, the amount of drug-receptor complex formed per unit time will be equal to the number of dissociations of drug-receptor complex per unit of time, and the system will be at equilibrium. That is equilibrium has occurred. Equilibrium can be defined as
or k1[R][D] = k2[RD]
This equation can be rearranged to give
Kd is the dissociation equilibrium constant. Kd has units of concentration as shown in the following equation.
Simple competitive antagonism: simple competitive antagonism is the most important type of the antagonism. In this type of antagonism the antagonist will compete with available agonist for same receptor site. Sufficient antagonist will displace agonist resulting in lower frequency of receptor activation. Presence of antagonist shifts agonist log dose response curve to right. A schild plot for a competitive antagonist will have a slope equal to 1 and the X-intercept and Y-intercept will each equal thedissociation constantof the antagonist.
This can be explained in equation as:
Occupancy for agonist
[RA] = [A] OR [A]/ KA
[RT] KA+ [A] [A]/ KA +1
In presence of competitive antagonist (B)
[RA] = [A]/ KA
[RT] [A]/ KA + [B]/ KB + 1
Occupancy reduced according to [B] and KB
To obtain same occupancy, must increase [A] to [A`]
r = [A’] / [A] = [B’] / [B]
r = [B] / KB +1
Where r depends on [B] and KB
Applying log on both sides
log (r-1) = log[B] – log KB
Aim: The main aim of the experiment is to measure the equilibrium dissociation constant (KB) for atropine at acetylcholine muscuranic receptors and to determine the drug receptor interactions.
The main objectives of the experiment are as follows
Ø To measure the equilibrium dissociation constant for atropine at acetylcholine muscuranic receptors
Ø To demonstrate the reversible competitive antagonism of atropine at acetylcholine muscuranic receptors
Ø To determine the equilibrium dissociation constant (KB) for atropine at acetylcholine muscuranic receptors by using schild plot.
MethodIsolation and mounting of Guinea-pig ileum in organ bath
Guinea-pig was first sacrificed and then the ileum was collected and transferred into physiological salt solution maintained at 370C. The food particles present in the ileum was expelled out through running Krebs solution through the lumen. Then tissue was tied with a thread at both the ends where one was tied to the mounting hook and the other was attached to the transducer.
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1) Preparation of serial dilutions of drug
The drugs used in the experiment were acetylcholine (Ach) and atropine. To determine the simple competitive antagonism of atropine at Ach muscuranic receptors serial dilutions of Ach were carried out. Ach was given as 1×10-2M and from the above concentration of the drug the following concentrations were prepared to the organ bath concentration such as 1×10-6M, 3×10-6M, 1×10-7M, 3×10-7M, 1×10-8M, 3×10-8M, 1×10-9M and 3×10-9M Ach. Then atropine was diluted to 1×10-8M (organ bath) from the given 1×10-2M concentration.
2) Determination of Organ bath concentration
The volume of physiological salt solution (pss) was 20 ml, and each time the volume of drug introduced into organ bath was 20µl.Therefore if 20µl of 1×10-2M drug was introduced into the organ bath then it gives 1×10-5M organ bath concentration.
Mathematical calculation of organ bath concentration:
In organ bath we have 20ml of pss which is equal to 20×103 µl of pss, if 20 µl of 1×10-2 M Ach was introduced then the organ bath concentration
= 20 µl x 10-2 M
20x 103 µl
= 1×10-5M (organ bath concentration).
The isolated guinea- pig ileum was mounted onto the organ bath and set up for recording isometric tension of the tissue using chart software in a Mac book.
Calibration of the experimental apparatus: The chart 5 software was calibrated and the sampling rate was adjusted to 10 samples per second with a maximum input voltage to 10 mV. The baseline was set to zero and then trace was started from the baseline zero then the force transducer was calibrated by placing 1 gram weight and after the calibration the trace produced was stopped for the moment to convert the units of tension into grams by selecting the trace produced previously.
Sensitisation of preparation: To check the viability of the tissue a response of suitable height was obtained by adding a little high concentration of the drug. Here in the experiment an appreciable recording was noted at 1×10-7M Ach.
The time cycle followed to construct a concentration- response curve was
0 seconds – to add the drug concentrations
30 seconds – to empty the organ bath and refill with fresh physiological salt solution
180 seconds – next drug concentration was added to the organ bath.
Concentration Response Curve:
By making use of the above drug concentrations a concentration response curve was constructed according to the provided time cycle.
1) 20 µl of 1×10-9M Ach was added into the organ bath at zero seconds at is allowed to stand for 30 seconds, then after 30 seconds the organ bath was emptied and refilled with pss. Pss was allowed to stand for 180 seconds. During the wash period if the peak does not return to the base then it was washed twice or thrice to make sure that all the drug dissociates from the receptors before the next addition of the other drug concentration. Each concentration was repeated twice or thrice until the two consecutive responses were reported with the same peak height.
2) By following the procedure and time cycle, the concentration response curve was constructed with different concentrations of acetyl choline such as 1×10-9M,3×10-9M, 1×10-8M, 3×10-8M, 1×10-7M, 3×10-7M,
1×10-6M and 3×10-6M Ach (organ bath concentration).
Equilibration of Acetylcholine receptors with acetylcholine
After step-2 the preparation was washed several times until the peak returned to the base line. Then atropine (1×10-8M organ bath concentration) was added to the preparation and then set aside for 40 minutes to allow atropine to equilibrate with acetylcholine muscuranic receptors.
Concentration response curve in the presence of atropine
The concentration response curve with acetylcholine was repeated again in the presence of atropine by following the time cycle and procedure, which was same as same step 2.Therefore in step 3 with each addition of acetylcholine concentration atropine was added simultaneously.
i) The graph pad prism in the Mac book was used to plot concentration response curves in the absence and presence of atropine.
Log concentration (acetylcholine) Vs response in grams
ii) From the above plot EC 50 values of acetylcholine in the presence and absence of atropine were obtained. Then the distance between the two curves control and response for the atropine presence was denoted by ‘r, where ‘r’ was called as shift.
iii) The shift was calculated mathematically as
r= EC 50 of response in the presence of atropine
EC 50 of Ach in the absence of atropine
iv) From the value of the shift, schild plot was plotted as log concentration of atropine presence against log(r-1).
v) From the schild plot the dissociation constant KB for atropine at acetylcholine muscuranic receptors was determined.
As explained above in the procedure serial dilutions of acetylcholine was added to the organ bath, where Ach has produced concentration dependent contractions of the guinea pig ileum as shown in the fig 1.
As shown in ‘ 1 the serial dilutions of acetylcholine are added into the organ bath from 1×10-7M to 3×10-6M Ach. Here in the trace it was clearly shown that contractions produced by the acetylcholine have been increased with respect to the concentrations.
In step-2 the preparation was washed and added with 1×10-8M atropine and set aside for 40 minutes to equilibrate the acetylcholine receptors.
In the trace it is clearly shown that, the contractions produced by serial dilutions of Ach from 1×10-8M to 3×10-4M in the presence of 1×10-8M atropine.
When Trace 1 and Trace 2 are compared it is evident that the contractions produced by Ach alone (trace 1) were greater than the contractions produced Ach in the presence of atropine (trace 2) which proves the simple competitive antagonism by atropine at muscuranic receptors.
A graph is plotted to the log concentration response curve produced by Ach alone against Ach in the presence of atropine. (graph is attatched to the report)
From the graph it is known that with the increase in the concentration of Ach, response have been increased when compared to Ach in the presence of atropine and also there is a shift towards right which shows the simple competitive antagonism produced by atropine.
From the results produced by Ach alone against Ach in the presence of atropine the fractional difference which is called as shift can be obtained as follows
Mathematical Calculation shift ‘r’
= EC50 of response after atropine (or) in the presence of atropine
EC50 of control (or) Ach in the absence of atropine
= 2.51×10-6 = 8.36
r-1 =8.36 -1=7.36
log(r-1)=log (7.36) =0.86
Partial dissociation constant (PKB) or PA2 is measured to confirm the simple competitive antagonism, where pKB values play an important role in classifying receptors.
Therefore PKB =log(r-1) -log [atropine]
=0.86 -log (1×10-8)
=0.86 – (-8)
From the above results log EC50 values for control (Ach alone) and Ach in the presence of atropine were given as 3.0e-007 and 2.51e-006 respectively.
This shows the molar concentration of Ach which produces 50% of the maximal possible response is higher than the molar concentration response produced by Ach in the presence of atropine.
If the antagonist is competitive, the dose ratio equals one plus the ratio of the concentration of antagonist divided by its Kd for the receptor. (The dissociation constant of the antagonist is sometimes called Kb and sometimes called Kd)
A simple rearrangement gives:
Here we have plotted a graph with log (antagonist) on the X-axis and log (dose ratio -1) on the Y-axis. If the antagonist has shown simple competitive antagonism then the slope should be 1.0, X-intercept and Y-intercept values should be both equal the Kd of the antagonist obtained.
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 of receptor sites.
From ‘ 5 and 6 it is evident that no concentrations of atropine have showed competitive antagonism perfectly. Therefore from the above results it is known that the concentrations of atropine has not shown simple competitive antagonism fairly.
Reversible competitive antagonism: The binding of drug to a receptor is fully reversible which produces a parallel shift of the dose response curve to the right in the presence of an antagonist.
The mechanism of action of acetylcholine at muscuranic receptors:
In various gastrointestinal smooth muscles, acetylcholine and its derivatives produce contractions by activating muscuranic receptors. It is generally assumed that the M3 muscuranic receptor plays a key role in mediating this activity. The M3 receptor is coupled preferentially to Gq-type G proteins, resulting in the activation of phospholipase C (PLC) and the formation of ionositiol trisphosphate (IP3) and diacylglycerol (DAG) which are likely to participate in muscuranic receptor-mediated smooth muscle contractions. IP3 causes Ca2+ release from intracellular store and can also mobilize Ca2+ secondarily through Ca2+-sensitive or store-dependent mechanisms. DAG, via activation of protein kinase C, phosphorylates various proteins and can directly activate non selective cationic channels.
From the above results the value of shift obtained was 0.378 which denotes the simple competitive antagonism produced by the concentration of atropine used (1×10-8 M).From the value of shift the pKB value was calculated as 8.4.If atropine has shown simple competitive antagonism then the value of pKB should be equal to 1-X intercept.
Therefore pKB=1-X intercept
We got value of pKB as 8.86.Therefore pKB is not equal to 1-X intercept.
Therefore the concentration of atropine (1×10-8M organ bath concentration) used by our group has not shown simple competitive antagonism effectively. The literature value of pKB is given as approximately 9 and we have obtained the value of pKB as 8.86 which does not fit with literature value.
Therefore from the above observations and results i can conclude that a little more high concentration of atropine may serve to produce complete simple competitive antagonism by atropine at acetylcholine muscuranic receptors.
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