Pharmacology: Dose and Response

• Pharmacology is based on measurements, therefore classifying drugs is based on how well it produces a response and how it is used
• In pharmacology, the needed quantity of a drug to produce an effect is referred to as the dose

Dose and Response

• Dosages can be described in units of weight, per kilogram of body weight, per square meter of body surface, or in concentration units
• As dosage increases, the measured effect becomes apparent until a maximum is reached
• The maximum level is considered the desired and therapeutic effect
• Side effects can be seen when dosages are increased
• The measure of a drug's selectivity measures the separation between doses, beneficial and harmful

Quantal Effects

• Some drug effects do not occur in a graded manner
• Epileptic fits, arrythmias, and death are "all-or-none" quantal effects
• The proportion of the population affected by a dose of a drug with these effects is graded

Drug action

• Many drugs act by reversibly binding to a cell component (a receptor)
• Response may include increased cyclic amp levels, isolated muscle contraction or blood pressure change

Sigmoid Curve & Hyperbola

• Graphs based on functions of the administered drug dose will take the form of a rectangular hyperbola
• This graph is limited when making quantitative measures, and comparing curves
• Logarithm of the dose forms a sigmoid curve
• The sigmoid curve shows qualitative aspects and enables quantifiable comparisons

Mathematical Expression of Dose-response

• This is based on a number of assumptions
• One molecule of a drug combines with one receptor
• Measured response depends on # of drug receptor complexes formed
• Maximum response comes if all receptors are occupied by a drug
• Number of receptors is less than the number of drug molecules

Expression

• The interaction of a drug and a receptor can be represented using an equation
• The Law of Mass Action is applied to this
• Equilibrium constant for the formation of drug-receptor complex = K₁ = K2/(k1) and equation (2) can be rewritten

Equilibrium

• The equilibrium constant KA is described in terms of concentration, characteristic to both the drug, and the receptor
• The higher a drug's affinity, the lower the value of KA
• Using Equation (3), KA can be measured from the dose-response relationship. When 50% of the receptors are occupied, the response should be 50% and the KA will equal the concentration of drug to produce this response (when P = 0.5, [A] = KA)

Agonists and Pharmacology

• Drugs that bind to a receptor to produce a positive effect are agonists in pharmacology
• Agonists possess receptor affinity and activity to induce a response

Dose Repsonse curve

• A drug that binds to a receptor and produces a positive effect is referred to as an Agonist.
• An indication of the relative affinities of the agonists for a common receptor is shown in the image and is given by their position on the log scale.
• This can be loosely considered the equivalent of potency, which means the quantity of drug required to produce a response.
• The maximum response obtained is an indication of the activity of an agonist which can be considered the equivalent of the term efficacy, which is used to describe the extent of the therapeutic response.
• The slope of the linear portion of the dose response curve is important as it indicates how great an increase in the response will follow a given increase in the dose.

Agonists

• Agonists can come in different forms
• Varying types can be illustrated by looking at dose-response curves
• Indication of relative agonist affinities for a common receptor is shown in the log position

Related Drugs

• Screening drugs at a particular receptor will often find drugs unable to produce the same maximum response
• Drugs that can produce the maximum response are full agonists, others are partial agonists
• Partial agonists will produce a lesser therapeutic effect
• Morphine acts at opioid receptors in the brain for pain relief and is a full agonist, while buprenorphine, which acts the same way, provides less pain relief and is a partial agonist

ED50

• ED50 stands for Effective Dose 50% (of max response)
• Affinity of an agonist can be estimated from drug experiments where a response is measured
• The dose that produces a response equal to half the maximum is recorded, since the drug penetrating the receptor site can't be determined
• ED50 is analogous to the ID50 value for enzyme inhibitors, and its value allows drugs to be ranked according to their pharmacological activities

CNS

• In the Central Nervous System, receptors are active without any bound agonist, and the nerves also operate
• Agonists can increase or decrease the nerve's operation by increasing or decreasing the receptor's activity
• Agonists which decrease the basal activity of receptors are known as inverse agonists

Antagonists

• Agents without activity to prevent agonist action are circumstantial evidence for receptors' existence
• Agents with receptor affinity but no activity are antagonists
• Effects cannot be measured directly, but their effects can be studied if they bind to a receptor to block agonist action

Competitive Antagonism

• Administering an agonist and antagonist at the same time makes them compete to occupy the receptors
• Any given dose of agonist will produce less response with an antagonist present compared to an agonist
• Increasing the agonist dose while keeping the antagonist dose fixed causes excess agonist molecules, creating a greater response
• The curve of an agonist alone vs that w antagonist produces the same maximum, just shifted to the right
• Successive increases in antagonist dose should be overcome by increases in the agonist dose if both act reversibly
• Series of rightward-shifted log dose-response curves will be plotted
• Competitive antagonism is shown to be true over many agonists and antagonists
• The name makes sense

Schild Plot

• Quantifying the effect of a competitive antagonist examines log dose curve displacement
• Expressed in terms of the dose ratio, where particular the amount of drug is measured to give a particular response if there is an antagonist versus none at all
• Equation shown to relate ratio and antagonist dose
• Where [b] is antagonist concentration and KB is the equillibrium constant

Schild relationship

• If the dose ratio (r - 1) vs log antagonist concentration is plotted
• The log dose of equillibrium constant and relationship between agonist and antagonist can be extracted

KB Drug

• Usually expressed as pA2 value, defined as negative logarithm of polar concentration of the agonist
• pA2 is analagous to pH and pK notations
• It reduces amount of concentration to simple number

Non-Competitive Antagonists

• Some antagonists decline in max response if does is increased
• Raising the agonist dose does not restore the resonse to pre-antagonist level
• Agents don't compete for the receptor, they usually bind covalently to prevent agonist binding
• A lower max results as an antagonist is added, lowering the count and resulting in covalent bonding preventiing the displacement of the molecule for a lower maximum response
• Antagonists = non-competitive and straight line Schild plots
• Phenoxybenzamine = non-competitive antagonist

Isotopes and action

• Radiolabeled compounds (14C, 3H, or 125I) and purification techniques measure the binding of drugs to receptors
• Since a response is not measured, binding is referred to as a ligand
• Using a linear plot, to produce the reअरेंजमेंट equation 4 must be followed, where B is the bounded amount, y is ligand concentration, Bmax=site number.
• Relationship provides straight line graph to aquire slope an constants

Research

• Allied to the measurement of the dosage-response, binding studies can elucidate structure-activity and structure-affinity relationships, often as a part of the drug screening process
• Scatchard Plot = valuable information to elucidate these relationships

Loss of effect

• Drug effects decrease gradually on occasion when repeatedly used
• Desensitzation and tachyphylaxis = effect w/in few minutes, Tolerance = period, Drug resistance is for chemotherapeutics
• Number of target receptors declines when loss of effect happens. Decrease is also evident in the binding to receptors.
• Depletion can occur through a mediator.
• Tolerance is a problem with transdermally administered substance

Summary

• Researchers can develop specific drugs that are targeted to a receptor or activation site
• Receptors may be in organisms as different forms
• Differences give rise to subtypes, even further subdivisions according to the affinity and activity of agonists and antagonists
• Simple log dose-response curve analysis and Schild plots enable H2-receptor, b1-receptor and adrenergic b2-receptor drugs to be tested
• Now that receptor isolation and ligand binding studies are possible this process should be easier but they should not always be characterized
• Some binding sites and isoforms may be desentisized.
• Dose is the most critical relationship