From Enzyme Kinetics to Drug Receptor Interactions by Marc Imhotep Cray, M.D.

Integrated Scientific and Clinical Pharmacology

From Enzyme Kinetics to Drug Receptor Interactions The Biochemical Bases of Pharmacodynamic Parameters Marc Imhotep Cray, M.D. BMS / CK-CS Teacher http://www.imhotepvirtualmedsch.com/

Objective:  To understand how Drug (Ligand)-Receptor interactions in pharmacodynamics (PD) are analogous to the EnzymeSubstrate reactions (enzyme kinetics models) of biochemistry  To demonstrate how Enzyme- Substrate interactions and Drug-Receptor interactions follow the same biochemical kinetic principles and have analogous parameters  To understand the relationship between Ligand-receptor binding curves Graded dose-response curves Companion string: MedPharm Guidebook, Pgs. 17-22

Michaelis-Menten kinetics  Km is inversely related to affinity of enzyme for its substrate  Vmax is directly proportional to enzyme concentration  Most enzymatic reactions follow a hyperbolic curve (i.e., Michaelis-Menten kinetics)  however, enzymatic reactions that exhibit a sigmoid curve usually indicate cooperative kinetics (i.e., hemoglobin)

[S] = concentration of substrate; V = velocity

Graph demonstrates the Michaelis-Menten kinetics model for relationship between an enzyme and a substrate: one of the parameters studies in pharmacokinetics, where the substrate is a pharmaceutical drug Km is the M-M constant Vmax is the maximum volorsity of the reaction 3

Michaelis-Menten kinetics (2)  As larger amounts of substrate are added to a reaction, the available enzyme binding sites become filled to the limit of Vmax  Beyond this limit the enzyme is saturated with substrate and the reaction rate ceases to increase  Saturation curve for an enzyme rxn showing relation between substrate concentration and reaction rate

From Enzyme kinetics Notes

Lineweaver-Burk plot (the inverse of M-M plots)  y-intercept , Vmax  The further to the right the x-intercept (i.e., closer to zero), the greater the Km and the lower the affinity Expressed mathematically: (only for sake of completeness) The y-axis is 1 / Vmax and the x-axis is 1 / [S]. The slope is Km / Vmax. 1 / Vo = (Km / Vmax) • (1 / S) + (1 / Vmax 5

Enzyme inhibition (1)  Reversible competitive inhibitors cross each other competitively, whereas noncompetitive inhibitors do not

REMEMBER  increase y-intercept means decrease Vmax  The further to the right the x-intercept (i.e., closer to zero), the greater the Km and the lower the affinity

Enzyme inhibition(2) Table Competitive inhibitors, reversible

Competitive inhibitors, irreversible

Noncompetitive inhibitors

Resemble substrate Yes

Yes

Bind active site

Yes

Effect on Vmax

Unchanged Unchanged

Unchanged

Effect on Km Overcome by [S] Pharmacodynamics

Yes potency

efficacy

Efficacy 7

Pharmacology Terminology  Most drugs evoke effects by interacting with receptors  Affinity  Efficacy [pharmacologic] or  (synonym) Intrinsic activity [molecular]  Agonists  Mimic physiologic activation  Have both high affinity and efficacy  Antagonists  Block actions of neurotransmitters or agonists  Have high affinity, but no efficacy  Often used as pharmacologic reversal agents

What are the differences between competitive and noncompetitive inhibitors? (1)  Competitive inhibitors (antagonist) bind to same active site of an enzyme (receptor) as substrate (ligand/drug) of interest  In competitive inhibition (antagonism) , the enzyme (receptor) is bound to either substrate (drug/agonist) or inhibitor (antagonist) at any given point  This is because inhibitor (antagonist) closely resembles substrate  Competitive inhibition (antagonist) can be overcome by overwhelming the system with increasing concentrations of substrate (agonist) , which compete with inhibitor (antagonist) for active site of catalytic enzyme (receptor) 9

What are the differences between competitive and noncompetitive inhibitors? (2) On the other hand,  Noncompetitive inhibitors (antagonist) bind to alternate sites of enzyme (receptor) other than the active binding site  Do not resemble substrate (ligand/drug)  binding of noncompetitive inhibitor to enzyme (receptor) of interest distorts enzyme (receptor) such that it can no longer bind to substrate (ligand/drug)  Noncompetitive inhibition (antagonism) is often irreversible and cannot be overcome by saturating system with increasing concentrations of substrate (ligand/drug)

Receptor binding: Agonist with Competitive antagonist Effect ď&#x201A;§ Shifts curve right ( potency), no change in efficacy ď&#x201A;§ Can be overcome by the concentration of agonist substrate Example Diazepam (agonist) + flumazenil (competitive antagonist) on GABA receptor 11

Receptor binding: Agonist with Non-Competitive antagonist Effect  Shifts curve down (efficacy)  Cannot be overcome by agonist substrate concentration Example  Norepinephrine (agonist) + Phenoxybenzamine (noncompetitive antagonist) on α-receptors

Receptor binding: Agonist with Partial Agonist (alone) Effect • Acts at same site as full agonist, but with lower maximal effect ( efficacy) • Potency is an independent variable Example • Morphine (full agonist) vs. buprenorphine (partial agonist) at opioid μ-receptors

Efficacy vs. potency Efficacy

RELATIVE EFFICACY

 Maximal effect a drug can produce  Represented by the y-value (Vmax)  y-value = Vmax = efficacy  Unrelated to potency (i.e., efficacious drugs can have high or low potency)  Partial agonists have less efficacy than full agonists

Efficacy vs. potency (2) Potency

RELATIVE POTENCY

 Amount of drug needed for a given effect  potency (EC50) = drug needed  Represented by the x-value (EC50)  Left-shifting = EC50 = potency  Unrelated to efficacy (i.e., potent drugs can have high or low efficacy)

Ligand-receptor binding curves

A. Linear

B. Semilogarithmic

A. Linear graphs of drug-receptor binding for two drugs with different values of Kd. B. Semilogarithmic graphs of the same drug-receptor binding. Kd = equilibrium dissociation constant for a given drug-receptor interaction. A lower Kd indicates a tighter drug-receptor interaction (higher affinity). Drug A, which has the lower Kd, will bind a higher proportion of total receptors than Drug B at any given drug concentration. Notice that Kd corresponds to the ligand concentration [L] at which 50% of receptors are bound (occupied) by ligand. [L] is concentration of free (unbound) ligand (drug), [LR] is concentration of ligandreceptor complexes, and [Ro] is total concentration of occupied and unoccupied receptors. Thus, [LR] /[R0] is the fractional occupancy of receptors, or fraction of total receptors that are occupied (bound) by ligand. Principles of Pharmacology: The Pathophysiologic Basis of Drug Therapy Cairo CW, Simon JB, Golan DE. (Eds.); LLW 2012, Pgs. 17-27

Graded dose-response curves

A. Linear

B. Semilogarithmic

Graded dose-response curves demonstrate effect of a drug as a function of its concentration. A. Linear graphs of graded dose-response curves for two drugs. B. Semilogarithmic graphs of same dose-response curves. Note close resemblance to Ligand-receptor binding curves: fraction of occupied receptors [LR]/[R0] has been replaced by fractional effect E/Emax, where E is a quantifiable response to a drug . EC50 is potency of t drug, or concentration at which the drug elicits 50% of its maximal effect. In the figure, Drug A is more potent than Drug B because it elicits a half-maximal effect at a lower concentration than Drug B. Drugs A and B exhibit the same efficacy Note that potency and efficacy are not intrinsically related-a drug can be extremely potent but have little efficacy, and vice versa. Principles of Pharmacology: The Pathophysiologic Basis of Drug Therapy Cairo CW, Simon JB, Golan DE. (Eds.); LLW 2012, Pgs. 17-27

Therapeutic index (TI) Measurement of drug safety TI =

   

TD50 (median toxic dose) ED50 (median effective dose)

Therapeutic window is measure of clinical drug effectiveness for a patient Therapeutic Index = TD50 / ED50 Safer drugs have higher TI values Drugs with lower TI values include digoxin, lithium, theophylline, and warfarin LD50 (lethal median dose) often replaces TD50 in animal studies 18

Further study:  eNotes: GP- General Principles of Drug Action  Drug-Receptor Interactions, Morris ZS, Golan DE and (or)  Brody’s Human Pharmacology: Ch.1 Pharmacodynamics- Receptors and Concentration-Response Relationships  Enzyme kinetics Notes

 MedPharm Wiki| PK and PD, Pgs. 73-88  Pharmacology Course Website