Pharmacology – Exam 4

 

 

 

 

Pharmacokinetics à Antibiotics Video

Pharmacokinetics = study of movement of drug molecules

Used to predict à 

Drug Dissolution	Time of dosage to disintegrate/dissolve
Drug Absorption and Distribution	Amount of drug absorbed vs. time Time of onset to target tissues Duration in target tissues
Drug Excretion	How and when the dose will be excreted

 

 

 

 

 

 

 

Classes of molecules behave according to physical/chemical laws

Individual molecules behave randomly

àOverall clinical response results from total of individual random interactions

 

Transport across lipid membranes is the key

 

Path of drug once ingested:

Gut wall à Capillaries/veins/portal vein à liver à vena cava à heart (to lungs, back to heart) à systemic circulation

 

Liver

* May enter the Bile Duct instead (Biliary Cycle)

   àfrom the bile duct to the gall bladder and then back to the duodenum

   àOptions once in duodenum

1.       Excretion through gut

2.     Re-absorbed, then to systemic circulation

3.     Re-absorbed, then to biliary cycle again

* Biliary Cycle is NOT a major route for drug excretion

          the drug concentration in the gall bladder may be up to 50 mg/mL (for a 1 gram dose)

          only about 200 mL of bile is produced each day

          this results in only 10 mg excreted per 1 gram dose via this route

 

Systemic

*  Drug will react with or against encountered molecules

*  Drug may or may not reach target organ

*  Drug may be excreted intact/unchanged/unutilized

*  Crossing Cell Membranes

          small molecules can pass through small pores, large molecules need help

          alternatives for large molecules à

                   Never Cross:  oral anti-fungals are designed to stay in the gut and not diffuse

                   Actively Transported:  utilize enzyme systems (e.g., transferases)

                   Passively Diffuse:  dissolve through membrane (lipophilic)

 

Rate of Transport

*Ionizability à ionized molecules CANNOT cross the lipid membrane

*Lipophilicity à    molecules repelled by lipids (lipophobic) may never get in

                             molecules attracted to lipids (lipophilic) may never get out

                             lipophilic molecues will just accumulate in cell membrane or fatty tissue

*Protein Affinity à protein bound molecules are temporarily tied up and unavailable for transport

 

Rates are represented by K_A (rate of absorption) and K_E (rate of excretion)

          à thus, absorption is rate-dependant

Example: Incomplete absorption in the duodenum is the initiator of side effects

          diarrhea, super-infections, candidiasis, destruction of normal gut flora that may result from antibiotics

 

Partition Coefficient à K_D

          Ratio of drug concentration in lipid to drug concentration in water

          Higher K_D indicates a drug is more lipophilic

Drug A	KD = 10 (10:1 ratio)	Drug A is 100 times more lipophilic than Drug B
Drug B	KD = 0.1 (1:10 ratio)

          There is continual exchange across membranes (or phases)

                   The rate in/across, K₁, and the rate out/across, K₂, determine K_D à K₁∕K₂

                   For Drug A, K₁ is 10x faster than K₂ (K_D = 10)

                   For Drug B, K₂ is 10x faster than K₁ (K_D = 0.1)

          At any given time, the drug concentration on one side of a membrane depends on the rates K₁ and K₂

          Equilibrium is eventually established and the ratio across both layers of a membrane will be the same

          Following the examples of Drugs A and B, we can see their equilibrium concentrations from the duodenum to the blood

KD	Duodenum Concentration (water phase)	Membrane (lipid phase)	Blood Concentration (water phase)	Action Into Membrane
Drug A = 10	1	10	1	Moves in quickly Stays in
Drug B = 0.1	10	1	10	Moves in slowly Rushes out

 

          An ideal drug is on that is lipophilic enough to get into the cell membrane and hydrophilic enough to get out

          Fortunately, there are determinants other than K_D that direct molecules into the blood…

 

Protein Affinity à molecules are bound to blood proteins (e.g., albumin), and are unable to cross the membrane

In general, á lipophilicity results in á protein binding

Donan Effect à reduced number of available (diffusible) molecules on one side of a membrane (due to protein-bound molecules) creates a vacuum of sorts on that side, pulling more across the membrane to re-establish equilibrium

          Protein-Binding creates a reservoir of potentially available drugs for tissue distribution

                   It does NOT inactivate the drug (as many people incorrectly think)

                   As non-bound molecules are used up, more molecules are released from protein to maintain equilibrium

Ionizability à drug molecules are ionized under specific conditions (remember, only non-ionized molecules can cross lipid membranes)

          pH greatly determines a molecules potential to ionize

          Acidic molecules do not ionize in acid (most antibiotics are acidic)

                   For these, the greater the pH (more alkaline, more basic), the greater tendency to ionize

          *An acid antibiotic will remain intact/non-ionized/undissolved in the stomach where pH = 2

          *In the duodenum where pH = 6 (only slightly acidic), the proportions of ionized and non-ionized are approximately equal

          *In the blood, pH = 7.4 (slightly alkaline) which induces two things:

                   1à a large portion of lipophilic, non-ionized molecules are ionized upon entering the blood

2à a Donan Effect is set up (reduced non-ionized molecules in the blood compared to the duodenum pulls more non-ionized molecules into the blood)

          Ionizability, similar to protein-binding, represents a reservoir of potentially available drug for tissue

 

Note: Drug is absorbed only from a short segment of the duodenum because of the pH.  The pH of the gut gets more alkaline which increases the amount of ionization which in turn decreases membrane transport from the gut.

 

Distribution to tissues depends largely on pH, as most tissues have a different pH range.

It also depends on blood flowà poor flow = poor distribution

 

Excretion depends on the same variables.

          Protein-bound molecules will not be filtered out in the glomerulus, thus remaining in the blood

          Only small, non-bound (meaning non-lipophilic and ionized) molecules are filtered out, into the tubule

                   àthis represents unused molecules that were not distributed during circulation through the blood

                   àthe protein-bound reservoir still remains, although the bound amount will â as equilibrium is re-established

          From the tubule, the drug may be excreted or resorbed (recycled)

          pH of the urine determines the amount of drug that is recycled

àDiets high in acidifying foods (oranges, vitamin C, etc) or high in carbohydrates will lower the pH of the urine and prevent/reverse ionization of antibiotics in the tubule and thus allow for resorption/recycling of the filtered drug

àDiets high in protein or in alkalizing agents will raise the pH of the urine and enhance ionization of antibiotics in the tubule and prevent resorption (more excretion of drug and less recycling)

          Penicillins are actively removed from the blood by transport enzymes

                   When the enzymes are transporting penicillin they are not transporting the normal intended molecules

                   For penicillin, probenecid competes for the active site on the enzyme

àthis reduces the amount of penicillin excreted in this manner

          Some drug is excreted through the feces due to higher pH (8 or 9) in the lower gut

 

Weights and Measures

Weight in grams (g or gm)

Volume in liters (l  or L)

giga (G)	109	= billion
mega (M)	106	= million
kilo (k)	103	= thousand
deci (d)	10-1	= tenth
centi (c)	10-2	= hundredth
milli (m)	10-3	= thousandth
micro (m or mc)	10-6	= millionth
nano (n)	10-9	= billionth
pico (p)	10-12	= trillionth

Rules for conversions

          If the unit changes to a larger unit (milli to deci) the number gets smaller (100 mm = 1 dm)

          If the unit changes to a smaller unit (milli to nano) the number gets larger (1 mm = 1,000,000 nm)

 

          1 kg = 2.2 lbs

          1 lb = 0.454 kg

         

          1 L = 1.06 qt

          1 gal = 4 qt

          1 pint = ½ qt

 

          1 mL = 1 cm³ = 1 cc

          1 mL of water = 1 g (1 L = 1 kg, 1 pint = 1 lb)

 

Concentration Units

          % à a weight to volume (w/v) ratio

                   defined relative to density of pure water à 100% = 1 g/mL

                   thus, 40% = 40 g / 100 mL à 0.4 g/mL or 400 mg/mL

          may also be written as 1:100 which equals 1%

          1:100,000 = 1g/10⁵mL, which is the same as 10^-5g/1mL, which is the same as 10mg/mL or 0.001% or 1mg%

 

Dose Response Curves and Population-Response Curves

Some definitions:

Dose à total concentration of drug present in the body, or amount administered to patient

Association constant à or drug-receptor affinity constant or equilibrium binding constant, K_eq

          Higher K_eq gives stronger receptor-binding, lower K_eq gives less receptor-binding

Dissociation constant à K_d = 1/ K_eq.  K_d is the value of [D] at which 50% of the receptors are occupied by drug

Receptor-occupation curve à shows the percent of receptors occupied as a function of the amount of drug present

Dose-response curve à shows the pharmacological response of a subject as a function of the amount of drug present

A pharmacologic response is directly proportional to the number of receptors that are bound to/occupied to/complexed with the drug molecules

ED₅₀ à the dose that produces a half-maximal response and equals K_d for the receptor mechanism

 

At low drug concentrations, fewer receptor sites are occupied, thus a decreased response

At higher drug concentrations, more receptor sites are occupied, thus an increased response

          There is a maximum saturation point of receptors above which increasing the concentration has no increased effect

Binding is reversible and described by the equation

          D = drug molecule, R = receptor, and DR = drug-receptor complex

The affinity for the drug to bind to the receptor is indicated by the drug-receptor affinity constant, K_eq (equilibrium constant)

A higher K_eq indicates that D binds very strongly to R (more DR)

A lower K_eq indicates that D does not bind very well to R (less DR)

K_eq is described by the following equation:

 

It is always true that the total number of receptors in the body, [R]_total = [R] + [DR], as some receptors are bound and others are not.

The values for [DR] and [R] may vary depending on the amount of drug present, but [R]_total remains constant

 

The relationship between [DR] and [D] of a given drug will indicate how the pharmacological response relates to the drug dose.

Manipulating the above equations will allow for the formation of the following equation:

from which a receptor-occupation curve and a dose-response curve is plotted (see handout for actual plots)

 

At low [D], receptor occupation goes to zero

At high [D], receptor occupation saturates at 100%

When [D] = 1/K_eq, then half of the receptors are bound

          Strong binding (high K_eq) reaches 50% occupancy at lower [D] (less of a dose)

          1/ K_eq is also referred to as the dissociation constant, K_d

          50% saturation, and 50% dissociation is achieved when [D] = K_d

          The effective dose for 50% of maximal response, or ED₅₀ is the value of [D] that causes 50% saturation

                   Therefore, ED₅₀ = K_d

 

More definitions:

Potency à relative measure of the dose of a drug required to produce a given response, and is inversely proportional to the dose

          The higher the required dose, the less potent the drug

          The lower the required dose, the more potent the drug

          Measured on the x-axis of the dose-response curve (log[D] values)

          á K_d results in â potency

increasing K_d shifts the curve to the right on the x-axis

this indicates that more drug is needed to achieve half-maximal response

since more drug is needed, it is less potent

Efficacy à relative measure of the response produced when a drug occupies a receptor

          Also called the intrinsic activity of the drug à does it do what it is supposed to do?

          Measures maximal response when all receptors are occupied (ceiling of activity)

          Measured on the y-axis of the dose-response curve

          A “higher” curve along the y-axis indicates a greater maximal response and thus a greater efficacy

 

Population-Response Curves

The susceptibility of a patient to a drug varies among individuals (varying K_d, intrinsic activity, etc.)

Because of biological variation, a population displays a log-normal distribution of drug sensitivities

These curves are quantal, in that they represent an all-or-none response (whereas the dose-response curves are graded)

Median effective dose, ED₅₀, is that dose required to produce the specific effect (unconsciousness) in half the population

          Other doses, ED₁₀ and ED₉₀, represent the same response for different percentages of the population

          The closer these values are to the ED₅₀, the less variation there is in response of the population to the drug (á predictability)

          ED₅₀ is also called the median effective therapeutic dose

Another quantal effect is death and is measured as the median lethal dose, or LD₅₀

Drug safety is determined by comparing LD₅₀ to ED₅₀

          The higher the LD₅₀ is compared to ED₅₀, the safer the drug is…

The ratio LD₅₀/ ED₅₀ is called the therapeutic index (TI)

          A higher TI is preferred à generally around 10

          Drugs with lower TI (general anesthetics are around 2) require special monitoring procedures

In some instances ED₉₀ will overlap with LD₁, and while 90% would lose consciousness, 1% would die

The certain safety factor (CSF) is the ratio LD₁/ ED₉₉ describes this overlap region

          It is desirable to have a CSF > 1 which indicates little or no overlap and suggests the drug is safe

 

More definitions:

Graded-response curve à response continually changes as the dose changes

          Also known as a dose-response curve

Quantal-response curve à change in the dosage within a population to elicit the same response

          Also known as a population-response curve

ED₅₀ à mean effective dose; dose required to produce a given effect in 50% of the population

          Can also have ED₁₀ and ED₅₀

LD₅₀ à median lethal dose; dose of the drug that will kill 50% of the population

Therapeutic Index àTI; LD₅₀/ED₅₀

Certain Safety Factor à CSF; LD₁/ED₉₉

 

 

Effect of pH on Drug Kinetics

Strong acids (proton donors) are always fully ionized

Weak acids and weak bases are only partially ionized

 

The following reactions describe the behavior of acids and bases

         

         

 

When considering the available form of a drug it is the non-ionized (or free) form

          AH is the free form of the acid

          B is the free form of the base

          These are also known as the permeant forms (able to cross the lipid membrane)

 

An á in pH (less H⁺ in the solution) causes a shift to the right for both equations  à these are basic solutions

          The effect is more free (available) base, and less free (available) acid

A â in pH (more H+ in the solution) causes a shift to the left for both equations  à these are acidic solutions

          The effect is less free (available) base, and more free (available) acid

 

K_a is the dissociation constant for each acid and base

          Measures how easily a molecule can donate protons (acids) or accept protons (bases) à become ionized

pK_a is the log value of K_a

          the lower the pK_a of an acid, the more it is ionized (unavailable)

          the higher the pK_a of a base, the more it is ionized (unavailable)

 

Henderson-Hasselbalch Equations

These are extremely important in pharmacology

à they allow a calculation of how much of the drug is permeant (non-ionized) and how much is non-permeant (ionized), as long as the pK_a and pH are known

For acids:

 

 

For bases:

 

 

A more useful quantity is the fraction/percent of total drug that is in one form or the other

          Acid:                                         Base: 

 

 

 

For a weak acid…

If pH > pK_a, then the ionic (non-permeant) form dominates

          If pH < pK_a, then the neutral (permeant) form dominates

          If pH = pK_a, then the forms are in equilibrium

          Remember, for the permeant form of an acid, the pH must be lower than the pK_a (more acidic)

For a weak base…

If pH < pK_a, then the ionic (non-permeant) form dominates

          If pH > pK_a, then the neutral (permeant) form dominates

          If pH = pK_a, then the forms are in equilibrium

          Remember, for the permeant form of a base, the pH must be higher than the pK_a (more basic)

 

It does not matter what the actual values are, but only the difference between pH and pK_a

Keys to solving problems:

1)      know whether the drug is an acid or a base

2)    know the pK_a of the drug

3)    know the pH of the body fluid where the drug is located

 

Equilibration of drugs across membranes follows this ruleà drugs accumulate where they are more ionized (non-permeant)

          Weak acids accumulate where it is more alkaline

          Weak bases accumulate where it is more acidic

          This is purely a passive processà no energy required (driven only by the pH gradient)

 

 

Kinetics of Drug Accumulation and Disappearance

Elimination of a drug is due to redistribution, metabolism, and excretion, and follows either zero-order kinetics or first-order kinetics

Zero-order à drug is eliminated at a constant amount over time

          C(t) = C₀ – k₀t represents zero-order kinetics

                    C(t) is the concentration at any time, t

                   C₀ is the peak concentration

                   k₀ is the rate constant

                   t is the amount of time since administration of the drug

          Alcohol is an example of a drug that is eliminated at a constant rate

First-order à drug is eliminated at a constant fraction over time (exponential decay)

          C(t) = C₀e^-kt represents first-order kinetics

                   C(t) is the concentration at any time, t

                   C₀ is the peak concentration

                   k is the first order rate constant

                   t is the amount of time since administration of the drug

          The time at which the drug concentration is one-half of its initial value is known as the biologic or plasma half-life (t_1/2)

          *Each drug has a unique t_1/2

          *Pharmacologic half-life is similar and refers to the time required for one-half of the pharmacologic response to decay

                   For reversible-receptor mechanisms, pharmacologic t_1/2 = plasma t_1/2

          *Method of drug administration affects the magnitude of C₀, but does not affect t_1/2

          *t_1/2 is independent of the initial concentration

          *The first-order rate constant, k, can be derived from the exponential decay equation…

                   k = 0.69/t_1/2

 

Multi-dosing and Drug Accumulation

Often a dose is administered repeatedly at equal time intervals (t_d is the dosing interval)

The drug accumulates in the plasma as the concentration rises further above C₀ with each dose

The concentration will eventually reach a maximal value (does not increase with additional doses)

          As C increases so does the amount eliminated during t_d (first-order kinetics)

          Eventually, the amount eliminated during t_d is equal to the single dose (no further accumulation)

          This is known as the maintenance or plateau state

          The concentration will have the same maximum and same minimum as the doses continue

 

Maintenance State Equation

          Dose = C_max(1-e^-ktd)

If any three of the four variables are known, the fourth can be found

A special case exists when td = t1/2

          Dose = ½C_max

 

Time to Reach Plateau State

The Plateau Principle shows that the accumulation half-time is equal to the elimination half-time

The amount of time to reach the plateau for therapeutic purposes is generally considered to be 4 half-lives

 

Loading Dose

An initial dose (loading or priming) which is larger than the maintenance dose in order to achieve plateau state more quickly

Only indicated when the TI is high (large margin of safety)

Example: Suppose tetracycline is to be loaded in two equal doses with t_d = 6 hours.  What are the loading and maintenance doses, if a peak maintenance level of 500 mg is desired?

          In this case t_d = t_1/2 = 6 hours, therefore the maintenance dose = ½C_max or ½(500) = 250 mg

          At the initial dose, the concentration is C_L

          After t_d, the concentration is ½ C_L, at which time the second loading dose is applied for a total of 3/2 C_L (½C_L + 1 C_L)

          The purpose of loading doses is to reach C_max quickly, so then here 3/2C_L = 500 mg

          Solving for C_L gives a loading dose of 333 mg

 

 

Asthma and COPD Drugs

COPD à chronic obstructive pulmonary disease

          Includes chronic obstructive bronchitis and emphysema

          Characterized by airflow limitation that is not fully reversible

          Symptoms include shortness of breath, cough, wheezing, and increased sputum production

 

 

 

 

Anti-Parkinson’s Disease Drugs

 

 

 

 

Gastrointestinal Drugs

 

 

 

 

Emergency Kit Drugs