Carriermediated Transport

Some drugs move into or out of cells against a concentration gradient, i.e. by active transport. These processes involve endogenous molecules, expend cellular energy and are more rapid than transfer by diffusion. The mechanisms show a high degree of specificity for particular compounds because they have evolved from biological needs for the uptake of essential nutrients or elimination of metabolic products. Thus, drugs that are subject to them bear some structural resemblance to natural constituents of the body. Examples of active transport systems are the absorption of iron by the gut, levodopa across the blood-brain barrier and the secretion of many organic acids and bases by renal tubular and biliary duct cells. Carrier-mediated transport that does not require energy is called facilitated diffusion, e.g. vitamin B12 absorption; carrier-mediated transport is subject to saturation and can be inhibited.

The order of reaction or process

In the body, drug molecules cross cell membranes, are transported across cells, and many are altered by being metabolised. These movements and changes involve interaction with membranes, carrier proteins and enzymes, either as individual chemical reactions or as processes. The rate at which these movements or changes can take place is subject to important influences that are referred to as the order of reaction or process. In biology generally, two orders of such reactions are recognised, and are summarised as follows:

• First-order processes by which a constant fraction of drug is transported/metabolised in unit time.

• Zero-order processes by which a constant amount of drug is transported/metabolised in unit time.

FIRST-ORDER (EXPONENTIAL) PROCESSES

In the majority of instances the rates at which absorption, distribution, metabolism and excretion of a drug occur are directly proportional to its concentration in the body. In other words, transfer of drug across a cell membrane or formation of a metabolite is high at high concentrations and falls in direct proportion to be low at low concentrations (an exponential relationship). This is because the processes follow the Law of Mass Action, which states that the rate of reaction is directly proportional to the active masses of reacting substances. In other words, at high concentrations, there are more opportunities for crowded molecules to interact with each other or to cross cell membranes than at low, uncrowded concentrations. Processes for which rate of reaction is proportional to concentration are called first-order.

In doses used clinically, most drugs are subject to first-order processes of absorption, distribution, metabolism and elimination. The knowledge that a drug exhibits first-order kinetics is useful. This chapter later illustrates how the rate of elimination of a drug from the plasma falls as the concentration in plasma falls and the time for any plasma concentration to fall by 50% (t^, the plasma halflife) will always be the same. Thus it becomes possible to quote a constant value for the t/, of the drug. This occurs because rate and concentration are in proportion, i.e. the process obeys first-order kinetics. The important calculations that depend on knowing t/2, i.e. time to eliminate a drug, time to achieve steady-state plasma concentration, and the construction of dosing schedules, will be correct when the order of reactions involved is known and, in the present case, are first-order.

Zero-order processes (saturation kinetics)

As the amount of drug in the body rises, any metabolic reactions or processes that have limited capacity become saturated. In other words, the rate of the process reaches a maximum amount at which it stays constant, e.g. due to limited activity of an enzyme, and further increase in rate is impossible despite an increase in the dose of drug. Clearly, these are circumstances in which the rate of reaction is no longer proportional to dose, and processes that exhibit this type of kinetics are described as rate-limited or dose-dependent or zero-order or as showing saturation kinetics. In practice enzymemediated metabolic reactions are the most likely to show rate-limitation because the amount of enzyme present is finite and can become saturated. Passive diffusion does not become saturated. There are some important consequences of zero-order kinetics.

Alcohol (ethanol) (see also p. 178) is a drug whose kinetics has considerable implications for society as well as for the individual, as follows.

Alcohol is subject to first-order kinetics with a t'/2 of about one hour at plasma concentrations below 10 mg/dl [attained after drinking about two-thirds of a unit (glass) of wine or beer]. Above this concentration the main enzyme (alcohol dehydrogenase) that converts the alcohol into acetaldehyde approaches and then reaches saturation, at which point alcohol metabolism cannot proceed any faster. Thus if the subject continues to drink, the blood alcohol concentration rises disproportionately, for the rate of metabolism remains the same (at about 10 ml or 8 g/h for a 70 kg man), i.e. a constant amount is metabolised in unit time, and alcohol shows zero-order kinetics.

Consider a man of average size whose life is unhappy to a degree where he drinks about half (375 ml) a standard bottle of whisky (40% alcohol), i.e. 150 ml of alcohol, over a short period, absorbs it and goes very drunk to bed at midnight with a blood alcohol concentration of about 250 mg/dl. If alcohol metabolism were subject to first-order kinetics, with a half-life (t/2) of one hour throughout the whole range of social consumption, the subject would halve his blood alcohol concentration each hour (see Fig. 7.2) and it is easy to calculate that, when he drove his car to work at 08.00 h the next morning, he would have a negligible blood alcohol concentration (less than 1 mg/dl); though, no doubt, a severe hangover might reduce his driving skill.

But at these high concentrations, alcohol is subject to zero-order kinetics and so, metabolising about 10 ml of alcohol per hour, after 8 h the subject will have eliminated 80 ml, leaving 70 ml in his body and giving a blood concentration of about 120 mg/dl. At this level his driving skill would be seriously impaired. The subject could have an accident and be convicted of drunk driving on his way to work despite his indignant protests that the blood or breath alcohol determination must be faulty since he has not touched a drop since midnight. He would be banned from the road, and thus have leisure to reflect on the difference between firstorder and zero-order kinetics.

This is an example thought up for this occasion, although no doubt something close to it happens in real life often enough, but an example important in therapeutics is provided by phenytoin. At low doses the elimination of phenytoin proceeds as a firstorder process and as dose is increased there is a directly proportional increase in the steady-state plasma concentration because elimination increases to match the increase in dose. But gradually the enzymatic elimination process approaches and reaches saturation, attaining a maximum rate beyond which it cannot increase; the process has become constant and zero-order. Since further increases in dose cannot be matched by increase in the rate of metabolism the plasma concentration rises steeply and disproportionately, with danger of toxicity. Salicylate metabolism also exhibits saturation kinetics but at high therapeutic doses. Clearly saturation kinetics is a significant factor in delay in recovery from drug overdose, e.g. with aspirin or phenytoin.

When a drug is subject to first-order kinetics and by definition the rate of elimination is proportional to plasma concentration, then the t\ is a constant characteristic, i.e. a constant value can be quoted throughout the plasma concentration range (accepting that there will be variation in t1/, between individuals), and this is convenient. If the rate of a process, e.g. removal from the plasma by metabolism, is not directly proportional to plasma concentration, then the t^ cannot be constant. Consequently, when a drug exhibits zero-order elimination kinetics no single value for its t\ can be quoted for, in fact, t/2 decreases as plasma concentration falls and the calculations on elimination and dosing that are so easy with first-order elimination (see below) become too complicated to be of much practical use.

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