A carrier molecule is involved in the transport of the drug across the membrane. This carriers can be very specific for a particular drug or a group of drugs. Carrier-mediated transport systems are saturable. This means that the rate of drug transport increases as the drug concentration increases until it reaches a plateau at very high drug concentration.
Carrier-mediated transport can be active transport where the drug is transported against the concentration gradient, i.e. from lower concentration to higher concentration. The active transport process requires energy.
The other kind of carrier-mediated transport is facilitated diffusion where drug transport is from higher concentration to lower concentration. The facilitated diffusion process does not require energy.
A zero-order process is a process that has a constant rate. The rate of the zero-order process does not depend on the amount of the reactant involved in the process.
If the elimination of a drug follows zero-order kinetics, this means that there is a constant amount of the drug eliminated per unit time, regardless of the administered dose.
Because the rate of drug elimination is constant (zero-order kinetics) the fraction of the dose eliminated per unit time after administration of a large dose, is much smaller than the fraction of the dose eliminated per unit time after administration of smaller doses.