Lecture 8 - Kinetics

CHE-30010 Lecture 8 - Natalie 11/02/2021 Kinetics For many chemical processes, the rate at which a chemical is processed is proportional to the concentration of the chemical – first order kinetics. Metabolism is often a first order process – the rate at which the drug is metabolised is proportional to the concentration of the drug, indications of foul play. Rate of loss (metabolism) = k[C]1 Where k = rate constant, exponent (order) = 1 with [] meaning the concentration. Rate of loss = positive Rate of reaction = negative On a graph, the rate of change can be seen as the slope of the line at a particular point – found taking the tangent of the curve. From the rate equation, the equation relating the concentration with time can be derived. 𝑪 = 𝑪𝟎 𝒆(−𝒌𝒕) CO = amount ingested so initial concentration. If we know what C0 is, we can calculate what C is at any time, if the rate constant K is known. The concentration will get smaller but would take forever in order to reach zero. CHE-30010 Lecture 8 - Natalie 11/02/2021 Manipulation in order to get an equation which links concentration and time. A = constant of integration Can also calculate time of ingestion or is a dose was poisonous and was a potential cause of death. First order kinetics Determine the rate at any point with a tangent but is not the most accurate. Linearising the equation (natural logs to remove the e factor) gives a straight line. Linearisation -> lnC = -kt + ln(C0) Follows the equation of a straight line graph y = mx + c Gradient = -K Intercept = ln(C0) Half-life For first order kinetics, the concept of half-life is useful time to reach half of its initial concentration in the body, with each drug having a different value. First order kinetics – independent of concentration, so is constant throughout the metabolic process. CHE-30010 Lecture 8 - Natalie 11/02/2021 Worked example A person has taken codeine tablets. The peak plasma concentration of codeine is found to be 0.2 mg/L and was reached after 30 minutes. If t1/2 = 2 hours, how long will it take after this before the plasma level of codeine falls below the limit of detection (LOD) for codeine of 2.0 ppb using a particular mass spectrometric method? Convert 2.0 ppb into mg/L so all concentrations are in the same units. 1 ppb = 1 µg of substance per kg (solid) or L (liquid). Divide by 1000 to convert from µg to mg. 2.0 ppb = 2.0 µ/L = 0.002 mg/L C = C0 x e(-kt) C = 0.002 mg/L C0 = 0.2 mg/L T = what we want to know K = unknown Assume it is a first order reaction, unless told otherwise. T ½ = (ln2)/K T ½ = 2 hours K = (ln2) / 2 hours K = 0.347 hour-1 C = C0 x e(-kt) 0.002 = 0.2 X e(-0.347 X t) Divide by 0.2: 0.01 = e(-0.347 X t) Remove e: ln(0.01) = -0.347t Divide by -0.347: ln(0.01)/-0.347 = t t = 13.27 hours Saturation – zero order kinetics For very high doses of drugs, the amount of material present may overwhelm the enzymes (and/or cofactors) responsible for processing them. In these cases, the metabolic process is saturated. The maximum rate of elimination is determined by the total amount of enzyme/cofactor. The drug molecules have to “wait their turn” for an enzyme to become available. CHE-30010 Lecture 8 - Natalie 11/02/2021 Starts first order with respect to the concentration of the drug, but then becomes saturated so is a pseudo zero order kinetic process with respect to the drug – independent of concentration. Basis for why we administer ethanol to those who have antifreeze poisoning to prevent the toxic metabolites. If overwhelmed, ethanol is metabolised first by this pathway as ethanol binds to the enzymes more effectively and the antifreeze isn’t metabolised further so bypasses the toxic metabolites. With saturation, the drug will follow zero-order kinetics (fixed elimination rate) until the concentration falls below the saturation point. An example is that zero order kinetics are observed when greater than 800 mg of aspirin is present in the body, but below that, first order kinetics resumes. Zero order rate of elimination = k [D]0 = k Therefore, rate is independent of concentration.