Reaction Rate (Kinetics) Reaction Rate

Transcription

1 Instructor: Allan Felsot Fall 2 Reaction Rate (Kinetics) ES/RP 3 Fundamentals of Environmental Toxicology Lecture / Pharmacokinetics (Toxicokinetics) & Pharmacodynamics (Toxicodynamics) Part 2 Importance of metabolism in detoxification or activation of a toxicant depends on Capability of detox. enzymes for catalyzing the reaction Dependent on ability of toxicant to form a complex with the detox. enzyme Rate of reaction Faster reactions will increase the rate of elimination of the toxicant Less re-circulating to blood and tissues Reaction Rate Described by mathematical functions known as rate laws Describe the relationship between tim and the concentration of the toxicant Two commonly used functions Power rate law First-order rate equation yperbolic kinetics Michaelis-Menton Kinetics Linear Function Logarithmic Function Reaction Kinetics Rate Law = a mathematical function or differential equation describing the turnover rate of a compound as a function of the concentration Linearization of First-Order Function Power Rate Law Rate = "dc dt = kc n First Order when n = ln ln t = "kt + ln T /2 = ln2/k =.693/k K = rate constant (/day) d [ C ] t dt or =! k [ C ] [ C ] t = [ C ] e! kt Differential eq. Integrated eq. alf-life is independent of concentration

2 yperbolic Kinetics Rate = "dc dt = Rate of Reaction, k k C k 2 +C Enzyme or surface catalyzed. Rate slows down as increases. V max Velocity of Rx.. V max K K3 E + S ES E + P K2 K [S] V max V = [S] + K m Concentration of Chemical, or [S] K m Substrate Concentration Double Reciprocal Plot for Calculation of Vmax & Km /v Lineweaver-urk Plot Slope: K m /V max Practical Application of Michaelis-Menton Kinetics Disappearance of toxicant speeds up as concentration decreases below the level associated with Vmax or enzyme saturation. owever, at sufficiently low concentration, metabolism might slow again because of necessity for complexation before reaction moves toward the product side. Intercept: -/K m Intercept: /V max /[S] Elimination Excretion The Ultimate Fate Excretion Metabolic reactions result in more water soluble compounds, facilitating excretion Reduction in amount of parent compound available to target sites earance Volume of blood (or plasma) cleared of chemical per unit time Routes Expired air, saliva, bile, feces, urine, milk, hair Extent less important than rate All compounds eventually % excreted 2

3 Insects have Malpighian tubules that function analogously to kidneys 2,-D Excreted y Ground Applicators Activity & Total Dosage mix/load/apply 7.8 µg/kg µg/kg 3 mix/load µg/kg apply.9 µg/kg Days After Application Application Area Under the Curve (AUC) Gives Information About Whole ody Dose Adapted from Nash et al. 82 Toxicokinetics & Exposure Route ased on Nolan et al. (98) Tox. Appl. Pharm. 73:8 Chlorpyrifos Elimination rate can differ among different development stages Experiment by sin & Coats (986) Pestic. iochem. Physiol. 2:336 Corn Rootworm Adult Corn Rootworm Larva S P O N O O O isofenphos Metabolism and Excretion Influences Selectivity Corn Rootworm ours After Dosing with Isofenphos sin & Coats (986) Pestic. iochem. Physiol. 2:336 Storage Type of elimination mechanism Influenced by rate of metabolism and hydrophobicity Example: DDT Slow metabolic rate igh Kow Temporary mechanism in that chemical is released from storage sites Equilibrium between adipose tissue and blood Of concern for very recalcitrant compounds Concept of bioconcentration factor (ecotox.) Ratio of matrix (or food) concentration to concentration in an organism 3

4 Case Study Uptake, metabolism, and elimination of two hydrophobic contaminants by midge larvae Experiment from Lydy et al. (2) Arch. Environ. Contam. Toxicol. 38:63 Exposed midge larvae in water to either or 2-chlorobiphenyl (2-C) larva pupa adult WS: ~ µg/l Log Kow: ~.7 Nominal Water Concentration: 7.3 µg/l 2-chlorobiphenyl WS: ~9 µg/l Log Kow: ~.9 Nominal Water Concentration:. µg/l (nmol/g) Uptake Phase 2 Elimination Phase Modified from Lydy et al. (2) Arch. Environ. Contamin. Toxicol. 38: (h) 2-C (nmol/g) Uptake Phase Elimination Phase Modified from Lydy et al. (2) Arch. Environ. Contamin. Toxicol. 38:63-68 Total chemical (C) 2-C parent Polar metabolites (h) Two Compartment Toxicokinetic Model k u Uptake clearance coefficient Cp [parent compound in animal] Metabolite formation constant k m k ep Parent elimination rate constant Toxicokinetic Functions C a = k u * C w * t C a = total in midge C w = concentration in water K u = uptake clearance coefficient Modified from Lydy et al. (2) Arch. Environ. Contamin. Toxicol. 38:63-68 Cm [metabolites in animal] k em Metabolite elimination rate constant 2-chlorobiphenyl dctot/dt = (k u Cw) - (k ep Cp) - (k em Cm) Ctot = total 2-C residues in midge larvae

5 Modeling Results (Lydy et al. 2) Parameter 2-C K u (ml/g/h) K ep (h - ). K em (h - ).73 K m (h - ).3 CF Toxicokinetics & Plants All mechanisms & processes same as in animals owever, must consider dose transfer from the environment (ditto if considering aquatic and soil dwelling animals) Other parameters important Soil sorption coefficient (Koc) Air:water transfer coefficient (K ) T/2 (days).7 Conceptual Model of Relationships