Enzyme Kinetics and Inhibition

Comprehensive vocabulary flashcards covering chemical kinetics, Michaelis-Menten enzyme kinetics, kinetic parameters, linear graphical transformations, and reversible and irreversible inhibition mechanisms.

Chemical Kinetics

The study of the rate of chemical reactions and a tool used to evaluate reaction mechanisms by characterizing the individual steps occurring along a reaction pathway.

Thermodynamics

The science relating the energy of a system to its distance from equilibrium, used to determine equilibrium constants and whether a reaction is spontaneous, but providing no information about reaction pathways or individual steps.

Elementary Reaction

A single step occurring at the molecular level with one or more intermediates whose characterization describes the reaction mechanism.

Molecularity

The number of reacting molecules involved in each elementary step of a chemical reaction, classified as unimolecular (one reactant), bimolecular (two reactants), or termolecular (three reactants).

Reaction Rate (Velocity)

The change in concentration of a reactant or product as a function of time, expressed in units of $\text{concentration}/\text{time}$ such as $M/s$, $mM/s$, or $\mu M/\min$.

Rate Equation

An expression relating reaction rate to reactant concentrations raised to specific powers, defined generally as $\text{Rate} = k[A]^a[B]^b[C]^c$.

Order of the Reaction ($n$)

The sum of the exponents in the rate equation ($n = a + b + c$), determining how the overall rate depends on reactant concentrations.

Rate Constant ($k$)

The proportionality constant in a rate equation that remains constant at a given temperature and has units of $[\text{concentration}]^{(1-n)}[\text{time}]^{-1}$.

Zero-Order Kinetics

A kinetic regime where the rate of product formation is independent of reactant concentration ($v = k[A]^0 = k$), described by the integrated rate law $[A] = [A_0] - kt$.

Heterogeneous Catalysis

Catalysis where the catalyst is a solid and reactants are dissolved in solvent; zero-order kinetics occur because the solid catalyst contains orders of magnitude more binding sites than reactant molecules.

First-Order Kinetics

A reaction pathway where rate depends linearly on reactant concentration ($v = k[A]$), resulting in an exponential decay of reactant ($[A] = [A_0]e^{-kt}$) and an exponential rise to maximum of product ($[P] = [A_0](1 - e^{-kt})$).

Half-Life ($t_{1/2}$)

The time required to consume half of the initial reactant concentration; for a first-order reaction, it is constant and equal to $\frac{\ln(2)}{k} = \frac{0.693}{k}$.

Initial Velocity Conditions

Experimental constraints used to simplify enzyme kinetic calculations: $[E_0] \ll [S]$, initial $[P] = 0$, only measuring the first few turnovers so $[S]$ remains constant, and holding temperature, pressure, pH, and ionic strength constant.

Rapid Equilibrium Assumption

A kinetic assumption where substrate binding and dissociation are significantly faster than chemical conversion to products ($k_2 \gg k_3$), allowing the first step to be defined by the equilibrium constant $K_S = \frac{k_2}{k_1} = \frac{[E][S]}{[ES]}$.

Presteady State

The brief initial period lasting a few milliseconds after initiating an enzyme-catalyzed reaction during which enzyme-substrate intermediates build up to stable concentrations.

Steady State

The phase of an enzyme-catalyzed reaction following the presteady state where the concentration of the enzyme-substrate complex remains constant ($\frac{d[ES]}{dt} = 0$) until substrate is exhausted.

Michaelis-Menten Equation

The fundamental mathematical equation $v = \frac{V_{\max}[S]}{K_m + [S]}$ describing the hyperbolic curve of initial reaction velocity as a function of substrate concentration.

Michaelis Constant ($K_m$)

The apparent dissociation constant defined as $K_m = \frac{k_2 + k_3}{k_1}$, which equals the specific substrate concentration required to achieve half of the maximal velocity ($\frac{1}{2}V_{\max}$).

Maximal Velocity ($V_{\max}$)

The theoretical maximum reaction rate achieved when the enzyme active sites are completely saturated with substrate ($V_{\max} = k_3[E_0]$ in the simplest model), representing the horizontal asymptote on a Michaelis-Menten plot.

Turnover Number ($k_{\text{cat}}$)

A concentration-independent parameter calculated as $k_{\text{cat}} = \frac{V_{\max}}{[E_0]}$ with units of $\text{time}^{-1}$, representing the number of substrate molecules converted to product per enzyme active site per unit time.

Specificity Constant ($k_{\text{cat}}/K_m$)

The apparent second-order rate constant with units of $M^{-1}s^{-1}$ that measures an enzyme's catalytic efficiency at low substrate concentrations ($[S] \ll K_m$), capped by the diffusion-controlled limit of $10^9\,M^{-1}s^{-1}$.

Lineweaver-Burk Plot

A double reciprocal linear transformation of the Michaelis-Menten equation ($\frac{1}{v}$ vs $\frac{1}{[S]}$) with a slope of $\frac{K_m}{V_{\max}}$, a y-intercept of $\frac{1}{V_{\max}}$, and an x-intercept of $-\frac{1}{K_m}$.

Reversible Inhibitors

Molecules that bind noncovalently to enzymes, readily associating and dissociating, classified into competitive, uncompetitive, pure noncompetitive, and mixed noncompetitive types.

Competitive Inhibitor

A reversible inhibitor that competes directly with substrate for the free enzyme's active site, increasing apparent $K_m$ while leaving $V_{\max}$ unchanged, whose Lineweaver-Burk plots intersect at a common y-intercept ($\frac{1}{V_{\max}}$).

Benzamidine

A competitive inhibitor of trypsin that fits into the enzyme's specificity pocket and binds to Asp 189, competing directly with the arginine side chain of polypeptide substrates.

Pure Noncompetitive Inhibitor

A reversible inhibitor that binds to a separate site on both free enzyme ($E$) and enzyme-substrate complex ($ES$) with equal affinity ($K_i = K_i'$), reducing apparent $V_{\max}$ while leaving $K_m$ unchanged, intersecting at $-1/K_m$ on a Lineweaver-Burk plot.

Mixed Noncompetitive Inhibitor

A reversible inhibitor that binds to an allosteric or distinct site on both $E$ and $ES$ with unequal affinities ($K_i \neq K_i'$), causing changes in both apparent $V_{\max}$ and apparent $K_m$.

Uncompetitive Inhibitor

A reversible inhibitor that binds exclusively to the enzyme-substrate complex ($ES$) and not free enzyme, reducing both apparent $V_{\max}$ and apparent $K_m$ by the same proportion to produce parallel lines on a Lineweaver-Burk plot.

Irreversible Inhibitor

An inhibitor that covalently inactivates an enzyme, decreasing the concentration of active sites; distinguished experimentally from noncompetitive inhibition by time-dependent loss of activity and failure of dialysis to restore function.

Iodoacetamide

An irreversible enzyme inhibitor that covalently alkylates the catalytic sulfhydryl group ($-SH$) of active-site cysteine residues, releasing $I^-$ and $H^+$ and permanently destroying enzymatic activity.