Chapter 8: Kinetics and Regulation

Vocabulary practice flashcards covering enzyme kinetics, the Michaelis–Menten model, Lineweaver–Burk analysis, allosteric regulation, concerted and sequential models, and single-molecule enzyme studies.

Enzyme Kinetics

The study of the rates of chemical reactions catalyzed by enzymes.

Reaction Velocity ($V$)

The quantity of reactant that disappears (or quantity of product that appears) per specified unit of time $t$, defined mathematically as $V = -\frac{d[A]}{dt} = \frac{d[P]}{dt}$.

Rate Constant ($k$)

The proportionality constant that directly relates the reaction velocity to the concentration of reactants in a rate equation, such as in $V = k[A]$.

First-Order Reaction

A reaction in which the velocity is directly proportional to a single reactant concentration, having rate constants expressed in units of $s^{-1}$.

Second-Order Reaction

A bimolecular reaction involving two reactants, characterized by rate constants with units of $M^{-1}s^{-1}$.

Initial Velocity ($V_0$)

The number of moles of product formed per second shortly after a reaction has begun, measured before significant substrate depletion or product inhibition occurs.

Michaelis–Menten Equation

An equation describing enzyme activity as a function of substrate concentration: $V_0 = V_{\max}\frac{[S]}{[S] + K_M}$.

Michaelis Constant ($K_M$)

The substrate concentration at which reaction velocity reaches half its maximal value ($V_{\max}/2$); it describes the affinity of the enzyme–substrate interaction independently of enzyme concentration.

Maximal Velocity ($V_{\max}$)

The theoretical maximum catalytic velocity attained when all active sites of the total enzyme ($[E]_T$) are fully saturated with substrate, defined as $V_{\max} = k_2[E]_T$.

Zero-Order Kinetics

The kinetic regime occurring when an enzyme is fully saturated with substrate ($[S] \gg K_M$), causing the reaction rate to equal $V_{\max}$ and become independent of further additions of substrate.

Maud Menten

Pioneering Canadian physician and scientist who co-developed the Michaelis–Menten model, invented a histochemical assay for alkaline phosphatase, and pioneered protein electrophoresis.

Aldehyde Dehydrogenase

A liver enzyme that processes acetaldehyde into acetate; individuals prone to alcohol flushing possess an inactive mitochondrial low-$K_M$ isozyme and rely solely on a cytoplasmic high-$K_M$ form.

Lineweaver–Burk Plot

A double-reciprocal plot of $1/V_0$ versus $1/[S]$ featuring a straight line with a y-intercept of $1/V_{\max}$, a slope of $K_M/V_{\max}$, and an x-intercept of $-1/K_M$.

Penicillinase

A $29.6\,\text{kDa}$ enzyme (also called $\beta$-lactamase) present in resistant bacteria like Staphylococcus aureus that hydrolyzes and inactivates penicillin.

Elasticity

The sensitivity of an enzyme's catalytic activity to changes in substrate concentration, which is highest when substrate concentration is approximately equal to $K_M$.

Turnover Number ($k_{\text{cat}}$; $k_2$)

The number of substrate molecules converted into product per active site per unit time when the enzyme is fully saturated with substrate, calculated as $k_{\text{cat}} = \frac{V_{\max}}{[E]_T}$.

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

A second-order rate constant measuring catalytic efficiency when $[S] \ll K_M$, accounting for both the rate of catalysis and enzyme-substrate interaction up to the diffusion-controlled limit of $10^8\text{--}10^9\,M^{-1}s^{-1}$.

Sequential Reaction

A bisubstrate reaction mechanism in which all substrates must bind to the enzyme to form a ternary complex before any product can be released.

Double-Displacement (Ping-Pong) Reaction

A bisubstrate reaction mechanism characterized by the formation of a temporarily modified enzyme intermediate, where one or more products are released before all substrates bind.

Allosteric Enzymes

Information-sensing enzymes with quaternary structure and multiple active sites that regulate flux through metabolic pathways by responding to environmental chemical signals.

Feedback Inhibition

A regulatory mechanism where the end product of a metabolic pathway binds to a distinct regulatory site on an enzyme catalyzing an early committed step to suppress its activity.

Sigmoidal Kinetic Curve

An S-shaped velocity-versus-substrate curve characteristic of allosteric enzymes displaying cooperative substrate binding and a sharp threshold response.

Concerted Model (MWC Model)

An allosteric model governed by the symmetry rule, postulating that all enzyme subunits transition simultaneously between the tense ($T$) and relaxed ($R$) states without hybrid conformations.

Tense (T) State

The less active and more stable conformation of an allosteric enzyme that predominates in the absence of substrate or positive modulators.

Relaxed (R) State

The active catalytic conformation of an allosteric enzyme that possesses higher affinity for substrate molecules.

Allosteric Constant ($L_0$)

The equilibrium ratio of the tense state to the relaxed state ($T/R$) in an allosteric enzyme in the absence of substrate or effectors, typically in the hundreds.

Threshold Effect

The switch-like cooperativity observed in allosteric enzymes, where enzyme activity transitions sharply from an off state to an on state across a narrow range of substrate concentration.

Heterotropic Effect

An allosteric effect mediated by non-substrate regulatory molecules (effectors) binding to distinct sites, shifting the sigmoidal curve left (activators) or right (inhibitors).

Homotropic Effect

An allosteric effect caused by the binding of identical molecules (usually substrate) to active sites, producing cooperative transitions.

Sequential Model (KNF Model)

An allosteric model proposing that substrate binding induces conformational changes sequentially in adjacent subunits, which readily accommodates negative cooperativity.

Gout

A painful joint disease caused by the precipitation of sodium urate crystals, often resulting from the loss of regulatory feedback inhibition in purine synthesis enzymes.

Phosphoribosylpyrophosphate Synthetase (PRS)

The enzyme synthesizing PRPP from ribose 5-phosphate and ATP; mutations abolishing its allosteric feedback inhibition by purine nucleotides cause excessive urate accumulation.

Ensemble Studies

Traditional biochemical assays conducted on bulk populations containing millions of enzyme molecules, which measure average kinetic parameters such as $K_M$.

Single-Molecule Experiments

Techniques evaluating individual enzyme molecules one at a time, capable of resolving molecular heterogeneity, transient intermediates, and mechanical forces.