chapter 7

Kinetics and Regulation

Kinetics is the Study of Reaction Rates

• Kinetics examines the rates of chemical reactions.
• Enzyme kinetics looks specifically at the rates of enzyme-catalyzed reactions.
• The rate (or velocity) of a reaction is the quantity of reactant that disappears or the quantity of product that appears over a certain time.
• Expressed as: V = -d[A]/dt = d[P]/dt, where 'd' indicates change.
• The velocity of a reaction is directly related to the concentration of the reactant by the rate constant k.
• For First-order reactions velocity is directly proportional to reactant concentration with a rate constant unit of s⁻¹.
• Second-order reactions involve two reactants and have a rate constant unit of M⁻¹s⁻¹.
• Pseudo-first-order reactions resemble first-order reactions when one reactant's concentration greatly exceeds the other's; the rate depends on the lower concentration reactant.
• Zero-order reactions have rates independent of reactant concentrations, which enzyme-catalyzed reactions can approximate.

The Michaelis-Menten Model Describes the Kinetics of Many Enzymes

• The initial velocity of catalysis is the rate right after a reaction starts, varying with substrate concentration when enzyme concentration remains constant.
• Substrate concentration can vary; enzyme concentration is constant.
• k₂ can be ignored when looking for initial velocity because product has not begun to accumulate at that point.
• Michaelis-Menten Equation relates initial velocity to substrate concentration: Vo = (Vmax[S]) / ([S] + KM)
• Michaelis constant (KM) is unique to each enzyme and independent of enzyme concentration, equal to (k₋₁+k₂)/k₁.
• Maximum velocity (Vmax) can only be obtained when all enzyme is bound with a substrate and is directly dependent on enzyme concentration.
• Vmax = k₂[E]T where [E]T is the total enzyme concentration.
• KM equals [S] when Vo = Vmax/2.
• When [S] < KM, velocity is directly proportional to [S]; an increase in [S] causes an increase in Vo, and Vo = (Vmax/KM)[S].
• When [S] > KM, the velocity is nearly equal to the max velocity to be reached, becoming independent of [S] and indicating zero-order kinetics.
• KM and Vmax values are important enzyme characteristics.
• KM depends on pH, temperature, ionic strength, and equals substrate concentration when half of active sites are filled.
• Best substrate concentrations are around KM if normal.
• The enzyme has significant activity, and the substrate concentration can vary and alter enzyme activity.
• Vmax reveals the turnover number of the enzyme.
• The number of substrate molecules an enzyme can convert into the product per unit of time when the enzyme is fully saturated with substrate.
• Turnover number = k₂ or kcat, which reveals the rate of catalysis where k₂ = Vmax/[E]T.
• Kcat/KM indicates catalytic efficiency.
• Enzymes are not usually saturated inside a cell; substrate is present at 10-50% of KM.
• When substrate concentration is much lower than KM the equation is Vo = (kcat[S][E]T) / KM.
• Kcat/KM, the specificity constant, is a measure of catalytic efficiency.
• Kcat is the rate of catalysis with a specific substrate, whereas KM considers the nature of enzyme-substrate interaction.
• Kcat/KM can be compared for different substrates to determine the enzyme's preference.
• If the rate of product formation exceeds the rate of dissociation of the ES-complex, then Kcat/KM approaches k₁, the rate of ES-complex formation.
• The upper limit to being no faster than the encounter of the enzyme and substrate (diffusion-controlled), ranging between 10⁸ to 10⁹ s⁻¹M⁻¹.
• Enzymes that reach this limit have achieved kinetic perfection and are the rate of catalytic efficiency is determined by how fast an enzyme encounters a substrate.
• Most biochemical reactions include multiple substrates.
• Sequential reaction have all substrates binding to the enzyme before any product is released, forming a ternary complex.
• In an ordered sequential reaction, substrates must bind in a specific order, whereas random sequential reactions do not binding requirement.
• Double-displacement (ping-pong) reactions have one or more products released before all substrates bind, with a substituted enzyme intermediate forming.

Allosteric Enzymes Are Catalysts and Information Sensors

• Michaelis-Menten enzymes are not regulated within the cell: if the required substrate is present, the enzyme catalyzes the reaction. Most enzymes in a cell are Michaelis-Menten enzymes.

• Allosteric enzymes regulate the flux of biochemicals through metabolic pathways.

• Enzyme activity is thusly regulated.

• Allosteric enzyme features contain: the regulation of catalytic activity by environmental signals, the uses of final products of a pathway to regulate the enzyme, more complex enzyme kinetics than Michaelis-Menten enzymes, and a quaternary structure with multiple active sites in each enzyme.

• Allosteric enzymes are regulated by products of the pathways under their control.

• In a hypothetical metabolic pathway A → B → C → D → E → F, five reactions each rely on a different enzyme

• Limited amounts of F are produced and F cannot be be stored.

• A needs to be conserved unless F is needed.

• A → B is the committed step.

• When plenty of F is present, it will reverse-binding process to e₁ preventing the pathway's other steps from occurring through feedback inhibition.

• F would not resemble the substrate or product and it would not bind to the active site.

• Allosteric enzymes always bind to the committed step of pathway.

• The product of one enzyme may lead to a common product when multiple pathways exist, with the end product feedback inhibiting of each pathway.

• The end product will feedback inhibit its own pathway and stimulate the allosteric enzyme that catalyzes the committed step of the other pathway to prevent too much of each end product from building up for the individual pathways.

• Allosterically regulated enzymes do not conform to Michaelis-Menten kinetics..

• Allosteric enzymes react to substrate concentration and regulation by other molecules, showing a sigmoidal velocity-versus-substrate curve.

• Enzymes in the curve show a sharp increase in velocity in the middle.

• Allosteric enzymes depend on alterations in quaternary structure.

• In the concerted model for allosteric enzymes:

  • Allosteric enzymes have multiple active sites on different polypeptide chains.
  • Enzymes can exist in two conformations:
    • R, the relaxed state, catalyzes chemical reactions.
    • T, the tense state, is less active.
    • No substrates or signaling molecules will cause these two to undergo equilibrium, with T being more stable and more common.
    • A change in stability can be caused with changes to environment.
  • The allosteric constant is typically in the hundreds.
  • All subunits/active sites must be in the same state following the symmetry rule - either all in T or all in R form.
  • Substrates bind more to the R form than the T form.

• At low substrate concentrations the substrate finds it difficult bind to the more prevalent T form, having little enzyme activity under such concentrations.

• There being more substrate concentration after a T transitions to an R has the substrate readily available, which results in:

  • One substrate binding to the R form and trapping other active sites in the R form so there is easier substrate-binding; this is considered cooperativity activity.
  • Subsequent substrates do not have collide unproductively withenzyme.
  • Sharp increase in V.

• Allosteric enzymes are more sensitive than Michaelis-Menten enzymes to substrate changes.

• Regulator molecules modulate the T and R equilibrium.

• Positive effector binds to R form at a regulatory site to stabilize, making things easier for binding and reducing concentration of needed substrates.

• Negative effector binds to T form at a regulatory site to stabilize, making it more difficult S to b, and raising the threshold concentration level of S needed.

• Heterotropic effects are the effect that regulatory molecules have on allosteric enzymes: shifting the curve to the left/right if they are activators/inhibitors.

• Homotropic effects show substrates' effect on allosteric enzymes.

• The sequential model can account for allosteric effects with the following conditions:

  • Subunits of allosteric enzymes go through sequential changes in structure.
  • One substrate binding does not change the rest of teh binding sites.
  • Each site of an allosteric enzyme only changes with substrate binding to the next site.
  • It can allow for negative cooperativity, meaning substrate-binding becomes harder for extra substrates

• The majority of enzymes in cells act as a combination of the sequential and concerted models.