BIOC*2580: Enzymes and Reaction Rates

nucleophilic catalysis

Enzymes can speed up reactions by providing a better nucleophile.

• e.g. Cys-SH, His-N: Asp or Glu -COO:-

• More rarely Tyr or Ser -:OH or Lys :NH₂

electrophilic catalysis

An electrophile is an electron-seeking group; there are no really good electrophilic amino acids.

An enzyme may contain a non-amino acid helper molecule called a prosthetic group as part of its structure (cofactors/coenzymes). They bind at the enzyme catalytic site and initiate reaction by withdrawing electrons from the substrate.

prosthetic group

A non-amino acid helper molecule that an enzyme may contain as part of its structure. It binds at the enzyme catalytic site and initiates reaction by withdrawing electrons from the substrate.

general acid catalysis

Catalysis by an amino acid side chain that donates H⁺ to the reaction.

• H⁺ exchange takes place right at the site of reaction, so the pH of surroundings is not affected (as enzymes must function at physiological pH)

• Gain or loss of one H⁺ in a small confined volume can have the same effect as strong acid or base

general base catalysis

Catalysis by an amino acid side chain that removes H⁺ from the reaction.

• H⁺ exchange takes place right at the site of reaction, so the pH of surroundings is not affected (as enzymes must function at physiological pH)

• Gain or loss of one H⁺ in a small confined volume can have the same effect as strong acid or base

chemical catalysis

1. Nucleophilic catalysis

2. Electrophilic catalysis

3. General acid catalysis

4. General base catalysis

These mechanisms can each contribute about an 100-fold increase in reaction rate, and work together to lower E_a.

Some reaction mechanisms use multiple of these!

stabilizing the transition state

Reactions must pass through a transition state to proceed, and key atoms may change shape (e.g. trigonal planar → tetrahedral), or a bond may stretch.

Less activation energy is needed if the enzyme active site is complementary to the transition state (the transition state differs chemically from the substrate).

The enzyme can help by binding the substrate in the ideal shape for the transition state (catalytic site set up to complement the transition state of the substrate, thus lowering energy content).

transition state

What reactions must pass through to proceed. Key atoms may change shape (e.g. trigonal planar → tetrahedral) or a bond may stretch. This state differs chemically from the substrate. If the active site is complementary, less activation energy is needed.

Activation energy can be lowered partly be choosing a different state, and partly by making the enzyme contribute to bond distortion that leads to this state.

enzyme assay

The process of measuring enzyme-catalyzed reaction rate.

• Enzymes speed up reaction rate in proportion to the amount of enzyme present!

enzyme kinetics

The mathematical analysis of how rate varies as a function of substrate concentration: can be used to test reaction mechanisms.

• Measure rates based on the rate of disappearance of reactant or rate of appearance of product

• Enzymes speed up reaction rate in proportion to the amount of enzyme present!

artificial substrate

A molecular “look-alike” for a real substrate. Often used in trypsin reactions to increase efficiency.

Trypsin hydrolyzes peptide bonds on the C-terminal side of Arg or Lys except when Pro is present in that position → we hydrolyze peptidyl nitroanilide, which releases p-nitroaniline which is distinctly coloured and thus makes it easy to measure the concentration and the rate.

UV absorbance change

Some natural substrates show UV absorbance change after conversion to product.

When pyruvate is converted to lactate, it converts NADH to NAD⁺ (oxidated). NADH absorbs ultraviolet light at 340 nm, whereas the NAD⁺ product does not absorb → Overall absorbance decreases as the reaction proceeds ([NADH] decrerases as it is converted to NAD⁺, thus, less absorbance).

chromophores

Parts of molecules with conjugated double bonds (alternating double and single bonds). Absorb visible or UV light.

• Coloured compounds absorb between 400-700 nm

• Natural biochemical forms frequently absorb in the UV range, 200-400 nm

• Larger forms absorb at longer wavelengths

conjugated double bonds

Alternating double and single bonds.

Beer-Lambert Law

Absorbance is proportional to sample concentration and sample thickness.

Absorbance

I_o = initial intensity

I = measured intensity

rate of reaction

Quantitative description of enzyme catalysis

Change in [substrate] or [product] per unit time (Mmin^-1 or molL^-1min^-1).

= [substrate used] / time or [product formed] / time (in M or mM)

enzyme activity

Quantitative description of enzyme catalysis

Moles of substrate converted per unit time (µmol/min). Represents the quantity of enzyme present.

= rate * volume

Also: (moles substrate or moles product) / time

specific activity

Quantitative description of enzyme catalysis

The number of enzyme units per milligram of total protein (µmol min^-1 mg^-1 or µmol min^-1 µg^-1).

Measure of enzyme purity during purification of enzymes and measure of enzyme efficiency when two different pure enzymes are compared.

= (Enzyme Activity) / (Total Protein)

molar activity

Quantitative description of enzyme catalysis

Activity per mole of enzyme (min^-1).

Equal to the turnover number, the number of catalytic reaction cycles per molecule of enzyme per second.

= (Specific Activity)(Molar mass of enzyme) → with necessary unit conversions!

If n moles of substrate are converted per second per mole of enzyme, then n molecules of substrate are converted per molecule of enzyme.

kinetics

The mathematical analysis of how reaction rate varies as a function of reactant concentration.

progress curve

Plot substrate or product concentration over period of time ([S]).

Initial rate v_o is taken from the slope of the curve at time zero.

Measure several rates at different initial [S].

normal chemical reactions

Follow simple rate laws.

enzyme reaction

Does not follow a simple rate law - instead, creates a hyperbolic curve that plateaus as [S] increases.

analysis of enzyme reaction as two steps

Since enzyme is recycled, it is not consumed; [E]_total is constant.

Work at time = 0 so [P] = 0, reverse reaction at step 2 can be ignored.

Individual steps have rate constant k₁, k_-1, k₂.

Michaelis-Menten equation

Equation that shows how initial rate (v_o) varies as a function of substrate concentration ([S]). May also be written in the fractional form, which is useful for solving enzyme kinetics problems.

Every enzyme has characteristic values of the two constants, V_max and K_M.

V_max

The upper limit for rate; indicates the catalytic rate when 100% of the enzyme is occupied by substrate (saturated with substrate). Higher rate means a faster reaction and better catalysis.

At high [S], all enzyme molecules have bound substrate and are engaged in catalytic activity, so reaction cannot go any faster (adding substrate cannot increase rate).

Considered a pseudo-constant (constant only if the amount of enzyme is fixed).

turnover number (k₂)

The rate that a singular molecule is working; how fast a single enzyme molecule can work. The true constant!

Michaelis constant (K_M)

Indicates how well the substrate fits the catalytic site.

The concentration of substrate [S] at which v_o is equal to 50% of the maximum rate V_max.

A low value indicates that the enzyme binds and utilizes substrate well; less [S] is needed to occupy the enzyme.

A high value indicates that the enzyme binds and utilizes substrate poorly; more [S] is needed to occupy the enzyme.

An enzyme with more than one substrate has a different value for each.

Lineweaver-Burk method

Method using linear transformations to convert the Michaelis-Menten equation into a straight line form; slopes and intercepts of the straight line give better estimates of V_max and K_M. Work well unless there are significant errors in the data.

• Take reciprocals of both sides of the Michaelis-Menten equation; obtain K_M by extending the graph onto the negative x-axis

• Why do this? Real experimental data often shows scatter due to measurement errors

inactivators

Usually react with enzymes irreversibly. Results from covalent chemical reactions. Reaction destroys catalytic activity and “uses up” the enzyme.

Many are highly toxic (e.g. nerve gases).

Simple stoichiometric relationship!

inhibitors

Decreases enzyme activity without destroying the catalytic function of enzyme molecule, usually bind to enzymes reversibly. Enzyme activity is restored if concentration is reduced.

Binds to site on the enzyme by non-covalent forces, similar to substrate (H-bonding, hydrophobic effect, etc.).

Degree of inhibition is governed by binding equilibrium, not simple stoichiometry.

Presence may affect different stages of the catalytic reaction, gives different modes of inhibition.

Can regulate enzyme activity in the cell → more economical for a cell to make and destroy a small inhibitor than a large enzyme.

modes of inhibition

The presence of inhibitor may affect different stages of the catalytic reaction, giving different modes.

• Competitive: affects ability to bind substrate

• Non-competitive: affects catalytic rate (also mixed)

competitive inhibition

Affects the ability to bind substrate.

Arises when inhibitor can only bind to unoccupied enzyme E.

Formation of EI complex means less available E available to bind substrate. Inhibitor and substrate compete for available enzyme - high [S] can overcome the inhibitor (in this case, can still reach V_max).

S and I often share the same binding site and may resemble one another in terms of chemical structure.

non-competitive inhibition

Affects the catalytic rate (also mixed inhibition).

Formation of EI and EIS means less ES to undergo catalysis, but substrate can still bind to EI without yielding product.

Inhibitor binding site is different from substrate binding site.

Bound inhibitor may disorganize the catalytic component of the enzyme.

If EI and EIS steps each have a different K_i, we get mixed inhibition.

regulation of enzyme activity

Can regulate enzyme activity in the cell → more economical for a cell to make and destroy a small inhibitor than a large enzyme.

• e.g. aspirin, ibuprofen

equilibrium constant K_i

Constant that governs inhibitor binding.

competitive inhibition Lineweaver-Burk plot

• Different lines represent different [I]

• No effect on V_max, so all graph lines have the same y-intercept (y-intercept = 1/V_max)

• K_M’ increases as [I] increases, so x-intercept gets smaller when considering absolute values (x-intercept = -1/K_M)

• Slope increases as [I] increases (slope = K_M’/V_max)

non-competitive inhibition Lineweaver-Burk plot

• Different lines represent different [I]

• No effect on K_M, so all graph lines have the same x-intercept (x-intercept = -1/K_M)

• V’_max decreases as [I] increases, so y-intercept gets bigger (y-intercept = 1/V’_max)

• Slope increases as [I] increases (slope = K_M/V’_max)

• For mixed, lines meet above the x-axis