Chapter 6: Enzymes Flashcards
cofactor
- reusable non-protein molecules that doesn’t contain carbon (inorganic)
- Usually are metal ions such as iron, zinc, cobalt, and copper that loosely bind to an enzyme’s active site
- a substance that increases the rate of a chemical reaction
- can be considered “helper molecules” that assist in
- They must also be supplemented in the diet as most organisms do not naturally synthesize metal ions.
coenzyme
- an organic non-protein compound that binds with an enzyme to catalyze a reaction
- often broadly called cofactors, but they are chemically different
- it cannot function alone, but can be reused several times when paired with an enzyme
prosthetic groups
- organic vitamins, sugars, lipids, or inorganic metal ions
- unlike coenzymes or cofactors, these groups bind very tightly or covalently to an enzyme to aid in catalyzing reactions
- often used in cellular respiration and photosynthesis.
A complete, catalytically active enzyme together with its bound coenzyme and/or metal ions is called a _____. The protein part of such an enzyme is called the _____ or _____
- holoenzyme
- apoenzyme
- apoprotein
active site
- region of an enzyme that binds substrate molecules
- This is crucial for the enzyme’s catalytic activity.
substrate, S
The molecule that is bound in the active site and acted upon by the enzyme
The surface of the active site is lined with _____ _____ _____ with substituent groups that bind the substrate and catalyze its chemical transformation. Often, the active site _____ a substrate, sequestering it completely from solution.
- amino acid residues
- encloses
Catalysts do not affect reaction _____
equilibria
energy in biological systems is described in terms of
free energy, G.
ground state
- starting point for either the forward or the reverse reaction
- the contribution to the free energy of the system by an average molecule (S or P) under a given set of condition
exothermic reactions
- the system loses heat as the surroundings warm up
- heat energy is being released from the system to the surroundings
- -ΔH = NEGATIVE
endothermic reactions
- the system gains heat as the surroundings cool down
- heat energy is being absorbed by the system from the surroundings
- ΔH = POSITIVE
exothermic reaction coodinate
- y axis = potential energy
- x axis = reaction pathway
- forward reaction: reactants on left, products on right
- reverse reaction: flip side reactants & products are on
- activated complex: is an intermediate compound w/higher energy than both reactants and products
- ΔH represents the difference between enthalpy of reactants and products
- ΔH = HPRODUCTS – HREACTANTS
- The step with the highest activation energy (ΔG‡) is the slowest step reaction
- The step with the lowest activation energy (ΔG‡) is the fastest step in the reaction
- The reaction cannot proceed faster than the rate of the slowest elementary step
endothermic reaction coodinate
- y axis = potential energy
- x axis = reaction pathway
- activated complex: is an intermediate compound w/higher energy than both reactants and products
- ΔH represents the difference between enthalpy of reactants and products
- ΔH = HPRODUCTS – HREACTANTS
- The step with the highest activation energy (ΔG‡) is the slowest step reaction
- The step with the lowest activation energy (ΔG‡) is the fastest step in the reaction
- The reaction cannot proceed faster than the rate of the slowest elementary step
reaction coordinate
- A: potential energy of reactants
- B: ΔG‡: activation energy: energy needed to start reaction
- C: ΔG‡: activation energy: reverse reaction
- D: ΔH: energy of reaction
- E: potential energy of products
ΔGo, the standard free-energy change
- describes the free-energy changes for reactions
- a standard set of conditions
- temperature 298 K
- partial pressure of each gas 1 atm, or 101.3 kPa
- concentration of each solute 1 M
ΔG’o, the biochemical standard free-energy change
- used because biochemical systems commonly involve H+ concentrations far below 1 M
- it is the standard free-energy change at pH 7.0
reaction coordinate diagram
- S = Substrate, P = Product
- free energy of the system is plotted against the progress of the reaction S → P
- description of the energy changes during the reaction
- horizontal axis (reaction coordinate) reflects the progressive chemical changes (e.g., bond breakage or formation) as S is converted to P
- activation energies, ΔG‡, for the S → P and P → S reactions are indicated
- ΔG’o
- standard free-energy change in the direction S → P
- exergonic: it’s negative, the free energy of the ground state of P is lower than that of S
- at equilibrium there is more P than S (the equilibrium favors P)
transition state
- The rate of a reaction is dependent on an energy barrier between reactants and products
- energy required for alignment of reacting groups, formation of transient unstable charges, bond rearrangements, and other transformations required for the reaction to proceed in either direction
- depicted by the energy “hill” in reaction coodinate
- molecules must overcome this barrier with a higher energy level
- the top of the energy hill represents a moment where things could go either way, decay to either substrate or product is equally likely
- not a chemical species with any significant stability and should not be confused with a reaction intermediate
activation energy, ΔG‡
- difference between the energy levels of the ground state and the transition state
- rate of a reaction reflects ΔG‡
- a higher ΔG‡ corresponds to a slower reaction
- Reaction rates can be increased by raising the temperature and/or pressure, thereby increasing the number of molecules with sufficient energy to overcome the energy barrier
- ΔG‡ can be lowered by adding a catalyst
reaction intermediates
- A reaction intermediate is any species on the reaction pathway that has a finite chemical lifetime (longer than a molecular vibration)
- occupy valleys in the reaction coordinate diagram
rate-limiting step
- the step (or steps) with the highest activation energy determines the overall rate
- it’s the highest-energy point in the reaction coordiante diagram
- can vary with reaction conditions, and for many enzymes several steps may have similar activation energies, which means they are all partially rate-limiting
- Reaction equilibria is linked to the _____ _____-_____ for the reaction
- reaction rates are linked to the _____ _____
- standard free-energy change ΔG’º
- activation energy ΔG‡
equilibrium constant, K’eq or K’
- denotes equilibrium: (S)ubstrate ⇔ (P)roducts
- K’eq = P / S
for thermodynamics the relationship between K’eq and ΔG’º can be described by the following formula
- ΔG’º = -RT ln K’eq
- R: gas constant, 8.315 J/mol • K
- T: absolute temperature, 298 K (25 8C)
- equilibrium constant is directly related to the standard free-energy change for the reaction
- A large negative value for ΔG’º reflects a favorable reaction equilibrium
- more product than substrate at equilibrium
- doesn’t mean the reaction will proceed at a rapid rate
rate law or
differential rate law
- rate law
- expresses the relationship between the rate of the reaction and the concentration of the reactant
- no products are involved
- differential rate law
- used to describe what is occurring on a molecular level during a reaction, whereas integrated rate laws are used for determining the reaction order and the value of the rate constant from experimental measurements
rate law formula
- V = k[S]n
- S: concentration of substrate (reactant)
- k: rate constant
- V: rate, velocity of the reaction. the amount of R that react per unit of time
- n: reaction order
rate constant (k)
- constant of proportionality
- changes only with change in temp
- Unit of k depends on order of reaction
reaction order (n)
- usually integer can be fraction
- determines how rate depends on [] of reactant
- can only b determined experimentally
overall order
the sum of the exponents for reactions with more than one reactant
reaction order values:
zero order
n = 0
rate = k[S]⁰
- S = substrate = reactant, P = product
- rate is independent of concentration of S
- because [S]⁰ = 1 so rate is equal to k
- concentration ↓ linearly
- slope of line is constant → constant rate
- occurs when amt of reactant available for reaction unaffected by changes to ttl amt of reactant
- units of Ms-1
reaction order values:
first order
n = 1
rate = k[S]¹
- S = substrate = reactant, P = product
- rate directly proportional to [S]
- rate ↓ as reaction proceeds cuz [S] ↓
- slope of curve (rate) less steep w/time
- If a first-order reaction has a rate constant k of 0.03 s-1 this means that 3% of the available S will be converted to P in 1 s
- units of s-1
reaction order values:
second order
n = 2
rate = k[S]² or rate = k[S1][S2]
- S = substrate = reactant, P = product
- If a reaction rate depends on the concentration of two different compounds
- rate proportional to square of [S] if the same compounds: rate = k[S]²
- or proportional to the product of the two [S]: rate = k[S1][S2]
- rate more sensitive to [S]
- rate proportional to [S]²
- slope flattens quicker than 1st order
- initial rate ↑ 4x when [S] doubles
rate / differential law
concentration vs time graph
rate / differential law
rate vs concentration graph
unit of k
(rate constant)
pattern
From transition-state theory we can derive an expression that relates the magnitude of a rate constant to the activation energy:
- k: Boltzmann constant = 1.38064852 × 10-23 m2 kg s-2 K-1
- h: Planck’s constant = 6.62607015 × 10−34 joule second
- The important point here is that the relationship between the rate constant k and the activation energy ΔG‡ is inverse and exponential
What are two sources of energy that lower the activation energy
Covalent and noncovalent interactions between enzymes and substrate
What are two sources of energy that lower the activation energy?
Covalent interactions between enzymes and substrates
- the rearrangement of covalent bonds during an enzyme-catalyzed reaction.
- Catalytic functional groups on an enzyme may form a transient covalent bond with a substrate and activate it for reaction
- or a group may be transiently transferred from the substrate to the enzyme
- In many cases, these reactions occur only in the enzyme active site
- these covalent interactions between enzymes and substrates lower the activation energy (and thereby accelerate the reaction) by providing an alternative, lower-energy reaction path.
What are two sources of energy that lower the activation energy?
noncovalent interactions
- critical to the formation of complexes between proteins and small molecules, including enzyme substrates
- Much of the energy required to lower activation energies is derived from weak, noncovalent interactions between substrate and enzyme
- interaction between substrate and enzyme in this complex is mediated by the same forces that stabilize protein structure, including hydrogen bonds and hydrophobic and ionic interactions
- Formation of each weak interaction in the ES complex is accompanied by release of a small amount of free energy that stabilizes the interaction called the binding energy, ΔGB
binding energy, ΔGB
- energy derived from enzyme-substrate interaction
- stabilizes the enzyme-substrate complex
- a major source of free energy used by enzymes to lower the activation energies of reactions
- contributes to specificity as well as to catalysis
- Weak interactions are optimized in the reaction transition state
- enzyme active sites are complementary not to the substrates per se but to the transition states through which substrates pass as they are converted to products
An enzyme completely complementary to its substrate would be a very _____ enzyme
poor
optimal interactions between substrate and enzyme occur only in the _____ _____
transition state
Some _____ interactions are formed in the enzyme substrate complex, but the full complement of such interactions is formed only when the substrate reaches the transition state. The _____ _____ released by the formation of these interactions partially offsets the energy required to reach the top of the energy hill. The summation of the unfavorable (positive) _____ _____ and the favorable (negative) _____ ______ results in a lower net activation energy
- weak
- free energy (binding energy)
- activation energy ΔG‡
- binding energy ΔGB
weak binding interactions between the enzyme and the substrate provide a substantial driving force for _____ _____
enzymatic catalysis
The weak interactions formed only in the transition state are those that make the _____ contribution to catalysis
primary
requirement for multiple weak interactions to drive catalysis is one reason why enzymes (and some coenzymes) are so _____. An enzyme must provide _____ _____ for ionic, hydrogen-bond, and other interactions, and also must precisely _____ these groups so that binding energy is optimized in the transition state
- large
- functional groups
- position
- There are 4 prominent physical and thermodynamic factors contributing to ΔG‡, the barrier to reaction:
- ____ _____ can be used to overcome all these barriers.
- 4 prominent physical and thermodynamic factors
- the entropy (freedom of motion) of molecules in solution, reduces the possibility that they will react together
- The solvation shell of hydrogenbonded water surrounds and helps to stabilize most biomolecules in aqueous solution
- distortion of substrates that must occur in many reactions
- Need for proper alignment of catalytic functional groups on the enzyme
- Binding energy
entropy reduction
- the large restriction in the motions of two substrates that are going to react
- obvious benefit of binding substrates to an enzyme.
- Binding energy holds the substrates in the proper orientation to react
Km, Michaelis constant
- The [S] at which V0 is half maximal
- Km = 1/2 • Vmax
- Km = (K-1 + K2) / K1
- Km = breakdown / formation
- k1 = rate constants, ES formation
- k-1 = rate constants, ES breakdown to reactants
- k2 = rate constants, ES breakdown to products
Michaelis-Menten equation
- the rate equation for a one-substrate enzyme-catalyzed reaction
- V0: initial reaction rate
- Vmax: maximum reaction rate
- KM: Michaelis constant
Enzyme-Substrate complex and Product formation steps
- k1 = rate constants, ES formation
- k-1 = rate constants, ES breakdown to reactants
- k2 = rate constants, ES breakdown to products
- K-2 = rate constant for the reverse reaction of catalysis
enzyme saturation
- At low [S] most of the enzyme is in the uncombined form E
- rate is proportional to [S] because
- Equilibrium is pushed toward formation of more ES as [S] increases
- When virtually all the enzyme is present as the ES complex and [E] is small the enzyme is said to be saturated
- maximum initial rate of the catalyzed reaction (Vmax) is observed
- further increases in [S] have no effect on rate
- distinguishing characteristic of enzymatic catalysts
- responsible for the plateau in saturation kinetics
An important relationship emerges from the Michaelis-Menten equation in the special case when V0 is exactly one-half Vmax
Kd, dissociation constant
- why is rate-limiting variable removed from the formula?
- When k2 is rate-limiting
- k2 << K-1
- k2
- Km = (K-1 + K2) / K1 → Km = k-1/k1
- When these conditions hold true, Km represents a measure of the substrate-binding affinity—does not apply for most enzymes
- k1 = rate constants, ES formation
- k-1 = rate constants, ES breakdown to reactants
- k2 = rate constants, ES breakdown to products
When k2 >> K-1, Km is
- k2 >> K-1,
- Km = (K-1 + K2) / K1 → Km = k<span>2</span>/k1
- Km DOES NOT represents a measure of the substrate-binding affinity
- k1 = rate constants, formation
- k-1 = rate constants, breakdown to reactants
- k2 = rate constants, breakdown to products
When k2 and K-1, are comparable, Km is
- Km remains a more complex function of all three rate constants
- Km = (K-1 + K2) / K1
- Km DOES NOT represents a measure of the substrate-binding affinity
- k1 = rate constants, formation
- k-1 = rate constants, breakdown to reactants
- k2 = rate constants, breakdown to products
kcat, turnover number
- a more general rate constant
- describes the limiting rate of any enzyme-catalyzed reaction at saturation
- If the reaction has several steps and one is rate limiting, it is equivalent to the rate constant for that limiting step
- a first-order rate constant
- units: s-1
- equivalent to the number of substrate molecules converted to product in a given unit of time on a single saturated enzyme
Enzymatic reactions with two substrates usually involve transfer of an ____ or a _____ _____ from one substrate to the other. These reactions proceed by one of several different pathways. In some cases, both substrates are bound to the enzyme concurrently at some point in the course of the reaction, forming a ____ ______ complex; the substrates bind in a random sequence or in a specific order. In other cases, the first substrate is converted to _____ and dissociates before the second substrate binds, so no ______ complex is formed
- atom
- functional group
- noncovalent ternary
- product
- ternary
In the case of bisubstrate reactions, steady-state kinetics can help determine whether a _____ _____ is formed during the reaction. In these examples double-reciprocal plots the concentration of substrate 1 is varied while the concentration of substrate 2 is held constant. This is repeated for several values of [S2], generating several separate lines. (a) _____ lines indicate that a ternary complex is formed in the reaction; (b) _____ lines indicate a Ping-Pong (double-displacement) pathway.
- ternary complex
- Intersecting
- parallel
Reversible Inhibition: competitive inhibitor
- competes w/substrate for the active site of an enzyme
- While inhibitor (I) occupies the active site, it prevents binding of the substrate to the enzyme
- Many are structurally similar to the substrate and combine with the enzyme to form an EI complex, but without leading to catalysis
Reversible Inhibition: competitive inhibitor
Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the Michaelis-Menten equation becomes
- αKm = the Km observed in the presence of the inhibitor, often called the “apparent” Km
- Km increases in the presence of inhibitor by the factor α when the [S] is at V0 = ½Vmax
- This effect on apparent Km, combined with the absence of an effect on Vmax, is diagnostic of competitive inhibition and is readily revealed in a double-reciprocal plot
- KI = equilibrium constant for inhibitor binding,
Reversible Inhibition: uncompetitive inhibitor
- observed only with enzymes having two or more substrates
- doesn’t bind at the substrate active site
- binds only to the ES complex
- at high [S], V0 approaches Vmax/α’
- lowers the measured Vmax
- αKm also decreases, because the [S] required to reach one-half Vmax decreases by the factor α’
- In the presence of an uncompetitive inhibitor, the MichaelisMenten equation is altered to
Reversible Inhibition: mixed inhibitor
- observed only with enzymes having two or more substrates
- doesn’t bind at the substrate active site
- binds to either E or ES
- usually affects both Km and Vmax
- special case of α = α’
- rarely encountered in experiments
- defined as noncompetitive inhibition
- The rate equation describing mixed inhibition is
Reversible Inhibition
- For all reversible inhibitors, the apparent Vmax = ______, because the right side of the equation always simplifies to _____ at sufficiently high [S]
- For competitive inhibitors, α’ = _____ and can thus be ignored
- αKm
- as always, equals the [S] at which V0 = 1/2 • Vmax
- or more generally when V0 = ______
- This condition is met when [S] = _____
- If only one of two reaction products is present, no _____ reaction can take place. However, a product generally binds to some part of the active site, thus serving as an ______
- Vmax/α’
- Vmax/α’
- 1.0
- Vmax/2α’
- αKm/α’
- reverse
- inhibitor
Reversible Inhibition: Duble Reciprocal Plots
- offers an easy way of determining whether an enzyme inhibitor is competitive, uncompetitive, or mixed
- In this example, [E] is constant
- 1st set: [S] is held constant to measure the effect of increasing [I] on initial V0
- 2nd set: [I] is held constant but [S] is varied
- Results are plotted as 1/V0 versus 1/[S]
Competitive Inhibition
- one set is obtained in the absence of inhibitor
- two at different concentrations of a competitive inhibitor
- Increasing [I] results in a family of lines with a common intercept on the 1/V0 axis but with different slopes
- Because the intercept on the 1/V0 axis equals 1/Vmax, we know that Vmax is unchanged by the presence of a competitive inhibitor
- Regardless of the competitive [I], a sufficiently high [S] will always displace the I from the enzyme’s active site
- The value of α can be calculated from the change in slope at any given [I]
- Knowing [I] and α, we can calculate KI in: α = 1 + ([I] / KI)
Uncompetitive / Mixed Inhibition
- Changes in axis intercepts signal changes in Vmax and Km
Allosteric Regulation / enzymes
- function through reversible, noncovalent binding of allosteric modulators or allosteric effectors
- regulatory compounds
- generally small metabolites or cofactors
- can be inhibitory or stimulatory
- enzymes have additional conformations induced by the binding modulators which can produce more or less active forms of enzyme
- enzymes tend to be multisubunit proteins, and in some cases the regulatory site(s) and the active site are on separate subunits
- homotrophic enzyme: when the modulator is the substrate itself, the active site and regulatory site are the same
- heterotropic enzyme: when the modulator is a molecule other than the substrate
- Enzymes with several modulators generally have different specific binding sites for each
Allosteric Regulation / enzymes
allosteric modulators should not be confused with _____ and _____ inhibitors. Although the latter bind at a second site on the enzyme, they do not necessarily mediate _____ changes between active and inactive forms, and the _____ effects are distinct
- uncompetitive
- mixed
- conformational
- kinetic
- The sigmoid curve of a homotropic enzyme, in which the substrate also serves as a positive (stimulatory) modulator, or activator
- resemblance to the oxygen-saturation curve of hemoglobin
- The sigmoidal curve is a hybrid curve in which the enzyme is present primarily in the relatively inactive T state at low substrate concentration, and primarily in the more active R state at high substrate concentration.
- The curves for the pure T and R states are plotted separately in color
- The effects of several different concentrations of a positive modulator (+) or a negative modulator (-) on an allosteric enzyme in which K0.5 is altered without a change in Vmax.
- The central curve shows the substrate-activity relationship without a modulator.
A less common type of modulation, in which Vmax is altered and K0.5 is nearly constant
