lecture 14 enzyme kinetics
how does the presence of a competitive inhibitor change the lineweaver burk plot of an enzyme? what are the similarities? what are the differences?
In the presence of a competitive inhibitor: 1. the slope is greater (the Km is increased)... which means that the affinity of the enzyme for [S] is reduced. 2. the y-intercept stays the same (unchanged vmax) 3. the x-intercept is less negative (-1/Km ratio will decrease, putting the x-intercept closer to the origin)
what is the purpose of using a lineweaver burk plot instead of a michealis-menten graph?
It is difficult to discern the Km from a Michealis-Menten graph because the Vmax is asymptotic. Thus, to find the Km, we need a linear view (aka lineweaver burk)
How will the vmax change in the presence of a uncompetitive inhibitor?
It will be smaller (less functional enzymes if they are bound to uncompetitive inhibitors)
how will the x-intercept of a lineweaver burk plot change in the presence of a competitive inhibitor?
It will become less negative because the Km is larger
what is a consequence of treating an organism with DIPF to irreversibly inhibit enzymes?
It will inhibit acetylcholinesterase, functioning as a neurotoxin
what is KI
KI is the dissociation constant for the [EI] complex in competitive inhibition
what is another name for K2? and what does it mean?
Kcat (turnover number of the enzyme) describes the maximum number of substrate molecules that can be transformed into product molecules by a single active site over a given period of time
what is the equation to calculate Kcat?
Kcat = Vmax/[E]total assumes complete saturation of active sites
What is the significance of Km (assuming that K2 <<<< K-1)
Km = K-1/K1 = [E][S]/[ES] = Kd (this is because K2 is small enough to neglect) thus, IF the formation of the product is the RLS, the Km is the dissociation constant for the ES complex!
what is the Michealis-Menten constant?
Km = [K(-1)+K(2)]/K1 = [E][S]/[ES] *the units are concentration
What is the DEFINITION of Km?
Km is the substrate concentration [S] at which Vo=Vmax/2
what is an example of a reactive substrate analog?
TPCK. adds its reactive group on chymotrypsin's His 57, inhibiting it.
How is the Km different than the Kcat?
The Km is basically the dissociation constant of the ES complex. based on affinity The Kcat depicts how QUICKLY the enzyme can convert substrates into products. has literally nothing to do with affinity. it assumes that all of the active sites are saturated.
how does the vmax change in the presence of a competitive inhibitor?
The Vmax does not change
describe the curve of a michealis-menten graph IF you only consider the END of the reaction. explain why this happens
The curve is zero order at the end of the reaction. use the assumption that Km<<<[S], and rewrite the Michealis menten equation making that assumption. Vo= Vmax *[S]/[S] = Vmax so..... Vo = Vmax. Vmax = the rate constant k, and [S] is risen to the zeroth power. Thus, it takes the form V=k[S]^0 which means that the rate of the reaction is independent of the substrate concentration
What does the inverse of Kcat signify?
The inverse of Kcat tells us the TIME that it takes for one active site to turn one substrate into one product. units are seconds
why does the velocity of a reaction go down as the reaction proceeds?
The substrate concentration of the reaction will decrease because it is being consumed by the reaction
how is Vmax defined in terms of rate and total enzyme concentration? what is the mathematical equation for Vmax?
Vmax describes the highest number of substrate molecules that can be transformed into product molecules over a given time period when all of the active sites are saturated with that substrate. Vmax = k2*[E]total
what is the equation for Vmax?
Vmax= K(2)* [E]total
what is the equation that describes the enzyme efficiency at low substrate concentrations (i.e. physiological conditions)? what assumptions must be made?
Vo = (Kcat/Km) [E]total[S] This equation was derived almost the exact same way as the Michealis-Menten equation. steady state assumption allowed us to state: (k-1 + k2)/k1 = Km = [E][S]/[ES] solving for ES and substituting into the rate law would give: Vo = Kcat ([E][S]/km) BUT UNLIKE THE MICHEALIS-MENTEN EQUATION we assume that [S] <<<[Km] (at t=0). thus, if there is no product yet formed, (because [S]=0) and hardly any [ES] in solution.... SO, all of the enzyme in solution will be unbound: [E] = [E]total Thus, [E]tot can be inserted for [E] Vo=(Kcat/Km)[E]tot[S]
what is another way to represent [ES] at maximum saturation?
[E]total *[E]nonbinded = 0
For a molecule to serve as a reactive substrate analog, what two features must it have?
a specificity group to bind to the active site of the enzyme and a reactive group to subsequently inhibit the enzyme
how do you define the velocity of a reaction (in words and mathematically)?
aka The reaction rate. it is equal to the disappearance of S and the formation of P over time v= -delta(S)/delta(t) = delta(P)/delta(t)
what is the "alpha" variable in the competitive inhibition michealis menten equation? use words and the formula
alpha = 1 + ([I]/Ki) alpha is the factor by which the [S] must increase to overcome the inhibitor
what is an uncompetitive inhibitor?
an uncompetitive inhibitor binds onto the site of the enzyme that is only created when the substrate binds onto that particular enzyme.
what kind of inhibition is methanol poisoning?
competitive inhibition
what is another name for the Lineweaver-Burk plot?
double reciprocal plot
at what substrate concentration does uncompetitive inhibition work best?
high [S].
how does the presence of a UNcompetitive inhibitor change the lineweaver burk plot of an enzyme? what is different and what is the same?
in the presence of an uncompetitive inhibitor: 1. the slope is the same.... (BUT the vmax and the Km are BOTH decreased) 2. the y-intercept is higher (because the vmax is smaller, meaning that the 1/vmax is going to be higher) 3. the x-intercept is more negative (because the Km is smaller, the ratio of -1/Km will be smaller and further away from the origin) vmax is decreased because the uncompetitive inhibitor actually reduces the amount of functional enzymes. the Km also decreases because the inhibitor will actually cause the enzyme to KEEP the substrate in its active site--->high affinity---->lower Km.
what does a competitive inhibitor do?
increases Km. does not affect Vmax or Kcat
what does an uncompetitive inhibitor do?
increases affinity of substrate, but rate of reaction goes down. vmax and Kcat--- decreased Km ---> decreased
what does a noncompetitive inhibitor do?
it affects the enzyme efficiency, but not the affinity to the substrate Vmax and Kcat --- decrease Km ----unchanged
how does the y-intercept of a lineweaver burk plot change in the presence of a competitive inhibitor?
it does not change (same vmax)
how does the slope of the lineweaver burk plot change in the presence of a competitive inhibitor?
it is increased (because Km is increased)
describe the curve of a michealis-menten graph IF you only consider the BEGINNING of the reaction (i.e. t=0). explain why this happens
it is linear. use assumption that Km >>>>[S] when t=0 ([S]= virtually zero at t=0). rewrite the michealis menten equation making that assumption Vo= Vmax * [S]/Km this can be arranged into y=mx + b form, which is linear. The beginning of the rxn is also first order because the [S] is directly proportional to the rate of the reaction
what is the substrate concentration usually found in nature?
it usually lies somewhere between zero and the Km.
How will the Y-intercept of a lineweaver burk plot change in the presence of a uncompetitive inhibitor?
it will be higher because the Vmax will be smaller
how will the x-intercept of a lineweaver burk plot change in the presence of a uncompetitive inhibitor?
it will become more negative because of the smaller Km.
How will the Km change in the presence of a uncompetitive inhibitor
it will decrease because the uncompetitive inhibitor will trap the substrate in the active site (i.e. high affinity, which means lower Km)
how does the Km change in the presence of a competitive inhibitor?
it will increase
how will the slope of a lineweaver burk plot change in the presence of a uncompetitive inhibitor?
it will not change, although vmax and Km will both be reduced
on a product v. time graph, what is the shape of the Vo curve?
linear
if the initial velocity of a reaction was plotted on a product v. time graph, describe the curve of the graph
linear. the velocity (rate of reaction) is going to be constant at first....
what are a couple of ways to irreversibly inhibit an enzyme?
modify an important active site residue 1. (non-targeted) react Cysteine (located in the active site) with iodoacetamide. Note: ALL accessible Cys will react, not just active site 2. (targeted) use DIPF to react with Ser residues that are ONLY in the active site.
what are the units for Kcat? what does this signify?
s^-1 this says that X amount of substrate molecules are converted to X amount of product molecules in one second
what does a mixed inhibitor do?
similar to noncompetitive inhibitor, but also affects affinity of the substrate. vmax and Kcat ---- decreased Km ---- increased
what is a reactive substrate analog?
specific irreversible inhibitor characterized by irreversible covalent modification combined with substrate recognition i.e. a substrate can react with an active site, and inhibit that active site forever.
What is the specificity constant? What does it represent?
specificity constant = Kcat/Km it represents the ability of an enzyme to convert substrate into product (accounts for turnover and affinity)
how does the Km change as alpha increases?
the Km increases (less affinity of the enzyme for the substrate)
what does a higher specificity constant imply?
the compound is a better substrate for the enzyme
what is K'i
the dissociation constant of ESI complex in uncompetitive inhibition K'i = [ES][I]/[ESI]
how do you determine the Vmax from a lineweaver-burk plot?
the y-intercept (b) in the lineweaver burke equation = 1/Vmax. Therefore, using the graph, you can find the y-intercept, set it equal to 1/Vmax, and solve for Vmax.
what is a common type of competitive inhibitor?
transition state analog
what does a non-hyperbolic curve in a michealis-menten graph signify?
typical of allosteric or cooperative behavior in an oligomeric enzyme
how do you determine the Ki from a lineweaver burk plot?
use slope slope = aKm/Vmax
describe the lineweaver burk plot of noncompetitive inhibition
vmax- decreased Km - unchanged y-axis - higher x-axis - unchanged
when is a reaction operating at maximum velocity?
when all of the active sites of an enzyme are saturated with substrate.
when is K-1 = K1?
when the concentration of reactants equals the concentration of products
What is negative feedback?
when the product of a reaction binds to the active site and down-regulates enzyme activity (form of competitive inhibition)
what is an assumption that must be made before stating Kcat = Vmax/[E]total?
you must assume that all of the active sites are completely saturated with enzyme
How do you find the Km using a lineweaver burk plot? (there are two different ways, but definitely know the simple way)
you would set the y in the lineweaver burk equation equal to zero, and plug in the [S] (x-intercept), and solve for Km. but more SIMPLY, you can find the x-intercept by setting it equal to -1/Km, and then solving for Km.
what are the three simplifications (assumptions) made by the Michealis-Menten equation?
1. EP can be ignored (because the formation of the product is the RDS, and the ES complex is formed promptly) i.e. [E total] = [E free]+[ES] 2. K(-2) = 0 and P=0 (if we consider only initial velocity at early time points) 3. steady-state assumption (the concentration of the ES intermediate is constant because K2 is so small (limiting) that its disregarded. i.e. [ES]K(-1) + [ES]K(2) = [E][S]K(1) is the same thing as [ES]K(-1) = [E][S]K(1) which would make ES stay the same 4. [S] is constant at early time points because [S] >>> [E]tot, so the concentration of S that binds with E [SE] can be disregarded. i.e. [S]tot = [S]unbound + [SE] is the same as [S]tot= [S]unbound
What does a small Km signify? What about a large Km?
A small Km signifies stronger binding, and a large Km signifies weaker binding (remember that Km is essentially the dissociation constant of the ES complex)
what is the rate law for an enzyme forming a product?
Assuming that the formation of the product is the rate limiting step, Vo = K2[ES]
