**Michaelis Menten Model**

**“E”+”S” ⇌ “E”∙”S” → “E”+”P”**

1st step is __REVERSIBLE__

2nd step is __irreversible__

(unidirectional)

**“E”+”S” ⇌ “E”∙”S” → “E”+”P”**

Enzyme contacts substrate by **diffusion** to form the **E-S Intermediate**

Which then passes over the **activation barrier** to yield:**Product = P**

OR**E-S** can **FALL APART** & the enzyme / substrate **diffuse away**

What is **k**_{+1}

- *
__BI-molecular__****rate constant** - (involves BOTH E & S, SEPERATELY)*

for **FORMING E-S**

L/mole-sec = molarity^{-1}sec^{-1} = **M ^{-1}-sec^{-1}**

What is **k _{-1}**

- *
__uni-molecular__****rate constant** - (starts with just ONE MOLECULE = E-S complex combined)*

for * DISSOCIATION of* E-S

**sec ^{-1}**

What is **k _{+2}**

- *
__uni-molecular__****rate constant** - (starts with just ONE MOLECULE = E-S complex combined)*

for **BREAKDOWN of E-S** into

**E + P**

**sec ^{-1}**

What is this?

**RATE LAW** for the **M-M Model**

**K _{m} = Michaelis Constant**

[**E _{0}]** =

**original enzyme concentration**

*NO simple interpretation of MOLECULARITY or ORDER*

What is **K _{m}**

**Michaelis Constant**

it *can be RELATED to a* **dissociation constant** (

**K**)

_{s}*but is NOT quite the same*

__just the SAME UNITS__

of __micromolar__

What is **k _{+2}** or

**k**

_{cat}__TURNOVER Number__

the **MAXIMUM #** of

substrate molecules **converted** / **turned over** into **product**

__per unit time__, per active site

What is the **Maximal Rate of Reaction?**

Rxn rate is maximixed when **ALL** of the **active sites**

on **ALL** of the **enzyme molecules** are **Filled w/ substrate**

Rate equation simplifies to:**V _{max} = k_{cat} [E_{0}]**

this occurs **ONLY** if the **enzyme** is ** SATURATED** with

**substrate**

- generally requires that*
**[S] >>> K**_{m} - If [
to saturate the enzyme*, you can’t use this simple expression, but must instead use__S] is not high enough____the original rate law__

When can this **rate equation NOT be used?**

**V _{max} = k_{cat }[E_{0}]**

if the **[S]** is **NOT** high enough to **saturate the enzyme***we can not use that expression,*

**we MUST use the** __Original Rate law__

**Traditional Unit = U**

vs

**katal = kat**

- *U** of enzyme activity is the
- *
__amount of ENZYME__** that can**convert ONE**ofmole__micro__**substrate**into**products**in__ONE MINUTE__ - *kat** =
**SI unit of activity**, thethat converts__amount of ACTIVITY__ - *ONE**
**mole**of**substrate**into**products**in__one SECOND__

**Equivilance of U** to **kat**

**1 microkat** =

**60**(traditional)

**U**

**nits of activity**

Since:__kat=1mole__ vs U=1*micromole*

__1 second__ vs 1 minute

What does this indicate? **Km vs kcat**

Km = micromolar

Takes **A LOT** of **CO2** to **saturate** the enzyme

kcat = per second

there is a **VERY FAST TURNOVER**

What does this indicate? **Km vs kcat**

Km = micromolar

does **NOT** take a lot of **substrate** to **saturate** the **enzyme**

kcat = per second

there is a **VERY FAST TURNOVER ** –> produce pyruvate quickly

What does this indicate? **Km vs kcat**

**elastase chews up on AA’s**

Km = micromolar

Takes **A LOT** of **substrate** to **saturate** the **enzyme**

kcat = per second

there is a __SLOW turnover__

What does this indicate? **Km vs kcat**

**fumarase is in the TCA cycle**

Km = micromolar

does **NOT** take a lot of **substrate to saturate the enzyme**

kcat = per second

there is a **VERY FAST TURNOVER **

When can **K _{m}**

_{ }be

**APPROXIMATED**by

**K**for the

_{s}**E-S complex?**

**K _{m}**

_{ }= Michaelis Constant

**K _{s} =**

**dissociation constant**

**K _{m} =~ K_{s}**

ONLY IF

**k**

_{+2}/**k**<<<

_{+1}

*K*_{s}** rate of catalysis** is

__MUCH SLOWER***__than__***rate of dissociation___k<sub>+2</sub>_ = _rate of **breakdown** of E-S --\> E + P_ k<sub>+1</sub> = rate of ***dissocation*** of E + S \<-- E-S

What is **K _{s}**

_k<sub>-1</sub> = rate of ***dissociation*** of **E + S** \<-- E-S_ k<sub>+1</sub> = rate of **formation** of E + S --\> **E-S**

- *RATE of
**__Dissociation__ __only approximates K__if the rate catalysis is_{m}than the rate at which__MUCH SLOWER____E-S dissociates back to E + S__*

How to determine the **INITIAL RATE** of an **enzyme reaction?**

and **[E _{o}]**

Set up the rxn with **measured #** of **enzyme & substrate**

then follow the progress by **measuring appearance of PRODUCT**

then ** PLOT** = [

**P**roduct] vs

**[t**ime

**]**

**SLOPE** = **Rate of Rxn**

(use the slope in the ** LINEAR REGION** of the plot)

then ** TRACE BACK TO T=1** for

**[E**

_{0}]**Initial Rate Determination**

**GRAPH**

use the **slope** in the ** LINEAR REGION** of the plot

How to find **Half-Maximal Velocity** = **1/2 V _{max}**

When [**S] = K _{m}** , then

**v**=

**1/2 V**

_{max}the

**for**

__numerical value__**[S**

_{0}] = K_{m}First find the **maximum** (plateau) for the **initial rate** = **v**

then **drop back** in **concentration of substrate = [S]** to where v is **half the maximal value**

then find the corresponding **initial concentration of S**

What is the **Lineweaver-Burk** Plot?

**Double-Reciprocal** Plot**1/v** vs **1/[S]**

(min/um) vs (M^{-1})

**K _{m} / V_{max}** =

**Slope**

should be a

__STRAIGHT LINE__**ONLY IF**the enzyme obeys the

__Michaelis-Menten model__x-intercept @ -1 / K_{m}

y-intercept @ 1 / V_{max}

What type of plot is this?

Double Reciprocal

__LINEWEAVER-BURK__

only a STRAIGHT LINE slope if enzyme obeys M-M model

Where is the **X-Axis Intercept** in the

**Lineweaver-Burk** (Double Reciprocal) **Plot?**

**-1 / K _{m}**

(micromolar

^{-1})

slope = Km / Vmax

Where is the **Y-Axis Intercept** in the** Lineweaver-Burk** (Double Reciprocal) **Plot**?

**1 / V _{max}**

slope = Km / Vmax

(min / micromole)

What plot is this?

**Lineweaver-Burk**

What plot is this?

- *
__Eadie - Hofstee Plot__** - not very useful*

What plot is this?

__Hanes - Wolf Plot__

Technically superior > lineweaver burk

because there is **least distortion** to experimental ERRORS

When do we see a *Non-Linear* / CURVED Plot?

and **WHY?**

When the **enzyme** is **NOT following that model**

2 common possibilities of curvature:

may be ** MORE Kinetic STEPS** in the mechanism that the M-M model allows

__ENZYME__*may have* __MULTIPLE ACTIVE SITES__

which may be **interacting** with one another**= cooperativity** (pos / neg)

What do we do with **CURVED PLOTS?**

**compare to “linear”** type plots to __diagnose deviations__

from the M-M model

USE __Curve-Fitting SOFTWARE**__ + __**full non-linear rate law__

to get **accurate estimates** of the kinetic parameters

**k _{cat}** and

**K**

_{m}k_{+2}= k_{cat} = turnover number

Basic ways to **measure the # of enzyme** (concentration)

**Assays**

__IMMUNOASSAY__

needs specific AB’s, *does NOT measure _inactive_* enzymes

__ELECTROPHORESIS__

stain -> scan **slow** also

*does NOT measure*

__active__*enzyme*

__STANDARDIZED RXN__

FAST, but *may call for _coupling_* of 2+ sucessive rxns in order to measure the product

__spectrophotometrically__**Immunoassay**

**Positives & Negatives**

(basic ways to measure enzyme concentration)

Need ** SPECIFIC ANTIBODIES** to the enzyme

*does NOT measure* * INACTIVE* enzyme

only measures the ACTIVE enzyme

think immuno**A**ssay = measures ACTIVE

**Electrophoresis**

Positives & Negatives

(basic ways to measure enzyme concentration)

Electrophoresis -> stain -> scan

*SLOW*

*NOT for measuring*__ACTIVE__**enzyme**

only measures the *inactive enzyme*

**Stantardized Reaction**

Positives & Negatives

(basic ways to measure enzyme concentration)

Measures the ACTIVITY of enzyme

**FAST**

*but may call for* ** COUPLING** of

**two or more successive rxns**in order to measure the

**product**

__SPECTROPHOTOMETRICALLY__

How do we **monitor an enzyme** that ** does NOT** use a

**substrate or form a product?**

__ENZYME COUPLED ASSAY__

__UV ABSORBANCE**__ or __**FLUORESENCE__

done DIRECTLY by coupling it to a **second INDICATOR REACTION** that *itself, does NOT give a useful signal*

need to add **EXCESS SUBSTRATE & Secondary ENZYME**

to ensure that the**rate limiting facto**r is the **#enzyme in the first rxn**

**Coupled Assay Time Course**

**Lag Phase -> up to Incubation time**

time **BEFORE** **products** are being made

To ensure that the:**Overall Rate-limiting Factor** =__Amount of Enzyme 1__

(1st enzyme that is or diagnostic quanitity)

we need:

**EXCESS** ** SUBSTRATES** for BOTH reactions to reach SS

**EXCESS** __ENZYME__** #2** the one for the indicator reaction

** Aspartate Amino Transferase** (

**AST**)

as an **Example of Coupled Enzyme Assay**

**AST** catalyzes this rxn:

Aspartate + a-Ketoglutarate ↔ Glutamate + **Oxaloacetate**

The **indicator rxn #2** uses **malate dehydrogenase** for:

**Oxaloacetate** + NADH + H+ ↔ Malate + __NAD+__

We then **follow** the ** PRODUCTION OF NAD+** using

__FLUORESCENCE**__or__**UV ABSORBANCE__we need excess:

reactants & 2ndary enzyme (malate dehydrogenase)

What type of **Inhibition** is this?

*Reversible* COMPETITIVE inhibition

**Competitive Inhibition**

- *inhibitor**
**blocks S from binding in the active site** - various ways to block / different points of contacts*

Formation of **E-S complex is Reduced,** new complex,

**E-I is formed**

*unlike* **K _{m},K_{i}**(

**) is**

*inhibitory constant***(K**

__really a EQ dissociation constant___{s})

*Competitive Inhibitor** has*on the***_NO EFFECT_****catalytic step**- *k
_{cat}= k_{+2}** is THE SAME &**V**is also THE SAME_{max}

In *Reversible* Competitive Inhibtion

Can the **addition of MORE substrate** **OVERCOME the inhibition?**

(restore the OG rate of rxn)

__YES__

**apparent Michaelis constant** is ** numerically LARGER** than

**K**

_{m}so it **INCREASES** as the concentration of **INHIBITOR RISES**

takes MORE substrate to HALF-SATURATE the enzyme when a competitive inhibitor is present

**Competitive Inhibition’s** **effects on:**

**k _{cat} &**

**V**

_{max }& K_{m}(k_{+2}) turnover rate / maximum velocity

**k _{cat} & V_{max} STAY THE SAME**

**K _{m}**

*decreases*__MORE substrate can OVERCOME inhibition__

What type of **Inhibition Graph?**

__Reversible____COMPETITIVE inhibition__

**Increasing** **[I]** = more inhibitor leads to:

Slope = **Steaper Slope**

Y-axis (vertical) = __Same Y-Intercept__**V _{max}**

__does NOT change__X-axis = *Different X-intercepts***K _{m}**

*decreases*What type of **Inhibition Graph?**

__UN-____COMPETITIVE inhibition__

**Increasing** **[I]** = more inhibitor concentration leads to:

Slope = **No Change** (

**Parallel Plot**)

Y-axis (vertical) = **Increase Y-Intercept****V _{max}** is

*progressively reduced*X-axis = **Increase X-intercept****K _{m}** is

*progressively reduced*What type of **Inhibition Graph?**

__NON-____COMPETITIVE inhibition__

**Increasing** **[I]** = more inhibitor concentration leads to:

Slope = **Increasing Slope**

Y-axis (vertical) = **Increase Y-Intercept****V _{max}** is

*reduced*X-axis = __SAME X-Intercept__**K _{m}**

__does NOT change__**UN-Competitive Inhibition’s** **effects on:**

**k _{cat} &**

**V**

_{max }& K_{m}(k_{+2}) turnover rate / maximum velocity

*kcat idk*

__REDUCE BOTH Vmax & Km__

__NOT POSSIBLE TO OVERCOME INHIBITION__

**NONCompetitive Inhibition’s** **effects on:**

**k _{cat} &**

**V**

_{max }& K_{m}(k_{+2}) turnover rate / maximum velocity

kcat ?

**V _{max} INCREASES**

**K _{m}**

**stays the SAME**

__NOT able to OVERCOME INHIBITION with more substrate__

What type of **Inhibition is this?**

__NONCompetitive / MIXED Inhibition__

**NONCompetitive = special case of mixed**

inhibitor has SAME AFFINITY for either E or E-S complex**K _{i} = K_{i}‘**

**MIXED**

K_{i} & K_{i}’ are **allowed to be different**

What type of **Inhibition** is this?

__UN-Competitive Inhibition__

parallel graph, vmax &km get smaller

__UN-Competitive Inhibition__

*relatively UNCOMMON*, **Parallel Plots**

- *Inhibitor –> E-S complex**
- does NOT bind to the FREE ENZYME*

__NO E-I complex is formed__

E-S-I complex is catalytically inert

still reversible

__NOT POSSIBLE toOVERCOME INHIBITION w/ MORE SUBSTRATE__

__Mixed / NON-Competitive Inhibition__

converge to the same **X-intercept** (-1/km), same Km

**Inhibitor** –> complex with **BOTH**: **E** & **E-S**

**E-I** & **E-S-I** complexes are __Both INACTIVE__

__ADDING MORE SUBSTRATE WILL NOT OVERCOME INHIBITION__

since inhibition can STILL OCCUR when the substrate binds

**alcohol dehydrogenase inhibition**

**by 3-butylthiolane 1-oxide**

Example of

__UN-Competitive Inhibition__

PARALLEL PLOTS

**NAMPT** inhibtion by **NAD / NADH**

__NON-Competitive Inhibition__

all **converge to same X-Intercept**

(-1/Km)

What is the difference between

__Mixed**__ & __**Noncompetitive Inhibition?__

__NON-Competitive Inhibition__

a **SPECIAL CASE** of **Mixed Inhibition** where

inhibitor has the ** SAME affinity** for BOTH

**E & E-S**complex

*numerically,* **K _{i} = K_{i}‘**

- *
__Mixed Inhibition__** - *K
_{i}& K_{i}‘** are**allowed to be DIFFERENT**