Download Michaelis-Menten Equation

Analyzing the
Michaelis-Menten Kinetics Model
G. Goins, Dept. of Biology
N.C. A&T State University
Advisors:
Dr. M. Chen, Dept. of Mathematics
Dr. G. Goins, Dept. of Biology
Sponsored by
Grant No. 1634598
http://blend.ncat.edu
Biological Background
• Spontaneous chemical reactions that take place in
living things often occur very slowly without a
catalyst called an enzyme
• The enzyme binds to molecules known as the
substrate, and converts substrate to product,
• Unbound enzyme repeats cycle
2
Michaelis-Menten Mechanism
• The model represents how an enzyme acts on a substrate. E is
the enzyme, S is the substrate, ES is the enzyme-substrate
complex and P is the product.
E  S 
ES


E

P
k
k
k1
k2
k-1
ES

ES  E  P
1
2
Substrate
Products
Active site
Enzyme
Enzyme-substrate
complex
Recycle
Enzyme
3
What is the Michaelis-Menten
Equation
• Commonly used in
biology, the
Michaelis-Menten
equation describes the
reaction time to
convert (binding and
conversion) substrate
to product
vmax [ S ]
v0 
K m  [S ]
4
Michaelis-Menten kinetics
V0 varies with [S]
Vmax
approached
asymptotically
V0 is moles of product
formed per sec. when [P]
is low (close to zero time)
E + SESE + P
Michaelis-Menten Model
V0 = Vmax x[S]/([S] + Km)
Michaelis-Menten Equation
5
Michaelis-Menten
system of ODEs
• The four differential equations that are used in
the model are
dE
  k1 E * S  ( ki  k 2 ) ES (1)
dt
dS
  k1 E * S  ki ES
(2)
dt
dES
 k1 E * S  ( ki  k 2 ) ES (3)
dt
dP
 k 2 ES
(4)
dt
6
What is Michaelis-Menton good for?
• Application: Any process involving an Enzyme (E) that
converts a resource material (substrate, S) into another
form product (P)
• Biochemist use the shape of the curve to determine the
binding specificity of an enzyme for a substrate
• Km is called the Michaelis Constant, if small, then
steeper curve and more specific binding
7
Determining initial velocity (when [P] is low)
Ignore the back reaction
8
Steady-state & pre-steady-state conditions
At equilibrium,
no net change of [S] & [P]
or of [ES] & [E]
At pre-steady-state,
[P] is low (close to zero
time), hence, V0 for
initial reaction velocity
9
At pre-steady state, we can ignore the back reactions
Molecular biology, proteomics and systems biology approaches
•
Molecular biology studies traditionally focused on 1 or a few proteins with a highly
mechanistic levels of detail
•
Proteomics seeks to catalogue many proteins
•
Systems biology seeks a mechanistic understanding of phenomena that involve
many proteins
systems
biology
molecular
biology
proteomics
Albeck et al. Nature Reviews Molecular Cell Biology 7,
803–812 (November 2006)