Protein Networks
Copyright © 2008: Sauro
1
Protein Cycles
20% of the human protein-coding
genes encode components of signaling
pathways, including transmembrane
proteins, guanine-nucleotide binding
proteins (G
proteins), kinases, phosphatases and
proteases.
The identification of 518 putative
protein kinase genes and 130 protein
phosphatases suggests that
reversible protein phosphorylation is
a central regulatory element of most
cellular functions.
2
Abundance of Kinases
Species
# of putative kinases
Saccharomyces cerevisiae
121
Drosophila melanogaster
319
C. elegans
437
Arabidopsis thal
1049
Human
518
Data from http://www.kinexus.ca
3
The Simple Cascade
v
2
v1
4
Response Characteristic
?
5
Linear Response
• A simple example of protein
dynamics: protein synthesis
and degradation.
6
Hyperbolic Response
Assume linear kinetics
7
Hyperbolic Response
8
Sigmoidal Response
Assume saturable kinetics
9
Sigmoidal Response
Assume saturable kinetics
10
Sigmoidal Response
M1 = R/(R+RP)
M2 = RP/(R+RP)
v1
v1
11
Sigmoidal Response
M1 = R/(R+RP)
M2 = RP/(R+RP)
v1
v1
12
Fundamental Properties
Ultrasensitivity
E1
E2
X
Kms = 0.5
13
Fundamental Properties
Ultrasensitivity
E1
E2
X
Kms = 0.1
14
Fundamental Properties
Ultrasensitivity
E1
E2
X
Kms = 0.02
15
Fundamental Properties
Ultrasensitivity
v1, v2
Km = 1, Vmax = 1
Vmax
v1
v2
E1
16
Fundamental Properties
Ultrasensitivity
v1, v2
Km = 0.03, Vmax = 1
Vmax
v1
v2
E1
17
Output
Collector Current
Device Analogs
Base Current
Input
Input
18
Digital Circuits
In ultrasensitive mode, cascades can be
used to build Boolean circuits.
NOT Gate
A
B
19
Ring Oscillator
20
NAND Gate
A B
A
B
C
C
21
Memory Units
Basic flip-flop
R = reset
S = set
Q = output
22
Memory Units
Clocked RS flip-flop
R = reset
S = set
C = clock
Q = output
23
Counters
Clock input
Binary Counter
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
Clock RS flip-flop
etc
24
Arithmetic
Half Adder (No carry input)
A
B
Sum
Carry
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
25
Sigmoidal Response
Multiple Cycles
The response of the cascade is the
product of the individual cycle
sensitivities.
Cascades can therefore have considerable
gain values (Hill coefficients >> 10).
26
Multiple Phosphorylation Sites
p53 is a transcription
factor that is involved
in preventing cancer
formation.
Physiologically it is
involved in a variety
of stress signals,
cell cycle and
programmed
death functions.
It has multiple
modification sites – 21
phosphorylation sites..
http://www.biology.bnl.gov/cellbio/human_p53.html
27
Multiple Phosphorylation Sites
Assume linear kinetics
S3
28
Multiple Phosphorylation Sites
Assume linear kinetics
S3
29
Sigmoidal Response
Oscillators
Cell-signalling dynamics in time and space
Boris N. Kholodenko Nature Reviews
Molecular Cell Biology 7, 165-176 (March
2006) |
30
Sigmoidal Response
Bistable Switches
Cell-signalling dynamics in time and space
Boris N. Kholodenko Nature Reviews Molecular
Cell Biology 7, 165-176 (March 2006) |
31
Sigmoidal Response
Oscillators
Cell-signalling dynamics in time and space
Boris N. Kholodenko Nature Reviews Molecular
Cell Biology 7, 165-176 (March 2006) |
32
Sigmoidal Response
Oscillators
Cell-signalling dynamics in
time and space
Boris N. Kholodenko
Nature Reviews Molecular
Cell Biology 7, 165-176
(March 2006) |
33
Amplifiers
Provided the feedback is below the
threshold to cause oscillations, feedback
systems can behave as robust amplifiers.
34
Cascades as Noise Filters
1
0.9
0.8
P2 / (P1 + P2)
0.7
30
0.6
0.5
20
0.4
0.3
0.2
10
0.1
0
0.5
1
1.5
2
V1 / V2
Cascades can act as
signal noise filters in
the most sensitive region
Magnitude
0
V1 = 1.7
0
V1 = 3.06
-10
V1 = 3.4
V1 = 3.74
-20
V1 = 5.1
-30
-40
-50
0.001
0.01
0.1
1
10
100
Frequency
Output
35
Why? Frequency Analysis
0
0
0.5
1
1.5
2
-5
Nr(dv/ds)L
-10
-15
Jacobian
-20
-25
-30
-35
V1/V2
1
0.9
0.8
P2 / (P1 + P2)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
V1 / V2
36