Download - Protein Networks
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Protein Networks
Week 5
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Linear Response• A simple example of protein
dynamics: protein synthesis and degradation
• Using the law of mass action, we can write the rate equation.
• S = signal strength (e.g. concentration of mRNA)
• R = response magnitude (e.g. concentration of protein)
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Linear Response
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Protein Cycles20% of the human protein-coding genes encode components of signalingpathways, including transmembrane proteins, guanine-nucleotide binding proteins (G proteins), kinases, phosphatases and proteases.
The identification of 518 putative protein kinase genes and 130 proteinphosphatases suggests that reversible protein phosphorylation is a central regulatory element of most cellular functions.
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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
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The Simple Cascade
v 1
v2
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Conservation laws
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Hyperbolic Response
Assume linear kinetics
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Hyperbolic Response
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Sigmoidal Response
Assume saturable kinetics
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Sigmoidal Response
Assume saturable kinetics
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Sigmoidal ResponseMemoryless Switch
Assume saturable kinetics
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Fundamental Properties
X
E1
E2
Ultrasensitivity
Kms = 0.5
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Fundamental Properties
X
E1
E2
Ultrasensitivity
Kms = 0.1
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Fundamental Properties
X
E1
E2
Ultrasensitivity
Kms = 0.02
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Colle
ctor
Cur
rent
Base Current
Input
Input
Out
put
Device Analogs
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Digital CircuitsIn ultrasensitive mode, cascades can be
used to build Boolean circuits.
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Basic Logic GatesNAND Gate – fundamental building block of all logic circuits
A B C
0 0 1
0 1 1
1 0 1
1 1 0
CBA
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Basic Logic GatesNOT Gate
A B
0 1
1 0BA
BA
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Basic Logic GatesNOT Gate
A
B
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Ring Oscillator
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NAND Gate
CBA
B
C
A
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Memory UnitsBasic flip-flop
R = resetS = setQ = output
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Memory Units
Clocked RS flip-flop
R = resetS = setC = clockQ = output
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Counters
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
Binary Counter
etc
Clock RS flip-flop
Clock input
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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
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Sigmoidal ResponseMultiple Cycles
Assume linear kinetics
S3
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Sigmoidal ResponseBistable Switches
Cell-signalling dynamics in time and spaceBoris N. Kholodenko Nature Reviews Molecular Cell Biology 7, 165-176 (March 2006) |
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Sigmoidal ResponseOscillators
Cell-signalling dynamics in time and spaceBoris N. Kholodenko Nature Reviews Molecular Cell Biology 7, 165-176 (March 2006) |
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Sigmoidal ResponseOscillators
Cell-signalling dynamics in time and spaceBoris N. Kholodenko Nature Reviews Molecular Cell Biology 7, 165-176 (March 2006) |
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Sigmoidal ResponseOscillators
Cell-signalling dynamics in time and space Boris N. Kholodenko Nature Reviews Molecular Cell Biology 7, 165-176 (March 2006) |
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Amplifiers – basic amplifier
Ktesibios, 270BC invented the float regulator to maintain a constant water flow which was in turn used as a measure of time.
http://www.control-systems.net/recursos/mapa.htm
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Amplifiers – basic amplifier
Centrifugal fly-ball governor, introduced by Watt in 1788 to control the speed of the new steam engines.
http://visite.artsetmetiers.free.fr/watt.html
By 1868 it is estimated that 75,000 governors were in operation in England
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Amplifiers – basic amplifier
Harold Black in 1927, invented the first feedback amplifier in order to solve the problem of signal distortion when American Telephone and Telegraph wanted to lay telephone lines all the way from the east to the west coast.
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Amplifiers – basic amplifier
Amplifier (A)
Feedback (k)
Output (y)Input (u)
e = error
-
+ e
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Amplifiers – basic amplifier
Amplifier (A)
Feedback (k)
Output (y)Input (u)e
-
+
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Amplifiers – basic amplifier
Amplifier (A)
Feedback (k)
Output (y)Input (u)e
-
+
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Amplifiers – basic amplifier
Amplifier (A)
Feedback (k)
Output (y)Input (u)e
-
+
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Amplifiers – basic amplifier
Amplifier (A)
Feedback (k)
Output (y)Input (u)e
If kA > 0 then
-
+
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Amplifiers – basic amplifier
Amplifier (A)
Feedback (k)
Output (y)Input (u)
1. Robust to variation in amplifier characteristics2. Linearization of the amplifier response3. Amplification of signal4. Preferential changes in input and output impedances5. Improved frequency response
741 op amp
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Feedback – basic amplifier
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Amplifiers – basic amplifier
Provided the feedback is below thethreshold to cause oscillations, feedbacksystems can behave as robust amplifiers.
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Amplifiers – Synthetic Amplifier
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Cascades as Noise Filters
Cascades can act assignal noise filters in the most sensitive region
Output
-50
-40
-30
-20
-10
0
10
20
30
0.001 0.01 0.1 1 10 100
Frequency
Mag
nitu
de
V1 = 1.7
V1 = 3.06
V1 = 3.4
V1 = 3.74
V1 = 5.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2
V1 / V2
P2 /
(P1
+ P2
)
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Why? Frequency Analysis
-35
-30
-25
-20
-15
-10
-5
00 0.5 1 1.5 2
V1/V2
Nr(
dv/d
s)L
Jacobian
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2
V1 / V2
P2 /
(P1
+ P2
)
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Homeostatic Systems – perfect adaptation
Simultaneous stimulation of input and output steps
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ThursdaySimulating other kinds of ‘computational’ behavior
1. Adaptive systems2. Amplifiers and feedback regulation3. Feed-forward networks4. Low an high pass filter