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Protein Networks Week 5. Linear Response A simple example of protein dynamics: protein synthesis and degradation Using the law of mass action, we can.

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Presentation on theme: "Protein Networks Week 5. Linear Response A simple example of protein dynamics: protein synthesis and degradation Using the law of mass action, we can."— Presentation transcript:

1 Protein Networks Week 5

2 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)

3 Linear Response

4 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.

5 Abundance of Kinases Data from http://www.kinexus.ca

6 The Simple Cascade v 1 v 2

7 Conservation laws

8 Hyperbolic Response Assume linear kinetics

9 Hyperbolic Response

10 Sigmoidal Response Assume saturable kinetics

11 Sigmoidal Response Assume saturable kinetics

12 Sigmoidal Response Memoryless Switch Assume saturable kinetics

13 Fundamental Properties X E1 E2 Ultrasensitivity Kms = 0.5

14 Fundamental Properties X E1 E2 Ultrasensitivity Kms = 0.1

15 Fundamental Properties X E1 E2 Ultrasensitivity Kms = 0.02

16 Collector Current Base Current Input Output Device Analogs

17 Digital Circuits In ultrasensitive mode, cascades can be used to build Boolean circuits.

18 Basic Logic Gates NAND Gate – fundamental building block of all logic circuits C B A

19 Basic Logic Gates NOT Gate B A B A

20 Basic Logic Gates NOT Gate A B

21 Ring Oscillator

22 NAND Gate C B A B C A

23 Memory Units Basic flip-flop R = reset S = set Q = output

24 Memory Units Clocked RS flip-flop R = reset S = set C = clock Q = output

25 Counters Binary Counter etc Clock RS flip-flop Clock input

26 Arithmetic Half Adder (No carry input)

27 Sigmoidal Response Multiple Cycles Assume linear kinetics S3

28 Sigmoidal Response Bistable Switches Cell-signalling dynamics in time and space Boris N. Kholodenko Nature Reviews Molecular Cell Biology 7, 165-176 (March 2006) |

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 Oscillators 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 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

33 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

34 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.

35 Amplifiers – basic amplifier Amplifier (A) Feedback (k) Output (y)Input (u) e = error - + e

36 Amplifiers – basic amplifier Amplifier (A) Feedback (k) Output (y)Input (u) e - +

37 Amplifiers – basic amplifier Amplifier (A) Feedback (k) Output (y)Input (u) e - +

38 Amplifiers – basic amplifier Amplifier (A) Feedback (k) Output (y)Input (u) e - +

39 Amplifiers – basic amplifier Amplifier (A) Feedback (k) Output (y)Input (u) e If kA > 0 then - +

40 Amplifiers – basic amplifier Amplifier (A) Feedback (k) Output (y) Input (u) 1.Robust to variation in amplifier characteristics 2.Linearization of the amplifier response 3.Amplification of signal 4.Preferential changes in input and output impedances 5.Improved frequency response 741 op amp

41 Feedback – basic amplifier

42 Amplifiers – basic amplifier Provided the feedback is below the threshold to cause oscillations, feedback systems can behave as robust amplifiers.

43 Amplifiers – Synthetic Amplifier

44 Cascades as Noise Filters Cascades can act as signal noise filters in the most sensitive region Output

45 Why? Frequency Analysis

46 Homeostatic Systems – perfect adaptation Simultaneous stimulation of input and output steps

47 Thursday Simulating other kinds of ‘computational’ behavior 1.Adaptive systems 2.Amplifiers and feedback regulation 3.Feed-forward networks 4.Low an high pass filter

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