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Protein Networks

Protein Networks. Week 5. 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). Linear Response.

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Protein Networks

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  1. Protein Networks Week 5

  2. 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) Linear Response

  3. Linear Response

  4. 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. Protein Cycles 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 2 v 1

  7. Conservation laws

  8. Assume linear kinetics Hyperbolic Response

  9. Hyperbolic Response

  10. Assume saturable kinetics Sigmoidal Response

  11. Assume saturable kinetics Sigmoidal Response

  12. Assume saturable kinetics Sigmoidal ResponseMemoryless Switch

  13. Fundamental Properties Ultrasensitivity E1 E2 X Kms = 0.5

  14. Fundamental Properties Ultrasensitivity E1 E2 X Kms = 0.1

  15. Fundamental Properties Ultrasensitivity E1 E2 X Kms = 0.02

  16. Device Analogs Output Collector Current Base Current Input Input

  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 A C B

  19. Basic Logic Gates NOT Gate B A A B

  20. Basic Logic Gates NOT Gate A B

  21. Ring Oscillator

  22. NAND Gate B A A C B C

  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 Clock input Binary Counter Clock RS flip-flop etc

  26. Arithmetic Half Adder (No carry input)

  27. Assume linear kinetics Sigmoidal ResponseMultiple Cycles S3

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

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

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

  31. Sigmoidal ResponseOscillators 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 By 1868 it is estimated that 75,000 governors were in operation in England 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

  34. 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. Amplifiers – basic amplifier

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

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

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

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

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

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

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

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