Robustness in protein circuits: adaptation in bacterial chemotaxis

1. Robustness in protein circuits:adaptation in bacterial chemotaxis Information in Biology 2008 Oren Shoval

2. Outline • Noise is a part of life • Overview of bacterial chemotaxis • Internal mechanism of chemotaxis control • The robust model of perfect adaptation • Perfect adaptation and control theory

3. Outline • Noise is a part of life • Overview of bacterial chemotaxis • Internal mechanism of chemotaxis control • The robust model of perfect adaptation • Perfect adaptation and control theory

4. Many biological processes are robust to external and internal fluctuations • Internal protein levels vary significantly between genetically identical cells • Humans keep body temperature at 36.7° despite: • External noise of surrounding temperature • Internal noise of body weight, size, food intake Elowitz et al., Science, 2002

5. Sensitivity to noise is a measure of biological system performance • Sensitivity is the change in system output (Y) due to changes in the internal parameter () • Robustness means zero sensitivity • For example, dependence of body temperature on body weight: Robust Savageau, Nature, 1971

6. Outline • Noise is a part of life • Overview of bacterial chemotaxis • Internal mechanism of chemotaxis control • The robust model of perfect adaptation • Perfect adaptation and control theory

7. Chemotaxis: Bacteria can “swim” towards an attractant and away from a repellent Repellant (poison) Attractant (food)

8. Swimming is done by a spiraling motor (flagella) • Flagella can rotate in two directions: • Speed of about 50m/sec. Is this fast? • Clock wise • (advancing ~sec) • Counter clock wise • (tumble ~0.1sec)

9. Bacteria find their way up a nutrient gradient by changing the tumbling rate • Bacteria are too small to measure gradient • Gradient found by temporal change during running • PositiveGradient • Biased random walk Lower tumbling rate Continue in correct direction Berg, Nature, 1972

10. Automated analysis of the bacteria trails enables extracting the chemotaxis parameters Berg, Nature, 1972 • Parameters: • Mean free path • Tumbling rate

11. Tumbling rate shows exact adaptation to nutrient level Steady state tumbling rate addition of nutrient bacteria stop tumbling Adaptation: slowly return to a steady state tumbling • Adaptation is commonly found in sensory systems • Adaptation is the focus of Barkai’s paper Addition of attractant reduces tumbling immediately Adaptation

12. Adaptation increases the dynamic range of sensors • Adaptation keeps sensor sensitive to changes regardless of average stimulus • Bacteria without adaptation show <1% chemotaxis ability System unable to sense changes Stimulus level Possible stimulus range System dynamic range

13. Outline • Noise is a part of life • Overview of bacterial chemotaxis • Internal mechanism of chemotaxis control • The robust model of perfect adaptation • Perfect adaptation and control theory

14. Motor control by a two component system: receptor and regulator Receptor without an attractant Activate Y by adding a P Y-P binds to motor Increase rate of tumbling Shorter runs Receptor Sensor activity level more tumbling P Y Y Motor Removal of P at constant rate

15. An attractant inhibits the receptor, thus reducing motor activity Sugar Adding attractant Less receptor activity Less Y-P is created Reduced tumbling Longer runs Receptor Sensor activity level Less tumbling P Y Y Motor Removal of P at constant rate Fast process (miliseconds)

16. Again: Sugar Less sugar Shorter runs More sugar Longer runs Receptor Receptor Sensor activity level Sensor activity level more tumbling Less tumbling P P Y Y Y Y Motor Motor Removal of P at constant rate Removal of P at constant rate

17. Adaptation is achieved by reactivating the receptor • Adding M (Methylation) overcomes deactivation due to sugar • R add M, B removes M M M Reactivation (R) Deactivation (B) Sensor activity level Negative feedback Slow process (minutes)

18. The adaptation cycle: Slow (minutes) Fast (miliseconds)

19. Outline • Noise is a part of life • Overview of bacterial chemotaxis • Internal mechanism of chemotaxis control • The robust model of perfect adaptation • Perfect adaptation and control theory

20. Is adaptation accuracy sensitive or robust to internal protein levels? • Example: If the level of protein R (reactivation) changes by 20%, will we still have adaptation? Two mechanisms for adaptation

21. Barkai proposed a robust model of adaptation that depends on two assumptions • Methylation (R) works at maximum rate (saturation) • Demethylation (B) occurs only on activated receptors Barkai, Nature, 1997 CheR

22. Let’s have fun with some equations • The attractant governs the active vs. inactive ratio: • Methylation rate: • At steady state: CheR Adaptation is robust!

23. Experiments can measure the sensitivity of chemotaxis parameters to internal protein level • Alon experimentally varied the level of proteins that make up chemotaxis • Three parameters were extracted for each mutant: Alon et al., Nature, 1999 Adaptation time Steady state tumbling Adaptation precision

24. Experiments have proven that adaptation precision is robust to variations in protein levels Alon et al., Nature, 1999 x3 receptors x50 CheR x0.5 CheY x12 CheB x0 CheZ x0 CheZ • Adaptation is precise in all cases • Steady state tumbling rate and adaptation time change

25. Perfect adaptation is important, so the network is designed to keep it robust • Partial adaptation leads to <1% of wild-type chemotaxis ability • Changing the tumbling frequency and adaptation time does not affect chemotaxis ability • Exact adaptation is displayed in taxis of many other bacterial species (B. subtillis, R. sphaeroides) However, nonessential features are sensitive to protein levels

26. Outline • Noise is a part of life • Overview of bacterial chemotaxis • Internal mechanism of chemotaxis control • The robust model of perfect adaptation • Perfect adaptation and control theory

27. Robust adaptation in chemotaxis is an example of integral feedback control A Error Yi et al., PNAS, 2001

28. Summary • Biochemical networks need to cope with noise • Chemotaxis is the ability of bacteria to swim towards an attractant • Chemotaxis adaptation is robust to internal protein levels