1. In-silico Implementation of Bacterial Chemotaxis Lin Wang Advisor: Sima Setayeshgar

2. Chemotaxis in E. coli Dimensions: Body size: 1 μm in length 0.4 μm in radius Flagellum: 10 μm long Physical constants: Cell speed: 20-30 μm/sec Mean run time: 1 sec Mean tumble time: 0.1 sec From Berg Lab From R. M. Berry, Encyclopedia of Life Sciences

3. From Single Cells to Populations … Chemotactic response of individual cells forms the basis of macroscopic pattern formation in populations of bacteria: Colonies Pattern formation in E. coli: From H.C. Berg and E. O. Budrene, Nature (1995) Biofilms Agrobacterium biofilm: From Fuqua Lab

4. Motivation  Chemotaxis as a well-characterized “ model ” signaling network, amenable to quantitative analysis and extension to other signaling networks from the standpoint of general information-processing concepts, such as signal to noise, adaptation and memory  Chemotaxis as an important biophysical mechanism, for example underlying initial stages of biofilm formation

5. Modeling Chemotaxis in E. coli Signal Transduction Pathway Motor Response [CheY-P] Stimulus Flagellar Response Motion

6. Outline  Chemotaxis signal transduction network in E. coli  Stochastic implementation of reaction network using Stochsim  Flagellar and motor response  Preliminary numerical results

7. Chemotaxis Signal Transduction Pathway in E. coli

8. Ligand Binding E: receptor complex a: ligand (eg., aspartate) Rapid equilibrium: Rates 1 : E: K D = 1.71x10 -6 M -1 E * : K D = 12x10 -6 M -1 [1] Morton-Firth et al., J. Mol. Biol. (1999)

9. Receptor Activation E n : methylated receptor complex; activation probability, P 1 (n) E n a: ligand-bound receptor complex; activation probability, P 2 (n) E n * : active form of E n E n * a: active form of E n a Table 1: Activation Probabilities nP 1 (n)P 2 (n) 00.020.00291 10.1250.02 20.50.125 30.8750.5 40.9970.98

10. Methylation R: CheR E n (a): E n, E n a E n (*) (a): E n, E n *, E n a, E n * a Rate constants: k 1f = 5x10 6 M -1 sec -1 k 1r = 1 sec -1 k 2f = 0.819 sec -1 (1) (2)

11. Demethylation Bp: CheB-P E n * (a): E n *, E n * a Rate constants: k 1f = 1x10 6 M -1 sec -1 k 1r = 1.25 sec -1 k 2f = 0.15484 sec -1 (1) (2)

12. Autophosphorylation E * :E n *, E n * a Rate constant: k f = 15.5 sec -1

13. CheY Reactions Y: CheY Yp: CheY-P Rate constants: k 1f = 1.24x10 -3 sec -1 k 1r = 4.5x10 -2 sec -1 k 2f = 14.15 sec -1

14. CheY Phosphotransfer Rate constants: k 1f = 5x10 6 M -1 sec -1 k 2f = 20 sec -1 k 2r = 5x10 6 M -1 sec -1 k 3f = 7.5 sec -1 k 3r = 5x10 6 M -1 sec -1

15. CheB Reactions B: CheB Bp: CheB-P Rate constant: k f = 0.35 sec -1

16. CheB Phosphotransfer Rate constants: k 1f = 5x10 6 M -1 sec -1 k 2f = 16 sec -1 k 2r = 5x10 6 M -1 sec -1 k 3f = 16 sec -1 k 3r = 5x10 6 M -1 sec -1

17. Simulating Reactions Stochastic 2 : Reaction has probability P of occurring a) Generate x, a uniform random number in [0, 1]. b) x <= P, reaction happens. c) x > P, reaction does not happen. How to generate P from reaction rates? [2] Morton-Firth et al., J. Mol. Biol. (1998) Two methods: Deterministic: ODE description, using rate constants,

18. Stochsim Package Stochsim package is a general platform for simulating reactions using a stochastic method.

19. Pseudo-molecule Pseudo-molecules are used to simulate unimolecular reaction. Number of pseudomolecule in simulating system: k 1max : fastest unimolecular reaction rate k 2max : fastest bimolecular reaction rate

20. From Rate Constant to Probability  Unimolecular reaction n: number of molecules from reaction system n 0 : number of pseudomolecules N A : Avogadro constant  Bimolecular reaction

21. Simulation Parameters Reaction Volume: 1.41 x 10 -15 liter Rate constants given above. Table 2: Initial Numbers of Molecules MoleculeNumberConcentration (μM) Y2128425.07 Yp00 R2000.24 E4246- B19282.27 Bp00

22. Output of Signal Transduction Network Fig 1. Number of CheY-P molecules as a function of time, the trace is smoothed by an averaging window of 0.3 sec. The motor switches state whenever threshold (red line) is crossed. It ’ s assumed that there is only 1 motor/cell.

23. Flagellar Response  Flagellar state directly reflects motor state, except that 20% of the motor changing from CCW to CW is dropped 3.  Assume there is only 1 flagellum/cell. [3] Alon et al., The EMBO Journal (1998)

24. Motion  Motion of the cell is determined by the state of flagellum. CCW  run CW  tumble

25. Run and Tumble Process  Run 4  Tumble 5 t t+Δt α v = 20 μm/s D r = 0.06205 s -1 γ = 4 μ = -4.6 β = 18.32 [4] Zou et al., Biophys. J. (2003)[5] Berg and Brown, Nature (1972)

26. Some Simulation Results  Distribution of run and tumble intervals.  Diffusion of a population of cells in an unbounded region in the absence of stimulus.  Diffusion of a population of cells in a bounded region (z>0), with and without stimulus.

27. Motor CW and CCW Intervals Fig 2. Fraction of motor CW/CCW intervals of wild-type cell in an environment without ligand. Left: Experiment (Korobkova et al., Nature 2004); Right: Simulation

28. Diffusion in Unbounded Region: No Stimulus Fig 3. Mean-squared distance from initial position as a function of time (averaged over 540 cells). Diffusion constant is found to be 4.4 * 10 -4 mm 2 /s, consistent with experimental results 6. [6] Paul Lewus et al., BioTech. and BioEng. (2001)

29. Diffusion in Bounded Region (z>0) Fig 4. Number of cells (out of a total of 540) above z=1.2 mm as a function of time. Red: constant linear gradient of aspartate 10 -8 zM/μM; Blue: no aspartate.

30. Future Directions  Optimal biochemical signal processing (role of “ adaptive ” network adaptation time)  Role of chemotaxis in initial stages of biofilm formation Realistic description of chemotaxis in E. coli to explore:

31. Thanks