Lin Wang Advisor: Sima Setayeshgar

Motivation: Information Processing in Biological Systems Chemical signaling cascade is the most fundamental information processing unit in biological systems.  Photoreceptor [1] Vertebrate photoreceptor converts external energy (light quanta) into a change in concentration intracellular signaling proteins ( Ca 2+ ?? Vesical release??).  Chemotaxis [2] E. coli chemotaxis network converts external change of stimulus into a change in concentration of signaling protein CheYp, which controls cell motile behavior. Use E. coli chemotaxis network as a prototype to explore the general information processing principle in biological systems. [1] Peter B. Detwiler et al. (2000). Biophysical Journal. 79, [2] Birgit E. Scharf et al. (1998) PNAS. 95,

Background: Introduction to Chemotaxis in E. coli Fluorescently labeled E. coli, from Berg lab Dimensions: Body size: 1 μm in length 0.4 μm in radius Flagellum: 10 μm long 45 nm in diameter From R. M. Berry, Encyclopedia of Life Sciences Physical constants: Cell speed: μm/sec Mean run time: 1 sec Mean tumble time: 0.1 sec One of the key features of E. coli chemotaxis network: Adaptation.

Background: Adaptation in E. coli Chemotaxis Network Adaptation is the restoration of pre-stimulus behavior following a change in external stimulus. Fig. 1 [3] Adaptation to addition /removal of stimuli. Attractant: 30 μM MeAsp. Repellent: 100 μM NiCl 2 YFP/CFP ~ [CheYp] Why does E. coli ’ s response vary? [3] Sourjik et al. (2002) PNAS [4] Howard C. Berg, (1975) PNAS Fig. 2 [4] The left most curve is the relation between the adaptation time of E. coli and step-wise change of [MeAsp] (1e-2 ~ 1e+4 μM).

Outline  Modeling E. coli chemotaxis network Chemical signal transduction pathway (reactions) Numerical implementation of transduction pathway (stochsim package) Couple motor response, output of transduction pathway, to cell motion  Preliminary numerical results Model validation (excitation and adaptation, motile behavior, etc) Input-output mutual information transmission Relates the role of adaptation.  Future work

Modeling Chemotaxis in E. coli: Picture of Numerical Implementation Signal Transduction Pathway Motor Response Stimulus Flagellar Response (?) Motion

Chemical Signal Transduction Pathway Table I: Signal Transduction Network

Simulating Reactions We use Stochsim [5] package, a general platform for simulating reactions using a stochastic method, to simulate reactions. Reactions have a probabilities p to occur.  Unimolecular reaction n: Number of molecules from reaction system n 0 : Number of pseudo-molecules N A : Avogadro constant p: Probability for a reaction to happen Δt: Simulation time step V: Simulation volume  Bimolecular reaction [6] Carl Jason Morton-Firth et al J. Theor. Biol

Parameters Values for 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 II: Activation Probabilities nP 1 (n)P 2 (n)

Parameters Values for Proteins Reaction Volume: 1.41 x liter Rate constants given above. Table III: Initial Numbers of Molecules MoleculeNumberConcentration (μM) Y Yp00 R E6276- B Bp00

Parameter Value for Motor Response Table IV: parameters values ParamterValueLiterature value KRKR 5.9 μM 3~12 μM KTKT 1.7 μM 1~7 μM K f (0) 1.0E-5 μM 3.35E-4 μM K b (0) 1.5E+4 μM 2.2E+4 μM μ Linda Turner et al. Biophysical Journal (1999), Philippe Cluzel et al., Science (2000)

From Motor Response to Cell Motion  Output of the chemotaxis network is the motor state which determines the motile behavior. R  runT  tumble  Run [6]  Tumble [7] t t+Δt v = 20 μm/s D r = s -1 α γ = 4 μ = -4.6 β = [6] Zou et al. (2003) Biophys. Journal [7] Berg and Brown (1972) Nature

Outline  Modeling E. coli chemotaxis network Chemical signal transduction pathway (reactions) Numerical implementation of transduction pathway (stochsim package) Couple motor response, output of transduction pathway, to cell motion  Preliminary numerical results Model validation (excitation and adaptation, motile behavior, etc) Input-output mutual information transmission  Future work

Model Validation: Step Response and Adaptation Time Fig. 3 E. coli motor response to 10 μM step-wise change of Asp at t=5 sec. The motor CCW bias is plotted as a funcion of time. Fig. 4 Adaptation time under various step-wise change of [Asp] from 0 to 0.1, 1, 10, 100, respectively. Adaptation time is defined as the motor CCW bias returns to its pre-stimulus value. (1000 is running)

Model Validation: Impulse Response of Wild-type Cell Fig. 5 Impulse response of wild-type cell ， impulse duration 0.2 sec. Left: Experimental result from Steven M. Block et all, Cell (1982) Right: Simulation result (data smoothed)

Model Validation: Running & Tumbling Intervals Fig. 6 The distribution of motor CCW and CW events. Left: korobkova et al., 2004 Right: Simulation results. (Red: CCW events; Black: CW events) (running to get a better looking result)

I/O Mutual Information: Preliminary Results  Construct Input-Output relation.  Construct a formula to calculate input-output mutual information.  Calculate IO information under different signals if we use the response to a specific signal.  Investigate the role of correlation time of signals in input-output information transmission.

I/O Mutual Information: Construct Input-output Relation  Artificial signal is presented to the simulation system. Fig. 7 Upper panel: Gaussian distributed artificial signal (μ=3 μM,σ 2 = 3 μM 2, correlation time 1 sec). Lower panel: Response to the input signal. Fig. 8 Response delays input by 0.1 sec. Input signal is binned first. Find response to input signal in each bin, then find the average response. Fig. 9 I-O relation under signals with different statistics. The correlation time of the signals is the same: 1 sec. Question: What is the role of varying response under different signals.

I/O Mutual Information: Calculation  s: Input signal; P(s): probability distribution of signal  r: response; P(r): probability distribution of response  r(s): I-O relation found as in last slide, mapping s to r.  n: noise;P(n|r): noise distribution conditioned on response  The following equation is used to calculate IO mutual information rate [7]. [7] Naama Brenner et al. (2000) Neuron

I/O Mutual Information: Effect of Correlation Time of Signal  The so found response function under an input signal maximizing information rate under such input. Fig. 10 All signals have correlation time of 1 sec. The response function, r(s), to (3, 3) is used to transform input signals with different statistical properties to output. The IO mutual information is calculated. The IO information rate maximizes at (3, 3) signal, which is the signal that is used to find r(s).

IO Mutual Information: Effect of Correlation Time of Signal Fig. 11 Information transmitted by E. coli chemotaxis network is plotted as a function of correlation time of signals, which have different statistic parameters. With the increasing correlation time, E. coli is able to extract more information out of the input signal. Typical impulse response time of wild-type E. coli is around 1 sec.

Conclusion

Outline  Modeling E. coli chemotaxis network Chemical signal transduction pathway (reactions) Motor and flagella response, and cell motion Numerical implementation (stochsim package)  Preliminary numerical results Model validation (excitation and adaptation, motile behavior, etc) Input-output mutual information transmission  Future work

Thank you.