1. The chemotaxis network is able to extract as much as information possible once the input signal varies slower relative to the response time of the chemotaxis network. Under an input signal with specific statistics, the chemotaxis network varies its response to optimize the cell’s performance, maximizing the mutual information between input signal and output response. Optimal Strategy of E. coli Chemotaxis Network from Information Processing View Lin Wang and Sima Setayeshgar Department of Physics, Indiana University, Bloomington, Indiana 47405 From R. M. Berry, Encyclopedia of Life Sciences Physical constants for motion: Cell speed: 20-30 μ m/sec Mean run time: 1 sec Mean tumble time: 0.1 sec Fluorescently labeled E. coli (Berg lab) Body size:1 μ m in length, 0.4 μ m in radius Flagellum:10 μ m long, 45 nm in diameter Motivation Chemical signaling cascade is the most fundamental information processing unit in biological systems. Generally, it converts an external stimulus to change in concentration of intracellular signaling molecules. E. coli Chemotaxis Chemotaxis, motion toward desirable chemicals (usually nutrients) and away from harmful ones, is achieved through continuous ‘runs’ and ‘tumbles’. Adaptation Adaptation is an important and generic property of signaling systems, where the response (e.g. running bias in chemotaxis) returns precisely to the pre-stimulus level while the stimulus persists. Adaptation functions from short time scale (impulse) to long time scale (evolution). It allows the system to compensate for the presence of continued stimulation and to be ready to respond to further stimuli. Numerical Implementation The chemotaxis signal transduction pathway in E. coli – a network of ~50 interacting proteins – converts an external stimulus (change in concentration of chemo-attractant / repellent) into an internal stimulus (change in concentration of intracellular response regulator, CheY-P) which in turn interacts with the flagella motor to bias the cell’s motion. Model Validation By utilizing this realistic and stochastic numerical implementation, we explore E. coli chemotaxis network from the standpoint of general information-processing concepts. Input-Output Relation Conclusions Motion Photoreceptor [1,2] Use E. coli chemotaxis network as a prototype to explore the general information processing principle in biological systems. [1] R. C. Hardie et al. (2001) Nature 413, 186-193 [2] J. Oberwinkler et al. (2000) PNAS 97, 8578-8583 Chemotaxis network Signal Transduction Pathway Motor Response [CheY-P] Stimulus Flagellar Bundling Numerical Adaptation [3] [3] Sourjik et al. (2002) PNAS. 99 123-127 [4] H. C. Berg, (1975) PNAS. 72 71-713 Attractant: 30 μ M aspartate. Repellent: 100 μ M NiCl 2 Adaptation to various step change of attractant serine (mM). nP 1 (n)P 2 (n) 00.020.00291 10.170.02 20.50.17 30.8740.5 40.9970.98 MoleculeNumber Concentration ( μ M) Y1568418 Yp00 R2500.29 E6276- B19282.27 Bp00 Parameter values of chemotaxis network Table I: Signal Transduction Network Table III: Initial Protein Levels Table II: Activation Probabilities Motor response [6] Motor response A simple threshold model is used to model motor response. The motor switches state whenever CheY-P trace (blue trace) crosses the threshold (red line) Simulating reactions Reactions are simulated using Stochsim [5] package, a general platform for simulating reactions stochastically. Reactions have a probability p to occur. Symbols: n: Number of molecules in reaction system n 0 : Number of pseudo-molecules N A : Avogadro constant p: Probability for a reaction to happen Δ t: Simulation time step V: Simulation volume Bi-molecular reaction Uni-molecular reaction Focus The preliminary result suggests that E. coli varies its response under signals with different statistics. My goal is to understand how signal transduction pathways, such as the chemotaxis network, may adapt to the statistics of the fluctuating input so as to optimize the cell’s response. My focus is to find out an approach to evaluate information transmission rate and then investigate the role of adaptation. Adaptation [9] Motor CCW and CW intervals [11] Adaptation time [10] [5] C. J. Morton-Firth et al. 1998 J. Theor. Biol.. 192 117-128 [6]T. Emonet et al. 2005 Bioinformatics 21 2714-2721 Discussion: the simulation results are in good agreement with experiments, although the adaptation times differ by a small factor. Cell response when exposed to a step change of aspartate from 0 to 0.1 mM (left), 10 μM (right) beginning at 5 sec. Transition time to step change of external attractant Distribution of wild-type E. coli motor CW (grey) and CCW (black) intervals. Upper: Gaussian distributed signal ( μ =3 μ M, σ 2 = μ, τ = 1 sec) Lower panel: Response to the input signal. I/O relation under signals with different statistics. ( τ = 1 sec) The response is the average of responses in each bin of signal. Mutual Information The average information that observation of Y provide about the signal X, is I, the mutual information of X and Y [7]. I is at minimum, zero, when Y is independent of X, while it is at maximum when Y is completely determined by X. The I/O mutual information rate can be calculated by the following equation [8]. s: Input signal; P(s): probability distribution of signal r: response; P(r): probability distribution of response r(s): I-O relation, mapping s to r. n: noise; P(n|r): noise distribution conditioned on response [7] Spikes, Fred Rieke et al. 1997, p122-123 [8] N. Brenner et al. (2000) Neuron. 26 695-702 Effect of Correlation Time τ My first step is to investigate the effect of correlation time τ to the I/O mutual information rate of the chemotaxis network. Response r(s) to signals: μ =1 μ M, σ 2 = μ, τ = 0.1, 0.3, 0.8, 1 sec, respectively. At τ > 0.8 sec, the response does not change any more. (This holds true for signals with different mean values) Effect of τ in I/O mutual information The I/O mutual information rate of E. coli chemotaxis network is plotted as a function of correlation time τ. The Gaussian distributed signals used here have means of 1, 3, 5, and 10, respectively. Use a realistic description of motor to replace the simple threshold model of motor response. Take into account the clustering effect among trans-membrane aspartate receptors to improve the performance of the numerical implementation. Investigate role of adaptation time. Future Work Effect of τ on I/O relation Effect of varying response Use r (s 1 ) under input signal s 1 ( μ 1 =1 μ M, σ 1 2 = μ 1, τ 1 = 1 sec) to find P(r) for different input signals, and calculate the mutual information between r (s 1 ) and s k. The calculated I/O mutual information rate of E. coli chemotaxis network maximizes under the condition that the response and the input signal matches. [9] S. M. Block et al. 1982 Cell 31 215-226 [10] H. C. Berg et al. 1975 PNAS 72 3235-3239 [11] T. Emonet et al. 2005 Bioinformatics 21 2714-2721 E. coli chemotaxis network Signal Output Input signal Artificially generated Gaussian distributed time series with correlation time τ. Output Number of CheY-P molecules Adaptation variation [3] E. Coli Chemotaxis [3] Photon Δ [Ca 2+ ] Ca 2+ Fluorescence Attractant Δ [CheY-P] Response of drosophila photoreceptor to photon absorption. Response of E. coli to external attractant. Yellow: CheY-P relative level. Run Bias Simulation Experiment