Team:ETHZ Basel/Modeling

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= Mathematical Modeling Overview =
= Mathematical Modeling Overview =
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[[Image:ETHZ_Basel_molecular_comb.png|thumb|400px|'''Schematical overview of the devices used in modeling the E.lemming.''' LSP refers to light switch protein, AP to anchor protein, anchor to the plasmid anchor and Che to the attacked protein of the chemotaxis pathway. The core component of E. lemming is the fusion of one light-sensitive protein (LSP1) to a protein of the chemotaxis pathway (Che). Upon change of wavelength of light pulses, this component will dimerize with the corresponding light-sensitive protein (LSP2), which is linked to an anchor protein, bound to an anchor (plasmid). The result is a change of the spatial localization of Che, perturbing the chemotaxis pathway, which ultimately leads to a different tumbling/directed movement state ratio.
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[[Image:ETHZ_Basel_molecular_comb.png|thumb|400px|'''Figure 1: schematical overview of the modeled processes in E. lemming.''' LSP refers to light switch protein, AP to anchor protein, and Che to the attacked protein of the chemotaxis pathway.]]
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In order to support [[Team:ETHZ_Basel/Biology|wet laboratory experiments]] and to create a test bench for the [[Team:ETHZ_Basel/InformationProcessing|information processing]] part, a complex mathematical model of E. lemming was created. This goal was achieved by implementing and combining deterministic molecular models of the [[Team:ETHZ_Basel/Modeling/Chemotaxis| chemotaxis pathway]] and the [[Team:ETHZ_Basel/Modeling/Light_Switch| light switch]] and probabilistic model for the [[Team:ETHZ_Basel/Modeling/Movement| bacterial movement]].
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A complex mathematical model of E. lemming from both literature inspired and self developed submodels was created that covers the processes displayed in Figure 1.
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== Model implementation ==
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In a first step, existing models for the individual processes of E. lemming have been identified by literature research, implemented, corrected and adapted to our needs. Where we could not rely on established models, we started modeling on our own and calibrated the model with regard to available literature knowledge.
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=== Individual molecular models ===
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In a first step, we implemented individual deterministic molecular models for the subdevices and a stochastic mathematical model of the bacterial movement.
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* [[Team:ETHZ_Basel/Modeling/Chemotaxis|'''Chemotaxis Pathway''']]: two similar models of the chemotactic receptor pathway.
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* [[Team:ETHZ_Basel/Modeling/Light_Switch|'''Light Switch''']]: based on the light-sensitive dimerizing Arabidopsis proteins PhyB and PIF3.
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* [[Team:ETHZ_Basel/Modeling/Movement|'''Bacterial Movement''']]: a probabilistic model of ''E. coli'' movement, determined by distribution of input bias.
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=== Combined mathematical models ===
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* [[Team:ETHZ_Basel/Modeling/Light_Switch|'''Light Switch''']]: both implementation approaches have been modeled:
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[[Image:ETHZ_Basel_models_overview_comb.png|thumb|400px|'''Combined models.''' Coupled individual models for the simulation of the entire process and their interfaces.]]
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** [[Team:ETHZ_Basel/Modeling/Light_Switch#Modeling_of_the_light_switch:_PhyB.2FPIF3|'''PhyB/PIF3''']]: a deterministic molecular model based on the light-sensitive dimerizing Arabidopsis proteins PhyB and PIF3.
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The next step, combining the individual models to a comprehensive and more complex model of E. lemming was achieved in two substeps:
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** [[Team:ETHZ_Basel/Modeling/Light_Switch#Modeling_of_the_PhyB.2FPIF3_light_switch#Archeal_light_receptor|'''Archeal Light Receptor''']]: a deterministic molecular model based on the archeal light receptor.
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* [[Team:ETHZ_Basel/Modeling/Combined#Light_switch_-_Chemotaxis |'''Light switch - Chemotaxis''']]: used to provide support for wet laboratory.
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* [[Team:ETHZ_Basel/Modeling/Chemotaxis|'''Chemotaxis Pathway''']]: two deterministic molecular models of the chemotaxis pathway.
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* [[Team:ETHZ_Basel/Modeling/Combined#Chemotaxis_-_Movement |''' Chemotaxis - Movement''']]: complete model of E. lemming.
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* [[Team:ETHZ_Basel/Modeling/Movement|'''Bacterial Movement''']]: a self developed stochastic model of ''E. coli'' movement on basis of the CheYp bias.
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== Experimental Design ==
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In a second part, we combined the submodels stepwise to more comprehensive models that we could use to address different important questions to:
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=== Insights for wet laboratory ===
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* [[Team:ETHZ_Basel/Modeling/Combined#PhyB.2FPIF3_light_switch_-_Chemotaxis |'''PhyB/PIF3 light switch - Chemotaxis''']]: this model was used to reduce [[Team:ETHZ_Basel/Biology|wet laboratory experiments]] by identification molecular targets by [[Team:ETHZ_Basel/Modeling/Experimental_Design|experimental design]].
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Since the design of E.lemming implies the existence of many possible biological combinations of the fundamental parts, the first steps in the modeling of our system were directed towards reducing the actual number of combinations implemented in the wetlab. Furthermore, by using the combined molecular models for ''in silico'' evaluation of the best possible devices, we derived theoretical results on choosing the biological parts which maximize the chance of a functional final ensemble.
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* [[Team:ETHZ_Basel/Modeling/Combined#Archeal_light_receptor_-_Chemotaxis |'''Archeal light receptor - Chemotaxis''']]: this model was combined identically to the one above.
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* [[Team:ETHZ_Basel/Modeling/Combined#Chemotaxis_-_Movement |'''Chemotaxis - Movement''']]: complete model of E. lemming as a simulative test bench for the [[Team:ETHZ_Basel/InformationProcessing/Controller|controller]] design and as a brick of the comprehensive simulation of [[Team:ETHZ_Basel/InformationProcessing|information processing]].
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[[Team:ETHZ_Basel/Modeling/Experimental_Design#Insights_for_wet_laboratory|''' Wet laboratory evaluation results''']] have showed that molecular modeling and experimental biology can interwork to gain new insight on both aspects of our project.
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=== Insights for information processing ===
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In order to adjust the controller to have optimal light pulse rates, the combined molecular model has been used to determine the corresponding time constants.
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[[Team:ETHZ_Basel/Modeling/Experimental_Design#Insights_for_information_processing|'''Information processing evaluation results''']] provide further information on how this task has been accomplished.
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== Test bench for information processing ==
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[[Image:ETHZ_Basel_models_overview_ip.png|thumb|400px|'''Test bench for information processing.''']]
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In order to create a first test bench for the information processing pipeline, the combined model has been used to set up and evaluate [[Team:ETHZ_Basel/InformationProcessing/Controller| the controller]].
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By providing input ports for the actual and the desired movement direction of the bacterium and boolean output ports for both light pulses (red light/far red light), it was possible to time - dependently control the E. lemming and close the loop in simulating the overall network.
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Latest revision as of 19:09, 27 October 2010

Mathematical Modeling Overview

Figure 1: schematical overview of the modeled processes in E. lemming. LSP refers to light switch protein, AP to anchor protein, and Che to the attacked protein of the chemotaxis pathway.

A complex mathematical model of E. lemming from both literature inspired and self developed submodels was created that covers the processes displayed in Figure 1.

In a first step, existing models for the individual processes of E. lemming have been identified by literature research, implemented, corrected and adapted to our needs. Where we could not rely on established models, we started modeling on our own and calibrated the model with regard to available literature knowledge.

  • Light Switch: both implementation approaches have been modeled:
    • PhyB/PIF3: a deterministic molecular model based on the light-sensitive dimerizing Arabidopsis proteins PhyB and PIF3.
    • Archeal Light Receptor: a deterministic molecular model based on the archeal light receptor.
  • Chemotaxis Pathway: two deterministic molecular models of the chemotaxis pathway.
  • Bacterial Movement: a self developed stochastic model of E. coli movement on basis of the CheYp bias.

In a second part, we combined the submodels stepwise to more comprehensive models that we could use to address different important questions to:

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