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 and change upon light pulse induction.''' 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 and perturbation of 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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== Implementation of mathematical models ==
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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 molecular and 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 whole 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, combination of the individual molecular and mathematical models to a comprehensive 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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To create the biological implementation of E. lemming, the parts of the core components had to be chosen in an order to improve chances to result in a functioning ensemble. By using the combined molecular models for ''in silico'' evaluation of the best possible parts, it was possible to reduce the amount of different combinations to be tested.
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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 for both perceptions of the problem.
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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 how this 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 create and evaluate the controller. By providing an input port for light pulse and an output port for bacterial movement, it was possible to close the loop and simulate the whole system.
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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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