IGEM:Cambridge/2008/Notebook/Turing Pattern Formation
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== [[IGEM:Cambridge/2008/Turing_Pattern_Formation/Modelling  Modelling ReactionDiffusion Systems]] ==  == [[IGEM:Cambridge/2008/Turing_Pattern_Formation/Modelling  Modelling ReactionDiffusion Systems]] ==  
  [[Image:Turing_moving.png   +  [[Image:Turing_moving.png  A moving, spatially unstable pattern  thumb  right ]] 
Mathematically, reactiondiffusion systems are coupled nonlinear differential equations that can be solved numerically. Our main goal is to create a system approximating the behaviour of the luxactivator and agrinhibitor systems that we intend to use with B. subtilis. This will include a detailed analysis of enzyme kinematics and we hope to deduce the parameter ranges in which our B.subtilis construct will be able to form patterns, thus feeding back into our design decisions (promoter choice, rbs choice).  Mathematically, reactiondiffusion systems are coupled nonlinear differential equations that can be solved numerically. Our main goal is to create a system approximating the behaviour of the luxactivator and agrinhibitor systems that we intend to use with B. subtilis. This will include a detailed analysis of enzyme kinematics and we hope to deduce the parameter ranges in which our B.subtilis construct will be able to form patterns, thus feeding back into our design decisions (promoter choice, rbs choice). 
Revision as of 11:03, 11 August 2008
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IntroductionWe are planning to implement a simple twocomponent ReactionDiffusion system in the grampositive model organism Bacillus subtilis. In 1952, Alan Turing famously described this system and suggested it as the basis for selforganization and pattern formation in biological systems. The simplest of these patterns, which we are planning to model in bacteria, mimic the spots and stripes seen on animal coats.
(A) The model consists of two diffusible signals secreted by every cell. The activator, which is controlled by a stochastic bistable switch, turns on itself and its own inhibitor. (B) A field of cells can be stably patterned into two different zones, so long as the inhibitor diffuses faster than the activator. The activator and inhibitor are synthesized in the source at the center, and turned off by accumulation of the inhibitor in the periphery.
We plan to use two wellcharacterized bacterial communication systems to generate this behavior. The agr peptide signalling system from S. aureus will serve as our activatory signal (pictured), while the lux system from V. fischeri will serve as our inhibitor. Bacillus subtilis serves as an excellent chassis for this project because of the ease with which chromosomal integration can be performed. This project will focus on a tight integration of modeling and experiment; we will test different promoter strengths and other variables, feed these system parameters into our multicell models, and then use those models to tweak the regulatory machinery that will control signal production. Grasshopper ExampleThe reactiondiffusion system depends on an activator and inhibitory signal that spread throughout the medium. The "grasshopper" example is quite intuitive: Imagine it is hot and there is a field of dry grass with grasshoppers. Suddenly, a fire starts burning at some point and spreads (the activator signal) so that the grasshoppers move away from that point to avoid the fire. However, the grasshoppers also generate moisture (the inhibitory signal) thus preventing the areas of dry grass the grasshoppers move to of catching fire. The initial patch will have burnt down. However, the surrounded area will be saturated by moisture generated by the grasshoppers thus preventing the fire from spreading. Imagine now that at the beginning, not a single patch, but numerous randomly distributed patches (resembling noise) of dry grass catch fire. The resulting patterning of charred grass and grasshoppers is called a Turing Pattern. It is important to note that the inhibitory signal (grasshoppers) must travel faster than the activation signal (fire) as to prevent the whole field from burning down which would result in no patterning at all. ObjectiveThis project seeks to generate Turing Patterns by creating a ReactionDiffusion system in the grampositive bacteria Bacillus subtilis. We need to integrate two signalling systems into this bacterium and use an autofeedback mechanism to generate selforganizing patterns from random noise. We plan to incorporate the agr peptide signalling system from S. aureus and the lux AHL system from V. fisheri. MaterialsBacillus StrainsBacillus strain 1A1 (derivative of standard strain 168)
Bacillus strain 1A771 (derivative of standard strain 168)
Bacillus strain 1A751 (derivative of standard strain 168)
Vectors
PrimersConstructs
Modelling ReactionDiffusion SystemsMathematically, reactiondiffusion systems are coupled nonlinear differential equations that can be solved numerically. Our main goal is to create a system approximating the behaviour of the luxactivator and agrinhibitor systems that we intend to use with B. subtilis. This will include a detailed analysis of enzyme kinematics and we hope to deduce the parameter ranges in which our B.subtilis construct will be able to form patterns, thus feeding back into our design decisions (promoter choice, rbs choice). We will also take a significant investigative approach and ask whether Turinglike patterns can originate from systems that do not resemble reactiondiffusion. In particular, we would like to ask whether pattern formation can occur with a single signalling molecule only.
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Experiments
