Team:Purdue/Modeling2

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Latest revision as of 21:03, 18 July 2012


Modeling

Levels of Investigation

  • How biofilm responds to shear, flow, temp, surface attachment, etc
  • How Silica traps the particle during flow
  • How Curli adheres and how OmpA-Silicatein Alpha polymerizes Silica/How the silica crystalizes (introduction of Salicylic Acid)
  • How protien expression responds to external and metabolic variation (e.g. introduction of IPTG to system)
  • How constructs work with each other/controls systems
  • How RBS/ Promoter effects protein expression

Distribution of Modeling

Matlab
  • Protein Production
  • Feed Forward Loop Control Structure
TinkerCell
  • Quorum sensing
  • Feed Forward Loop
JMP
  • Experimental Design and Characterization Experiments
Comsol/Other
  • Waterflow and shear force on final system
  • Silica formation

Design

  • Desired Outcomes of Models
  • Levels of Abstractions

    • Biofilter response to Environmental conditions
      • Shear
      • Flow
      • Temperature
      • Abiotic Surface (Adhesion)
    • Formation of Silica Matrix
    • BioFilm Development
      • Model of Bacterial Growth, Death, Breaking Off
    • Expression of Proteins
      • Response to addition of IPTG
      • Optimal Production rate/expression of Curli and OmpA-Silicatein Alpha protiens
      • Control Systems
      • Fine Tuning of Protein Expression with RBS/Promoter combination variants

  • Platforms
  • Considerations and Assumption
  • Parameters

Equations

    The growth of the Biofilm can be modeled with modified continuous growth models. Traditional models of population growth make use of basic differential equations to measure the change in population over unit time. At the most fundamental level

    Population Change Rate = dN = bN-dN
    dt

    Where N is the population of individuals, b is the rate of births or immigration, and d is the rate of deaths or emigration.

    To understand these dynamics of population in the context of biofilm growth, we treat the bacterial attachment and detachment as a reversible reaction of the form

    N Bacteria Attached < k1 > N Bacteria Detached
    k2

    Where k1 is the rate constant of detachment and k2 is the rate constant of attachment. Because we have chosen to simplfily the cell attachment and detachment as a reaction, we are able to employ reaction kinects to predict the rate of binding that will dictate the constants to population growth.

    Such assumptions allow us to make use of basic principles of reaction kinetics such as the Law of Mass Action , which dictates that a rate of reaction is always proportional to the concentration of its reactions. Therefore, using the attached and detached cells as the reactants in the equation the rate of attachment becomes

    Rate of Growth of Attached Bacteria = dNatt = k2Ndet + βNdet - k1Natt - αNatt
    dt

    introducing the constants α, which is degredation and dilution, and β, which is reproduction rate.

Assumptions and Simplifications

Outcomes

Parameter Theoretical Value Experimental Value Analysis
Parameter 1 ____ ____ ____
Parameter 2 ____ ____ ____
Parameter 3 ____ ____ ____
Parameter 4 ____ ____ ____

References

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