Team:Purdue/Modeling
From 2012.igem.org
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 | ||
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} < | k_{1} | > N _{Bacteria Detached} |
k_{2} | ||
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 = | dN_{att} | = k_{2}N_{det} + βN_{det} - k_{1}N_{att} - αN_{att} |
dt | ||
Interation One
In the first iteration, certain simplifying assumptions were made. We assume that the LacI protein has reached a steady state level in the cell. Upon the introduction of lactose into the media, LacI is inactivated immediately, resulting in activation of repressed genes. All interactions are modeled with Michaelis-Menten binding kinetics, running the expression of each protein as a differential equation and plots it against the time the circuit runs, with addition of Lactose at the 10 unit mark. It is evident at this point that promoter regulating expression of the ompR234 protein (which is directly proportional to the variable 'XCurli' in the model) is switched off, leading to gradual degradation of the protein in the system. Each term, X_Curli, X_Sila, and X_tetR, are designed to have a primary expression term (the first term in each differential equation) followed by a term which accounts for the degradation and dilution of the protein within the cell. The parameters entered are system-independent estimates, stable over a range of behaviors. Sensitivity analysis of the parameters in the system shows that time-evolution is robust to the initial parameter estimates.
Interation Two
The second iteration addresses interactions of the OmpR234 protein with the activators EnvZ, and EnvZ's interaction with upregulation of the Curli expression gene. The visualization of this model reveals the sensitivity of the feedback loop.
Interation Three
The final iteration of the model creates a mathematical model that more correctly assumes that OmpR234 interacts at the protein level rather than the transcriptional level. The model provides evidence that OmpR234 provides too much a time delay for optimal deactiviation of the Curli adhesion and protein, providing an avenue for future project improvement.