Team:Michigan/Modeling
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Mathematical models are very important in the design of an iGEM project. The Michigan modeling team is composed of [[User:Evolver|Josh]], [[User:Kevijose|Kevin]], [[User:htwong|Candy]], [[User:Jejihong|Jennifer]], and [[User:seongkyu|John]]. To construct our models, we have taken advantage of MATLAB's Simbiology toolset. More information and tutorials on Matlab and Simbiology can be found here: [http://www.mathworks.com/academia/student_center/tutorials/launchpad.html?s_cid=0410_webg_igem10_294031 MATLAB Tutorial] | Mathematical models are very important in the design of an iGEM project. The Michigan modeling team is composed of [[User:Evolver|Josh]], [[User:Kevijose|Kevin]], [[User:htwong|Candy]], [[User:Jejihong|Jennifer]], and [[User:seongkyu|John]]. To construct our models, we have taken advantage of MATLAB's Simbiology toolset. More information and tutorials on Matlab and Simbiology can be found here: [http://www.mathworks.com/academia/student_center/tutorials/launchpad.html?s_cid=0410_webg_igem10_294031 MATLAB Tutorial] | ||
- | There are several components to a good mathematical model. These include assumptions, parameters, and equations. | + | There are several components to a good mathematical model. These include assumptions, variables, parameters, and equations. |
- | *Assumptions | + | *Assumptions help to decide how to describe each part of the system, as well as to identify which parts (if any) to deem negligible. Almost always, these assumptions yield an idealized version of the system, and it is within this framework that the model is truly valid. Outside of this ideal model, the real system deviates. However, if the assumptions are sufficiently comprehensive and reasonably valid, then this ideal model can be a very good approximation to the real system. |
- | *Parameters are | + | |
- | * | + | *Variables are quantities that are "measured" independently, e.g. in a simulation or experiment. As the name implies, they are not defined to be constants in the system, although occasionally a variable may maintain a [nearly] constant value in a particular simulation or trial of an experiment. The behavior, relationships, and responses of the variables are of utmost interest in the model, as they are what allow conclusions to be drawn. |
- | + | ||
+ | *Parameters are quantities, in particular defined to be constant, that the model takes to be part of the inherent description of the system. They help to characterize the properties and relations between variables. For example, the relationship between two variables is defined by the functional form and the parameters, used as "coefficients". Often, parameters are used to characterize a relationship that cannot or need not be described in an explicit functional form (e.g. reaction rate constants in a differential rate equation). | ||
+ | |||
+ | *Equations relate variables to each other, and they essentially translate the [idealized] system into the language of mathematics. The form of each equation is dictated by the assumptions and the parameters. For example, a system of ordinary differential equations constitutes the mathematical representation of the model. In this case, one seeks the solution to the system of ODEs to acquire a full understanding of the dynamic behavior of the idealized system. Often, an analytic solution may be impossible to find, so numerical simulations/solutions are extensively used. Alternatively, one can examine other aspects, such as steady-state behavior. | ||
==Pili== | ==Pili== | ||
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<u>Parameters</u> | <u>Parameters</u> | ||
<br> | <br> | ||
+ | These parameters were determined through running various assays. These parameters are not exact values yet, but are meant to convey a sense of which factors were faster than others. | ||
'''Rate of piliation= 10''' | '''Rate of piliation= 10''' | ||
*From experimental observation, the pili growth factor is greater than the rate of flocculation. | *From experimental observation, the pili growth factor is greater than the rate of flocculation. | ||
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[[Image:Pili_floc_model.jpg|500px]] | [[Image:Pili_floc_model.jpg|500px]] | ||
- | This results graph shows that the population of both the algae and the flocs stabilize to a constant level over time. We need to conduct more | + | ===Conclusions and Further Work=== |
+ | This results graph shows that the population of both the algae and the flocs stabilize to a constant level over time. We need to conduct more laboratory assays to determine if this is the actual case. If it is, we can adjust the model and start running more simulations to relate it to the lab setting. Possible solutions to increase the amount of the flocs would be to add more E. coli, but this is not ideal in the industrial setting due to the cost. | ||
[[#top|Back to top]] | [[#top|Back to top]] | ||
<br style="clear: both" /> | <br style="clear: both" /> | ||
==Quorum Sensing== | ==Quorum Sensing== | ||
- | Quorum sensing has been modeled by other iGEM teams for previous competitions, including: [ | + | Quorum sensing has been modeled by other iGEM teams for previous competitions, including: [https://2007.igem.org/Bangalore Bangalore] and [https://2008.igem.org/Team:NTU-Singapore Singapore] |
[[Image:LuxS- Modeling001.jpg|right]] This model is based on the paper [http://jb.asm.org/cgi/content/short/189/16/6011 Quorum Sensing in Escherichia coli Is Signaled by AI-2/LsrR: Effects on Small RNA and Biofilm Architecture (doi:10.1128/JB.00014-07)] and was created with the help of [[User:infekt|Alex]] who is also on the quorum sensing team. More information about quorum sensing can be found here: [[Team:Michigan/Project]] and their notebook can be found here: [[Team:Michigan/Quorum_Sensing]]. | [[Image:LuxS- Modeling001.jpg|right]] This model is based on the paper [http://jb.asm.org/cgi/content/short/189/16/6011 Quorum Sensing in Escherichia coli Is Signaled by AI-2/LsrR: Effects on Small RNA and Biofilm Architecture (doi:10.1128/JB.00014-07)] and was created with the help of [[User:infekt|Alex]] who is also on the quorum sensing team. More information about quorum sensing can be found here: [[Team:Michigan/Project]] and their notebook can be found here: [[Team:Michigan/Quorum_Sensing]]. | ||
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Note: Although concentration and time are in arbitrary units, they are consistent across all plots. | Note: Although concentration and time are in arbitrary units, they are consistent across all plots. | ||
- | [[Image: | + | [[Image:log_dec_NAs.jpg|500px]] |
[[Image:influent entry unlim nutr.jpg|500px]] | [[Image:influent entry unlim nutr.jpg|500px]] | ||
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'''Conclusions''' | '''Conclusions''' | ||
- | From this model, we can extrapolate that the longer the bioreactor, the more NAs will be degraded, as the ''Pseudomonas'' species are present along the entire length of the bioreactor. We also find that, when described with a logistic equation, ''Pseudomonas'' populations eventually reached a steady state in each unit, coupled with the plateau of NA concentration in the corresponding units. In future studies, if an estimate of NA degradation efficiency is described along the length of the bioreactor, we can model NA degradation assuming that ''Pseudomonas'' population are in a steady state. | + | From this model, we can extrapolate that the longer the bioreactor, the more NAs will be degraded, as the ''Pseudomonas'' species are present along the entire length of the bioreactor. We also find that, when described with a logistic equation, ''Pseudomonas'' populations eventually reached a steady state in each unit, coupled with the plateau of NA concentration in the corresponding units. In future studies, if an estimate of NA degradation efficiency is described along the length of the bioreactor, we can model NA degradation assuming that ''Pseudomonas'' population are in a steady state. In addition, it is made clear in the semi-log plot of NA concentration of each unit that efficiency per length of bioreactor in degrading NAs decrease exponentially. It is thus unnecessary to produce a bioreactor beyond a certain length, where the NAs degraded along the additional length contribute very little to the NA concentration in the effluent. |
Ideally, a drip flow bioreactor should be modeled by a plug flow reactor model, which describes a fluid flowing through a pipe with perfect mixing in the radial direction and no mixing in the axial direction. However, we deemed the method above to be sufficient for our purposes and more intuitive in design. [https://2009.igem.org/Team:uOttawa/Modeling uOttawa] used plug flow model to describe nutrient flow in the intestines. | Ideally, a drip flow bioreactor should be modeled by a plug flow reactor model, which describes a fluid flowing through a pipe with perfect mixing in the radial direction and no mixing in the axial direction. However, we deemed the method above to be sufficient for our purposes and more intuitive in design. [https://2009.igem.org/Team:uOttawa/Modeling uOttawa] used plug flow model to describe nutrient flow in the intestines. |
Latest revision as of 05:30, 27 October 2010