Imperial/Dry Lab/Modelling

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=Model Development for Infector Detector <font color = red> ''(page population in progress)''</font>=
 
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==Formulation of the problem==
 
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As described earlier, catheter-associated urinary tract infection (CAUTI) in the clinical setting is a prevalent problem with extensive economic impact. The underlying cause of many such infections can be attributed to the formation of biofilm, by aggregating-bacteria on the surface of urinary catheters.
 
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[[Image: IC07_QS.png|right|thumb|500px| Role of AHL (HSL) quorum-sensing in biofilm formation]]
 
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Infector Detector (ID) is a simple biological detector, which serves to expose bacterial biofilm. It functions by exploiting the inherent AHL (Acetyl Homoserine Lactone)  production employed by certain types of quorum-sensing bacteria, in the formation of such structures.<br>
 
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Our project attempts to improve where previous methods of biofilm detection have proven ineffective: first and foremost, by focussing on the sensitivity of the system, to markers of biofilm: in this case, low levels of AHL production (which represents the bacterial "chatter" of such aggregating bacteria).
 
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In doing so, a complete investigation of the level of sensitivity to AHL concentration needs to be performed - in other words, what is the minimal AHL concentration for appreciable expression of a chosen reporter protein. Furthermore, establish a functional range for possible AHL detection. How does increased AHL concentration impact on the maximal output of reporter protein?<br>
 
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Finally, how can the system performance be tailored, by exploiting possible state variables (e.g. varying initial LuxR concentration and/or concentration of pLux promoters). 
 
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The system performance here revolves most importantly around AHL sensitivity; however, the effect on the maximal output of fluorescent reporter protein and response time is, likewise, of great importance.
 
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==Selection of Model Design and Structure==
 
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Since the novelty of our solution revolves around the use of cell-free systems as a "bacterial-free" solution in the clinical setting, a simple system is selected. Our approach involves a modified version of the bioluminescence machinery employed by the bacterium ''Vibrio Fischeri''.
 
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In fact, the characterization of this machinery, forms the setting for the first detailed description of the above-mentioned quorum-sensing phenomenon (Engebrecht and Silverman, 1984 and Engebrecht et al., 1983).
 
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A system which employs two regulatory proteins LuxR and LuxI, which, together with the autoinducer protein, AHL, control the expression of the in-house reporter (luciferase).
 
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Our system maintains the general flavour of this configuration; involving a marginally-varied sensor and reporter element.
 
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In fact, an already present system is utilized, for its simplicity and good definition - [http://partsregistry.org/Part:BBa_T9002 T9002]. This forms our construct 1.
 
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One of the questions posed in the formulation of the model, involved exploring means of "tweaking" the system to achieve improved performance (sensitivity/maximal output/response time). A possible solution could involve introducing purified LuxR into the system, and in this way impose steady-state far sooner than for construct 1. Theoretically, this should shorten response time. It is for this reason, that a second construct will be investigated. Construct 2 thus differs only w.r.t the elimination of the constitutive promoter pTET. (here, LuxR is introduced directly).
 
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<font color = red>~~Insert diagram illustrating both constructs </font><br>
 
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<font color = red>~~Insert diagram illustrating both interaction of molecules </font><br>
 
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<font color = red>~~Insert diagram illustrating sensor and reporter elements </font><br>
 
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==Establishing a model==
 
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===Approach===
 
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At reasonably high molecular concentrations of the state variables, a continuous model can be adopted, which is represented by a system of ordinary differential equations.
 
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It is for this reason that our approach to modelling the system follows a deterministic, continuous approximation. In developing this model, we were interested in the behaviour at steady-state, that is when the system has equilibrated and the concentrations of the state variables remain constant.
 
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We can condition the system in various manners, but for the purposes of our project, we will seek a formulation which is valid for both constructs considered, i.e. the governing equations are a represenation of both constructs.
 
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The only difference is with regards to the parameter k<sub>1</sub>, the maximum transcription rate of the constitutive promoter (pTET) in Construct 1. <br> Thus k<sub>1</sub> = 0 for construct 2 (which lacks pTET).
 
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Furthermore, we generate two models based upon the available system energy:
 
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'''Model 1''':  Infinite Energy<br>
 
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'''Model 2''':  Limited Energy<br>
 
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The system kinetics are determined by the following coupled-ODEs. For a derivation of the governing equations,  please access
 
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[https://2007.igem.org/wiki/index.php?title=Imperial/Dry_Lab/Modelling/Model_Derivation Model Derivation]
 
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===Model 1===
 
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Our initial approach assumed that energy would be in unlimited supply, and that our system would eventually reach steady-state.
 
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[[Image: IC07 Model1.png|600px]]
 
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===Model 2===
 
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Experimentation suggested otherwise; our system needed to be amended. This lead to the development of model 2, an energy-dependent network, where the dependence on energy assumes Hill-like dynamics:<br>
 
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[[Image: IC07 Model2.png|600px]]
 
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====''Model Parameters''====
 
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{| class="wikitable" border="1" cellspacing="0" cellpadding="2" style="text-align:left; margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
 
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! Parameter                   
 
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! Description
 
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|-
 
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|<font color = blue>''Kinetic <br> Constants'' </font>
 
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|
 
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|-
 
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| k<sub>1</sub>
 
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| Maximal constitutive transcription of LuxR by pTET
 
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|-
 
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|k<sub>2</sub>
 
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|Binding between LuxR and AHL
 
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|-
 
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|k<sub>3</sub>
 
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|Dissociation of protein complex LuxR-AHL (A)
 
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|-
 
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|k<sub>4</sub>
 
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|Binding between A and pLux promoter
 
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|k<sub>5</sub>
 
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|Dissociaton of A-pLux complex
 
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|k<sub>6</sub>
 
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|Transcription of FP
 
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|<font color = blue>''Degradation <br> Rates'' </font>
 
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|&delta;<sub>LuxR</sub>
 
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|Degradation rate of LuxR
 
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|&delta;<sub>AHL</sub>
 
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|Degradation rate of AHL
 
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|&delta;<sub>GFP</sub>
 
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|Degradation rate of GFP
 
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|-
 
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|<font color = blue>''Hill Co-operativity''</font>
 
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|-
 
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|n
 
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|Co-operativity coefficient describing the degree <br>of energy dependence, which follows Hill-like dynamics
 
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|<font color = blue>''Energy consumption <br> of transcription''</font>
 
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|&alpha;<sub>1</sub>
 
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|Energy consumption due to constitutive transcription of LuxR
 
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|&alpha;<sub>2</sub>
 
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|Energy consumption due to transcription of ''gfp'' gene
 
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|}
 
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==References==
 
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==Log==
 
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*Images - black borders, pastel backgrounds (pale) - see QS image; stretch to fill gaps - no white spaces
 
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*Equations - bordered
 
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*Improve appearance of eqns - presentation? symmetry?
 
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*LaTeX on MIT wiki?
 

Revision as of 23:39, 25 October 2007