IGEM:IMPERIAL/2008/New/Growth Curve
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<br>  <br>  
<font size=6px color=#E5EBFF><b>Growth Curve</b></font>  <font size=6px color=#E5EBFF><b>Growth Curve</b></font>  
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+  ==Results==  
+  [[Image:Log_graph.tifthumbcenter300pxLogGraph used to determine the growth rate]]  
+  The model for the growth curve was fitted to the experimental results as shown below. The experimental results is depicted by the red curve, while our model is shown by the green curve. The resource curve was also plotted as a function of time and is shown below. Based on our experimental results from the Wet Lab, a log graph was plotted to determine the growth rate. The growth rate was then determined from the gradient of the log graph. This value was included when simulating the growth model using MATLAB.  
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+  The following constants used to generate the model were found to yield the best fit to experimental results.  
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+  '''GROWTH CONSTANT: A = 1.3494  
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+  '''INITIAL NUTRIENT CONCENTRATION: R_0 = 2'''  
+  
+  '''HILL COEFFICIENT: n = 1.25'''  
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+  '''INITIAL OD = 0.4'''  
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+  '''CONSTANT: <math>\alpha</math> = 0.64516'''  
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+  <br>  
+  { border="1" cellpadding="5" cellspacing="0" align="center"  
+    
+  [[Image:Experimental_Result.JPG thumbcenter300px]]  
+  [[Image:Fitted_Curve.JPG thumbcenter300px]]  
+  [[Image:Resource_Curve.JPG thumbcenter300px]]  
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+  <center>Experimental Results</center>  
+  <center>Fitted Curve</center>  
+  <center>Resource Curve</center>  
+    
+  }  
+  <br>  
+  
<br><br>  <br><br>  
+  ==Background Information of Modelling the Growth Curve==  
{{Imperial/Box1The aim of modelling the growth curve is to characterise the ''B. subtilis'' chassis used in the project. Characterisation increases the predictability of the growth of '' B. subtilis'' by determining, for example, its growth rate and the duration of its distinctive growth phases.  {{Imperial/Box1The aim of modelling the growth curve is to characterise the ''B. subtilis'' chassis used in the project. Characterisation increases the predictability of the growth of '' B. subtilis'' by determining, for example, its growth rate and the duration of its distinctive growth phases.  
  == How to model the growth curve? ==  +  
+  
+  ==[[How to model the growth curve?]]==  
In order to model the growth of ''B. subtilis'', the process was broken down into three main steps, where a separate submodel is produced in MATLAB for each step. Each submodel is an ODE model, which can be simulated using MATLAB. The variables in each submodel can be adjusted according to the boundary conditions (from experimental results).  In order to model the growth of ''B. subtilis'', the process was broken down into three main steps, where a separate submodel is produced in MATLAB for each step. Each submodel is an ODE model, which can be simulated using MATLAB. The variables in each submodel can be adjusted according to the boundary conditions (from experimental results).  
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In the final step, a combination of Submodels 1 and 2 are superposed with Submodel 3, resulting in a more complex model which enhances the accuracy of illustrating bacterial growth. For more details about the submodels, please click on the following link: [[Media:Modelling_Growth_Curve.pdf]]. For more information on our modelling strategy, please click on the following: [[Tutorial for Growth Curve]].  In the final step, a combination of Submodels 1 and 2 are superposed with Submodel 3, resulting in a more complex model which enhances the accuracy of illustrating bacterial growth. For more details about the submodels, please click on the following link: [[Media:Modelling_Growth_Curve.pdf]]. For more information on our modelling strategy, please click on the following: [[Tutorial for Growth Curve]].  
  ==The Model==  +  ==[[The Model]]== 
The model illustrates the main growth phases the ''B. subtilis'' undergoes. These are identified as the '''lag phase''', the '''exponential phase''' and the '''stationary phase'''. The death phase is a constitutive event and it is possible that it exerts an influence on the three phases discussed below. However, to simplify a complicated model, it is less relevant in this case and therefore is not included in this model.  The model illustrates the main growth phases the ''B. subtilis'' undergoes. These are identified as the '''lag phase''', the '''exponential phase''' and the '''stationary phase'''. The death phase is a constitutive event and it is possible that it exerts an influence on the three phases discussed below. However, to simplify a complicated model, it is less relevant in this case and therefore is not included in this model.  
The Mfile used to generate the model below is located in the Appendices section, its link can be found at the bottom of this page.  The Mfile used to generate the model below is located in the Appendices section, its link can be found at the bottom of this page.  
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{{Imperial/Box1  {{Imperial/Box1 
Revision as of 04:59, 30 September 2008
 
ResultsThe model for the growth curve was fitted to the experimental results as shown below. The experimental results is depicted by the red curve, while our model is shown by the green curve. The resource curve was also plotted as a function of time and is shown below. Based on our experimental results from the Wet Lab, a log graph was plotted to determine the growth rate. The growth rate was then determined from the gradient of the log graph. This value was included when simulating the growth model using MATLAB.
GROWTH CONSTANT: A = 1.3494 INITIAL NUTRIENT CONCENTRATION: R_0 = 2 HILL COEFFICIENT: n = 1.25 INITIAL OD = 0.4 CONSTANT: α = 0.64516
Background Information of Modelling the Growth Curve
