IGEM:IMPERIAL/2008/New/Growth Curve: Difference between revisions

From OpenWetWare
Jump to navigationJump to search
No edit summary
No edit summary
Line 1: Line 1:
__NOTOC__
__NOTOC__
{{Imperial/StartPage2}}
{{Imperial/StartPage2}}
 
<br>
{{Imperial/Box1|Growth Curves|The 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.
<br>
&nbsp; <font size=6px color=#E5EBFF><b>Growth Curve</b></font>
<br><br>
{{Imperial/Box1||The 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? ==

Revision as of 07:01, 27 September 2008

<html> <style type="text/css"> .firstHeading {display: none;} </style> </html> <html> <style type="text/css"> 

   table.calendar          { margin:0; padding:2px; }

table.calendar td { margin:0; padding:1px; vertical-align:top; } table.month .heading td { padding:1px; background-color:#FFFFFF; text-align:center; font-size:120%; font-weight:bold; } table.month .dow td { text-align:center; font-size:110%; } table.month td.today { background-color:#3366FF } table.month td { 

   border:2px;
   margin:0;
   padding:0pt 1.5pt;
   font-size:8pt;
   text-align:right;
   background-color:#FFFFFF;
   }
  1. bodyContent table.month a { background:none; padding:0 }

.day-active { font-weight:bold; } .day-empty { color:black; } </style> </html>

<html><script language="JavaScript">

var timeout = 250; var closetimer = 0; var ddmenuitem = 0;

// open hidden layer function mopen(id) { // cancel close timer mcancelclosetime(); // close old layer if(ddmenuitem) ddmenuitem.style.visibility = 'hidden'; // get new layer and show it ddmenuitem = document.getElementById(id); ddmenuitem.style.visibility = 'visible'; } // close showed layer function mclose() { if(ddmenuitem) ddmenuitem.style.visibility = 'hidden'; } // go close timer function mclosetime() { closetimer = window.setTimeout(mclose, timeout); } // cancel close timer function mcancelclosetime() { if(closetimer) { window.clearTimeout(closetimer); closetimer = null; } } // close layer when click-out //document.onclick = mclose; </script> <table background="http://i59.photobucket.com/albums/g305/Timpski/ToolbarBackground.png" style="color:#ffffff;" link="#ffffff" cellpadding="0" cellspacing="1" border="0" bordercolor="#ffffff" align="center" width="100%"><tr><td colspan="6" class="wetlab"><br><br><br></td></tr> <tr><td align="center" width="10%" valign="bottom"><ul id="sddm"><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Home"> Home </a></ul> </td><td align="center" width="20%" valign="bottom"><ul id="sddm"><a href="#" 

       onclick="mopen('m1')" 
       onmouseover="mopen('m1')" 
       onmouseout="mclosetime()">Biofabricator Subtilis</a>
       <div id="m1" 
           onmouseover="mcancelclosetime()" 
           onmouseout="mclosetime()">
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Project">Project Specifications</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Chassis_1">Why B. subtilis?</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Chassis_2">B. subtilis: Benefits vs Challenges</a>
       </div></ul>

</td><td align="center" width="18%" valign="bottom"><ul id="sddm"><a href="#" 

       onclick="mopen('m2')" 
       onmouseover="mopen('m2')" 
       onmouseout="mclosetime()">Wet Lab</a>
       <div id="m2" 
           onmouseover="mcancelclosetime()" 
           onmouseout="mclosetime()">
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Wet_Lab">Wet Lab Hub</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Cloning_Strategy">Cloning Strategy</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Protocols">Experiments & Protocols</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Major_Results">Experimental Results</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/BioBricks">BioBricks & Characterisation</a>
       </div></ul>

</td><td align="center" width="18%" valign="bottom"><ul id="sddm"><a href="#" 

       onclick="mopen('m3')" 
       onmouseover="mopen('m3')" 
       onmouseout="mclosetime()">Dry Lab</a>
       <div id="m3" 
           onmouseover="mcancelclosetime()" 
           onmouseout="mclosetime()">
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Dry_Lab">Dry Lab Hub</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Growth_Curve">Growth Curves</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Genetic_Circuit">Genetic Circuits</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Motility">Motility Analysis</a>
       <a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Appendices">Appendices - Code etc.</a>
       </div></ul>

</td><td align="center" width="17%" valign="bottom"><ul id="sddm"><a href="http://2008.igem.org/Team:Imperial_College/Notebook"> Notebook </a></ul> </td><td align="center" width="17%" valign="bottom"><ul id="sddm"><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Team"> Our Team </a></ul> </td></tr></table></html>

<html><style type="text/css">

div.Section { font:11pt/16pt Calibri, Verdana, Arial, Geneva, sans-serif; background-image: url(http://openwetware.org/images/a/a0/Background.PNG); background-size: 100%; background-origin: content; }

/* Text (paragraphs) */ div.Section p { font:11pt/16pt Calibri, Verdana, Arial, Geneva, sans-serif; text-align:justify; margin-top:0px; margin-left:30px; margin-right:30px; }

/* Headings */ div.Section h1 { font:22pt Calibri, Verdana, Arial, Geneva, sans-serif; text-align:left; color:#3366FF; font-weight:bold; }

/* Subheadings */ div.Section h2 { font:18pt Calibri, Verdana, Arial, Geneva, sans-serif; color:#3366FF; margin-left:5px; font-weight:bold; }

/* Subsubheadings */ div.Section h3 { font:22pt Calibri, Verdana, Arial, sans-serif; color:#E5EBFF; margin-left:10px; font-weight:bold; }

/* Subsubsubheadings */ div.Section h4 { font:22pt Calibri, Verdana, Arial, sans-serif; color:#2B48B3; margin-left:10px; font-weight:bold; }

/* Subsubsubsubheadings */ div.Section h5 { font:12pt Calibri, Verdana, Arial, sans-serif; color:#3366FF; margin-left:20px; }

/* References */ div.Section h6 { font:12pt Calibri, Verdana, Arial, sans-serif; font-weight:bold; font-style:italic; color:#3366FF; margin-left:25px; }

/* Hyperlinks */ div.Section a { }

div.Section a:hover { }

/* Tables */ div.Section td { font:11pt/16pt Calibri, Verdana, Arial, Geneva, sans-serif; text-align:justify; vertical-align:top; padding:2px 4px 2px 4px; }

/* Lists */ div.Section li { font:11pt/16pt Calibri, Verdana, Arial, Geneva, sans-serif; text-align:left; margin-top:0px; margin-left:30px; margin-right:0px; }

/* TOC stuff */ table.toc { margin-left:10px; }

table.toc li { font: 11pt/16pt Calibri, Verdana, Arial, Geneva, sans-serif; text-align: justify; margin-top: 0px; margin-left:2px; margin-right:2px; }

/* [edit] links */ span.editsection { color:#BBBBBB; font-size:10pt; font-weight:normal; font-style:normal; vertical-align:bottom; }

span.editsection a { color:#BBBBBB; font-size:10pt; font-weight:normal; font-style:normal; vertical-align:bottom; }

span.editsection a:hover { color:#3366FF; font-size:10pt; font-weight:normal; font-style:normal; vertical-align:bottom; }

/* Drop-down Menu */

  1. sddm {

margin: 0; padding: 0; z-index: 30 margin: 0; padding: 0; float: center; font: bold 12pt Calibri, Verdana, Arial, Geneva, sans-serif; border: 0px; list-style: none; }

  1. sddm a {

display: block; margin: 0px 0px 0px 0px; padding: 0 0 12px 0; color: #FFFFFF; text-align: center; text-decoration: none; }

  1. sddm a:hover {

border: 0px }

  1. sddm div {

position: absolute; visibility: hidden; margin: 0; padding: 0; background: #66aadd; border: 1px solid #66aadd } #sddm div a { position: relative; left: 0; display: block; margin: 0; padding: 5px 10px; width: auto; white-space: nowrap; text-align: left; text-decoration: none; background: #FFFFFF; color: #2875DE; font: 11pt Calibri, Verdana, Arial, Geneva, sans-serif } #sddm div a:hover { background: #66aadd; color: #FFFFFF } </style></html>



  Growth Curve

The 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?

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 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 Tutorial for Growth Curve.


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 M-file used to generate the model below is located in the Appendices section, its link can be found at the bottom of this page.



LAG PHASE

During the lag phase, the rate of growth is slow due to two main reasons, B. subtilis is absorbing nutrients in the medium and the replication machinery is being switched on. The higher the concentration of nutrients in the medium, the faster the rate of bateria growth.

As a result, the volume of the bacteria increases, followed by an increases in the number of bacteria.

EXPONENTIAL PHASE

Both colony number and cell volume increase exponentially during this phase. Our model assumes concentration of the nutrients inside the bacteria is constant.

STATIONARY PHASE

The growth of the colony ceases in number and in volume due to a finite concentration of nutrients, hence its does not have a gradient. Other causes may be death and cell division.

According to the model, the maximum growth of the bacteria is determined by the concentration of nutrients available initially.

To further enhance the accuracy of the model, the following information will be extracted from experimental data:

  • Time span of lag phase, stationary phase and exponential phase
  • The growth rate

Results

Log-Graph 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. From experimental results, 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.

The following constants used to generate the model were found to yield the best fit to experimental results.

GROWTH CONSTANT: A = 1.3494

INITIAL NUTRIENT CONCENTRATION: R_0 = 2

HILL COEFFICIENT: n = 1.25

INITIAL OD = 0.4

CONSTANT: [math]\displaystyle{ \alpha }[/math] = 0.64516


Experimental Results
Fitted Curve
Resource Curve


Discussion

Dry lab hub

Growth Curve

Genetic Circuit

Motility

Appendices


<html><center><table style="color:#ffffff;background-color:#66aadd;" cellpadding="3" cellspacing="1" border="0" bordercolor="#ffffff" align="center"> <tr><td><ul id="sddm"></html>< Previous<html></ul> </td><td><ul id="sddm"><a href="#">Back to top</a></ul> </td><td><ul id="sddm"></html>Next ><html></ul> </td></tr></table> </center></html>

Retrieved from "https://openwetware.org/mediawiki/index.php?title=IGEM:IMPERIAL/2008/New/Growth_Curve&oldid=246510"