Difference between revisions of "Team:Warwick/Modeling"

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<h4>Modelling</h4>
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Modelling is a key part of synthetic biology. Some experiments take too long, are far too expensive, or the information required just can’t be found via lab work. This is where modelling comes in. We take information from the biologist, construct a theoretical framework, and then feed back to people in the lab about what they should do.
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<h4>Binding Affinity Modelling</h4>
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<br>In our project we have come up with a number of models, ranging from cell division to equilibrium reactions.
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<br><br><b>Click on the images below to explore more.</b>
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<br><b>Law of Mass Action</b>
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<br>When modelling chemical reactions, we used the law of mass action which explains and predicts behaviours of solutions in dynamic equilibrium. The basis for this law stems from the research conducted by Cato M. Guldberg and Peter Waage in the mid 18 hundreds. Guldberg and Waage recognized that chemical equilibrium is a dynamic process in which rates of reaction for the forward and backward reactions must be equal at chemical equilibrium. In order to find the equilibrium values for the chemicals involved, the differential equation governing the process must be found.
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<br><br>We have found said differential equation and then analytically solved it. After substituting in empirical data from the experiments, it is impossible to solve the equations to find the binding and unbinding constants (association and disassociation constants). We then used a computational method to find these constants. These results tell the biologists which zinc fingers have the best binding ability.
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<br><br>Another piece of code then uses these new found values to find out how much reactant to use, the related expenses, and how long the reaction will take.
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<br>We are currently working on a piece of code that will test the DNA sequence to see if they are viable options for our experiment.
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<br><b>The Equations</b><br>
 
  
  
  
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We will call the amount (concentration multiplied by volume) of the bacteria A, and the amount of binding site on the DNA (concentration multiplied by volume multiplied by binding sites per DNA sequence) as B.
 
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<br><i>The rate of change of A= the rate of unbinding-the rate of binding. </i>
 
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<br>These rates are proportional to the amount of unbinded or binded molecules there are.
 
  
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<p><img src="https://static.igem.org/mediawiki/2015/5/54/Warwickmodeling1.png" align="left" height="300px" width="400px" border="1px"></p>
 
  
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<p><a href="BindingAffinity"><h5>Binding Affinity Modelling</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/6/66/Warwickmodeling5.png" align="right" height="100px" width="100px" border="1px"></p></p> </a>
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A big problem biologists encounter is the uncertainty of binding especially in our design where zinc fingers bind to their sites. Therefore it is important to come up with a model which can calculate the number of cell and zinc finger binding sites required for a given output. This page discusses this and shows a program designed to dictate concentrations for the biologists to use.
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<br>By letting
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<p><img src="https://static.igem.org/mediawiki/2015/2/25/Warwickmodeling2.png" align="left" height="300px" width="400px" border="1px"></p>
 
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<br>We can solve this differential equation using separation of variables.
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<p><img src="https://static.igem.org/mediawiki/2015/6/64/Warwickbubbles1.png" height="120px" width="800px" border="1px"></p>
  
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<p><img src="https://static.igem.org/mediawiki/2015/4/4f/Warwickmodeling3.png" align="left" height="300px" width="400px" border="1px"></p><br><br>
 
  
  
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<br>Where χ is an unknown constant. To find χ we set A=A_0  at t=0.
 
  
  
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<p><img src="https://static.igem.org/mediawiki/2015/d/d4/Warwickmodeling4.png" align="left" height="300px" width="400px" border="1px"></p><br><br>
 
  
  
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<br>Note that 4ac-b^2 is negative, so the square root cannot be calculated. We now rearrange to cancel out imaginary parts.
 
  
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<p><a href="Modelling4"><h5>DNA Beading Model</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/a/a0/WarwickBead_Drawing.png" align="right" height="100px" width="100px" border="1px"></p></p> </a>
  
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<p><img src="https://static.igem.org/mediawiki/2015/6/66/Warwickmodeling5.png" align="left" height="300px" width="400px" border="1px"></p><br><br>
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Once we  had a method of calculating the concentration of cells needed we had to model the number of cells required to make a certain shape. We also needed to invent a novel approach to creating 2D shapes using cells, this page discusses binding them to a longer string of DNA to form a pattern.
  
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<p><img src="https://static.igem.org/mediawiki/2015/2/29/Warwickbubbles2.png" height="120px" width="800px" border="1px"></p>
  
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<br>Therfore
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<br>Substituting the values for a, b, and c.
 
  
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<p><a href="Modelling2"><h5>DNA Origami Glue Modelling</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/7/74/WarwickE.coli_Bonded_to_Origami.png" align="right" height="100px" width="100px" border="1px"></p></p> </a>
  
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<p><img src="https://static.igem.org/mediawiki/2015/1/1f/Warwickmodeling7.png" align="left" height="300px" width="400px" border="1px"></p><br><br>
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After the inherent problems and issues found from using the first model of 2D shapes we came up with a second, which discusses the use of DNA as an oligonucleotide adhesive to create 2D and 3D structures and shapes.<br>
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<p><img src="https://static.igem.org/mediawiki/2015/5/5b/Warwickbubbles3.png" height="120px" width="800px" border="1px"></p>
  
  
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<br>Let
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<br>Then
 
  
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<p><a href="Modelling6"><h5>Cell Growth Interactions</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/c/c1/Warwickcellgrowthgraph.png" align="right" height="100px" width="100px" border="1px"></p></p> </a>
  
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The previous model works but would change over time as the cells grow. To combat this we came up with a model to shows cell growth which could then be used to come up with starting pattern for the previous model so that the interactions remain contant over time.
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<p><img src="https://static.igem.org/mediawiki/2015/4/42/Warwickbubbles4.png" height="120px" width="800px" border="1px"></p>
  
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<p><img src="https://static.igem.org/mediawiki/2015/d/d6/Warwickmodeling11.png" align="left" height="300px" width="400px" border="1px"></p>
 
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<p><a href="modelling3"><h5>Tetrahedron Construction</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/0/05/WarwickCaddy.png" align="right" height="100px" width="100px" border="1px"></p></p> </a>
  
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The previous model of using DNA as a glue could create 3D shapes but would need vast amounts of unique zinc fingers. This wasn't possible with our time frame so we came up with a model which could create a 3D structure from the minimum amount of unique DNA using tetrahedrons as a base to build from. Cells would then be bound to the outside.<br>
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<video id="ModellingClip" src="https://static.igem.org/mediawiki/2015/4/48/Warwickmodellingvideo.mp4" controls></video>
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<p><img src="https://static.igem.org/mediawiki/2015/b/be/Warwickbubbles5.png" height="120px" width="800px" border="1px"></p>
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<p><a href="Modelling5"><h5>Cube Construction</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/c/c5/Sexalea.png" align="right" height="100px" width="100px" border="1px"></p> </p></a>
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The tetrahedron construction model could only create sphere shaped 3D structures. The cells that bound to the outside couldn't be controlled as well as we hoped so we came up with a new model that could. This page discusses the use of cube shaped DNA to create a shape where the cells bonded to the outside could be chosen.<br><br>
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<p><img src="https://static.igem.org/mediawiki/2015/0/03/Warwickbubbles7.png" height="120px" width="800px" border="1px"></p>
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<p><a href="Modelling3"><h5>3D Lithography</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/e/e3/Warwickfdm.png" align="right" height="100px" width="100px" border="1px"></p></p>
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Once we had an idea of how we could create small shapes using cells we wanted a quick overview how larger objects could be made. This discusses the different possibilities of the creation of 3D structures and shapes in a general sense, using different forms of bio-printng.<br><br>
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<p><img src="https://static.igem.org/mediawiki/2015/c/c4/Warwickbubbles8.png" height="120px" width="800px" border="1px"></p>
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<p><a href="Modelling1"><h5>NTNU Collaboration</h5><p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/1/13/Warwickntunuloo.png" align="right" height="100px" width="100px" border="1px"></p></p>
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We dcided to get help for some of the modelling and NTNU were kind enough to oblige. This model deals with calculating bonding and binding affinities.<br><br>
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Latest revision as of 10:10, 18 September 2015

Warwick iGEM 2015

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