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width: 500px ; height: ;"img src="https://static.igem.org/mediawiki/2018/0/0b/T--Lethbridge_HS--Copper2.png "> | width: 500px ; height: ;"img src="https://static.igem.org/mediawiki/2018/0/0b/T--Lethbridge_HS--Copper2.png "> | ||
− | <figcaption style="font-size: 16px; font-family: 'Open Sans'"><b>Figure 13a.</b></figcaption><figure></div> | + | <figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 13a.</b><center></figcaption><figure></div> |
<div class="col-sm"> | <div class="col-sm"> | ||
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<img class="img-fluid"style="float:left; margin-right: 15px;margin-bottom:5px;margin-top:0px; | <img class="img-fluid"style="float:left; margin-right: 15px;margin-bottom:5px;margin-top:0px; | ||
− | width: 500px ; height: ;"img src="https://static.igem.org/mediawiki/2018/f/f2/T--Lethbridge_HS--Copper3.png "><figcaption style="font-size: 16px; font-family: 'Open Sans'"><b>Figure 13b.</b></figcaption></figure> | + | width: 500px ; height: ;"img src="https://static.igem.org/mediawiki/2018/f/f2/T--Lethbridge_HS--Copper3.png "><figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 13b.</b><center></figcaption></figure> |
</div></div></div> | </div></div></div> | ||
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width: 500px ; height: ;"src="https://static.igem.org/mediawiki/2018/d/dd/T--Lethbridge_HS--Copper1.png"></center> <figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 13c.</b></center></figcaption><figure> | width: 500px ; height: ;"src="https://static.igem.org/mediawiki/2018/d/dd/T--Lethbridge_HS--Copper1.png"></center> <figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 13c.</b></center></figcaption><figure> | ||
<figure> | <figure> | ||
+ | |||
+ | <p style="font-size: 18px; font-family: 'Open Sans'">Copper-binding models showing the concentrations of free enzyme (CUT A), formed complex (CUT A – Copper complex), and free copper. The change in concentration of free enzyme and formed complex over time as the enzyme binds to free copper is quite evident, and the result shows that the higher the initial concentration of copper (i.e. the higher the concentration of CuSo4), the faster the rate of change. However, there is no detectable change in the concentration of free copper at all regardless of the initial concentration. Why? We realized that this is because our copper concentration was too high compared to our enzyme concentration. The lowest copper concentration we used in the experiment was 0.2365 molar, whereas the enzyme concentration used was 1 micromolar, or 1E-6 molar. The tiny amount of enzyme is too insignificant to cause a change in the concentration of free copper.</p> | ||
+ | |||
+ | <p style="font-size: 18px; font-family: 'Open Sans'"><b>Improve</b></p> | ||
+ | |||
+ | <p style="font-size: 18px; font-family: 'Open Sans'">With further research in elementary kinetics, we realized that our enzyme, CUT A, is capable of binding to six copper ions simultaneously. Previously, we have assumed that there is a 1:1 ratio of enzyme to copper ions. This assumption turns out to be false. With multiple binding, the new equations are as follows (where n represents the number of substrates each enzyme can bind to):</p> | ||
+ | |||
+ | <center><img class="img-fluid"style="margin-bottom:5px;margin-top:0px; | ||
+ | |||
+ | width: 400px ; height: ;"src="https://static.igem.org/mediawiki/2018/5/57/T--Lethbridge_HS--cooperative_equation.png"></center> | ||
+ | |||
+ | |||
+ | <p style="font-size: 18px; font-family: 'Open Sans'"><b>Results and Interpretation:</b></p> | ||
+ | |||
+ | <div class="container"><div class="row"><div class="col-sm"> | ||
+ | <figure> | ||
+ | <img class="img-fluid"style="float:right; margin-left: 15px;margin-bottom:5px;margin-top:0px; | ||
+ | |||
+ | width: 500px ; height: ;"img src="https://static.igem.org/mediawiki/2018/b/b3/T--Lethbridge_HS--coorperative2.png "> | ||
+ | <figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 14a.</b><center></figcaption><figure></div> | ||
+ | |||
+ | <div class="col-sm"> | ||
+ | <figure> | ||
+ | <img class="img-fluid"style="float:left; margin-right: 15px;margin-bottom:5px;margin-top:0px; | ||
+ | |||
+ | width: 500px ; height: ;"img src="https://static.igem.org/mediawiki/2018/3/32/T--Lethbridge_HS--coorperative3.png "><figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 14b.</b><center></figcaption></figure> | ||
+ | |||
+ | </div></div></div> | ||
+ | |||
+ | <figure> | ||
+ | <center><img class="img-fluid"style="margin-bottom:5px;margin-top:0px; | ||
+ | |||
+ | width: 500px ; height: ;"src="https://static.igem.org/mediawiki/2018/6/6f/T--Lethbridge_HS--coorperative1.png"></center> <figcaption style="font-size: 16px; font-family: 'Open Sans'"><center><b>Figure 14c.</b></center></figcaption><figure> | ||
+ | <figure> | ||
+ | |||
+ | <p style="font-size: 18px; font-family: 'Open Sans'">Copper-binding models where each free enzyme (CUT A) may bind to six substrates (copper ions). Compared with previous results, the rate of change of the concentrations of free enzyme and ion-enzyme complexes are faster, but there is still no detectable change to the concentration of free copper. This is expected as the difference between the copper concentration and enzyme concentration is too great (of a 6th order). Successful removal of copper ions will require a much higher concentration of enzymes.</p> | ||
+ | |||
+ | |||
+ | |||
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+ | |||
Revision as of 03:10, 18 October 2018
MODELLING
The evolution of our bacteria-phage dynamic model helped us gain a better understanding of the interaction between a bacteria population and a phage population and its impact on the viability of our design. After defining a variety of parameters and making several assumptions, we showed that it is possible for our system of bacteria and phages to be self-sustainable. Comparing our model with our experimental results, we developed a second model where we accounted for additional factors such as a possible mutation in the bacteria’s DNA that results in resistance against phage infection. Furthermore, we modelled the copper-binding efficiency of CUP I (our copper-binding protein) to estimate the optimal ratio of enzyme and copper concentrations that would result in the most efficient binding in the implementation of our system.
DISCRETE TIME MODEL
Purpose:Given an initial Multiplicity of Infection (MOI) and infection onset point (during a bacteria lifecycle), determine how the populations of bacteria and phages change over discrete time intervals.
Assumptions:
- There is no delay in infection
- All bacteria are susceptible to infection, and all infections are successful.
- All bacteria death is caused by infection (i.e. there is no natural death)
Definitions of Parameters and Variables:
Multiplicity of Infection (MOI): The MOI represents the initial ratio between the number of phages and number of bacteria at the time of inoculation. It is a decisive factor in calculating the probability that a bacteria will be infected by at least one phage particle. The equation that relates the MOI to this probability is:
where P is the probability, and m represents the multiplicity of infection. (reference Wikipedia page) Although it is possible that a bacterium is infected with more than one phage particles, a research study conducted by Ellis and Delbruck suggests that bacteria infected with multiple phage particles had similar burst sizes than bacteria that were infected with only one phage. (insert reference)
Burst Size: the number of phages produced per infected bacteria.
Lysis Time: the time it takes for a phage to infect and lyse a bacteria host.
Both the burst size and the lysis time depend on the point during a bacteria lifecycle when inoculation begins. One research study conducted by Zachary Storms and Tobin Brown shows how the burst size—the squares, and the lysis time—the circles, vary with when the infection starts. Storms and Brown suggest that the burst size is the highest and the lysis time is the shortest if the infection starts when the bacteria cell enters the division stage, because at that point the cell has the richest intracellular resources.
Bacteria doubling time: the time it takes a bacteria population to double in size.
Equations:
Results and Interpretation:
The following graphs are constructed with an initial bacteria population of 1,000 and an initial phage population calculated according to the MOI used. However, the actual numbers of bacteria and phages do not influence the trends observed in the graph, as it is the ratio between these numbers (the MOI), not the actual numbers, that matters.