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+ | <div style='padding-top: 30px;'></div> | ||
+ | <center><img src="https://static.igem.org/mediawiki/2017/3/36/T--William_and_Mary--descript.jpeg" width=380px;/></center> | ||
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<div style = 'padding-left: 190px; padding-bottom: 10px;font-size: 25px' ><b>Motivation</b></div> | <div style = 'padding-left: 190px; padding-bottom: 10px;font-size: 25px' ><b>Motivation</b></div> | ||
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<div style='padding-top: 0px;'></div> | <div style='padding-top: 0px;'></div> | ||
− | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' > | + | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' >The relationship between the degradation rate of a gene's protein product and the response speed of its expression is a well-established concept in the theoretical biology community. Consider the following simple mathematical model presented by Uri Alon [5]. X is an inducible gene which, once activated, produces its protein product x at rate α. If x is degraded at rate γ, then we can use the following differential equation to track the concentration of protein x over time:</div> |
<figure style='padding-left: 200px;'> | <figure style='padding-left: 200px;'> | ||
− | <img src='https://static.igem.org/mediawiki/2017/ | + | <img src='https://static.igem.org/mediawiki/2017/0/02/T--William_and_Mary--truDescriptionMath1.png' height = "70%" width = "70%"/> |
− | <figcaption><div style='padding-left: 5px;padding-top: 15px; color: #808080; font-size: 14px;'>Figure 1: A simple kinetic model tracking the changing concentration of protein x over time. </div></figcaption> | + | <figcaption><div style='padding-left: 5px;padding-top: 15px; color: #808080; font-size: 14px;'>Figure 1: A simple kinetic model tracking the changing concentration of protein x over time. </div><div style='padding-left: 5px;color: #808080; font-size: 14px;'>Gene circuit component images adapted from Newcastle iGEM 2010; protein images adapted from Cameron and Collins 2014 [7]. </div></figcaption> |
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<div style='padding-top: 15px;'></div> | <div style='padding-top: 15px;'></div> | ||
− | <div style = 'padding-right: 190px; padding-left: 190px; line-height: 25px;' > | + | <div style = 'padding-right: 190px; padding-left: 190px; line-height: 25px;' >We solve the above differential equation to obtain the following function, which gives the protein concentration at a given time t after activation of X: </div> |
<figure style='padding-left: 200px;'> | <figure style='padding-left: 200px;'> | ||
− | <img src='https://static.igem.org/mediawiki/2017/ | + | <img src='https://static.igem.org/mediawiki/2017/7/71/T--William_and_Mary--truDescriptionMath2.png' height = "30%" width = "30%"/> |
<figcaption><div style='padding-left: 5px;padding-top: 15px; color: #808080; font-size: 14px;'>Figure 2: Concentration of protein x as a function of time; the solution to the differential equation in Figure 1. </div></figcaption> | <figcaption><div style='padding-left: 5px;padding-top: 15px; color: #808080; font-size: 14px;'>Figure 2: Concentration of protein x as a function of time; the solution to the differential equation in Figure 1. </div></figcaption> | ||
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<div style = 'padding-right: 190px; padding-left: 190px; line-height: 25px;' >We are able to graph this function and determine that the steady state concentration for x is equal to production rate over degradation rate. Finally, defining т<sub>1/2</sub> as the time it takes for x to reach half its steady-state concentration, we find the following: </div> | <div style = 'padding-right: 190px; padding-left: 190px; line-height: 25px;' >We are able to graph this function and determine that the steady state concentration for x is equal to production rate over degradation rate. Finally, defining т<sub>1/2</sub> as the time it takes for x to reach half its steady-state concentration, we find the following: </div> | ||
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+ | <figure style='padding-left: 200px;'> | ||
+ | <img src='https://static.igem.org/mediawiki/2017/6/65/T--William_and_Mary--DescriptionMath3.png' height = "70%" width = "70%"/> | ||
+ | <figcaption><div style='padding-left: 5px;padding-top: 15px; color: #808080; font-size: 14px;'>Figure 3: We find that т<sub>1/2</sub> is a function of γ, the degradation rate for protein x. </div></figcaption> | ||
+ | </figure> | ||
<div style='padding-top: 15px;'></div> | <div style='padding-top: 15px;'></div> | ||
− | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' >Thus in order to create a plug-and-play style system to control gene expression speed, we developed and characterized a suite of BioBrick parts which allow for simple, modular and predictable changes to the gene expression speed of arbitrary proteins.</div> | + | <div style = 'padding-right: 190px; padding-left: 190px; line-height: 25px;' >The above expression reveals that in this model, it is not only sufficient but also necessary to tune the degradation rate γ in order to control the gene expression speed (represented here as т<sub>1/2</sub>). This property remains true for more complex circuit architectures like feedforward loops, provided that the steady-state concentration is held constant [5]. </div> |
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+ | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' >Thus in order to create a plug-and-play style system to control gene expression speed, we developed and characterized a suite of BioBrick parts which allow for simple, modular and predictable changes to the gene expression speed of arbitrary proteins via protein degradation.</div> | ||
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− | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' >When we created our gene expression control system, we wanted to make sure that it was both usable across a variety of biological systems and circuits, and easily accessible to other iGEM teams. To this end, we chose to use the Mesoplasma florum Lon (mf-Lon) protease system | + | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' >When we created our gene expression control system, we wanted to make sure that it was both usable across a variety of biological systems and circuits, and easily accessible to other iGEM teams. To this end, we chose to use the <i>Mesoplasma florum</i> Lon (mf-Lon) protease system which was characterized by Gur and Sauer in 2008 [6] and developed into a modular suite of genetic parts by Cameron and Collins in 2014 [7]. This system consists of of a AAA+ protease and its associated protein degradation tags (pdt), which operate in a mechanistically similar manner to the E. Coli endogenous protease ClpXP and its associated ssrA tags. However, unlike ClpXP and ssrA tags, mf-Lon and pdts are completely orthogonal to the endogenous protein degradation systems in E. coli. Using this orthogonal degradation system helps eliminate cross-talk between our system and endogenous E. coli proteins. Further, since there are pdts with a wide range of different affinities, we are able to tune degradation rate, and thus gene expression speed to a wide variety of values. This represents not only a practical advancement in the tuning of circuits, but also an important contribution in our theoretical understanding of biological processes, as to our knowledge there has so far been no direct experimental measurement in the literature of the predicted 1/γ scaling of a gene's speed with its degradation rate. See our <a href='https://2017.igem.org/Team:William_and_Mary/Results' style='text-decoration: underline;'>results</a> page for more details.</div> |
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− | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' > | + | <div style = 'padding-right: 190px; padding-left: 190px; text-indent: 50px;line-height: 25px;' >Finally, by constructing a mechanistic model of our degradation system, we were able to rigorously analyze our timeseries datasets using Bayesian Parameter Inference and obtain parameter distributions (Figure 4). We then used this analysis to feed back into our predictive saturation model, which we used to develop the beginnings of a theoretical framework for understanding the relationship between protease-driven speed control and saturation effects on the protease. By combining our characterization measurements with our conceptual insights, future iGEM teams are now enabled to use the pdt system to predictably control the temporal dynamics of their genetic circuits. See our <a href='https://2017.igem.org/Team:William_and_Mary/Model' style='text-decoration: underline;'>modeling</a> page for details |
+ | </div> | ||
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+ | <center> | ||
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+ | <img src='https://static.igem.org/mediawiki/2017/5/5a/T--William_and_Mary--MCMC-F2.png' width = "45%"/> | ||
+ | <figcaption><div style='padding-left: 20%;padding-right:20%; padding-top: 15px; color: #808080; font-size: 14px;'>Figure 4: MCMC parameter estimation for a simple protein production model correctly estimates the simulated values for both beta and gamma (15 and .03 respectively). In addition, the MCMC identifies a strong positive correlation between beta and gamma. This makes sense as steady-state levels of protein are set by the ratio Beta/Gamma. Therefore as beta goes up we should see a corresponding increase in gamma to best fit the model. | ||
+ | </div></figcaption> | ||
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<div style='padding-top: 60px;'></div> | <div style='padding-top: 60px;'></div> | ||
Latest revision as of 03:07, 2 November 2017