Revision as of 15:21, 18 November 2018

<head> <meta charset="utf-8"> <title>C-lastin, Interlab</title> <style> @charset "utf-8"; /* CSS Document */ .ec--modeling--container{ padding-top: 100px; padding-right: 14%; padding-bottom: 100px; padding-left: 38%; } .ec--main--title{ text-align: center; padding-top: 30px; padding-right: 30px; padding-bottom: 30px; padding-left: 30px; } .ec--img--wwd--cont{ text-align: center; padding-top: 20px; padding-right: 20px; padding-bottom: 20px; padding-left: 20px; } .ec--modeling--items{ width: 270px; display: block; position: fixed; float: left; top: 250px; /*position: -webkit-sticky; position: sticky; padding-bottom: 0px; margin-top: 11.4em;*/ left: 14%; line-height: 1.3; text-indent: inherit; } ul.circle {

   list-style-type: circle;

} .ec--biob--cont{ padding-top: 20px; padding-right: 20px; padding-bottom: 20px; padding-left: 20px; } .textdis{

   display:none;

} .loc-neg-c{ display: none; } .loc-pos-c{ display: none; } .loc-td1{ display: none; } .loc-td2{ display: none; } .loc-td3{ display: none; } .loc-td4{ display: none; } .loc-td5{ display: none; } .loc-td6{ display: none; }

input:hover {

   background-color: brown;

}

bigBox {

 width:800px;
 height: 300px;

}

leftBox {

float: left; height: 300px; width: 390px; margin: 0; }

rightBox {

 float:right;
 height:300px;
 width: 390px;

} .ec--biobr--location--container{ padding-top: 50px; padding-right: 25px; padding-bottom: 25px; padding-left: 25px; } .ec--h2{ font-size: 25px; font-weight: bolder; display: block; margin-top: 15px; margin-bottom: 15px; clear: both; padding-top: 20px; padding-bottom: 20px; color: black; line-height: 40px; } .ec--p{ display: block; line-height: 2; text-align: justify; font-size: 16px; } .ec--coll--video{ display: block; clear: both; text-align: center; padding-top: 30px; padding-bottom: 30px; } .ec--coll--letter{ text-align: justify; display: block; margin-left: 20px; margin-right: 20px; margin-top: 20px; margin-bottom: 20px; width: 900px; } .ec--img--surv{ top: 0; bottom: 0; left: 0; right: 0; margin: auto; padding-top: 20px; padding-bottom: 20px; } .anchorOffset{

display: block !important; position: relative !important; top: -135px !important; visibility: hidden !important;

} a.lateral{

 color: black;
 text-decoration: inherit;
 opacity: 1;
 color: gray;
 font-weight: 500;
 font-size: 16px;

} a.inner-link--active {

 opacity: 1;
 animation: bulge .5s ease;
 -webkit-animation: bulge .5s ease;

} .ec--h3{ font-size: 22px; font-weight: bolder; display: block; margin-top: 15px; margin-bottom: 15px; clear: both; padding-top: 20px;

}

</style>

</head>

<body>

MATHEMATICAL MODELLING

</a>

Index

<a href="#LOV" style="color:black; text-decoration: none">List of variables and constants</a>
I<a href="#IND3" style="color:black; text-decoration: none">PTG-inducible model</a>

<a href="#IND4" style="color:black; text-decoration: none">Entry of IPTG into the cell</a>
<a href="#IND5" style="color:black; text-decoration: none">CBD cipA-BMP2 expression</a>
<a href="#IND6" style="color:black; text-decoration: none">Kinetic constants</a>

<a href="#IND7" style="color:black; text-decoration: none">Results of the IPTG-inducible model</a>

<a href="#IND8" style="color:black; text-decoration: none">Calculation of entry of IPTG into the cell</a>
I<a href="#IND9" style="color:black; text-decoration: none">PTG-LacI repressor interaction</a>
<a href="#IND10" style="color:black; text-decoration: none">Calculation and validation of CBD cipA-BMP2 expression</a>

<a href="#IND11" style="color:black; text-decoration: none">Conclusions</a>

INTRODUCTION

</a>

                   This  is an IPTG-inducible model for the expression of the fusion protein CBD  cipA-BMP2 under the control of Plac promoter and cloned in psb1c3. The vector  does not contain the ORF of LacI and thus the LacI repressor protein concentration  is that in E. coli strains (10nM per cell).1

                   <a name="LOV" style="text-decoration:none;"></a>The  model consists of systems of differential equations that were solved in Python  using Spyder 3.6 (Anaconda).

LIST OF VARIABLES AND CONSTANTS

</a>

Variable/Constant	Definition	Unit/Value
[IPTG] TOTAL	Total IPTG concentration in the medium	nM
[IPTG]ext	IPTG concentration outside E. coli	nM
[IPTG]int	IPTG concentration inside E. coli	nM
[IPTG]TOTAL	Total LacI concentration in E. coli	nM
[LacI]act	Active LacI concentration in E. coli	nM
[CB]mRNA	CBD-BMP2 mRNA concentration in E. coli	nM
[CB]	CBD-BMP2 protein concentration in E. coli	nM
δ[CB]	Degradation rate of CBD-BMP2 mRNA	min-1
β[CB]	Translational rate of CBD-BMP2 protein	min-1
σ[CB]	Degradation rate of CBD-BMP2 protein	min-1
t	time	min
α[CB]	Transcriptional leakage of Plac promoter	%
kPlac	Maximum transcription rate of Plac promoter	0.5 nM min-1
kIPTGupt	Rate constant of IPTG uptake	0.92 min-1
kIPTGout	Rate constant of IPTG output	0.05 min-1
KIPTG	Michaelis constant of IPTG-LacI binding	600 nM
<a name="IND3"></a>hIPTG	Hill coefficient of IPTG-LacI binding	2
HLacI	Hill coefficient of LacI-Plac promoter binding	2

<a name="IND4"></a>IPTG-INDUCIBLE MODEL FOR CBD CIPA-BMP2 PROTEIN EXPRESSION IN E. coli

Entry of IPTG into E. coli
Mimicking lactose, IPTG is a chemical widely used in scientific research because it cannot be metabolized. IPGT induces the expression of genes under the control of Plac promoter.

IPTG enters into E. coli cells in a concentration dependent manner. This uptake is mediated by lactose permease and passive diffusion at low and high concentrations respectively.2 The IPTG uptake through passive diffusion can be described with the law of mass action expressing the balance between IPTG concentration outside (IPTGext) and inside (IPTGint) of E. coli :

<img src=""/>
Eq 1.

 The first term on the right side of Eq 1  represents the forward rate where kIPTGupt is the rate constant of IPTG uptake (0.92 min-1)3 while the second term has negative  sign because it represents the backward rate where kIPTGout is the rate constant of IPTG output (0.05 min-1).3 Because of [IPTG]ext = [IPTG]TOTAL - [IPTG]int, it can be replaced in equation 1 in order to have IPTGint as the unique independent variable:

<img src=""/>
Eq 2.

 The LacI-IPTG interaction is assumed to be so  fast and when the IPTG concentration largely exceeds that of lacI. The LacI  active ([LacI]act), i.e that unbounded to IPTG, can be described  with the Hill repression function.4,2

<img src=""/>
Eq 3.

Equation 3 (Eq 3) describes the amount of unbounded LacI that actively repress the expression of a protein driven by the Plac promoter; the expression of CBD cipA-BMP2 in the present study. <a name="IND5"></a>[LacI]TOTAL is the concentration of LacI inside E. coli, KIPTG is the Michaelis constant of IPTG-LacI binding (6000 M) 5 and hIPTG is the associated Hill coefficient (2).3,6

CBD cipA-BMP2 EXPRESSION

CBD cipA-BMP2 mRNA

The CBD cipA-BMP2 mRNA concentration ([CB]mRNA) at time t can be described as follows:

<img src=""/>
Eq 4.

The first term on the right side of the equation 2.6 represents the synthesis of mRNA. kPlac is the maximum transcriptional rate corresponding to the Plac promoter (0.5 nM min-1).3 αCEB+(1-αCEB) is the leakiness factor where αCEB is the transcriptional leakage of Plac promoter. is the repressing Hill function of Plac promoter where KLacI is the Michaelis constant of LacI-Plac promoter binding (6000 M), 3 and hLacI is the associated Hill coefficient(2).3 The second term represents the degradation of the [CB]mRNA where δ[CB] is the degradation rate.3,6,7

 Because there is not constitutive expression of  LacI protein from the plasmid cloned in E. coli carrying the CBD cipA-BMP2 construct and based on our preliminary measurements of total  protein concentration using BCA method, the transcriptional leakage can be  taken to be 0.8 and thus the balance for [CB]mRNA becomes:

<img src=""/>
Eq 5.

CBD cipA-BMP2 protein

 

 The concentration of CBD cipA-BMP2 protein  ([CB]) can be described as follows:

<img src=""/>
Eq 6.

<a name="IND6"></a>The first term on the right side of the equation 6 represents the synthesis of [CB] where β[CB] is the translational rate of [CB]. The second term represents the degradation of [CB] where σ[CB] is the degradation rate.

KINETIC CONSTANTS

 The time cell division of E. coli is function of factors such as pressure, temperature and culture medium  and ranging from 20-30 min under optimal conditions. Culturing in universal  common medium such as Nutrient Broth and Luria-Bertani at 35 ℃, the time cell division can be assumed to be 30  min.8,9,10

 The half life of mRNAs in E. coli has been well reported by Bernstein and coworkers who determined that it  depends of culture medium. In, LB 99% of mRNAs had a half-life time between  1-15 min with a mean of 5.2 min.11 Therefore, 5.2 min can be assumed as the  half-life time of CBD cipA -BMP2 mRNA. Consequently, δ[CB]= 0.226 min-1.

In E. coli , the translation takes place at 12-21 amino acids per second (aa s-1).12 We choose 19 aa s-1 because the codon optimization. <a name="IND7"></a><a name="IND8"></a>Because CBD cipA-BMP2 contains 292 aa, β[CB] can be taken to be 3.904 min-1.The half life of CBD cipA-BMP2 protein can be assumed to be 60 min-1, 13 consequently, σ[CB]= 0.05min-1:

RESULTS OF THE IPTG-INDUCIBLE MODEL FOR CBD cipA-BMP2 PROTEIN EXPRESSION IN E. coli

Calculation of entry of IPTG into E. coli

 Figure 1 is a rate balance plot derived from  Equation 1 whith both forward and backward rates as functions of the normalized  [IPTG]int concentration whose value in the equilibrium (steady  state) can be obtained where the two functions intersect. Analitically, this  point is [IPTG]int =0.9485[IPTG]TOTAL

rate

Figure 1. Rate balance of IPTG diffusion through E. coli membrane. Forward and backward rates are plotted versus normalized [IPTG]int

IPTG-LacI repressor interaction
Because of IPTG is the inducer, it is important to evaluate its interaction with LacI repressor at different initial concentrations added to the system ([IPTG]TOTAL). For these values the [LacI]act can be calculated with Equation 3 (Table 1). From table 1 and figure 4, it can be deduced that a concentration of IPTG = 0.1 mM is saturating because the solutions derived from higher IPTG values converge.

Table 1. [LacI]act for different initial IPTG concentrations.

[IPTG]TOTAL (mM)	[LacI]act (nM)
0,001	9.7562
0,02	0.9095
0,03	0.4257
0.1	0.0399
1.0	0.0004

Calculation and validation of CBD cipA-BMP2 expression

The mathematical model for the expression of CBD cipA-BMP2 is:

<img src=""/>
Eq 7.

The stability of the system can be analyzed with the Jacobian matrix associated to the system of differential equations:

JACOBIAN

Because the two igenvalues (λ1= -0.226 y λ2 = -0.05) are negative, the equilibrium point is a stable node.

Time step selection and phase plane
A reasonable error less than 0.01 for both mRNA and protein concentrations was obtained with a time step Dt=0.1/8. Therefore, this Dt was considered to evaluate a phase plane plot which indicates the equilibrium points of the mathematical model. To determine the maximum concentrations of CBD cipA-BMP2 mRNA and CBD cipA-BMP2 protein, a saturating concentration of IPTG (IPTG=0.1 mM) was evaluated. This is a monostable system where the equilibrium point at the steady state (Figure 2) is 2.21 nM and 172.69nM for CBD cipA-BMP2 mRNA and CBD cipA-BMP2 protein respectively.

Plano

Figure 2. Phase plane plot of the molecular species of CBD cipA-BMP2 with IPTG=0.1 mM as saturating concentration. The stable equilibrium point is at 2.21 nM and 172.69 nM for [CB]mRNA and [CB], respectively.

Expression at different IPTG inducer concentrations
Different values of [LacI]act cause a different effect in the mathematical model for expression of [CB]mRNA and [CB]. Figure 3 and Figure 4 show the concentrations of [CB]mRNA and [CB], respectively, as functions of time with a time step size Dt=0.1/8. It is worth to note that the higher IPTG dosage the higher [CB]mRNA and [CB] until the saturating level of IPTG = 0.1 mM.

RNA

Figure 3. CBD cipA-BMP2 mRNA concentration as function of time. The concentration is dependent of levels of IPTG inducer until the saturating concentration (IPTG=0.1 mM).

CB protein

Figure 4. CBD cipA-BMP2 protein concentration as function of time. The concentration is dependent of the IPTG inducer until the saturating level (IPTG=0.1 mM).

CONCLUSIONS

The present IPTG-inducible mathematical model, where a fusion protein CBD cipA-BMP2 was cloned in psb1c3, can be analyzed in two stages. First, the concentration of the IPTG inducer added to the culture medium interacts with the repressor protein LacI following the Hill equation. Then, the expression of CBD cipA-BMP2 becomes relieved, and at saturating concentrations of IPTG ≥ 0.1 mM it reaches the highest value (CBD cipA-BMP2 protein = 172.69nM, CBD cipA-BMP2 mRNA=2.21 nM).

The IPTG concentration inside E. coli is 94,845% of the total IPTG added to the culture medium. Moreover, the phase line analysis of the ODE representing the IPTG concentration inside E. coli as function of time showed that the equilibrium point is stable.

The linearization of the mathematical model revealed an stable equilibrium point for the expression of CBD cipA-BMP2 because two negative igenvalues,

REFERENCES

 1. Oehler, S.  (2009). Feedback Regulation of Lac Repressor Expression in Escherichia coli. Journal of Bacteriology, 191(16), 5301–5303.  http://doi.org/10.1128/JB.00427-09

 2. Ukkonen, K.  Vasala, A. (2015). Protein expression by IPTG autoinduction in EnPresso  B:Protocol with minimal manual work and superior yields compared to other  media.BioSilta. Retrieved on june 24th, 2018 from  https://bioscience.co.uk/userles/pdf/Application%20Note%20-%20Protein%20expression%20by%20IPTG%20autoinduction%20in%20EnPresso%20B.pdf.

3. Team TUDelft. (2009).Bacterial Relay Race. International Genetically Enginereed Machines. Retrieved on june 25th, 2018 from https://2009.igem.org/Team:TUDelft.

4. Semsey, S., Jaured, L., Csiszovszki, Z., Erdssy, J., Stger, V., Hansen, S. Krishna, S. (2014).The effect of LacI autoregulation on the performanceof the lactose utilization system in Escherichia coli. Nucleic Acids Research,41 (13),6381?6390.https://academic.oup.com/nar/article/41/13/6381/1120421.

5. University of California Berkeley.(2006).Berkeley. International Genetically Enginereed Machines.Retrieved on july 14th, 2018 from https://2006.igem.org/wiki/index.php/Berkeley
6. Ozbudak, E., Thattai, M., Lim, H., Shraiman, B. Van Oudenaarden, A. (2004).Multistability in the lactose utilization network of Escherichia coli. Nature, 427 (1476-4687), 737?740.https://www.nature.com/articles/nature02298.

7. Michel, D. (2013). Kinetic approaches to lactose operon induction and bimodality. Journal of Theoretical Biology 325, 6275.https://www.sciencedirect.com/science/article/pii/S0022519313000659?via

8. Moulton, G. (2014). Fed-Batch Fermentation A Practical Guide to Scalable Recombinant Protein Production in Escherichia coli. Retrieved from <a href="https://books.google.com.ec/books?id=MTpYc3fAyICpg=20lpg=PA20dq=doubling+time+recombinant+e+coli+30+minutessource=ots=97TxFmAXwsig=W3OJJYLqLEF5Z48fXRfVTPqPP4hl=essa=Xved=ahUKEwi505aivqTcAhVSuVkKHVaDTgQ6AEwCHoECAgQAQv=onepageq=20-30">Google Books</a>.

9. Galli, E., Midonet, C., Paly, E. Barre, F. (2017).Pressure and Temperature Dependence of Growth and Morphology of Escherichia coli:Experiments and Stochastic Model. Plos Genetics,13(3):e1006702.https://doi.org/10.1371/journal.pgen.1006702. ://jour-nals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1006702

10. Hovgaard, L., Frokjaer, S. van de Weert, M. (2013).Pharmaceutical Formulation Development of Peptides and Proteins. Second Edition. Retrieved from <a href="https://books.google.com.ec/books?id=MTpYc3fAyICpg=PA20lpg=20dq=doubling+time+recombinant+e+coli+30+minutessource_blots=p97TxFmAXwsig=W3OJJYLqLEF5Z48fXRfVTPqPP4hl=essa=Xved=ahUKEwi505aivqTcAhVSuVkKHVaDTgQ6AEwCHoECAgQAQv=onepageq=20-30">Google Books</a>.

11. Bernstein, J., Khodursky, A., Lin, P., Chao, S. Cohen, S. (2002). Global analysis of mRNA decay and abundance in Escherichia coli at single-gene resolution using two color fluorescent DNA microarrays. Proceedings of the National Academy of Sciences of the United States of America. 99 (15) 9697-9702. ://www.pnas.org/content/99/15/9697

12. Bremer, H., Dennis, P. P. (1996) Modulation of chemical composition and other parameters of the cell by growth rate. Neidhardt, et al. eds. Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd ed. chapter 97, pp. 1559, Table 3

13. Team PKU Beijing.(2009).PKU IGEM . International Genetically Enginereed Machines. Retrieved on july 16th, 2018 from://2009.igem.org/Team:PKU Beijing/Modeling/Parameters

The main goal of our work is to develop a functionalized cellulose-based biomaterial for bone and cartilage regeneration in order to allow a faster injuries recovery time and overcome remaining challenges in repairing these connective tissues. In biomedicine, emergent strategies have focused the use biomaterials loaded with drugs.1-3 We aimed to use bacterial cellulose, a biocompatible biomaterial, as scaffold for the delivery of the human bone morphogenetic protein 2 (BMP2). It is worth to note that the diffusion of a drug far of the action site can become ectopic tissue formation, representing a serious problem. Therefore, we focused to attach the BMP2 by the use of a cellulose binding domain (CBD). We choose the CBD of the scaffolding protein of C. thermocellum (CBD cipA) because the higher affinity compared to other CBDs, reported by the Team Imperial_2014. Moreover, in an effort for a longer broad application of a functionalized bacterial cellulose, such as wound healing, we also fused the CBD cipA with an elastin like polypeptide (ELP_C5) derived from the ELP- [V-150].

</div> <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script> <script> $(document).ready(function(){ $("#type").mouseenter(function(){

   	$(".textdis").show();

}); $("#label-neg-c").mouseenter(function(){

   	$(".loc-neg-c").show();

}); $("#label-pos-c").mouseenter(function(){

   	$(".loc-pos-c").show();

}); $("#label-td1").mouseenter(function(){

   	$(".loc-td1").show();

}); $("#label-td2").mouseenter(function(){

   	$(".loc-td2").show();

}); $("#label-td3").mouseenter(function(){

   	$(".loc-td3").show();

}); $("#label-td4").mouseenter(function(){

   	$(".loc-td4").show();

}); $("#label-td5").mouseenter(function(){

   	$(".loc-td5").show();

}); $("#label-td6").mouseenter(function(){

   	$(".loc-td6").show();

});

$("#type").mouseleave(function(){ $(".textdis").hide(); }); $("#label-neg-c").mouseleave(function(){ $(".loc-neg-c").hide(); }); $("#label-pos-c").mouseleave(function(){ $(".loc-pos-c").hide(); }); $("#label-td1").mouseleave(function(){ $(".loc-td1").hide(); }); $("#label-td2").mouseleave(function(){ $(".loc-td2").hide(); }); $("#label-td3").mouseleave(function(){ $(".loc-td3").hide(); }); $("#label-td4").mouseleave(function(){ $(".loc-td4").hide(); }); $("#label-td5").mouseleave(function(){ $(".loc-td5").hide(); }); $("#label-td6").mouseleave(function(){ $(".loc-td6").hide(); });

});

</script>

@@ Line 1: / Line 1: @@
-{{Ecuador}}
-<html>
 <head>
@@ Line 383: / Line 381: @@
    The half life of mRNAs in E. coli has been well reported by Bernstein and coworkers who determined that it  depends of culture medium. In, LB 99% of mRNAs had a half-life time between  1-15 min with a mean of 5.2 min.11 Therefore, 5.2 min can be assumed as the  half-life time of CBD cipA -BMP2 mRNA. Consequently, δ[CB<strong>]</strong>= 0.226 min-1. <br>
    In <em>E</em>. <em>coli</em> , the translation takes place at 12-21 amino  acids per second (aa s-1).12 We choose 19 aa s-1 because  the codon optimization. <a name="IND7"></a><strong><a name="IND8"></a></strong>Because CBD cipA-BMP2 contains 292 aa, β[CB]<strong> </strong>can be taken to be 3.904 min-1.The  half life of CBD cipA-BMP2 protein can be assumed to be 60 min-1, 13 consequently,  σ[CB]= 0.05min-1:</div>
-<div class="ec--p"><strong>RESULTS OF THE IPTG-INDUCIBLE MODEL FOR CBD cipA-BMP2  PROTEIN EXPRESSION IN </strong><strong><em>E</em></strong><strong><em>. </em></strong><strong><em>coli</em></strong></div>
+<div class="ec--h2">RESULTS OF THE IPTG-INDUCIBLE MODEL FOR CBD cipA-BMP2  PROTEIN EXPRESSION IN E. coli</div>
 <div class="ec--p"><strong>Calculation of entry of IPTG into </strong><strong><em>E</em></strong><strong><em>. </em></strong><strong><em>coli</em></strong><br>
    Figure 1 is a rate balance plot derived from  Equation 1 whith both forward and backward rates as functions of the normalized  [IPTG]int concentration whose value in the equilibrium (steady  state) can be obtained where the two functions intersect. Analitically, this  point is [IPTG]int =0.9485[IPTG]TOTAL <br>
@@ Line 490: / Line 488: @@
 <div class="ec--p"><strong>Figure 4.</strong> CBD cipA-BMP2 protein concentration  as function of time. The concentration is dependent of the IPTG  inducer until the saturating level (IPTG=0.1 mM).</div>
 <div class="ec--p">&#160;</div>
-<div class="ec--p"><strong>CONCLUSIONS</strong></div>
+<div class="ec--h2">CONCLUSIONS</div>
-<div class="ec--p">The present IPTG-inducible mathematical model,  where a fusion protein CBD cipA-BMP2 was cloned in psb1c3, can be analyzed in  two stages. First, the concentration of the IPTG inducer added to the culture  medium interacts with the repressor protein LacI following the Hill equation.  Then, the expression of CBD cipA-BMP2 becomes relieved, and at saturating  concentrations of IPTG ≥ 0.1 mM it reaches the highest value (CBD  cipA-BMP2 protein = 172.69nM, CBD cipA-BMP2 mRNA=2.21 nM).<br>
+<div class="ec--p">The present IPTG-inducible mathematical model,  where a fusion protein CBD cipA-BMP2 was cloned in psb1c3, can be analyzed in  two stages. First, the concentration of the IPTG inducer added to the culture  medium interacts with the repressor protein LacI following the Hill equation.  Then, the expression of CBD cipA-BMP2 becomes relieved, and at saturating  concentrations of IPTG ≥ 0.1 mM it reaches the highest value (CBD  cipA-BMP2 protein = 172.69nM, CBD cipA-BMP2 mRNA=2.21 nM).</div><br>
-  The IPTG concentration inside E. coli is 94,845% of the total IPTG added to the culture  medium. Moreover, the phase line analysis of the ODE representing the IPTG  concentration inside <em>E</em><em>. </em><em>coli</em> as function of time showed that the equilibrium point  is stable.<br>
+	<div class="ec--p">
+		The IPTG concentration inside E. coli is 94,845% of the total IPTG added to the culture  medium. Moreover, the phase line analysis of the ODE representing the IPTG  concentration inside <em>E</em><em>. </em><em>coli</em> as function of time showed that the equilibrium point  is stable.</div>
    The linearization of the mathematical model revealed  an stable equilibrium point for the expression of CBD cipA-BMP2 because two  negative igenvalues,</div>
 <div class="ec--p">&#160;</div>
 <div class="ec--p">&#160;</div>
-<div class="ec--p"><strong>REFERENCES</strong><br>
+	<div class="ec--h2">REFERENCES</div>
+	<div class="ec--p">
 . Oehler, S.  (2009). Feedback Regulation of Lac Repressor Expression in <em>Escherichia coli</em>. Journal of Bacteriology, 191(16), 5301–5303.  http://doi.org/10.1128/JB.00427-09<br>
 . Ukkonen, K.  Vasala, A. (2015). Protein expression by IPTG autoinduction in EnPresso  B:Protocol with minimal manual work and superior yields compared to other  media.BioSilta. Retrieved on june 24th, 2018 from  https://bioscience.co.uk/userles/pdf/Application%20Note%20-%20Protein%20expression%20by%20IPTG%20autoinduction%20in%20EnPresso%20B.pdf.<br>
@@ Line 583: / Line 583: @@
 </script>
-</html>
-{{Ecuador/footer}}

Difference between revisions of "Team:Ecuador/Model"

Revision as of 15:21, 18 November 2018

MATHEMATICAL MODELLING

Index