Biomod/2013/NanoUANL/Nucleation

From OpenWetWare

(Difference between revisions)
Jump to: navigation, search
Line 53: Line 53:
<p>Mathematical models that represent the dynamic behavior of biological systems are a quite prolific field of work and are pillar for Systems Biology. A number of deterministic and stochastic formalisms have been developed at different abstraction levels that range from the molecular to the population levels.</p>
<p>Mathematical models that represent the dynamic behavior of biological systems are a quite prolific field of work and are pillar for Systems Biology. A number of deterministic and stochastic formalisms have been developed at different abstraction levels that range from the molecular to the population levels.</p>
<div id="title">
<div id="title">
-
<p><a name="Model Description"><h3>Model Description&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h3><hr></p></div>
+
<p><a name="Model Description"><h3>Model Description&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h3><hr></p></div>
<p>We present a model for the relation between time, temperature and the change in fluorescence (measured in Relative Fluorescent Units or RFUs) of an <i>E. coli</i> culture that harbors a genetic construction where a fluorescent protein is under control of a RNAT.</p>
<p>We present a model for the relation between time, temperature and the change in fluorescence (measured in Relative Fluorescent Units or RFUs) of an <i>E. coli</i> culture that harbors a genetic construction where a fluorescent protein is under control of a RNAT.</p>
<div id="title">
<div id="title">
-
<p><a name="Model"><h4>Model Conditions&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h4><hr></p></div>
+
<p><a name="Model"><h4>Model Conditions&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h4><hr></p></div>
\begin{equation}
\begin{equation}
\large F_{R} = \frac{F_{sample}}{F_{standard}}
\large F_{R} = \frac{F_{sample}}{F_{standard}}
Line 62: Line 62:
<p>where F<sub>sample</sub> is the OD<sub>600</sub>-normalized fluorescence emited by a sample, while F<sub>standard</sub> is the OD<sub>600</sub>-normalized fluorescence measurement for the corresponding standard culture (again, BBa_E1010 for RFP and BBa_E0040 for GFP).</p>
<p>where F<sub>sample</sub> is the OD<sub>600</sub>-normalized fluorescence emited by a sample, while F<sub>standard</sub> is the OD<sub>600</sub>-normalized fluorescence measurement for the corresponding standard culture (again, BBa_E1010 for RFP and BBa_E0040 for GFP).</p>
<div id="title">
<div id="title">
-
<p><a name="Fixed_temperature_model"><h4>Fixed Temeperature Model&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h4><hr></p></div>
+
<p><a name="Fixed_temperature_model"><h4>Fixed Temeperature Model&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h4><hr></p></div>
<div id="title">
<div id="title">
-
<p><a name="Dynamic"><h4>Dynamic Model&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h4><hr></p></div>
+
<p><a name="Dynamic"><h4>Dynamic Model&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h4><hr></p></div>
<p>In <a href="http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0011308" target="3">Shah and Gilchrist, (2010)</a>, it was found that the probability of openness of a ribosome binding site (RBS) of an mRNA with respect to temperature, fits well into a logistic equation. However, the authors did not find significant differences in the behaviour of known RNATs and non-RNAT elements and admit that RBS openness cannot be assumed to be directly correlated to translational activity. Therefore, their RBS-melting probability equation would not be recommendable to be used directly in gene expression models for RNATs.</p>
<p>In <a href="http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0011308" target="3">Shah and Gilchrist, (2010)</a>, it was found that the probability of openness of a ribosome binding site (RBS) of an mRNA with respect to temperature, fits well into a logistic equation. However, the authors did not find significant differences in the behaviour of known RNATs and non-RNAT elements and admit that RBS openness cannot be assumed to be directly correlated to translational activity. Therefore, their RBS-melting probability equation would not be recommendable to be used directly in gene expression models for RNATs.</p>
<div id="title">
<div id="title">
-
<p><a name="Gaussian Function Fitting"><h3>Gaussian Function Fitting&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h3><hr></p></div>
+
<p><a name="Gaussian Function Fitting"><h3>Gaussian Function Fitting&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h3><hr></p></div>
<div id="title">
<div id="title">
<p><a name="Gaussian Function"><h4>Gaussian Function</h4></a><hr></p></div>
<p><a name="Gaussian Function"><h4>Gaussian Function</h4></a><hr></p></div>
Line 75: Line 75:
<p><a name="Justification"><h4>Justification</h4></a><hr></p></div>
<p><a name="Justification"><h4>Justification</h4></a><hr></p></div>
<div id="title">
<div id="title">
-
<p><a name="Fitting Results"><h3>Fitting Results&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h3><hr></p></div>
+
<p><a name="Fitting Results"><h3>Fitting Results&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h3><hr></p></div>
<div id="title">
<div id="title">
<p><a name="RNAT Comparison"><h4>RNAT Comparison</h4></a><hr></p></div>
<p><a name="RNAT Comparison"><h4>RNAT Comparison</h4></a><hr></p></div>
Line 83: Line 83:
<p><a name="M12 Special Case"><h4>M12 Special Case</h4></a><hr></p></div>
<p><a name="M12 Special Case"><h4>M12 Special Case</h4></a><hr></p></div>
<div id="title">
<div id="title">
-
<p><a name="References"><h3>References&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h3><hr></p></div>
+
<p><a name="References"><h3>References&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h3><hr></p></div>
<ol>
<ol>
<li>ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique?  
<li>ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique?  
Line 97: Line 97:
<div id="title">
<div id="title">
-
<p><a name="Appendix"><h3>Appendix&nbsp;&nbsp;<a href="#" class="btn btn-info"><font color="#fff">Back to top</font></a></h3><hr></p></div>
+
<p><a name="Appendix"><h3>Appendix&nbsp;&nbsp;<a href="#" class="btn btn-info">Back to top</a></h3><hr></p></div>
</div>
</div>

Revision as of 23:29, 12 October 2013

Math Model

Mathematical models that represent the dynamic behavior of biological systems are a quite prolific field of work and are pillar for Systems Biology. A number of deterministic and stochastic formalisms have been developed at different abstraction levels that range from the molecular to the population levels.

We present a model for the relation between time, temperature and the change in fluorescence (measured in Relative Fluorescent Units or RFUs) of an E. coli culture that harbors a genetic construction where a fluorescent protein is under control of a RNAT.

\begin{equation} \large F_{R} = \frac{F_{sample}}{F_{standard}} \end{equation}

where Fsample is the OD600-normalized fluorescence emited by a sample, while Fstandard is the OD600-normalized fluorescence measurement for the corresponding standard culture (again, BBa_E1010 for RFP and BBa_E0040 for GFP).

In Shah and Gilchrist, (2010), it was found that the probability of openness of a ribosome binding site (RBS) of an mRNA with respect to temperature, fits well into a logistic equation. However, the authors did not find significant differences in the behaviour of known RNATs and non-RNAT elements and admit that RBS openness cannot be assumed to be directly correlated to translational activity. Therefore, their RBS-melting probability equation would not be recommendable to be used directly in gene expression models for RNATs.

  1. ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique? PLoS ONE,5(7):e11308.doi:10.1371/journal.pone.0011308.
  2. H. A. Von Fircks, T. Verwijst,(1993)Plant Viability as a Function of Temperature Stress(The Richards Function Applied to Data from Freezing Tests of Growing Shoots Plant Physio ,103(1):125–130.
  3. Hoops S, et al. (2010)COPASI–a COmplex PAthway SImulator Bioinformatics ,22,3067-3074,2006,http://dx.doi.org/10.1093/bioinformatics/btl485
  4. COPASI Documentation 2.Steady State calculation(2013,May 16).Retrieved from http://www.copasi.org/tiki-integrator.php?repID=9&file=ch07s02.html
  5. Ting Chen, et al. Modeling gene expression with differential equations (1999) Pacic Symposium of Biocomputing
  6. Gaussian function(Consulted on 2013,September 27)Retrieved from http://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4282164/Gaussian%20function.pdf

Personal tools