Biomod/2013/NanoUANL/Nucleation
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Math Model
<a name="Introduction">
Introduction</a>
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.
<a name="Model Description">
Model Description <a href="#" class="btn btn-info">Back to top</a>
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.
<a name="Model">
Model Conditions <a href="#" class="btn btn-info">Back to top</a>
\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).
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Fixed Temeperature Model <a href="#" class="btn btn-info">Back to top</a>
<a name="Dynamic">
Dynamic Model <a href="#" class="btn btn-info">Back to top</a>
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.
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Gaussian Function Fitting <a href="#" class="btn btn-info">Back to top</a>
<a name="Gaussian Function">
Gaussian Function
<a name="Biological Antecedents">
Biological Antecedents
<a name="Justification">
Justification
<a name="Fitting Results">
Fitting Results <a href="#" class="btn btn-info">Back to top</a>
<a name="RNAT Comparison">
RNAT Comparison
<a name="Parameters">
Parameters
<a name="M12 Special Case">
M12 Special Case
<a name="References">
References <a href="#" class="btn btn-info">Back to top</a>
- ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique? PLoS ONE,5(7):e11308.doi:10.1371/journal.pone.0011308.
- 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.
- Hoops S, et al. (2010)COPASI–a COmplex PAthway SImulator Bioinformatics ,22,3067-3074,2006,http://dx.doi.org/10.1093/bioinformatics/btl485
- COPASI Documentation 2.Steady State calculation(2013,May 16).Retrieved from http://www.copasi.org/tiki-integrator.php?repID=9&file=ch07s02.html<il>
- Ting Chen, et al. Modeling gene expression with differential equations (1999) Pacic Symposium of Biocomputing
- Gaussian function(Consulted on 2013,September 27)Retrieved from http://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4282164/Gaussian%20function.pdf
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