# Biomod/2013/NanoUANL/Nucleation

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**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.

where F_{sample} is the OD_{600}-normalized fluorescence emited by a sample, while F_{standard} is the OD_{600}-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.

- ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique?
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- 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