# Biomod/2013/NanoUANL/Nucleation

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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.

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.

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.

\large F_{R} = \frac{F_{sample}}{F_{standard}} \large F_{R} = \frac{F_{sample}}{F_{standard}} Line 62: Line 62:

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).

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.

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.

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Justification

Justification

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M12 Special Case

M12 Special Case

1. ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique?
2. ShahP ,Gilchrist MA(2010)Is Thermosensing Property of RNA Thermometers Unique? Line 97: Line 97:

## Math Model

### Introduction

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.

### Model Description

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.

#### Model Conditions

$$\large F_{R} = \frac{F_{sample}}{F_{standard}}$$

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).

#### Dynamic Model

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.

### References

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