# Biomod/2013/NanoUANL/Nucleation

(Difference between revisions)
 Revision as of 23:29, 12 October 2013 (view source)← Previous diff Revision as of 23:33, 12 October 2013 (view source)Next diff → Line 57: Line 57: + \large F_{R} = \frac{F_{sample}}{F_{standard}} \large F_{R} = \frac{F_{sample}}{F_{standard}} + +
$F_{R} - F_{Rst} = e^{C} \ e^{- \delta {t}}$
+

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).

## 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

$$\large F_{R} = \frac{F_{sample}}{F_{standard}}$$
$F_{R} - F_{Rst} = e^{C} \ e^{- \delta {t}}$

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