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Team:Fudan Lux/Modeling
From 2012.igem.org
Mathematical Model
The model has two elements: the light sensor, which exists as a dimer, and Lux protein. The light sensor dimer has the capability to bind to downstream promoter, as above mentioned which is “Tet on” promoter, and regulate the expression of Lux. Once the dimer binds to the promoter, the transcription rate of the Lux is decreased by a factor of 100. The parameters of the system are listed in Table 1. We built the corresponding deterministic mathematical model for this system as follows:
equation (1), the variables Ls, Ls1, Lux refer to the concentration of the light sensor, the active light sensor and Lux protein in the system, respectively. The variables Z , Z1 and Z2 denote the total light strength, intrinsic light strength and external light strength. The initial values of these variables are set to zero. N is the copy number of plasmid, K1 and K2 are expression capability of light sensor gene and Lux, respectively, K3 is the parameter describe the ability of give out light by Lux, K4 is attenuation rate of light propagation in colonial, K5 and K6 are parameters of logistic eqution, d is the degradation rate of light sensor and Lux protein, r means the dilution rate caused by cell volume grow. δ denotes the noise of gene expression. In order to calculate the total extern light strength, we used multiple integral to describe the contribution of whole colonial to this unit. Multiple logistic method was also be used to describe concentration of the active light sensor change by light sensor and total light strength.
Simulation
| Paramemter | Value |
| N | row 2, cell 1 |
| K1 | 0.01 umol/min |
| K2 | 0.01umol/min |
| K3 | 8.4 |
| K4 | 0.05 |
| K5 | 20 |
| K6 | 20 |
| d2 | 0 |
| d1 | 0 |
| r | 0.02 |
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Spectrum analysis
Randomly, we chased more than 2000 sampling points, and extracted time serials data of each sampling points from our time lapse images. Use customized matlab code, we analyzed the spectrum of each sampling point, and then shown the distribution of frequency of all sampling points by histogram.
