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Analytical Solutions of Fluroscent Reporters to auxin influx in plantcells

Mehala N, Ananthaswamy V, Rajendran L

A Mathematical model of biosensors for phytohormone quantification has been developed. The model is based on the system of five coupled non-linear ordinary differential equations that describes the dynamics of DII-VENUS transcriptional reporter degradation in response to external application of Auxin . The nonlinear relationship that exists between the target molecule and the reporter necessitates the development of mathematical models which are used to relate the sensor fluorescence with hormone abundance quantitatively. In this article the analytical expressions for various levels of degradation of DII-VENUS for various doses of Auxin have been derived by using homotopy perturbation method. The analytical results are compared with simulation results using Mat lab program. It is found that the numerical results agree with the analytical results and with the appropriate theories.