Finding parameters

Our model now considers the maturation of KillerRed and the accumulation of damages done to the bacteria. It is able to explain and predict properly the behaviour observed. But we still have to find the best parameters to do so. These are 6 parameters to find :

$r$ : the speed of growth of bacteria. in $min^{-1}$

$a$ : the production of KillerRed per bacteria. in $UF.OD^{-1}.min^{-1}$

$b$ : the efficiency of photobleaching. in $UF.UL^{-1}.min^{-1}$

$m$ : the maturation rate of KillerRed. in $min^{-1}$

$k$ : the toxicity of KillerRed. in $OD.UF^{-1}.UL^{-1}.min^{-1}$

$l$ : the ability of the bacteria to repear damages of ROS. unitless

With the units :

$OD$ is the Optical Density for $\lambda = 600nm$

$UF$ is an arbitrary Unit of Fluorescence

$UL$ is an arbitrary Unit of Light, related to the energy received by the bacteria. $1 UF$ shall be the energy of light received by an erlenmeyer with a MR16 LED on its side.

A regression requieres the solutions to be analytic functions, such as polynomials or exponentials to project the points on it.

Gradient or Newton methods requiere a regularity in the effect of parameters that we don't have.

The technique of design of experiments is also unusable for the same reason.

Methods to find our parameters