Team:Paris/Modeling/estimation
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(→how to control the concentration of the transcription factor ?) |
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<center> [[Image:Bilan_lacR.png]]</center> | <center> [[Image:Bilan_lacR.png]]</center> | ||
- | where [IPTG] denotes the concentration of IPTG we introduced in the medium, that will stay constant in all the bacteria along time, assuming that its degradation is near 0, and that the diffusion is quick. (We can already notice an other limitation in our protocol : this formula has got sense only for [IPTG] < (K + [LacR*]), that limits the range of [IPTG] we can use to determine the functions below. Notice that this limitation is conditionned by [LacR*], which depends of the constitutive promoter we put before ''lacR''.) | + | where [IPTG] denotes the concentration of IPTG we introduced in the medium, that will stay constant in all the bacteria along time, assuming that its degradation is near 0, and that the diffusion is quick. (We can already notice an other limitation in our protocol : this formula has got sense only for [IPTG] < (K + [LacR*]), that limits the range of [IPTG] we can use to determine the functions below. Notice that this limitation is conditionned by [LacR*],which depends of the constitutive promoter we put before ''lacR''.) |
According to the [[Team:Paris/Modeling#first_Hypothesis|hypothesis '''(3)''']], the activity of ''Plac'' would verify (keeping the same notations) : | According to the [[Team:Paris/Modeling#first_Hypothesis|hypothesis '''(3)''']], the activity of ''Plac'' would verify (keeping the same notations) : | ||
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* better but much longer and requiring much more precision, we can use the already noticed properties : [IPTG] < (K + [LacR*]). By having a look on the first equation of this section, we understand that beyond this limit, [LacR_IPTG] will no more evoluate. By observing the evolution of the influence of a growing (by steps as small as possible) concentration of [IPTG] introduced, we should be able to approximate the critic concentration when it no more changes, ~(K + [LacR*]). Less is the order n, better is the detection of this critic concentration, because of the greater derivative of the Hill function for small values of LacR. Therefore we should keep this estimation only if we find n ~ 1. Then, by considering k*((K + [LacR*])/[LacR*]) instead of k, we should easily determine all the parameters we need, only thanks to [[Team:Paris/Modeling/Programs|'findparam']]. | * better but much longer and requiring much more precision, we can use the already noticed properties : [IPTG] < (K + [LacR*]). By having a look on the first equation of this section, we understand that beyond this limit, [LacR_IPTG] will no more evoluate. By observing the evolution of the influence of a growing (by steps as small as possible) concentration of [IPTG] introduced, we should be able to approximate the critic concentration when it no more changes, ~(K + [LacR*]). Less is the order n, better is the detection of this critic concentration, because of the greater derivative of the Hill function for small values of LacR. Therefore we should keep this estimation only if we find n ~ 1. Then, by considering k*((K + [LacR*])/[LacR*]) instead of k, we should easily determine all the parameters we need, only thanks to [[Team:Paris/Modeling/Programs|'findparam']]. | ||
- | * Finally, since the repression of ''Plac'' by LacR in ''E.Coli'' has been well studied, and also the binding of IPTG on LacR, we could probably find the dissociation constant K (see above) of the complexation reaction | + | * Finally, since the repression of ''Plac'' by LacR in ''E.Coli'' has been well studied, and also the binding of IPTG on LacR, we could probably find the dissociation constant K (see above) of the complexation reaction LacR + IPTG ⇄ LacR_IPTG, in order to find directly by calculus the amount of free IPTG, function of the expression of the constitutive promoter before ''lacR'' and of the added IPTG. |
- | LacR + IPTG ⇄ LacR_IPTG, in order to find directly by calculus the amount of free IPTG, function of the expression of the constitutive promoter before ''lacR'' and of the added IPTG. | + | |
Then, it is still interesting to compare the three possibilities, if we have enough time... | Then, it is still interesting to compare the three possibilities, if we have enough time... |
Revision as of 18:28, 12 August 2008
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