# Team:Paris/Modeling/hill approach

(Difference between revisions)
 Revision as of 14:02, 12 August 2008 (view source)Hugo (Talk | contribs) (New page: ==First Mathematical Approach== ===Introduction=== As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were exp...)← Older edit Latest revision as of 07:06, 30 October 2008 (view source) (35 intermediate revisions not shown) Line 1: Line 1: - ==First Mathematical Approach== + {{:Team:Paris/MenuBackup}} + = Model of the ''APE modelisation'' = + ==What kind of Mathematical Simulation ?== - ===Introduction=== + One of the strength of the synthetic biology is that precise knowledge and caracterisation of certains interactions allow very good predictions and simulations. So, our second model intends to get the best precision in the modelisation, consistent with the simpliest (but still logical) hypothesis possible. - As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were expected to be Hill functions. Obvisouly, this modeling requires a huge number of parameters. To obtain them, we had planed to devise specific experiments (described below). + To determine interactions like Michaëlis-Menten's or Hill's, we start from the basical chemicals equations and try to caracterise their consequences on the behaviour of the system with few parameters. For instance, each ''complexation reactions'' will be caracterised at their steady-state, for all sets of initial concentrations (see [[Team:Paris/Modeling/Programs|complexations]]). - Nonetheless, after reading some more articles, we have decided to change several assumptions of the modeling choice. Therefore, we have devised a perhaps more biologically relevant framework (see above). + We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells. - This part describes in detail the first approach and the codes that have been produced. + ==Bio-Chemical General Assumptions== -
So, if I understand well,the model above does not include Hill functions -is a simplification-  and is your second approach, right? + We know that the following equations do not describe properly what ''really'' happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an ''hexamere'' FlhD4C2. But, as we will surely not get access to the ''dissociation constant'' of the ''hexamerisation'', we just treat it as an ''abstract'' inducer protein "FlhDC", with an order (''n'') in its ''complexation caracterisation'' probably around 2*4 = 8 (but perhaps completly different ! ; the estimation of the error by the [[Team:Paris/Modeling/Programs#Finding_Parameters|'findparam']] program will tell us if we are right to do so). - ===First Approach=== + For the moment, at each part of our modelisation, we reduce the expression of a gene at its '''transcription'''. The '''translation''' process is not taken into acount (see however [[Team:Paris/Modeling/estimation#RBS_Issue|considerations on RBS]]). + Besause of that, our caracterisations doesn't allow us to know the ''real concentrations'' of the proteins we produce, but only their "real times effects" on the promoters they influence. - As a first approximation, we have proposed a set of 5 ordinary differential equations, without taking into account the translation step. Besides, we have had not introduced yet a synchronizaton module. Therefore, the repression of FlhDC is directly modeled by the presence of the 'Z3' gene (that is the last that is turned on). + Every complexations we deal with are the supposed to reach ''immediatly'' their '''steady-states'''. So, the only phenomenon we are observing along time is the protein production ; that's why this model can't really simulate the possible delay a complexation could introduce, and which could be important for the stiffness of our oscillations... - In this framework, we have found parameters that have provided oscillations as well as a function that automatically detects whether the output of the ode system is oscillating. This has allowed to screen a little the parameters used, in order to evaluate the robustness of the system. + As we need to keep our cells in the exponential phase of growth (and since we can't use the already mentioned system of Ron Weiss, see [[Team:Paris/Project|description of the project]]), our system works in a '''chemostat'''. We will also be able to estimate the Cell Density, and we will have to take into acount the ''renewal phenomenon''. Under this conditions, we assume the following constants to be true : - The methods employed are described there : [[Team:Paris/Modeling/first approach| First Approach]]. + * Cell Division : every 35 minutes + → Dilution Rate : 0.0198 min-1 + * Cell Density : cell.L-1 + → Average Intracellular Volume : L
+ → Average Extracellular Volume (in the chemostat) : L + * Renewal Rate : L.min-1 + (→ Dilution Rate : min-1) - ===More precise Bio-Mathematical Description=== + To see more details about the values of the involved constants, see [[Team:Paris/Modeling/Bibliography|the bibliography]] and the [[Team:Paris/Modeling/estimation|estimation section]]. - After trying to obtain oscillations from a simple model, we have tried to described more precisely the studied system. Therefore, we have obtained the following formalism : [[Team:Paris/Modeling/description|Bio-Mathematical Description]]. + ==Incrementally detailed Parts of our Project== - ===Bibliography=== + * [[Team:Paris/Modeling/Oscillations|Oscillations]] - In order to choose a proper modeling approach for our system, we have decided to list all the chemical reactions we will take into account. Afterwards, we will find the needed parameters reading articles or devising the required experiments. + * [[Team:Paris/Modeling/FIFO|FIFO]] - An overview of the work that has to be done can be found here : [[Team:Paris/Modeling/Bibliography|Parameters we have to use]]. + * [[Team:Paris/Modeling/Synchronisation|Synchronisation]] - ===Estimation of parameters=== +
- + - Then, we will need many parameters to fully desribe the system according to the asumptions of the previous section. A natural way to have access to their value, after searching in the litterature, is to devise specific experiments. As a consequence of the characterization of the promoters activity, some Hill functions could be obtained. + - + - Thus, we have described the experimental approach required : [[Team:Paris/Modeling/estimation|Estimation of the parameters]]. + - + - Nonetheless, as mentioned above, we have changed the way to model the biological reactions. As a result have stopped investigating in this way to focus on the [[Team:Paris/Modeling#An_Oscillatory_Biological_Model|An Oscillatory Biological Model]]. + - + - + - |}
+ - + - [[Too be continued]] +

## Latest revision as of 07:06, 30 October 2008

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# Model of the APE modelisation

## What kind of Mathematical Simulation ?

One of the strength of the synthetic biology is that precise knowledge and caracterisation of certains interactions allow very good predictions and simulations. So, our second model intends to get the best precision in the modelisation, consistent with the simpliest (but still logical) hypothesis possible.

To determine interactions like Michaëlis-Menten's or Hill's, we start from the basical chemicals equations and try to caracterise their consequences on the behaviour of the system with few parameters. For instance, each complexation reactions will be caracterised at their steady-state, for all sets of initial concentrations (see complexations).

We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells.

## Bio-Chemical General Assumptions

We know that the following equations do not describe properly what really happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an hexamere FlhD4C2. But, as we will surely not get access to the dissociation constant of the hexamerisation, we just treat it as an abstract inducer protein "FlhDC", with an order (n) in its complexation caracterisation probably around 2*4 = 8 (but perhaps completly different ! ; the estimation of the error by the 'findparam' program will tell us if we are right to do so).

For the moment, at each part of our modelisation, we reduce the expression of a gene at its transcription. The translation process is not taken into acount (see however considerations on RBS). Besause of that, our caracterisations doesn't allow us to know the real concentrations of the proteins we produce, but only their "real times effects" on the promoters they influence.

Every complexations we deal with are the supposed to reach immediatly their steady-states. So, the only phenomenon we are observing along time is the protein production ; that's why this model can't really simulate the possible delay a complexation could introduce, and which could be important for the stiffness of our oscillations...

As we need to keep our cells in the exponential phase of growth (and since we can't use the already mentioned system of Ron Weiss, see description of the project), our system works in a chemostat. We will also be able to estimate the Cell Density, and we will have to take into acount the renewal phenomenon. Under this conditions, we assume the following constants to be true :

• Cell Division : every 35 minutes

→ Dilution Rate : 0.0198 min-1

• Cell Density : cell.L-1

→ Average Intracellular Volume : L
→ Average Extracellular Volume (in the chemostat) : L

• Renewal Rate : L.min-1

(→ Dilution Rate : min-1)

To see more details about the values of the involved constants, see the bibliography and the estimation section.