Modeling+gene+regulaton+(lac+operon)

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 * TODO LIST**
 * REF Monod and Jaqcet? LAC Operon
 * REF for ecological modeller scottish lake?
 * REF 70's bistability hysteresis for lactose use
 * REF Setty & Alon
 * REF Wong et al
 * Clarification: why graded regulation rather than switch
 * Clarification: why more regulation in spatial system with stochasticity?

=Modelling gene regulation=

Monster of Loch Ness syndrome
The LAC operon is a prototype for gene regulation (Monod and Jaqcet??). However as is typical of a complex system we shall first issue a warning about the **monster of lochness** (Nessy):
 * she is a monster in folk tales
 * once in a while there a still sightings
 * she lives in a very foggy lake in Schotland (Loch Ness)
 * fossils were found!

In the 70's there was an ecological modeller (REF?) who decided that using state of the art modelling it was possible to make a full scale model of a specific lake system, which could predict everything. All that was needed was **to know all living things and all parameters**. This was done for Loch Ness and with the model they could prove the existance of Nessy, since what was needed in the model was a top predator to make everything work given reasonable parameters!
 * i.e. you can get everything out that you want, even a monster
 * such models are monsters!
 * same for regulation models: huge monster of **Loch Ness syndrome**

LAC operon evolution
[|van Hoek and Hogeweg (2006)] formulated a model about the LAC operon, which can be seen as an AND-gate:
 * if there is no glucose AND lactose => activated, otherwise off
 * if lactose => ON

Moreover: **beta-galactosidase** transforms lactose and **permiase** brings lactose into the cell. However there is a problem: permiase is switched on by lactose, but needs to bring lactose in first! Therefore already in the 70's (REF) bi-stability (histeresis) switch was predicted for lactose use:
 * if OFF stay OFF: no lactose since no permiase

Setty / Alon (2003 REF) showed however with direct measurement of the LAC operon activity that is was not really an AND-gate, but a more gradual regualtion. So: //Q: Why bring in lactose when it is not needed?// By 2005 experimental evidence was available showing bi-stability in the LAC operon using an artificial inducer IPTG (which is not metabolized). Moreover in only in the supplementary material they mention that bi-stability does not happen with lactose!


 * Model**:
 * many reaction equations based on literature
 * parameters: based on literature from last 50 years
 * not measured in one cell, or same conditions! can differ by three orders of magnitude (witness the surfacing of Nessy!)
 * parameters mainly from Wong et al. (REF) and model adapted
 * metabolism of lactose and glucose
 * cell growth and division
 * protein dynamics are slow for degradation
 * growth quite fast
 * in a spatial environment: glucose and lactose influx and diffusoin and consumption
 * environment was varied in a relevant way:
 * period of both lactose and glucose and both not, i.e. **tuned** in such a way that the system sees everything
 * used measured parameters **except for LAC operon**: these are evolved (and not the dimension reducing variables but the actual kinetic parameters
 * i.e. evolution operated within the constraints of **other** parameters


 * Results:**

First interesting observation:
 * if evolve dimension reduction parameters (i.e. lumped variables) one gets bad LAC operon and different replica give very different results because the system gets **stuck on local optima**
 * if evolve kinetic parameters (unlumped variables) one gets good LAC operon because this allows for **neutrality** and don't get stuck on local optima.

Since we are here question whether bi-stability evolves we take **hard-case initial conditions**: for this some background parameters were chosen to be unrealistically large.

However there is a problem. It is a huge model with different time-scales (rates) which requires a very small time step and so the model runs for weeks. Inevitably the number of possible runs in limited and results are not very stable. Therefore:
 * from each run the last common ancestor was taken (LCA): i.e. it was a successful individual
 * the LCA was then allowed to compete with other LCAs.
 * the LAC operons of the winner were then studied.


 * Results**


 * the promoter function becomes quite similar to that found by Setty / Alon 2003 REF?
 * however: histeresis is not observed for lactose, but only for the artificial inducer!

Thus from an evolutionary point of view we don't expect a switch but instead a more graded regulation. //Q: so why is that good?//
 * faster regulatory adaptation (?)
 * what is needed is high peak of infllux concentrations (?)
 * moreover: protein dynamics are slow so fast environmental change doesn't "affect" cell. If it is faster, promoter activity doesn't matter, if it is too slow, it gets stuck in one corner with no regulation
 * recent experiments: long high lactose etc, in a few weeks can loose promoter function (actually faster than in the model)


 * Conclusion**

First of all there is no such thing as the **real parameters**: changes in a few weeks! (compare that to Nessy!).

//Q: so what is the effect of stochasticity? (vs previous differential equation model)//
 * more regulation in a spatial system (?)

If we look at evolutionary time (2000 days):
 * paramters change constantly
 * mixed vs space is hardly perceptible

Idea of a **solution**: hard to show due to **compensatory mutations** in the whole kinetics of the system. Multi-level modelling is **indispensible for understanding single-level phenomena!**

Next: Genetic pattern formation and modelling morphogenesis (Paulien's critters)


 * References**

**van Hoek MJ & Hogeweg** (2006) In silico evolved lac operons exhibit bistability for artificial inducers, but not for lactose.  //Biophys. J.//, **91**: 2833-2843. [|MEDLINE]. [|DownLoad PDF].