an allosteric Ising model

AUTHORS Vincent Danos

Foreword
This model is after a recent paper [Science 327, pp.685-689] where among other things one finds an allosteric model (with an ANC-style energy function) of the E. Coli flagellar switch at the effector end of the chemotactic system.

The switch comprises two types of agents:
- a protomer P with two states f=0=inactive (favoured) or ccw (counter clockwise), f=1=active or cw (clockwise).

- and a regulator CheY-P that favours f=1.

To make a switch one takes 34 copies of P organised as a ring. CheY-Ps might bind any P, which means the ring can be in an astonishing approx. 10^20 different configurations (that is the number of species one would need in a traditional approach). The energy of the entire system is described by 3 different types of terms (in total 8 constants):

1. Ising term

E(P(f~1,x!1)P(y!1,f~0)) =
E(P(f~0,x!1)P(y!1,f~1))
>

E(P(f~0,x!1)P(y!1,f~0))  =
E(P(f~1,x!1)P(y!1,f~1))

an Ising penalty term for neighbours not being in the same conformation which will "spread conformation"

2. P conformational term
E(P(f~0)) < E(P(f~1))
saying that P prefers conformation 0 ("desir de nullite" as they say in french),

3. CheY-P binding:

E(P(f~0,s!1),CheY(s!1)) > E(P(f~0,s!1),CheY(s!1))
which says that when bound to CheY, P prefers conformation 1.

The simulation uses perturbations to control the amount of CheY-P, sending the entire ring in an homogeneously 0 or 1 conformation when it appears, and back to 0 when it disappears.

Created

February 10th by Vincent Danos

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