simple allosteric model

Author: Vincent Danos

This is a simple allosteric model. There are two agents called A and R, R has an internal state 0/1 that represents his conformation. Absent any A, R conformation is uniform. When A binds R, R prefers state 0.

Thermodynamic consistency forces a relation between the equilibrium constants for binding and flipping:

K(R flips 0 to 1 with an A) = K(attach to A in state 1) * K(flip 0 to 1 free) * 1/K(attach to A in 0) = 1/10

We activate the A's at T=10 time units to observe the difference on the conformational distribution of R.

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# Reversibility forces relations between equilibrium constants
# expressed as products of K's:
 
# K(bind A in state 0) * K(flip to 1 busy) = 1/10 * 10/1 =
# K(flip to 1 free) * K(bind A in state 1) = 1/1 * 1/1

%agent: B()
%agent: A(x)
%agent: R(i~0~1,x)

%init: 1000 (B(), R(i~0,x))

# flips	                     	# - Delta E =
R(i~0,x)	-> R(i~1,x)	  @1	# 0 
R(i~1,x)	-> R(i~0,x)	  @1

R(i~0,x!_)  -> R(i~1,x!_) @1 	# ln(1/10) = -ln(10) + 0 + 0
R(i~1,x!_)  -> R(i~0,x!_) @10

# binds
A(x),R(i~0,x) -> A(x!1),R(i~0,x!1) @10
A(x!1),R(i~0,x!1) -> A(x),R(i~0,x) @1 

A(x),R(i~1,x) -> A(x!1),R(i~1,x!1) @1
A(x!1),R(i~1,x!1) -> A(x),R(i~1,x) @1 


# we observe the number of Rs in conformation 0

%obs: 'free R0' R(i~0) 
%obs: 'bound R' R(x!_)

# ln(10) 
# ln(1)=0
# we activate the A's at T=10 time units to observe the difference
'inj' B() -> A(x) @0 

%mod: [T] >  10 do 'inj':= [inf]