Biocham 4.1.22 Copyright (C) 2003-2019 Inria, EPI Lifeware, Saclay-ÃŽle de France, France, license GNU GPL 2, http://lifeware.inria.fr/biocham4/

# TD7 Doctor in the Cell¶

### Algorithm for the differential diagnosis of diabetes¶

• logical circuits

# Questions¶

### 1) Write a CRN for implementing the GluONe circuit¶

• Out1: Â¬A âˆ§ G

• notA + A => _
• notA + G => O1
• Out2: A âˆ§ G

• A + G => O2
In [1]:
MA(k1) for notA + A => _.
MA(k2) for notA + G => O1.

MA(k3) for A + G => O2.

parameter(k1=1, k2=1, k3=1).
present(notA, 0.01).
list_ode.

\begin{align*} O2_0 &= 0\\ G_0 &= 0\\ A_0 &= 0\\ O1_0 &= 0\\ notA_0 &= 0.01\\ k1 &= 1\\ k2 &= 1\\ k3 &= 1\\ \frac{dO2}{dt} &= k3*A*G\\ \frac{dG}{dt} &= - (k2*notA*G)-k3*A*G\\ \frac{dA}{dt} &= - (k1*notA*A)-k3*A*G\\ \frac{dO1}{dt} &= k2*notA*G\\ \frac{dnotA}{dt} &= - (k1*notA*A)-k2*notA*G\\ \end{align*}

### $G_0 = 0, A_0 = 0$¶

In [2]:
present(G,0).
present(A,0).

numerical_simulation.
plot(show:{O1,O2}).

In [3]:
numerical_simulation(method:ssa).
plot(show:{O1,O2}).


### $G_0 = 1, A_0 = 0$¶

In [4]:
present(G,1).
present(A, 0).
numerical_simulation.
plot(show:{O1,O2}).

In [5]:
numerical_simulation(method:ssa).
plot(show:{O1,O2}).


### $G_0 = 0, A_0 = 1$¶

In [6]:
present(G,0).
present(A, 1).

numerical_simulation.
plot(show:{O1,O2}).

In [7]:
numerical_simulation(method:ssa).
plot(show:{O1,O2}).


### $G_0 = 1, A_0 = 1$¶

In [8]:
present(G,1).
present(A, 1).

numerical_simulation.
plot(show:{O1,O2}).

In [9]:
numerical_simulation(method:ssa).
plot(show:{O1,O2}).


The continuous and stochatic semantics yield what was expected, in accordance with the corresponding truth values table.

### 3) Play with the kinetic parameters of your CRN and describe the sensitivity of the circuit to their values¶

In [10]:
%slider k1 k2 k3

• the higher $k_1$, the fastest one of the species $A$ and $notA$ (the one with the lowest initial concentration) disappears ("consumed" by the other, due to the first reaction)
• the higher $k_2$ (resp. $k_3$), the steepest the variation of $O1$ (resp. $O2$) toward its final value is, looking more and more like a "step function", what we aim to approximate ultimately: so we'd better increase $k_1$ and $k_2$ as much as possible, to simulate as faithfully as possible the logic gates.