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The Bio-PEPA Eclipse Plug-in
User Manual : The Bio-PEPA plugin syntax : Syntax Example: Activator and Inhibitor

A.8 Syntax Example: Activator and Inhibitor

As an example, we will use a model of a general genetic network with a negative feedback through dimmers (see Figure 1).

\includegraphics[scale=0.9]{screenshots/screenshots/GeneticNetworkPng}
Figure 75: Genetic Network model

The model, which is shown in Table 4, is composed of three biological entities that interact with each other through five reactions (of which one is reversible). The biological entities are the mRNA molecule ($M$), the protein in monomer form ($P$) and the protein in dimeric form ($P2$). The first reaction (1) is the transcription of the mRNA ($M$) from the genes/DNA (not considered explicitly). The protein $P$ in the dimer form ($P2$), which is the final result of the network, has an inhibitory effect ($\ominus $, (-)) on this process. The second reaction (2) is the translation of the protein $P$ from $M$, in which $M$ acts as an activator ($\oplus $, (+)). The other two reactions represent the degradation of $M$ (3) and the degradation of $P$ (4). Finally there is the dimerization of $P$ and its inverse process (5, 5i). All the reactions are described by mass-action kinetics with the exception of the first reaction, which has a Michaelis-Menten kinetics [11] (see section A.4 for more information on mass-action and Michaelis-Menten kinetics) .

The Outline View of the model can be seen in Figure 76.

The Bio-PEPA syntax

//The Bio-PEPA plugin syntax

Locations:

//Locations

$v_{cell}: 1 (nM)^{-1}$

location v_cell: size = 1;

$ $

Parameter Definitions

//Parameter Definitions

$K_{M} = 356nM;$

KM = 356;

$v = 2.19 s^{-1};$

v = 2.19;

$k_2 = 0.043 s^{-1};$

k2 = 0.043;

$k_3 = 0.039 s^{-1};$

k3 = 0.039;

$k_4 = 0.0007 s^{-1};$

k4 = 0.0007;

$k_5 = 0.025 s^{-1};$

k5 = 0.025;

$k_{5_{i}} = 0.5 s^{-1};$

k5i = 0.5;

$ $

Species Attributes

 

$M: H = 1, N = 1,V = v_{cell},unit = nM;$

 

$P: H = 30, N = 2, V = v_{cell}, unit = nM;$

 

$P2: H = 30, N = 6, V = v_{cell}, unit = nM;$

 

$ $

Functional Rates

//Functional Rates

$f_{\alpha _{1}} = \frac{v}{K_{M}+P2};$

a1 = [v/(KM+P2)];

$f_{\alpha _{2}} = fMA(k2);$

a2 = [fMA(k2)];

$f_{\alpha _{3}} = fMA(k3);$

a3 = [fMA(k3)];

$f_{\alpha _{4}} = fMA(k4);$

a4 = [fMA(k4)];

$f_{\alpha _{5}} = fMA(k5);$

a5 = [fMA(k5)];

$f_{\alpha _{5_{i}}} = fMA(k5i);$

a5i = [fMA(k5i)];

$ $

Species Components

//Species Components

$M\; \rmdef (\alpha _{1}, 1) \product M + (\alpha _{2}, 1) \activator M + (\alpha _{3}, 1) \reactant M$

M = a1 >> + a2 (+) + a3 << ;

$P\; \; \rmdef (\alpha _{2}, 1) \product P + (\alpha _{4}, 1) \reactant P + (\alpha _{5}, 2) \reactant P + (\alpha _{5_{i}}, 2) \product P $

P = a2 >> + a4 << + (a5,2) << + (a5i,2) >>;

$P2 \rmdef (\alpha _{1}, 1) \inhibitor P2 + (\alpha _{5}, 1) \product P2 + (\alpha _{5_{i}}, 1) \reactant P2$

P2 = a1 (-) + a5 >> + a5i <<;

$ $

Model Component

//Model Component

$M[0] \sync{\alpha _{2}} P[0] \sync{\alpha _{5},\alpha _{5_{i}}} P2[0]$

M[0] <a2> P[0] <a5, a5i> P2[0]

Table 4: Bio-PEPA mathematical syntax and Bio-PEPA Eclipse Plug-in syntax for the Genetic Network model
\includegraphics[scale=0.5]{screenshots/screenshots/gennetworkoutline}
Figure 76: The Outline View of the Genetic Network model
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