Biomedical Engineering Reference
In-Depth Information
Tabl e 2
Biochemical stochastic -calculus specification for a heterodimer complex
formation and breakage
SYSTEM
WWD
Molecule
1
j
Moelcule
2
Molecule
1
WWD
.
backbone
/:
.bind
h
backbone
i
;
RA
/:
Molecule
1
bound
.
backbone
/
Molecule
1
bound
.
bb
/
WWD
.bb; RD/ :
Molecule
1
Molecule
2
WWD
.
bind
.
cross backbone
/; RA/ :
Molecule
2
bound
.
cross backbone
/
Molecule
2
bound
.
cbb
/
WWD
.
cbb
;
RD
/:
Molecule
2
RA and RD are the channel communication rates between processes
The first axiom of the BioSpi reduction semantics corresponds to usual reactions
involving two different molecules, the second one corresponds to homodimerization
reactions, involving the same molecular species.
2.2
The Approach
The kinetic approach, treating the cell adhesion as a reactive rate process of the
receptor and ligand molecules, is fit for a modeling and a simulation with BioSpi.
This framework [
1
] is a stochastic extension of the -calculus, a formal language
originally developed for specifying concurrent computational systems [
20
]. In
such systems, multiple processes interact with each other by synchronized pair-
wise communication on complementary communication channels, and modify each
other by transmitting channels names from one process to another. This feature,
named
mobility
, allows the network structure to change with the interaction between
processes.
The basic idea of the stochastic variant of the -calculus is to model a system as
a set of concurrent processes selected according to a suitable probability distribution
to quantitatively accommodate the rates and the times at which the reactions
occur. The stochastic -calculus is particularly suitable to model biochemical
networks as mobile communication systems. This language represents molecules
and their domains as computational processes, where their complementary determi-
nants correspond to communication channels. Chemical interaction and subsequent
modification of the state of reagents coincide with communication and channel
names transmission. In a stochastic -calculus model of a system of interacting
molecules, the time evolution of molecular populations levels is governed by the
initial number of processes and by the communication rates between them. The
communication rate associated to a channel is the parameter of an exponential
probability distribution that characterizes the stochastic behavior of the activity
corresponding to that channel. Precisely in this context activities denote actions with
an associated duration. Therefore, the communication rate is the abstraction of the
basal rate of a biochemical reaction, concerning the time that a molecular species
takes to undergo a reaction.
