Biomedical Engineering Reference
In-Depth Information
describe concurrent and parallel interactions. The basic idea of this calculus is to
model a system as a set of concurrent processes that interact according to a suitable
probability distribution to quantitatively accommodate the rates and the times at
which the reactions occur.
We adopted the framework of the stochastic -calculus to model and simulate
the molecular mechanism involved in encephalitogenic lymphocyte recruitment in
inflamed brain microvessels. Here we review the data we obtained from simulations
concerning the prediction of the rolling lymphocytes percentage versus vessels
diameters and of the adhesion probability versus contact time [
7
,
17
]. Our study,
started in 2004 in collaboration with the Department of Pathology of University of
Verona (Italy) [
17
], can also be interpreted as a comparison between the mechanical
and kinetic methods to point out the ability of this new tool to perform a stochastic
simulation of chemical interactions in a highly expressive and predictive way.
2
The Biochemical Stochastic
-Calculus Approach
In this section we first recall the basic syntax and intuitive semantics of the
biochemical stochastic -calculus, hereafter called
BioSpi
. We then discuss how
the language is used to model generic biological phenomena and how its composi-
tionality can be exploited to represent complex systems.
2.1
The Formalism
At the microscopic scale, biological processes are carried out by networks of
interacting molecules. The interaction between molecules causes their biochemical
modification. These modifications affect the potential of the modified molecules
to interact with other molecules. The -calculus represents the molecules as
computational processes and the network of interacting molecules as a mobile
concurrent systems. This kind of systems are composed of a community of co-
existing computational process that communicate each other and that change their
interconnection structure when they execute. Each computational process is defined
by its potential communication activity. The communication between process, that is
the abstraction of chemical interaction, occur via channels, denoted by their names.
In order for two concurrent processes to communicate, they must share a common
channel name on which the sender outputs a message with the receiver receives. The
only content of messages transmitted in communication is channel names or tuples
of channel names, which may be used for further communication. The -calculus
formally consists of a
syntax
for writing formal descriptions of the concurrent
system state (specification), a set of
congruence laws
, that determine when two
syntactic expressions are equivalent and an
operational semantics
consisting of
reduction rules
to define the potential changes in the state of the system induced
