Stochastic and executable models of synaptic processes

Neurons communicate with each other at synapses. These are plastic
 communication units that modulate signal transmission. Synaptic
 plasticity, i.e. the possibility of being modified by activity,
 contributes to neuro-computational capabilities, underlying phenomena
 like memory and learning. The synaptic signal transduction involves 
complex intra- and inter-cellular biochemical reactions, which, under
 several respects, appear to be most suitably described by stochastic 
models.

 On these bases, we have developed a stochastic and computationally 
executable model of the calyx of Held synapse. The aim of this work is 
to provide formal descriptive techniques for the analysis of such a 
complex and systemic behaviour. We exploit an interpretation of the
 structure of life systems as interacting computational entities from 
which the overall behaviour of the system emerges. We have exploited 
"process calculi", developed within concurrency theory in computer 
science, as representation language. These calculi describe the
 interactive behaviour of a system in terms of the behaviour of its 
active processes. A distinguished feature is that these 
representations have a direct executable interpretation, which allows 
the behaviour of a system, like the calyx, to be qualitatively
 simulated. Often, these models and their analysis enjoy nice 
compositional properties.

 Process behaviour is defined starting from basic interaction steps,
 which model simple molecular interactions, and compositional 
operators, through which we build up the complex behaviour of a
 structured system. The semantics of process calculi is generally 
expressed by a transition system, with states representing the current
 configuration of a system and transition representing its capability
 to act and move to one or more future states. Stochastic semantics has 
been developed in order to study system performances when relevant 
events occur according to a given probability distribution. Many of 
these semantics are based on the Gillespie’s Stochastic Simulation 
 Algorithm, originally proposed within chemical reaction modeling. This 
has further fostered the use of process calculi for biology and lead
 to the definition of new calculi for this purpose.

 The approach we followed benefits from conjugating the abstract and
 compositional algebraic models, the possibility of precisely describe
 their semantics and formally reasoning about them, and the
 quantitative analysis provided by stochastic semantics, accounting for
 the non-continuous, nor discrete, nature of many phenomena. Building
 on available data in literature, fitting some unknown parameters and
 developing working hypotheses, we have defined a model which, to our
 knowledge, is the first computational model of synaptic activity based 
on process calculi. The in-silico simulations performed are coherent
 with experimental data in literature and faithfully comprise
 short-term synaptic plasticity phenomena, like facilitation,
 depression and potentiation. Overall, the simulation results represent 
a quite articulate description of the presynaptic and postsynaptic
 activity.

 Additionally, this multidisciplinary work validates the application of
 the technique in life sciences, suggesting possibly improvements, such
 as a refined representation of space that overcomes the standard
 assumption of spatial uniformity (well-stirred space).