We are faced with a great challenge: the cross-fertilization between the fields of formal methods for concurrency, in the computer science domain, and systems biology in the biological realm

A. Dovier

E.M. Clarke

H. Jong

M. Elowitz

O. Müller

P.D. Karp

R. Alur

R. Paige

R.W. Brockett

T.A. Henzinger

English

Many biological systems can be modeled using systems of ordinary differential algebraic equations (e.g., S-systems), thus allowing the study of their solutions and behavior automatically with suitable software tools (e.g., PLAS, Octave/Matlab tm). Usually, numerical solutions (traces or trajectories) for appropriate initial conditions are analyzed in order to infer significant properties of the biological systems under study. When several variables are involved and the traces span over a long interval of time, the analysis phase necessitates automation in a scalable and efficient manner. Earlier, we have advocated and experimented with the use of automata and temporal logics for this purpose (XS-systems and Simpathica) and here we continue our investigation more deeply. We propose the use of hybrid automata and we discuss the use of the notions of bisimulation and collapsing for a “qualitative ” analysis of the temporal evolution of biological systems. As compared with our previous proposal, hybrid automata allow maintenance of more information about the differential equations (S-system) than standard automata. The use of the notion of bisimulation in the definition of the projection operation (restrictions to a subset of “interesting ” variables) makes possible to work with reduced automata satisfying the same formulae as the initial ones. Finally, the notion of collapsing is introduced to move toward still simpler and equivalent automata taming the complexity of the automata whose number of states depends on the level of approximation allowed

ANTONIOTTI M

MISHRA B

PIAZZA C

POLICRITI A

SIMEONI M.

Name not available

Modeling Cellular Behavior with Hybrid Automata: Bisimulation and Collapsing

Most of the observable natural phenomena exhibit a mixed discrete-continuous behavior characterized by laws changing according to a phase cycle. Such behaviors can be modeled in a very natural way by a class of automata called hybrid automata. In this class the evolution of measurable quantities, such as concentrations, is represented according to both dynamical system evolutions - on dense domains - and rules phases through a discrete transition structure. Once the real systems are modeled in such a framework, one may want to analyze them by applying automatic techniques, such as model checking or abstract interpretation. Unfortunately, the interleaving of dense and discrete evolutions soon leads to undecidability results on hybrid automata. This paper addresses questions regarding the decidability of reachability problem for hybrid automata (i.e., "can the systems reach a state a from a state b?") by proposing a more "Nature"-oriented semantics. In particular, after observing that dense domains are abstractions of real world, we suggest that, for any biological system, there should be a value ε such that if the distance of two objects are less than ε, we cannot distinguish them. Using the above considerations, we propose a new semantics for hybrid automata which guarantees the decidability of reachability. Moreover, we provide a biological example showing that the new semantics mimics the real world behaviors better than the "classical" one

ANTONIOTTI, M.

MISHRA, B.

SIMEONI, M.

PIAZZA, Carla

POLICRITI, Alberto

Archivio istituzionale della ricerca - Università degli Studi di Udine

DEGANO, PIERPAOLO

PRIAMI CORRADO

Archivio della Ricerca - Università di Pisa

Enhanced Operational Semantics in Systems Biology

Degano, Pierpaolo

Priami, Corrado

Unitn-eprints Research

  
 
 
 
 
 
UNIVERSITY 
OF TRENTO 
 DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY 
  
38050 Povo – Trento (Italy), Via Sommarive 14 
http://www.dit.unitn.it 
 
 
 
 
 
 
 
 
 
 
 
 
 
ENHANCED OPERATIONAL SEMANTICS 
IN SYSTEMS BIOLOGY 
 
Pierpaolo Degano  and Corrado Priami 
 
 
August 2003 
 
Technical Report # DIT-03-046 
 
 
 
 
 
 
 
 
 
 
 
Also: in proceedings of CMSB 2003 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
. 
 
Enhanced Operational Semantics in
Systems Biology. ?
Pierpaolo Degano1 and Corrado Priami2
1 Dipartimento di Informatica, Universita` di Pisa
Via Filippo Buonarroti, 2 – I-56127 Pisa, Italy – degano@di.unipi.it
2 Dipartimento di Informatica e Telecomunicazioni, Universita` di Trento
Via Sommarive, 1438050 Povo (TN), Italy – priami@dit.unitn.it
We are faced with a great challenge: the cross-fertilization be-
tween the fields of formal methods for concurrency, in the computer
science domain, and systems biology in the biological realm.
From the one side, re-using the theories developed in the last
years for mobile and distributed systems may spread light in the
systems biology field. Being based on sound and often deep math-
ematics, these theories may offer solid ways to describe biological
systems and to safely reason upon them. Also, formal methods may
provide biologists with software tools that can make them save time
and efforts. On the other hand, biological systems often have a size
of one or two order of magnitude bigger than that of computer sys-
tems. More importantly, their efficiency, flexibility and reliability is
incredibly superior to that of any computing machinery. So, an effort
of understanding biological mechanisms in terms of computer tech-
nology will bring over the computer science field new techniques to
develop and analyse complex systems that will be more robust, reli-
able and efficient than the present ones. As an example, we certainly
lack now linguistic primitives suitable to model biological systems.
A programming language rich enough will help biologists in formal-
izing biological systems and in predicting their behaviour. At the
very same time, such new primitives will help e.g. the computer sci-
entists to design and program systems in the so-called disappearing
computer scenario — a foreseen world where everyday life object is
equipped with microchips constantly interacting each other.
Process calculi are maybe the most popular framework to study
global computing, in which a great number of computing agents that
? Work partially supported by EU project DEGAS (IST-2001-32072) funded within
the FET proactive initiative on Global Computing.
cooperate to achieve common goals, possibly exchanging information
through communications or interactions. These agents are geograph-
ically dispersed, may move from one site to another, without possi-
bly stopping their ongoing calculations. Also, the knowledge of the
running environment is limited and no centralized point of control
is assumed. The long term objective of these calculi and their re-
lated formal theories is then to design applications, certified to have
some clearly stated properties, that may involve thousands or mil-
lions of ubiquitous, cooperating entities. Typically, process calculi
are built out from a very restricted number of primitives focused on
the description of process interaction. They have extensively being
investigated in the last three decades since the pioneering work by
Hoare [6] and Milner [9]; a closely related sub-field is that of Petri
nets, that studies concurrent sytems from the point of view of au-
tomata theory. A main result of the reasearch on process calculi are
formal theories that deal with several aspects of this fascinating new
computing paradigm. Among these aspects, particularly important
are the qualitative ones, that mainly consider the behaviour of com-
puting agents in terms of equivalences, as well as the quantitative
aspects, that measure somehow systems behaviour, taking care of
probability distributions, time constraints, and so on.
Systems biology [7] is a field that studies the system-level struc-
ture and behaviour of complex systems made up of molecular com-
ponents. In turn, the nature and the behaviour of the components,
when taken in isolation, is well-known from molecular biology. The
overall goal of this discipline is to control the evolution of these com-
plex systems and to design modifications to them, guaranteeing that
some specific properties are satisfied.
As a matter of fact, the goals of systems biology are quite simlar
to those of global computing application design. So, if we succeed in
modelling biological systems as computer systems, e.g. as computing
agents in some process calculus, we shall advance the state of the art
in both disciplines.
The connection between the computer and biological world is
very well described by the methaphor cells as computations [16].
Biological components (at various level of abstractions) are repre-
sented as processes and their interactions result to be communica-
tion between processes. Relying on calculi for mobility the effect of
a communication can change the future interaction of processes as
it happens on the biological side for interacting components.
The above methaphora has been reified exploiting a revised ver-
sion of the stochastic pi-calculus [13] implementd in the BioSPI sys-
tem [17, 14]. Recently, a biological version of the ambient calculus as
well has been considered to model biological systems [15].
Here, we propose to adopt enhanced operational semantics [5]
as a descritpion tool to attack the complexity of biological systems
within a uniform framework.
The enhanced operational semantics, EOS for short, is an opera-
tional way of specifying the behaviour of complex systems in terms
of their components, reagrdless of their actual nature, computational
or biological or whatelse. It enables its users to design, simulate and
analyse systems keeping distinct the various aspects they may have,
in particular the many facets related to qualitative and quantitative
analysis. Being each aspect orthogonal to the others, it is then pos-
sible to combine some of them at a later stage, so taking advantage
of a clear separation of concerns.
Recent developments in the EOS theory show that many differ-
ent families of calculi can be simulated relying on a core pi-calculus
formalism. The main idea is that the annotations introduced on la-
bels of transitions can be used to control the possible interaction
of communicating systems [3]. A further result is that most of the
transitions systems originated by calculi for mobility turns out to be
a subset of the pi-calculus [10] transition system. As a consequence,
we can study properties of the selected formalism in the pi-calculus
by suitable assignment of parameters to transitions. This unifying
framework allows us to select the most suitable formalism to design
biological systems and relying on the implementation of a pi-calculus
kernel (e.g., the BioSPI system) to study properties and performing
simulations.
As mentioned above, an important aspect of enhanced opera-
tional semantics is that it allows to describe various aspect of sys-
tems without changing the actual syntax (that remains the standard
syntax of many process calculi). Thus, it is possible to define causal
or locational relations between actions, so expressing, e.g., the need
of some bio-chemical reactions to occur before a selected one or the
need of the co-location of some reactants to enable an interaction.
In a similar, independent way, one can derive or assign stochastic
information to the system activities, in terms of the probabilities or
the statistical rates they have to occur. In this way, we describe sys-
tem evolutions closer to reality, and we mechanically calculate the
probability that a(n un)wanted chain of reactions has to show up.
Exploiting a notion of behavioural equivalence between processes, one
can then group apparently different biological systems, that however
exhibit the same dynamics. This equivalence can take as a param-
eter the wanted (qualitative or quantitative) aspects of the systems
under analysis: the user selects what has to be observed and a me-
chanical (and up to now inefficient) tool is able to detect similarities
and dissimilarities. As another application of the equivalences men-
tioned above, one can study a property known in the sub-field of
computer security as non-interference [2, 4]: a given system will not
interfere with its surrounding environment, whichever it could be, or,
in biological terms: does a selected component in a system interfere
with others and produce unwanted effects while the whole system
evolves?
We end this position paper by noting that although operational
semantics is one of the most simple formal tools that can be used
in the design of complex systems, it is quite far from the common
practice of biologists.
An essential ingredient for the success of the challenge outlined
at the beginning is the identification of a communication language
between computer scientists and biologists. Such a language must
have the following characteristics:
- it must hide as much technical details as possible from the user
so that the biologists need not to have strong background in
mathematics and formal methods to use it;
- it must be sufficiently structured (i) to avoid as much ambiguities
as possible and (ii) to derive consistent formal methods to analyse
and simulate systems;
- it must be possible to automatically translate specifications in
this language into process calculi specification and to reflect back
in the interface language the results of the formal analysis.
To satisfy all the above requirements we think that a graphical,
semi-structured language could be a solution at the right level of
abstraction. Indeed, biologists already have in use many graphical
languages (e.g., [1, 8, 11]) and so computer scientists do. Additionally,
software engineers make use of graphical standards as UML to model
systems, and there are already definitions of extractors from UML
specifcations to pi-calculus descriptions [12] that show the feasibility
of the approach and that allow reuse of existing tools.
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Enhanced Operational Semantics in Systems Biology

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