Classical modeling approaches for biology are mainly grounded in mathematics, and specifically on ordinary differential equations (ODE). Process calculi-based conceptual and computational tools are an alternative and emergent approach. Here we focus our analysis on BlenX (a beta-binders inspired programming language) showing how it is possible to easily re-use ODE models within this framework. An example will show then the advantages of moving into a stochastic approach. This is the preliminary version of a paper that was published in Proceedings of Pacific Symposium on Biocomputing (PSB 2009), January, 2009. The original publication is available at http://psb.stanford.edu/psb-online/proceedings/psb09

Palmisano, Alida

Priami, Corrado

English

University of Trento : UNITN-eprints

Technical Report CoSBi 10/2008
From Solvable to Executable Models
of Biological Systems
Alida Palmisano
CoSBi, Trento, Italy
Dipartimento di Ingegneria e Scienza dell’Informazione,
Universita` di Trento, Italy
palmisano@cosbi.eu
Corrado Priami
CoSBi, Trento, Italy
Dipartimento di Ingegneria e Scienza dell’Informazione,
Universita` di Trento, Italy
priami@cosbi.eu
This is the preliminary version of a paper that will appear in
Proceedings of Pacific Symposium on Biocomputing (PSB 2009), January, 2009
available at http://psb.stanford.edu/psb-online/proceedings/psb09/
From solvable to executable models
of biological systems
A. Palmisano, C. Priami
Abstract
Modeling in biology is mainly grounded in mathematics, and specif-
ically on ordinary differential equations (ODE). The programming lan-
guage approach is a complementary and emergent tool to analyze the
dynamics of biological networks. Here we focus on BlenX showing how
it is possible to easily re-use ODE models within this framework. A
budding yeast cell cycle example demonstrates the advantages of using
a stochastic approach. Finally, some hints are provided on how the
automatically translated model can take advantage of the full power of
BlenX to analyze the control mechanisms of the cell cycle machinery.
Abstract models of biological systems are becoming an indispensable
conceptual and computational tool for biologists. In order to be use-
ful, a model has to be computable, to allow automatic analysis, and
extensible, to permit the addition of further details without changing
too much the already modeled knowledge.
Chemical kinetics has traditionally been analyzed using a mathe-
matical formalism in which continuous (real) variables evolve deter-
ministically, even if molecular populations in a biological/chemical
systems are integer variables that evolve stochastically [1]. There is
not yet a precise and agreed upon characterization of what is the
best “usable form” in modeling biology, because some aspects are
better handled with the deterministic approach, while for others the
stochastic one is more suitable. For example, in the literature, beside
deterministic ordinary differential equations (ODE for short), we find
stochastic cell cycle models built with stochastic ODE Langevine type
[2], with the Gillespie method [3] and with stochasticity on transitions
[4].
After the work of Regev et al. [5], a promising trend is to use
programming languages to generate executable models of biological
1
systems. This strategy diverge from classical mathematical model-
ing, because it is executable and not just simply solvable [6]. Execu-
tion means that we can describe the flow of control between species
and reactions, e.g. not only the time, but also the causality rela-
tion among the events that constitute the history of the dynamics of
the model. This interpretation is very similar to programming the
behaviour of a system rather than describing only its outcome with
respect to time. As a consequence, a number of process calculi have
been adapted or newly developed for building biological models and
performing stochastic simulations (i.e. stochastic pi-calculus [7, 8],
BioAmbients [9], Brane Calculi [10], CCS-R [11], k-calculus [12], Bio-
PEPA [13]).
The main contribution of this work will be a semi-automatic method
to translate existing deterministic models written with ODEs into pro-
grams written in the stochastic modeling language BlenX [14, 15]. The
simple translation from general terms of the differential equations into
the transitions of the stochastic BlenX model is possible because of the
expressive power of the language that allows the definition of general
rate functions for the transitions. The level of abstraction of a biolog-
ical model, indeed, has important implications on the selection of the
modeling formalism used to define its stochastic counterpart.
The translation procedure of existing ODE models into BlenX can-
not be completely automatized, because it has to face the inverse
problem of reaction kinetics [16]: more than one structurally different
network of chemicals can produce the same set of ODEs. To disam-
biguate between those networks we need to have the knowledge of
the interactions between all the species, but usually this knowledge
is hidden in wiring diagrams that are not following strict or general
conventions.
Our translation creates a model that can be stochastically simu-
lated in order to answer questions that cannot be directly tackled by
deterministic models. The simple mapping is possible because of the
expressive power of BlenX that allows the definition of general rate
functions for reactions. However the usage of the SSA algorithm with
simple and complex kinetic laws leaves to the user the responsibility
to validate simulation results. The example that we want to consider
uses those different levels of abstraction and it will be be validated
against experimental results.
2
References
[1] D. Gillespie, Annual Review of Physical Chemistry 58, 35 (2007).
[2] R. Steuer, Journal of Theoretical Biology 228, 293 (2004).
[3] M. Sabouri-Ghomi, A. Ciliberto, S. Kar, B. Novak and J. Tyson,
Journal of Theoretical Biology 250, 209 (2007).
[4] P. Lecca and C. Priami, Cell cycle control in eukaryotes: A BioSpi
model, in Proceedings of BioConcur 2003 , (ENTCS, Elsevier,
2007).
[5] A. Regev and E. Shapiro, Nature 419, 353 (2002).
[6] J. Fisher and T. Henzinger, Nature Biotechnology 25, 1239
(2007).
[7] C. Priami, The Computer Journal 38, 578 (1995).
[8] C. Priami, A. Regev, E. Shapiro and W. Silvermann, Information
Processing Letters 80, 25 (2001).
[9] A. Regev, E. Panina, W. Silverman, L. Cardelli and E. Shapiro,
Theoretical Computer Science 325, 141 (2004).
[10] L. Cardelli, Brane Calculi - Interactions of Biological Membranes,
in Computational Methods in System Biology 2004 , (LNCS,
Springer, 2005).
[11] V. Danos and J. Krivine, Reversible communicating systems, in
Proceedings of CONCUR 2004 , (LNCS, Springer-Verlag, 2004).
[12] V. Danos and C. Laneve, Theoretical Computer Science 325, 69
(2004).
[13] F. Ciocchetta and J. Hillston, Bio-PEPA: an extension of the
process algebra PEPA for biochemical networks, in FBTC 2007 ,
(ENTCS, Springer, 2007).
[14] L. Dematte´, C. Priami and A. Romanel, Briefings in Bioinfor-
matics (2008), on-line, doi: 10.1093/bib/bbn023.
[15] L. Dematte´, C. Priami and A. Romanel, The BlenX language: a
tutorial, in SFM 2008 , (LNCS, Springer-Verlag, 2008).
[16] P. E´rdi and J. To´th, Mathematical Models of Chemical Reactions
(Princeton University Press, 1989).
3


From Solvable to Executable Models of Biological Systems

Unitn-eprints Research

Technical Report CoSBi 10/2008From Solvable to Executable Modelsof Biological SystemsAlida PalmisanoCoSBi, Trento, ItalyDipartimento di Ingegneria e Scienza dell’Informazione,Universita` di Trento, Italypalmisano@cosbi.euCorrado PriamiCoSBi, Trento, ItalyDipartimento di Ingegneria e Scienza dell’Informazione,Universita` di Trento, Italypriami@cosbi.euThis is the preliminary version of a paper that will appear inProceedings of Pacific Symposium on Biocomputing (PSB 2009), January, 2009available at http://psb.stanford.edu/psb-online/proceedings/psb09/From solvable to executable modelsof biological systemsA. Palmisano, C. PriamiAbstractModeling in biology is mainly grounded in mathematics, and specif-ically on ordinary differential equations (ODE). The programming lan-guage approach is a complementary and emergent tool to analyze thedynamics of biological networks. Here we focus on BlenX showing howit is possible to easily re-use ODE models within this framework. Abudding yeast cell cycle example demonstrates the advantages of usinga stochastic approach. Finally, some hints are provided on how theautomatically translated model can take advantage of the full power ofBlenX to analyze the control mechanisms of the cell cycle machinery.Abstract models of biological systems are becoming an indispensableconceptual and computational tool for biologists. In order to be use-ful, a model has to be computable, to allow automatic analysis, andextensible, to permit the addition of further details without changingtoo much the already modeled knowledge.Chemical kinetics has traditionally been analyzed using a mathe-matical formalism in which continuous (real) variables evolve deter-ministically, even if molecular populations in a biological/chemicalsystems are integer variables that evolve stochastically [1]. There isnot yet a precise and agreed upon characterization of what is thebest “usable form” in modeling biology, because some aspects arebetter handled with the deterministic approach, while for others thestochastic one is more suitable. For example, in the literature, besidedeterministic ordinary differential equations (ODE for short), we findstochastic cell cycle models built with stochastic ODE Langevine type[2], with the Gillespie method [3] and with stochasticity on transitions[4].After the work of Regev et al. [5], a promising trend is to useprogramming languages to generate executable models of biological1systems. This strategy diverge from classical mathematical model-ing, because it is executable and not just simply solvable [6]. Execu-tion means that we can describe the flow of control between speciesand reactions, e.g. not only the time, but also the causality rela-tion among the events that constitute the history of the dynamics ofthe model. This interpretation is very similar to programming thebehaviour of a system rather than describing only its outcome withrespect to time. As a consequence, a number of process calculi havebeen adapted or newly developed for building biological models andperforming stochastic simulations (i.e. stochastic pi-calculus [7, 8],BioAmbients [9], Brane Calculi [10], CCS-R [11], k-calculus [12], Bio-PEPA [13]).The main contribution of this work will be a semi-automatic methodto translate existing deterministic models written with ODEs into pro-grams written in the stochastic modeling language BlenX [14, 15]. Thesimple translation from general terms of the differential equations intothe transitions of the stochastic BlenX model is possible because of theexpressive power of the language that allows the definition of generalrate functions for the transitions. The level of abstraction of a biolog-ical model, indeed, has important implications on the selection of themodeling formalism used to define its stochastic counterpart.The translation procedure of existing ODE models into BlenX can-not be completely automatized, because it has to face the inverseproblem of reaction kinetics [16]: more than one structurally differentnetwork of chemicals can produce the same set of ODEs. To disam-biguate between those networks we need to have the knowledge ofthe interactions between all the species, but usually this knowledgeis hidden in wiring diagrams that are not following strict or generalconventions.Our translation creates a model that can be stochastically simu-lated in order to answer questions that cannot be directly tackled bydeterministic models. The simple mapping is possible because of theexpressive power of BlenX that allows the definition of general ratefunctions for reactions. However the usage of the SSA algorithm withsimple and complex kinetic laws leaves to the user the responsibilityto validate simulation results. The example that we want to consideruses those different levels of abstraction and it will be be validatedagainst experimental results.2References[1] D. Gillespie, Annual Review of Physical Chemistry 58, 35 (2007).[2] R. Steuer, Journal of Theoretical Biology 228, 293 (2004).[3] M. Sabouri-Ghomi, A. Ciliberto, S. Kar, B. Novak and J. Tyson,Journal of Theoretical Biology 250, 209 (2007).[4] P. Lecca and C. Priami, Cell cycle control in eukaryotes: A BioSpimodel, in Proceedings of BioConcur 2003 , (ENTCS, Elsevier,2007).[5] A. Regev and E. Shapiro, Nature 419, 353 (2002).[6] J. Fisher and T. Henzinger, Nature Biotechnology 25, 1239(2007).[7] C. Priami, The Computer Journal 38, 578 (1995).[8] C. Priami, A. Regev, E. Shapiro and W. Silvermann, InformationProcessing Letters 80, 25 (2001).[9] A. Regev, E. Panina, W. Silverman, L. Cardelli and E. Shapiro,Theoretical Computer Science 325, 141 (2004).[10] L. Cardelli, Brane Calculi - Interactions of Biological Membranes,in Computational Methods in System Biology 2004 , (LNCS,Springer, 2005).[11] V. Danos and J. Krivine, Reversible communicating systems, inProceedings of CONCUR 2004 , (LNCS, Springer-Verlag, 2004).[12] V. Danos and C. Laneve, Theoretical Computer Science 325, 69(2004).[13] F. Ciocchetta and J. Hillston, Bio-PEPA: an extension of theprocess algebra PEPA for biochemical networks, in FBTC 2007 ,(ENTCS, Springer, 2007).[14] L. Dematte´, C. Priami and A. Romanel, Briefings in Bioinfor-matics (2008), on-line, doi: 10.1093/bib/bbn023.[15] L. Dematte´, C. Priami and A. Romanel, The BlenX language: atutorial, in SFM 2008 , (LNCS, Springer-Verlag, 2008).[16] P. E´rdi and J. To´th, Mathematical Models of Chemical Reactions(Princeton University Press, 1989).3

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From Solvable to Executable Models of Biological Systems

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