Reaction constraints for the pi-calculus [Elektronische Ressource] : a language for the stochastic and spatial modeling of cell-biological processes / vorgelegt von Mathias John
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Reaction constraints for the pi-calculus [Elektronische Ressource] : a language for the stochastic and spatial modeling of cell-biological processes / vorgelegt von Mathias John

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Reaction Constraints for the Pi-CalculusA Language for the Stochastic and Spatial Modeling ofCell-Biological ProcessesDissertationzurErlangung des akademischen GradesDoktor-Ingenieur (Dr.-Ing.)der Fakultät für Informatik und Elektrotechnikder Universität Rostockvorgelegt vonDipl. Inf. Mathias John, geb. am 1982/02/14 in Teterowaus RostockRostock, 2010/07/07Principal Advisor: Prof. Dr. rer. nat. habil. Adelinde M. UhrmacherUniversity of Rostock, GermanyExternal Reviewers: Prof. Dr. Corrado PriamiMicrosoft Research / University of Trento, ItalyDr. rer. nat. habil. Joachim NiehrenINRIA Lille Nord Europe, FranceDate of Defense: 2010/08/26AbstractFor cell-biological processes, it is the complex interaction of their bio-chemical components, affected by both stochastic and spatial consid-erations, that create the overall picture. Formal modeling provides amethod to overcome the limits of experimental observation in the wet-lab by moving to the abstract world of the computer. The limits ofthe abstract world again depend on the expressiveness of the modelinglanguage used to formally describe the system under study. In this the-sis, reaction constraints for the pi-calculus are proposed as a languagefor the stochastic and spatial modeling of cell-biological processes.The goal is to develop a language with sufficient expressive power tomodel dynamic cell structures, like fusing compartments.

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Published 01 January 2010
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Reaction Constraints for the Pi-Calculus
A Language for the Stochastic and Spatial Modeling of
Cell-Biological Processes
Dissertation
zur
Erlangung des akademischen Grades
Doktor-Ingenieur (Dr.-Ing.)
der Fakultät für Informatik und Elektrotechnik
der Universität Rostock
vorgelegt von
Dipl. Inf. Mathias John, geb. am 1982/02/14 in Teterow
aus Rostock
Rostock, 2010/07/07Principal Advisor: Prof. Dr. rer. nat. habil. Adelinde M. Uhrmacher
University of Rostock, Germany
External Reviewers: Prof. Dr. Corrado Priami
Microsoft Research / University of Trento, Italy
Dr. rer. nat. habil. Joachim Niehren
INRIA Lille Nord Europe, France
Date of Defense: 2010/08/26Abstract
For cell-biological processes, it is the complex interaction of their bio-
chemical components, affected by both stochastic and spatial consid-
erations, that create the overall picture. Formal modeling provides a
method to overcome the limits of experimental observation in the wet-
lab by moving to the abstract world of the computer. The limits of
the abstract world again depend on the expressiveness of the modeling
language used to formally describe the system under study. In this the-
sis, reaction constraints for the pi-calculus are proposed as a language
for the stochastic and spatial modeling of cell-biological processes.
The goal is to develop a language with sufficient expressive power to
model dynamic cell structures, like fusing compartments. To this end,
reaction constraints are augmented with two language constructs: pri-
ority and a global imperative store, yielding two different modeling
languages, including non-deterministic and stochastic semantics. By
several modeling examples, e.g. of Euglena’s phototaxis, and exten-
sive expressiveness studies, e.g. an encoding of the spatial modeling
language BioAmbients, including a prove of its correctness, the useful-
ness of reaction constraints, priority, and a global imperative store for
the modeling of cell-biological processes is shown. Thereby, besides
dynamic cell structures, different modeling styles, e.g. individual-
based vs. population-based modeling, and different abstraction levels,
as e.g. provided by reaction kinetics following the law of Mass action
or the Michaelis-Menten theory, are considered.
Keywords: spatial and stochastic modeling, pi-calculus, computa-
tional systems biologyContents
1 Introduction 1
1.1 Formal Modeling to Study Cell-Biological Processes . 5
1.2 Thep-Calculus to Model . . 10
1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.1 The Attributedp-Calculus . . . . . . . . . . . 22
1.3.2 The Imperativep . . . . . . . . . . . 25
1.4 Related Work . . . . . . . . . . . . . . . . . . . . . . 27
1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.6 Bibliographic Note . . . . . . . . . . . . . . . . . . . 33
2 Thep-Calculus with Priority 39
2.1 Thep-Calculus with Priority . . . . . . . . . . . . . . 39
2.1.1 Design Decisions . . . . . . . . . . . . . . . . 40
2.1.2 Syntax of Processes . . . . . . . . . . . . . . . 41
2.1.3 Non-deterministic Operational Semantics . . . 45
2.1.4 Uniqueness of Convergence . . . . . . . . . . 48
2.1.5 Stochastic Operational Semantics . . . . . . . 51
v2.1.6 Type System . . . . . . . . . . . . . . . . . . 57
2.2 BioAmbients with Priority . . . . . . . . . . . . . . . 61
2.2.1 Syntax of Processes . . . . . . . . . . . . . . . 62
2.2.2 Non-deterministic Operational Semantics . . . 68
3 The Attributedp-Calculus 73
3.1 Language . . . . . . . . . . . . . . . . . . . . . . . . 73
3.1.1 Idea of Communication Constraints . . . . . . 74
3.1.2 Attribute Languages . . . . . . . . . . . . . . 75
3.1.3 Syntax of Processes . . . . . . . . . . . . . . . 80
3.1.4 Non-deterministic Operational Semantics . . . 82
3.1.5 Uniqueness of Convergence . . . . . . . . . . 86
3.1.6 Stochastic Operational Semantics . . . . . . . 88
3.1.7 Type System . . . . . . . . . . . . . . . . . . 89
3.2 Modeling Techniques and Biological Examples . . . . 98
3.2.1 Spatial Aspects: Euglena’s Phototaxis . . . . . 98
3.2.2 Cooperative Enhancement: Gene Regulation
at the Lambda Switch . . . . . . . . . . . . . . 106
3.2.3 Population-based Modeling . . . . . . . . . . 110
3.2.4 Global Information in Individual-Based Mod-
eling . . . . . . . . . . . . . . . . . . . . . . 114
3.2.5 Species-Based Modeling . . . . . . . . . . . . 116
3.3 Expressiveness . . . . . . . . . . . . . . . . . . . . . 116
3.3.1 Encoding of thep-Calculus with Priority . . . 118
3.3.2p[@;=] for Dynamic Compartments 125
3.3.3 Variants of the Stochastic Pi-Calculus . . . . . 131
63.4 Stochastic Simulator . . . . . . . . . . . . . . . . . . 135
3.5 Implementation and Performance Evaluation . . . . . . 142
4 The Imperativep-Calculus 147
4.1 Language . . . . . . . . . . . . . . . . . . . . . . . . 148
4.1.1 Idea of a Global Imperative Store . . . . . . . 149
4.1.2 Design Decisions . . . . . . . . . . . . . . . . 151
4.1.3 Attribute Languages . . . . . . . . . . . . . . 153
4.1.4 Syntax of Processes . . . . . . . . . . . . . . . 158
4.1.5 Non-Deterministic Operational Semantics . . . 162
4.1.6 Uniqueness of Convergence . . . . . . . . . . 168
4.1.7 Stochastic Semantics . . . . . . . . . . . . . . 172
4.2 Modeling Techniques and Biological Examples . . . . 177
4.2.1 Osmosis: Variable Volumes and Surfaces . . . 178
4.2.2 Michaelis-Menten kinetics à la sCCP . . . . . . 184
4.3 Expressiveness . . . . . . . . . . . . . . . . . . . . . 194
4.3.1 Conservativeness . . . . . . . . . . . . . . . . 194
4.3.2 Encoding BioAmbients . . . . . . . . . . . . . 200
4.4 Stochastic Simulator . . . . . . . . . . . . . . . . . . 210
5 Conclusion 215
A Experiment Results 223
B Remaining Proofs 225
B.1 Section 3.1.7 (Type System) . . . . . . . . . . . . . . 225
B.2 Section 3.3.1 (Encoding thep-Calculus with Priority) . 227B.3 Section 3.3.2 (Encoding p[@;=] for Dynamic Com-
partments) . . . . . . . . . . . . . . . . . . . . . . . . 238
Bibliography 243
6List of Figures
1.1 A realization of a CTMC based on the kinetic law of
Mass action. . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Syntax of thep-calculus with priority. . . . . . . . . . 42
2.2 Free channel names of thep-calculus with priority. . . 42
2.3 Axioms of the structural congruence of thep-calculus
with priority. . . . . . . . . . . . . . . . . . . . . . . 43
2.4 Rules of the non-deterministic semantics ofp-calculus
with priority. . . . . . . . . . . . . . . . . . . . . . . 46
2.4 Rules of the semantics ofp-calculus
with priority. . . . . . . . . . . . . . . . . . . . . . . 47
2.5 Rules of the stochastic semantics of the p-calculus
with priority. . . . . . . . . . . . . . . . . . . . . . . 52
2.6 Example of a CTMC generated by the stochastic se-
mantics of thep-calculus with priorities. . . . . . . . 55
2.7 Type system forp-calculus with priority. . . . . . . . 59
2.8 Syntax of BioAmbients with channels x;x˜;y˜2 Vars
and priorities r2 R. . . . . . . . . . . . . . . . . . . . 63
ix2.9 Free channel names of BioAmbients. . . . . . . . . . . 65
2.10 Rules of the structural congruence of BioAmbients. . . 66
2.11 Communication directions and rearrangement capabil-
ities of BioAmbients. . . . . . . . . . . . . . . . . . . 67
2.12 Rules of operational semantics of BioAmbients with
priorities in(R;<). . . . . . . . . . . . . . . . . . . . 69
2.12 Rules of the operational semantics of BioAmbients
with priorities in(R;<)(continued). . . . . . . . . . . 70
2.12 Rules of the operational semantics of BioAmbients
with priorities in(R;<)(continued). . . . . . . . . . . 71
3.1 Big-step evaluator of call-by-value l-calculus with
pairs and conditionals. . . . . . . . . . . . . . . . . . 77
3.2 Additional rules of big-step evaluator of the attribute
languagel(N ;+;=) . . . . . . . . . . . . . . . . . 770 <1
3.3 Syntax ofp(L), where x;x˜2 Vars, and e ;e ;e˜2 Exprs. 801 2
3.4 Non-deterministic operational semantics ofp(L). . . 83
3.5 Rules of the stochastic semantics ofp(L). . . . . . . 88
3.6 Type system forp(L). . . . . . . . . . . . . . . . . . 93
3.6 Type system forp(L) (continued). . . . . . . . . . . 94
3.7 A model of Euglena’s light-dependent motion with
two light sources. . . . . . . . . . . . . . . . . . . . . 101
3.8 Master Equation to compute the numbers of Euglenas
on each depth level in equilibrium. . . . . . . . . . . 103
3.9 Euglena model, Experiment A. . . . . . . . . . . . . . 104
3.10 model, B. . . . . . . . . . . . . . 105