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Immune Response Enhancement Strategy via Hybrid Control Perspective Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Exploring Synthetic Mass Action Models

Authors : Oded Maler, Ádám M. Halász, Olivier Lebeltel, Ouri Maler

Published in: Hybrid Systems Biology

Publisher: Springer International Publishing

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Abstract

In this work we propose a model that can be used to study the dynamics of mass action systems, systems consisting of a large number of individuals whose behavior is influenced by other individuals that they encounter. Our approach is rather synthetic and abstract, viewing each individual as a probabilistic automaton that can be in one of finitely many discrete states. We demonstrate the type of investigations that can be carried out on such a model using the Populus toolkit. In particular, we illustrate how sensitivity to initial spatial distribution can be observed in simulation.

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previous chapter Optimal Observation Time Points in Stochastic Chemical Kinetics
next chapter Exploiting the Eigenstructure of Linear Systems to Speed up Reachability Computations
Footnotes
1
Actually bilinear if one assumes the probability of triple encounters to be zero, as is often done in Chemistry.
 
2
A probabilistic automaton [15] is a Markov chain with an input alphabet where each input symbol induces a different transition matrix. It is also known as a Markov Decision Process (MDP) in some circles.
 
3
We export the primed variable notation from program verification where x stands for x[t] and \(x'\) denotes \(x[t+1]\).
 
4
We write the algorithm using the normalized state notation x but the combinatorial calculation underlying the derivation of probabilities will be based on the particle count X.
 
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Metadata
Title
Exploring Synthetic Mass Action Models
Authors
Oded Maler
Ádám M. Halász
Olivier Lebeltel
Ouri Maler
Copyright Year
2015
Book
Hybrid Systems Biology

Print ISBN: 978-3-319-27655-7

Electronic ISBN: 978-3-319-27656-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-27656-4_6

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