Article

Lumpability abstractions of rule-based systems

Theoretical Computer Science (Impact Factor: 0.52). 05/2012; 431:137--164. DOI: 10.1016/j.tcs.2011.12.059
Source: OAI

ABSTRACT The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics.
In this paper we prove that this quotienting yields a sufficient condition for \emph{weak lumpability} and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.

0 Bookmarks
 · 
306 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In synthetic biology, a common application field for compu-tational methods is the prediction of knockout strategies for reaction networks. Thereby, the major challenge is the lack of information on re-action kinetics. In this paper, we propose an approach, based on abstract interpretation, to predict candidates for reaction knockouts, relying only on partial kinetic information. We consider the usual deterministic steady state semantics of reaction networks and a few general properties of re-action kinetics. We introduce a novel abstract domain over pairs of real domain values to compute the differences between steady states that are reached before and after applying some knockout. We show that this ab-stract domain allows us to predict correct knockout strategy candidates independent of any particular choice of reaction kinetics. Our predictions remain candidates, since our abstract interpretation over-approximates the solution space. We provide an operational semantics for our abstrac-tion in terms of constraint satisfaction problems and illustrate our ap-proach on a realistic network.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. However, such a detailed description comes with complexity and computationally costly execution. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. Our method consists of searching for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). The reduced model is efficiently obtained by static inspection over the rule-set, and it represents a particular theoretical limit of the original model. The Bhattacharyya distance is proposed as a metric to estimate the reduction error for a given observable. The tool is tested on a detailed rule-based model of a $\lambda$-phage switch, which lists $96$ rules and $16$ agents. The reduced model has $11$ rules and $5$ agents, and provides a dramatic reduction in simulation time of several orders of magnitude.
  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.
    Journal of Mathematical Biology 11/2013; 69(3). DOI:10.1007/s00285-013-0738-7 · 2.39 Impact Factor

Full-text (2 Sources)

Download
59 Downloads
Available from
Jun 1, 2014