Elsevier

Biosystems

Volume 112, Issue 2, May 2013, Pages 122-130
Biosystems

Computational models of signalling networks for non-linear control

https://doi.org/10.1016/j.biosystems.2013.03.006Get rights and content

Abstract

Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.

Introduction

Cellular signalling needs to engage in many forms of communication to enable cells to sense and respond to the outside world. This capability is vital for cells to survive and adapt to constantly fluctuating environments. In multicellular organisms, the role of cellular signalling is especially significant as it is responsible for the coordination of complex multicellular interactions and the production of collective responses.

Broadly speaking, cellular signalling is a sequence of events triggered by a biochemical signal that requires a cellular response. Signalling pathways are the simplest cellular structures connecting the outside environment with the genes they regulate. A closer inspection reveals that cellular signalling starts when a surface receptor binds an extracellular messenger, which diffuses an intracellular signal to an effector protein inside the cell. This then produces secondary messengers, which transmit the information further into the cell along signalling pathways. Spatially or temporally variable catalytic reactions or cascades of protein kinases lead to changes in gene expression, bringing about a change in cellular activity. Cells also show a complex internal organisation, which regulates the number of cellular components activated by secondary messengers and guides the interactions between cellular regions. Crosstalk (Schwartz and Baron, 1999) captures the interaction between signalling pathways that leading to the formation of complex networks that produce a coordinated response.

In this paper, we extend our previous work on artificial signalling networks (ASNs) (Fuente et al., 2012) and suggest the use of crosstalk as a mechanism to model the structural and temporal topologies of cellular signalling, capturing its intrinsic dynamics. In order to test our model, we apply it to the control of a numerical dynamical system, whose properties mirror the complexity of the cellular environment.

This paper is organised as follows: Section 2 presents a brief overview of dynamical systems, Section 3 reviews the modelling of ASNs, highlighting the challenges this involves, Section 4 presents the new model and proposes the evolutionary algorithm used to induce model instances, Section 5 presents results and analysis and Section 6 concludes the paper.

Section snippets

Dynamical systems

A dynamical system is a mathematical model consisting of a state space and a function, or evolution rule, that specifies its current state within the space state based on an initial condition (Stepney, 2011). The evolution rule defines the motion and behaviour of the system across the state space. Dynamical systems can be autonomous or non-autonomous. The former is a closed system whose dynamics are not perturbed by the outside word. The latter defines an open system changing over time, as

Artificial signalling networks

Activities and functions of biological organisms emerge from the interactions amongst the biochemical networks operating within cells. These networks are categorised in three domains: genetic networks, which derives new behaviours via genetic regulation (Banzhaf, 2004); metabolic networks, preserving the physiological equilibrium inside cells (Fontana, 1992); and signalling networks, translating externals inputs into meaningful biological signals (Bray, 1995). Computational models of these

State space targeting with ASNs

The signal transduction processes inside cells depend on complex interactions between enzymes. Although these interactions vary in number of participants, they are essential in the generation of a cellular response. In fact, enzymes are not functional unless they are assembled together into a biological structure. Likewise, some of the main cellular functions are only achievable under certain configurations.

Despite the diversity of models aiming to capture the properties of intracellular

Results

Fig. 3 shows the distribution of the number of steps needed to traverse Chirikov's standard map for the evolved controllers at the end of the 100 evolutionary runs. The results indicate that both representations, the stand-alone ASN and the coupled-ASN, led to valid controllers, with scores approaching 100 and 300 steps respectively (see Fig. 4(a)–(b) for an example of map traversing using both models). The best performance arises from the Michaelis–Menten regulatory function in both scenarios.

Conclusions

In this paper, we have presented an interaction graph-based approach to the modelling of signalling pathways using evolutionary algorithms. The evolved ASN attains promising results in chaos targeting within Chirikov's standard map. Notably, our results illustrate that effective controllers can be found when signalling networks are interpreted as an individual pathway or a set of pathways, thereby demonstrating how the topology and adaptability of signalling networks can be evolved. Likewise,

Acknowledgement

This research is supported by the EPSRC Grant (Ref.: EP/F060041/1), Artificial Biochemical Networks: Computational Models and Architectures.

References (35)

  • D. Bray

    Protein molecules as computational elements in living cells

    Nature

    (1995)
  • R. Cavill et al.

    Multi-chromosomal genetic programming

  • Chirikov, B.V., 1962. Research concerning the theory of nonlinear resonance and stochasticity. Tech. rep., Institute of...
  • K. Dale

    Evolving Reaction–Diffusion Controllers for Minimally Cognitive Animats

    (2006)
  • A. Deckard et al.

    Preliminary studies on the in silico evolution of biochemical networks

    Biochemistry

    (2004)
  • J. Decraene et al.

    Evolving artificial cell signalling networks: perspectives and methods

    Stud. Comput. Intell.

    (2009)
  • W. Fontana

    Algorithmic chemistry

  • Cited by (6)

    View full text