Computational models of signalling networks for non-linear control
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)
- et al.
Computer simulated evolution of a network of cell signalling molecules
Biophys. J.
(1994) - et al.
Fuzzy modeling of signal transduction networks
Nearly linear mappings and their applications
Phys. D: Nonlin. Phenom.
(1980)- et al.
Quantification of information transfer via cellular signal transduction pathways
FEBS Lett.
(1997) - et al.
Interaction between mitogenic stimuli, or, a thousand and one connections
Curr. Opin. Cell Biol.
(1999) - et al.
The gene expression matrix: towards the extraction of genetic network architectures
Nonlin. Anal. Theory Methods Appl.
(1997) An Introduction to System Biology: Design Principles of Biological Circuits
(2007)- et al.
Filtering transcriptional noise during development: concepts and mechanisms
Nat. Rev. Genet.
(2006) Artificial chemistries: towards constructive dynamical systems
Solid State Phenom.
(2004)- et al.
Emergent properties of networks of biological signaling pathways
Science
(1999)
Protein molecules as computational elements in living cells
Nature
Multi-chromosomal genetic programming
Evolving Reaction–Diffusion Controllers for Minimally Cognitive Animats
Preliminary studies on the in silico evolution of biochemical networks
Biochemistry
Evolving artificial cell signalling networks: perspectives and methods
Stud. Comput. Intell.
Algorithmic chemistry
Cited by (6)
Bio-inspired smog sensing model for wireless sensor networks based on intracellular signalling
2019, Information FusionCitation Excerpt :Cell signalling technique makes this task possible and is a heart of biological process. It is a series of events produced by a biochemical signal [7]. The intracellular signalling process is highly sensitive and produces various cellular responses, like proliferation, differentiation [8].
Evolving ensembles: What can we learn from biological mutualisms?
2015, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)Harmonic versus chaos controlled oscillators in hexapedal locomotion
2015, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)Evolving classifiers to recognize the movement characteristics of parkinson's disease patients
2014, IEEE Transactions on Evolutionary ComputationBiochemical connectionism
2013, Natural ComputingAdaptive robotic gait control using coupled artificial signalling networks, hopf oscillators and inverse kinematics
2013, 2013 IEEE Congress on Evolutionary Computation, CEC 2013