Briefings in Bioinformatics 2001 2(3):258-270; doi:10.1093/bib/2.3.258

FREE Full Text (PDF) Freely available

© Henry Stewart Publications

Special issue papers

Systems biology: The reincarnation of systems theory applied in biology?

Olaf Wolkenhauer

Holds a joint appointment between the Department of Biomolecular Sciences and the Department of Electrical Engineering and Electronics (Control Systems Centre) at UMIST. His research interests include mathematical modelling and identification of dynamic systems with particular consideration of uncertainty in modelling, data and prediction.

[there’s Category Theory lurking here, although Rosen did not invoke it in 1960s]

Natural Transformations Models in Molecular Biology

IC Baianu - SIAM Natl. Meeting, Denver, CO, USA, 1983

This is available as a Word file from panmere.com

which can be downloaded by plugging the title into Google Scholar

Olaf Wolkenhauer, Department of Biomolecular Sciences and Department of Electrical Engineering and Electronics, Control Systems Centre, UMIST, Manchester M60 1QD, UK Tel/Fax: +44 (0)161 200 4672 E-mail: o.wolkenhauer@umist.ac.uk

With the availability of quantitative data on the transcriptome and proteome level, there is an increasing interest in formal mathematical models of gene expression and regulation. International conferences, research institutes and research groups concerned with systems biology have appeared in recent years and systems theory, the study of organisation and behaviour per se, is indeed a natural conceptual framework for such a task. This is, however, not the first time that systems theory has been applied in modelling cellular processes. Notably in the 1960s systems theory and biology enjoyed considerable interest among eminent scientists, mathematicians and engineers. Why did these early attempts vanish from research agendas? Here we shall review the domain of systems theory, its application to biology and the lessons that can be learned from the work of Robert Rosen. Rosen emerged from the early developments in the 1960s as a main critic but also developed a new alternative perspective to living systems, a concept that deserves a fresh look in the post-genome era of bioinformatics.

Keywords: genomics, systems biology, causality, relational biology, (M,R)-systems, linear systems theory

Advertisement

Biosystems

Volume 64, Issues 1-3, January 2002, Pages 63-72

I am not recommending that you actually purcahe ANYTHING from Elservier, but I’ll point to it.

Purchase PDF (305 K)

Mobilising knowledge models using societies of graphs

Studies in Multidisciplinarity, Volume 2, 2005, Pages 135-146

R.C. Paton

Abstract

This chapter discusses a way of mobilising knowledge by using models of knowledge based on graphs. These models are informal and geared to ease of use. A key feature of the approach is concerned with the idea that as knowledge about a domain unfolds, a society of graphs can be used to seed, generate and elaborate the emerging model. This society can help the exploration of a domain to unfold and the graphs satisfy a number of roles that we describe in terms of some key metaphors. A simple case study is followed to illustrate the approach concerned with the notion of a network.

Metaphors, models and bioinformation

Biosystems, Volume 38, Issues 2-3, 1996, Pages 155-162

Ray Paton

Abstract

The notion of bioinformation is central to the biosciences. This short paper examines a number of metaphors which are intimately related to this idea. These include metaphors about ‘system’ as well as metaphors associated with biosystem as ‘text’. A framework is presented which allows ideas about biosystems and computer systems to be displaced and a number of specific topics are then discussed. Firstly, information processing in non-neural tissues is given as an example of parallel distributed processing. This is followed with a number of metaphors associated with ‘text’, including ‘glue’, ‘verbs’ and ‘interpretation’. The paper concludes with a proposal on how to integrate general ideas of bioinformation using the idea of the ‘ecology of domains’.

Process, structure and context in relation to integrative biology

Ray Paton

Corresponding Author

Department of Computer Science, The University of Liverpool, Liverpool L69 3BX, UK

Received 8 May 2001;

revised 18 July 2001;

accepted 19 July 2001.

Available online 18 December 2001.

Abstract

This paper seeks to provide some integrative tools of thought regarding biological function related to ideas of process, structure, and context. The incorporation of linguistic and mathematical thinking is discussed within the context of managing thinking about natural systems as described by Robert Rosen. Examples from ecology, protein networks, and liver function are introduced to illustrate key ideas. It is hoped that these tools of thought, and the further work needed to mobilise such ideas, will continue to address a number of issues raised and pursued by Michael Conrad, such as the seed-germination model and vertical information processing.

Author Keywords: Ecology; Proteins; Category theory; Modelling; Function; Liver

Article Outline

1. Introduction

2. Graphs, processes, and objects

3. Context, ecology, and collection concepts

4. Proteins in context—graphs and ‘glues’

4.1. Proteins as verbs

4.2. Proteins, verbs and ‘glue’

5. ‘Glue’, categories, and functions

6. Concluding remarks

Acknowledgements

References

## Re: Category Theory and Biology

Nils Baas has been talking to me about the idea of “hyperstructures” a lot lately – and I have tried to think hard about it.

To me it seems like the main basic idea is this:

We might want to have something like an $n$-graph and equip it with a notion of composition (“fusion”) which does

notdistinguish between source and targets.Tom Leinster once told me that this is pretty close to saying “cyclic operad”, as far as I rememeber. But it seems to me that there might still be a good point in looking for more:

whatever the right notion of “$n$-graphs with fusion” is, the “morphisms” between them should

notsimply be morphisms, but should be “bonds” ($n$-graph elements), too.With Konrad Waldorf I was talking about this a bit. We came up with the following idea which might be a good guiding example:

Let $C$ be any category with all pullback. Then we know that

spansin $C$ form a bicategory.But now, what if I considered

multispansin $C$?Here a multispan is, clearly, an object on $C$ equipped with an arbitrary number of morphisms out of it.

Given two multispans, I can check if they have any “leg” in common, pull them back along this common leg and obtain a new multispan.

Clearly, the structure of multispans together with this fusion operation does not form a category – unless one artificially introduces labels that mark certain legs as incoming and other legs as outgoing.

Moreover, it is pretty clear that we can consider multispans of multispans in the obvious way, ad infionitum.

So I am guessing that multispans in a category $C$ might be a good guiding example for a definition of hyperstructure.

Even more so, since the other main motivating example that Nils Baas is emphasizing is hyperstructures of cobordisms with corners and singularities. Given that a cobordism can be regarded as a cospan, and naturally actually as a multi-cospan if we stop distinguishing between in- and out-parts of its boundary, this might actually be a special case of the more general multi(co)-span situation I just described.

Does anyone have any ideas on this??

I remeber John Baez pointing out how mutlispans of groupoids naturally appear as higher-rank tensors in the groupoidification program. Possibly there is some room for convergence here.

Where do multispans live?