Complex biological systems

There are many circumstances in real life where patterns of connectivity are important. For example, to understand how a disease may spread around a population, how a virus may spread around a computer network or how signals are passed around the brain, we must have some idea of the `wiring' between components. By studying the typical patterns in many real life networks, including data concerning connectivity between brain neurons, computers, web pages, people, co-authors and telephone users, scientists have discovered common features that seem to be universal. Also, they have come up with rules that appear to govern the development of real life networks. Often, it is necessary to summarize such an enormously complex set of information, perhaps by finding clusters of objects that behave similarly or by ordering the objects in a natural manner, so that neighbours have similar features. This project will develop new computational tools for organizing large data sets and for explaining the patterns of connectivity that are observed. To give the work a firm grounding, all ideas will be tested on real, cutting-edge data concerning the behaviour of genes and proteins in the cell. This aspect of the project work will be done in close collaboration with colleagues from the life sciences, notably cancer researchers from the Beatson Institute in Glasgow. These colleagues will help us to formulate the right questions. Further, after we have designed the new computational algorithms, these colleagues will also help us to interpret the answers. Any new findings in this important biological application could have direct benefits to healthcare and drug design.

This project developed new computational tools and analytical techniques
within complexity science. These were road tested in the cutting edge
context of large biological networks.
The work built on the proposers' track record
in computational analysis of large, sparse, complex networks,
and exploited the added value
of their close contacts with researchers in the life sciences.

Complex networks are a universal feature across a vast
range of applications, and many of the key
challenges
revolve around the issue
of how to unravel this complexity.
Our project developed novel, generic computational and modelling
tools through new ideas in (A) matrix factorization methods,
(B) sensitivity analysis, and (C) random network theory.
To give the work a solid grounding
and an immediate payoff, we embedded these topics
within the context of complex biological networks.

Highlights were the novel ideas and algorithms published in
more than 10 high quality refereed journals and
several invited talks (with expenses paid)
at international conferences, including
Multi-scale Stochastic Modeling of Cell Dynamics, Banff,
BIT 50: Trends in Numerical Computing, Lundh,
Opening Workshop of 2010-11 Program on Complex Networks, North Carolina,
Conference on Scientific Computing, Geneva,
Computational Mathematics Symposium, Maxwell Institute, Edinburgh
Applied Mathematics/Statistics Interface, Warwick,
Mathematical Tools for Systems Biology (MATSYB), Manchester.
Also, in 2008 Higham presented the invited Magnus Lectures at the University of
Colorado State, including a public lecture on Network Science: Joining the Dots.

The research from this project has led on to other externally funded research,
including in 2011: 30K from The Leverhulme Trust for a personal one year Research
Fellowship on Fundamental Issues in Stochastic Simulation for Systems Biology
and in 2010: 180K EPSRC and Research Councils UK Digital Economy Programme, for the
project MOLTEN: Mathematics Of Large Technological Evolving Networks.
It also directly spawned a 50K Knowledge Exchange grant that is allowing the research
to be used immediately at the Beatson Institutue for Cancer Research, Glasgow.