Computing robustness in biology
Robustness is the fundamental organising principle of evolving dynamic systems such as biological systems. One could say that robustness allows evolution to happen and that evolution favours robustness. For example, a biological signalling pathway may be robust not only to changes in molecular concentrations, but also to the loss of what appear, at first sight, to be essential genes.
So a robust system carries on with its essential functions despite perturbations (internal or external), unpredictable environments, and unreliable components. There is a large number of definitions of robustness - see discuss.santafe.edu/robustness.
Robustness is a system-level phenomenon. The individual components of a system may or may not be robust themselves - robustness is a property of the assembly of components and it cannot be fully understood by examining them individually.
Robustness is not immutability - if a system cannot change then it cannot adapt to changes to its internal or external environment. Robustness does not inhibit evolution; rather, it seems to be a fundamental and inevitable property of complex, evolvable systems.
One view of robustness, called Highly Optimised Tolerance (HOT) developed by J. M. Carlson, John Doyle [1-3] and others, suggests that biological systems that have evolved to be robust to run-of-the-mill perturbations are extremely sensitive to rarely encountered perturbations. So, paradoxically, we can say that many biological systems are 'robust yet fragile'. There is a trade-off between robustness, fragility, performance, and resource demands. Csete and Doyle  argue that robustness may be regarded as a conserved quantity. This 'conservation of robustness' implies that every robust system, for example every pernicious disease, has an Achilles heel - a fragility that, if found, may be used to destroy the system. For example, a robust biological system can be disrupted by tiny perturbations to genes, by trace amounts of toxins, or by microscopic pathogens . The hope is that in the long term these counter-intuitive insights, derived from studying the behaviour of the system as a whole, may inspire new medical treatments or practices.
Robustness has been a topic of interest since the 1930s, when Harry Nyquist , working at Bell Telephone Laboratories, provided the first two measures of robustness - Gain Margin and Phase Margin. An important event in March 2005 was the publication of Robust Design - a repertoire of biological, ecological, and engineering case studies  (edited by Erica Jen of the Santa Fe Institute). This book summarises the recent work done at the Santa Fe Institute on robustness as a fundamental design principle and describes how leading researchers are currently thinking about the concept of robustness.
Many details about the concept of robustness in biology and medicine are given in the reviews by Hiroaki Kitano [7, 8]. The specific example of Type 2 Diabetes is discussed by Kitano et al .
Most robust biological systems share a set of characteristic architectural features. Feedback control, both positive and negative, are ubiquitous. Negative feedback (also called autoregulation) is the main mechanism used to achieve a robust response to perturbations. Negative feedback operates when a signal causes its own inhibitor to be produced. Positive feedback (or autocatalysis) amplifies sensitivity. Such amplification is necessary if a cell is to make decisions robustly, based on 'noisy' information. Feedback control is coupled with redundancy to enhance robustness.
Homogeneous redundancy is where multiple copies of components are used to support the main system with many identical standby systems. This is rare in biological systems, but common in engineered systems. Such a design is susceptible to common-mode failure.
Heterogeneous redundancy is where cells possess genetic variability and so are not vulnerable to the same insult. Tumours achieve their robustness mainly by heterogeneous redundancy. Each cell in a tumour may be fragile to a particular drug, but the system of cells will be robust. Such cellular heterogeneity leads to functional redundancy, as cells have the flexibility to take on new functions. Although providing these alternatives is a costly business for any biological entity, the cellular heterogeneity evident in tumours would lead one to doubt the existence of a magic bullet that could be targeted at a single molecular abnormality.
Some other architectural features described by Krakauer  are decoupling and purging. Decoupling isolates and buffers high-level functionality from low-level damage. Purging amplifies the effect of perturbations, so as to ensure the purity of a population and the eradication of any vulnerable component.
Antibiotics can remove cholera because the pathogen has not hijacked the robustness mechanisms of the cell to protect itself. Cancer, HIV, and diabetes, however, are more pernicious. These diseases pervert the cells' natural robustness to their own ends. They usurp the mechanisms that normally defend the body against attack and use them to defend themselves. This misappropriation of the body's defences is both the strength and the weakness of these diseases. The weakness results from the conservation of robustness mentioned above. Some chemical perturbation directed at the fragility can be used to exorcise the pathogen or render it harmless. Robustness is always accompanied by some fragility - discover the fragility and you may have discovered a path to a clinical treatment.
One clinical strategy for the treatment of cancer that has been suggested by studies of robustness is to induce dormancy in the tumour cells (by inducing cell cycle arrest) rather than aiming at eradication of the tumour. A similar approach has been adopted in the treatment of HIV infection and is described by Kitano . HIV infects CD4-positive T cells and the virus replicates when the cell activates its anti-virus response. But in the approach to treatment suggested by robustness analysis, instead of being removed, HIV is forced into a latent state. This targeting of the cellular dynamics instead of specific molecules represents a new approach to treatment of disease. System-level modelling of disease can lead to counter-intuitive insights into the operation of the system and then to new clinical strategies. With greater understanding of complex evolvable systems, it might be possible to identify a set of medications and a detailed schedule for administrating them that would drive abnormal cells to some desired state with minimal side effects.
Mathematicians, engineers, and biologists involved in the study of biological systems all need to use similar modelling strategies in their research, so they can compare their results in a meaningful way. Many diverse and complex modelling tools are required in this area. Systems Biology Workbench (sbw.sourceforge.net) provides a framework that allows these different tools to interact with each other. Also, Systems Biology Markup Language - SBML - (SBML.org/index.psp) is a model-representation language that provides a common format for describing models of biochemical reaction networks. This software offers a very extensive range of applications and it is available for free on the web.
There have been recent developments in commercial software too. At the end of August, Wolfram Research released a new Mathematica application package. It is a version of a systems-biology modelling package called PathwayLab (www.wolfram.com/products/applications/pathwaylab). Originally developed by InNetics AB of Sweden (innetics.com), PathwayLab can be used for modelling and analysis, as well as experimentation and visualisation with biochemical networks. A model of the network is first created in Microsoft Visio, using customised drag and drop graphical building blocks. The model is then transformed into a *.m file and exported to Mathematica. This *.m file consists of a set of coupled non-linear differential equations. Such equations are grist for Mathematica's mill and they can be simulated and analysed using not only the usual extensive Mathematica functionality, but also the extended functionality offered by the PathwayLab application. Steady-state analysis, transient analysis, non-linear stability analysis, model reduction, transformation and formatting of reaction rate equations, and automated sweeping over parameter values are some of the facilities offered by this package.
 J. M. Carlson and J. Doyle, 'Complexity and robustness,' Proceedings of the National Academy of Sciences USA, vol. 99, pp. 2538-2545, 2002.
 J. M. Carlson and J. Doyle, 'Highly optimized tolerance: A mechanism for power laws in designed systems,' Physical Review E, vol. 60, pp. 1412-1427, 1999.
 J. M. Carlson and J. Doyle, 'Highly Optimized Tolerance: Robustness and Design in Complex Systems,' Physical Review Letters, vol. 84, pp. 2529-2532, 2000.
 M. Csete and J. Doyle, 'Reverse engineering of biological complexity,' Science, vol. 295, pp. 1664-1669, 2002.
 H. Nyquist, 'Regeneration Theory,' Bell Systems Technical Journal, vol. 2, pp. 126-147, 1932.
 E. Jen, 'Robust Design -- a repertoire of biological, ecological, and engineering case studies,' in Santa Fe Institute Studies in the Sciences of Complexity: Oxford University Press, 2005.
 H. Kitano, 'Biological Robustness,' Nature Reviews - Genetics, vol. 5, pp. 826-837, 2004.
 H. Kitano, 'Cancer as a robust system: implications for anticancer therapy,' Nature Reviews - Cancer, vol. 4, pp. 227-235, 2004.
 H. Kitano, K. Oda, T. Kimura, Y. Matsuoka, M. Csete, J. Doyle, and M. Muramatsu, 'Metabolic Syndrome and Robustness Tradeoffs,' Diabetes, vol. 53, Supplement 3, pp. S6-S15, 2004.