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Mathematics explains puzzles of icy dust in the outer space

One of the most impressive discoveries of the Cassini spacecraft was the cryo-volcanic activity of the icy Saturnian satellite Enceladus. Water vapour and tiny ice particles, ejected from geyser like sources, form a spectacular plume that towers over the south pole of the moon up to hundreds of kilometers. The icy particles (dust), which make the visible part of the plume, are the main source of Saturn's E ring.

However, the physical process of grain formation is not understood to date. Recent work by Dr Nikolay Brilliantov and colleagues present a new quantitative mathematical model, which basically explains the observed properties of the plume. The core of the model is subsurface condensation of ice grains in the vapour. The gas is produced at depth and escapes to vacuum through cracks in the ice shell at the south pole of the moon.

The model reproduces well all the available data obtained by Cassini. The results favor conditions of liquid water near Enceladus' surface, implying an 'underground' ocean which may be a habitat for life.

Most Accessed Paper in BMC Systems Biology in November 2008

Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions.

In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.

We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as 'pseudo-monomolecular' subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalised theory of the limiting step.

Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model.

The methods are demonstrated for simple examples and for a more complex model of NF-κB pathway. Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in 'middle-out' approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

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