Eindhoven NETIAM Report
The full report of the NETIAM workshop on "Complexity in modelling proteins and interfaces at the molecular level" may be downloaded in pdf format by using the link at the bottom of this page. The executive summary of the report is given below.

Executive Summary

This workshop identified two important areas of physical and biological science where mathematical innovation could enlighten our understanding of fundamental molecular processes. Despite the apparent disparity between these areas, the emergence of new insights would rely in each case on bringing new multiscale analyses to bear.

Understanding Interfaces at the Molecular Level
The more physically based topic is that of the bonding of two disparate materials at an interface, and specifically that of a polymer coating a metal substrate. Despite the importance of such interfaces to the automotive, semiconductor, metal and food industries, there is still no reliable basic understanding of the atomic configurations that are adopted even in the simplest configuration when the interface is nearly flat and the coating and substrate are infinite in extent. Here the new mathematical idea is to systematically use multiscale methodologies to ‘match’ together

1. a classical statistical physics theory for the atoms in the relatively wide sublayer where energy and entropy compete in the polymer between its ‘long chain’ bulk and the nominal interface;
2. a density functional theory for the relatively even mixture of atoms in a nanolayer around the interface;
3. an atomistic theory for metal atoms deeper into the substrate.

These three theories have a completely different mathematical character but they all highlight the role played by the Gibbs free energy, and this will be of vital importance when matching the theories together. The resulting composite theory will not only allow cohesive forces to be predicted with confidence, but stage (2) will reveal defect structure in the interface itself. This is the all important stage at which quantum mechanical effects cannot be avoided and the only way this can be done for the least realistic number of ten atoms is by exploiting the dramatic reduction in the dimensionality of the governing differential equations that density functional theory offers.

If this methodology can be perfected on this paradigm class of problems, it should be relatively easy to generalise it to study cases of imperfect contrast (so called `loops' and `trains' in the polymer), steps and / or ledges at the metal interface, the effect of impurity atoms such as oxygen and perhaps even to areas like quantum dot fabrication.

Understanding protein molecules in the cellular environment
There is an urgent need to gain a better quantitative understanding of the behaviour of protein molecules in a cell. From a physico-chemical viewpoint the principal challenge is to predict the evolution of both large and small protein molecules as they move through the complicated pathways between each other and the deformable cell skeleton and its microtubules and lipid bilayers. This is not just a problem in mechanics because of the numerous reactions that can occur between all the kinds of molecules in the cell and because of the important effects of electrical, thermal and chemical gradients. However it is clear that the geometry of the protein molecule is its most important mathematical characteristic as far as its reactivity is concerned (the geometry being most conveniently defined by its van der Waals surface). Moreover, user-friendly three-dimensional visualisations of this geometry are now becoming readily available, and there is much current interest in the apparently close relation between geometry and biological functionality .

In this highly complex situation, it was proposed that the first requisite was to understand how the classical theory of immiscible multiphase flow in a porous medium could be generalised to highlight the roles played by both the geometry of the dispersed phase in the pores and by the highly deformable nature of the porous ‘matrix’. This multiscale approach will be similar in spirit to the well-developed Buckley-Leverett theory as used so successfully in the oil recovery industry.

Such a paradigm will ignore reactions in the first instance but it is anticipated that these reactions will ultimately be incorporated as a body force distributed through the disperse phase in a way that is crucially dependent on the protein molecule geometry. It is also hoped that the model will provide a basis for understanding transport across the ‘bridges’ between the cytoplasm and the nucleus.

The programme of each of the NETIAM workshops is highly flexible, interactive, and responsive to emergent ideas, so distinguishing them from more traditional conference and seminar events. The Firenze, Ventspils and Kaiserslautern workshops have provided insight into the mechanisms and challenges in stimulating ideas for novel multidisciplinary research topics and collaborations; these aspects will be addressed more fully in the subsequent capstone Plenary Workshop in March 2005.

The proceedings and output from the Eindhoven workshop are recorded in this report for dissemination amongst the workshop participants and the wider public and research communities. The report is intended as a resource of ideas for future multidisciplinary research activity on the topic of Complexity in modelling proteins and interfaces at the molecular level and related areas. It is also the final of four Thematic Workshop reports which will form the basis of the final Plenary Workshop in March 2005, in which the ideas emerging from the Thematic Workshops will be integrated into substantial themes and collaborations for novel and multidisciplinary research.

The full report from the Eindhoven workshop can be downloaded here, or a shorter version (not including workshop presentations) is also available.

Download 'NETIAM Eindhoven report.pdf' (4 Mb).