A toolbox for modelling stochastic molecular networks
Plus: what celestial constellations can teach us about molecular networks
Modelling stochastic molecular networks such as polymers is quite a challenge since they are complex, flowing and changing systems. While a classical molecular dynamics approach works fine for simple networks with a repetitive pattern, it often collapses with stochastic networks because of the inability of modelling in a reasonable time. Now Ivan Kryven of the Van 't Hoff Institute for Molecular Sciences has found a solution for this. He developed a mathematical toolbox for the study of evolving molecular networks expanding on any spatial or time scale. Last week Kryven obtained his PhD cum laude with professor Piet Iedema of the Computational Polymer Chemistry group.
Polymers are a versatile class of materials with a broad range of physical properties. Their application diverges from nano-robots transporting drugs in the human body to tables and chairs in our households.
On a molecular level a polymer consists of an arrangement of many identical molecules - of one or just a few kinds - into a complicated structure usually referred to as a network. During synthesis, processing or under a load this molecular network expands, flows or changes. Modelling these stochastic molecular networks, for instance for the prediction of material properties, poses a great challenge for computational chemists.
Ivan Kryven now introduces a molecular topology approach that greatly reduces the complexity of modelling stochastic molecular networks. The underlying idea is that in conditions of fluidity and constant change the connection between the molecules (the molecular topology) remains a constant feature.
To be able to refer to this molecular topology regardless of the spatial network configuration Kryven uses a so-called graph description. This description is comparable to a subway map where abstract lines denote connections between stations, or to a map of the night sky with lines connecting the stars into mythological figures.
Already fields such as transportation, computing and social network research equally benefit form graph theoretic formalism by sharing common properties. In the molecular world it turns out that the topology of a molecular network defines many physical properties, even with a random connectivity pattern.
Evolution of topology
In his PhD dissertation Ivan Kryven views the assembly of molecular networks (the polymerization) from a perspective of evolving graph topology. His mathematical approach with continuously evolving distributions facilitates the description of the randomly fluctuating polymerization process that takes the molecular network from a very simple topology to a complicated interconnected structure.
Depending on the conditions of the process these distributions are obtained as time-dependent or steady-state solutions to a specific integro-differential equation denoted population balance equation. In view of the required high detail these distributions are often multidimensional.
When less is more
A remarkable result of Kryven's research is that the bigger molecular network, the more its properties are encoded by the graph representation rather than by the underlying chemistry. This means that the material properties can be explained by as simple structures as the collections of dots and their interconnecting sticks. So, Kryven remarks, no 'monsters' should be seen in large molecular networks, just as in modern celestial cartography there is no place for mythological creatures behind the constellations.
Ivan Kryven's research was part of the research programme of the Dutch Polymer Institute (DPI) and supported by the EU through the FP 7People NANOPOLY project.
I.Kryven. Topology evolution in macromolecular networks. University of Amsterdam 2014 (233 p.)