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Possible principle of controling the self-assembly
of biomolecular materials

Wlodzimierz Kozlowski*

Institute of Biocybernetics & Biomedical Engineering
of the Polish Academy of Sciences

This is an abstract for a poster to be presented at the
Fifth Foresight Conference on Molecular Nanotechnology.
The full paper is available here.


One reports computational study aimed at possible principle of controlling the biomolecular self-assembly for development of new materials of medical and technical importance. Objective is the self-assembling whose course may be specified by features characterising changes in the patterns of expanding spatial regions in which molecular components exhibit appearance of the required properties. In course of the study, diversity in ways of the expansion realisation influenced by stochastic factors is simulated by random expansion process (REP) whose states at subsequent stages of its development are finite random sets being multiplicity of sets-realisations that have evolved independently (parallel) within the same spatial domain. The state at each stage is represented by the pattern constructed so that it is as close as possible , after situation in space and measure , to all the various realisations at the stage ; this is mean measure set (MMS). The study on controlling mechanisms contributing to changes in the MMS features would suggest directions of searching for practical methods of controlling features of changes in actual pattern of the expanding spatial regions. With this purpose, a set-theoretical formula expressing the simulated REP is to model adequately mechanisms of information transmission about covering area in the actual expansion where chemical information is transmitted within supramolecular structures and due to displacement of the structures while self-assembling the material (manifestation of that transmission is identified as finite-size effects). This is satisfied by simulating REP as Markov process of covering nodes of a regular two-dimensional grid and so that information about covering a node is transmitted : between members of a pair of neighbour nodes and due to conditional displacement of this pair. Displacement of information about organisation of two nodes into a pair identifies the effective displacement of the pair of neighbour nodes. This is generalisation of the discrete displacement method (DDM) developed previously for modelling similar finite-size effects peculiar to turbulent transport and verified for example of developed turbulent pipe flow.

We have considered variant of the REP simulation which admitted specification by unique parameter; conditions assumed permitted for development constrained to one half plane from straight chain of covered nodes. It has been found that for certain interval of the parameter, there are appear jumps of increment in the MMS measure Imms preceded and followed by resident times for which Imms remains constant or varies not remarkably. It has been observed a number of those events in course of the REP development for different values of the control parameter. There are pairs of the subsequent events for which increments in the MMS area covered exhibit qualitative change in form , from sedimentation-like increment to percolation-like one. The DDM modelling of the finite size effects have appeared to be responsible for presence of the change. We discuss conditions for using the REP parameter to control appearance of the qualitative change and try to suggest actual methods used to control the self-assembly which would correspond to the simulations.

*Corresponding Address:
Dr Wlodzimierz Kozlowski, Institute of Biocybernetics & Biomedical Engineering of the Polish Academy of Sciences, Ks. Trojdena 4, Warsaw 02-109, POLAND, fax: +(48)-22-658-70-30, email :

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