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
: [email protected]
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