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ON (dis)ORDERED AGGREGATION OF PROTEINS

ON (dis)ORDERED AGGREGATION OF PROTEINS. Adam Gadomski & Jacek Siódmiak Institute of Mathematics and Physics University of Technology and Agriculture Bydgoszcz, Poland . Workshop on Structure and Function of Biomolecules May 13 - 15, 2004, Będlewo near Poznań, Poland. OBJECTIVE.

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ON (dis)ORDERED AGGREGATION OF PROTEINS

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  1. ON (dis)ORDERED AGGREGATION OF PROTEINS Adam Gadomski & Jacek Siódmiak Institute of Mathematics and Physics University of Technology and Agriculture Bydgoszcz, Poland Workshop on Structure and Function of Biomolecules May 13 - 15, 2004, Będlewo near Poznań, Poland

  2. OBJECTIVE TO PROPOSE A CONCEPTUAL AND THEORETICAL STRATEGY, BASED ON THE GROWTH RULE AND GROWTH MECHANISM, POSSIBLY OF USEFULNESS FOR QUALITY AND MANUFACTURE TESTS IN PROTEIN-BASED TECHNOLOGY AND PROTEIN-CLUSTER DESIGN

  3. Matter aggregation models, leading to (poly)crystallization in complex polyelectrolytic environments: (A) aggregation on a single seed in a diluted solution, (B) agglomeration on many nuclei in a more condensed solution

  4. GENERAL RULE BASED ON THE GROWTH RATE - time - mechanism – dependent continuous function - system’s main variables - control parameters (desirable behavior in time: )

  5. ONE-NUCLEUS BASED SCENARIO - volume - internal concentration (density) - surface - external concentration - time - position vector GENERAL SCHEME FOR THE MASS CONSERVATION LAW

  6. EMPHASIS PUT ON A CLUSTER – CLUSTER MECHANISM: - time- and size- dependent diffusion coefficient interaction (solution) parameter of Flory-Huggins type geometrical parameter (fractal dimension) - initial cluster mass - characteristic time constant

  7. Na+ion Lysozyme protein water dipole random walk DOUBLE LAYER surface of the growing crystal Cl-ion PIVOTAL ROLE OF THE DOUBLE LAYER (DL):

  8. Growth rates for the DL-controlledon-one-nucleus-based aggregation model supersaturation parameter deterministic: Frenkel-like macroion velocity an (un)correlated noise stochastic (an example):

  9. MANY-NUCLEI BASED SCENARIO GRAIN (CLUSTER)-MERGING MECHANISM

  10. RESULTING 2D-MICROSTRUCTURE: VORONOI-like MOSAIC FOR AGGREGATION INITIAL STRUCTURE FINAL STRUCTURE

  11. RESULTING FORMULA FOR VOLUME-PRESERVING d-DIMENSIONAL MATTER AGGREGATION time derivative of the specific volume (inverse of the polycrystal density) adjusting time-dependent kinetic prefactor responsible for spherulitic growth hypersurface inverse term

  12. ADDITIONAL FORMULA EXPLAINING THE MECHANISM (to be inserted in continuity equation) drift term diffusion term surface - to - volume characteristic exponent - hypervolume of a single crystallite - independent parameters scaling: holds !

  13. where TAKEN USUALLY FOR THE d-DEPENDENT MODELING AFTER SOLVING THE STATISTICAL PROBLEM is obtained USEFUL PHYSICAL QUANTITIES:

  14. CONCLUSION • THERE ARE PARAMETER RANGES WHICH SUPPORT THE AGGREGATION AS A RATE-LIMITING STEP, MAKING THE PROCESS KINETICALLY SMOOTH, THUS ENABLING THE CONSTANT CRYSTALLIZATION SPEED TO BE EFFECTIVE (AGGREGATION AS A BENEFACTOR) • OUTSIDE THE RANGES MENTIONED ABOVE AGGREGATION SPOILS THE CRYSTALLIZATION OF INTEREST (see lecture by A.Gadomski)

  15. LITERATURE:- A.Danch, A.Gadomski.a; A.Gadomski, J.Łuczkab • aJournal of Molecular Liquids, vol.86, no.1-3, June 2000, pp.249-257 • b IBIDEM, pp. 237-247 • J.Łuczka, M.Niemiec, R.Rudnicki • Physical Review E., vol.65, no.5, May 2002, pp.051401/1-9 • J.Łuczka, P.Hanggi, A.Gadomski • Physical Review E., vol.51, no.6, pt.A, June 1995, pp.5762-5769 • - A.Gadomski, J.Siódmiak • *Crystal Research & Technology, vol.37, no.2-3, 2002, pp.281-291 • *Croatica Chemica Acta, vol 76 (2) 2003, pp.129–136 • - A.Gadomski • *Chemical Physics Letters, vol.258, no.1-2, 9 Aug. 1996, pp.6-12; *Vacuume, vol50, pp.79-83 ACKNOWLEDGEMENT !!! This work was supported by KBN grant no. 2P03B 03225 (2003-2006).

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