By Rubem P. Mondaini, Rui Dilao

This helpful quantity includes the contributions from the keynote audio system of the BIOMAT 2006 symposium in addition to chosen contributions within the parts of mathematical biology, organic physics, biophysics and bioinformatics. It comprises new effects, contributions and accomplished reports to the mathematical modeling of infectious illnesses corresponding to HIV, tuberculosis and hepatitis B. Mathematical versions for physiological issues together with tumors, aneurysms and metabolic ailments are mentioned and analyzed. This publication additionally comprises unique contributions to de novo protein constitution prediction and multi-objective optimization suggestions utilized to protein tertiary constitution prediction. DNA evolutionary concerns, stem mobilephone biology, dynamics of biologic membranes, reaction-diffusion mechanisms, inhabitants dynamics, and bioeconomics are coated and mentioned all through this e-book.

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Additional info for Biomat 2006: International Sysposium on Mathematical and Computational Biology, Manaus, Brazil, 27-30 November 2006

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26. 27. 28. 29. 30. 31. 32. 33. 34. EMERGENCE OF A COLLECTIVE STEADY STATE AND SYMMETRY BREAKING IN SYSTEMS OF TWO IDENTICAL CELLS ˜ RUI DILAO Nonlinear Dynamics Group, Instituto Superior T´ ecnico Av. com We consider a system of two coupled identical cells. The dynamics of the chemical substances in the individual cells are the same, and the coupling is proportional to the differences in the concentrations of its chemical constituents. Without coupling, the cells have a unique and identical stable steady state — the quiescent state.

Habibian, M. , Blood Cell. Mol. Dis. 27, 934-937 (2001). 9. P. Quesenberry, M. Abedi, J. , Blood Cell. Mol. Dis. 32, 1-4 (2004). 10. G. Bradford, B. Williams, R. , Exp. Hematol. 25, 445-453 (1997). 11. S. Cheshier, S. Morrison, X. Liao et al. Proc. Natl. Acad. Sci. USA 96, 31203125 (1999). 12. M. Goodell, Blood 94, 2545-2547 (1999). 13. G. Van Zant, K. Scott-Micus, B. Thompson, et al. Exp. Hematol. 20, 470-475, (1992). 14. J. Abkowitz, S. Catlin, P. Guttorp, Nat. Med. 2, 190-197 (1996). 15. L. Kamminga, L.

K42 2(Bk2 − k4) − 4µ 0<µ< (14) In this case, the chemical substance X (or U ) is a repressor and Y (or V ) is an activator. Also, X is a self-activator and Y is a self-repressor. 33 For the choice of parameters, A = 2, k1 = k2 = k3 = k4 = 1, the local system (12) has a supercritical Hopf bifurcations for B = 5, and the instability conditions (14) become, B−1 2 1 + 2µ ν>4 . 2(B − 1) − 4µ 0<µ< (15) Taking, B, µ and ν as free parameters, the two-cell coupled system (2) with the local vector field (12) becomes, B dX1 = (B − 1)X1 + 4Y1 + X12 + 4X1 Y1 + X12 Y1 + µ(X2 − X1 ) dt 2 dY1 B 2 = −BX1 − 4Y1 − X1 − 4X1 Y1 − X12 Y1 + ν(Y2 − Y1) dt 2 dX2 B = (B − 1)X2 + 4Y2 + X22 + 4X2 Y2 + X22 Y2 + µ(X1 − X2 ) dt 2 dY2 B 2 = −BX2 − 4Y2 − X2 − 4X2 Y2 − X22 Y2 + ν(Y1 − Y2) .

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