Mathematical modelling of ciliary movement mechanism

• Autorzy: Krivovichev G.V. , Tregoubov V.P.
• Języki publikacji: EN

Abstrakty

EN

The main purpose of the paper was to present a new approach to the mathematical modelling of ciliary movements. This approach is based on the solution of the inverse problem of the dynamics, which is described by Lagrange's equations for the system of successively hinged rigid rods. In this case, as is well known, the generalized forces may be found as the time functions. It is proposed to represent these functions by the functions of generalized coordinates and velocities and also of the model parameters, whose values are determined as a solution of the parametric optimization problem. Besides, a special algorithm of ciliary movement control was elaborated. This algorithm is based on the hypothesis of variation of the equilibrium positions for cilia during one cycle of beating. The numerical results are in a good agreement with the cilia movements observed in Paramecium multimicronucleatum.

Słowa kluczowe

EN

cilium; model; movement mechanism; infusorian; movement control; identification

PL

migawka; model; mechanizm ruchu; kontrola ruchu; identyfikacja

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2011
• Tom: Vol. 13, no. 2
• Strony: 73--81
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Krivovichev G.V.

autor

Tregoubov V.P.

• Department of Modelling of the Electromechanical and Computer Systems, Saint-Petersburg State University, Russian Federation,

Bibliografia

• [1] RIKMENSPOEL R., RUDD W.G., The contractile mechanism In cilia, Biophysical Journal, 1973, 13, 955–993.
• [2] RIKMENSPOEL R., Contractile events in the cilia of Paramecium, Opalina, Mytilus, and Phragmatopoma, Biophysical Journal, 1976, 16, 445–470.
• [3] DILLON R.H., FAUCI L.J., An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating, Journal of Theoretical Biology, 2000, 207, 415–430.
• [4] FOSTER W.M., Mucociliary transport and cough in humans, Pulmonary pharmacology and therapeutics, 2002, 15, 277–282.
• [5] ALBERTS B., JOHNSON A., LEWIS J., RAFF M., ROBERTS K., WALTER P., Molecular biology of the cell, 3rd edition, Garland, New York, 1994.
• [6] MURASE M., The dynamics of cellular motility, John Wiley & Sons, USA, NY, 1992.
• [7] FAUCI L.J., DILLON R.H., Biofluid mechanics of reproduction, Annual Review of Fluid Mechanics, 2006, 38, 371–394.
• [8] CAMALET S., JULICHER F., Generic aspects of axonemal beating, New Journal of Physics, 2000, 2, 24.1–24.23.
• [9] CAMALET S., JULICHER F., PROST J., Self-organized Betting and swimming of internally driven filaments, Physical Review Letters, 1999, 82, No. 8, 1590–1593.
• [10] GUIRAO B., JOANNY J.F., Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia, Biophysical Journal, 2007, 92, 1900–1917.
• [11] GUERON S., LEVIT-GUREVICH K., A three-dimensional model for ciliary motion based on the internal 9+2 structure, Proceedings of the Royal Society of London B, 2001, 268, 599–607.
• [12] HOLWILL M.E., COHEN H.J., SATIR P., A sliding microtubule model incorporating axonemal twist and compatible with three-dimensional ciliary beating, Journal of Experimental Biology, 1979, 78, 265–280.
• [13] MITRAN S.M., Metachronal wave formation in a model of pulmonary cilia, Computers and Structures, 2007, 85, 763–774.
• [14] TOKIN I.B., TREGOUBOV V.P., SOKOLOFF A.B., Hypotheses and modelling of ciliary motility, Acta of Bioengineering & Biomechanics, 1, Supp. 1, 1999, 515–518.
• [15] KRIVOVICHEV G.V., TREGOUBOV V.P., Computer modelling of ciliary motility, Acta of Bioengineering and Biomechanics, 2008, 10, 3, 61–64.
• [16] TOKIN I.B., TREGOUBOV V.P., Mathematical modelling of generation and control of flagellar and ciliar motility, 11th European Cytoskeleton Forum, Book of Abstracts, 1996, 70.
• [17] VASILIEV F.P., Methods of optimization (Metody optimizatsii), Factorial Press, Moscow, 2002 (in Russian).
• [18] HAIRER E., NORSETT S.P., WANNER G., Solving ordinary differential equations. I. Nonstiff problems, 2nd edition, Springer-Verlag, 2008.