Resonance Condition in Microtubules Using Ultrasound Plane Waves
Microtubules (MTs) are protein filaments forming a major part of the cytoskeleton of all eukaryotic cells which directly contribute to the process of cell division by forming mitotic spindles and providing force for the segregation of chromosomes. MTs exhibit mechanoelastic properties of considerable interest in view of their functional roles in cell division and cell shape. In this work by introducing a new method, we have analytically solved equations of motion for the vibrational dynamics of an MT that is attached at its two ends. This is especially relevant for MTs during mitosis when they attach to chromosomes and centrosomes at the plus and minus ends, respectively. Our analysis applies to MTs present inside a viscous solution and when driven by an ultrasound plane wave. We have shown that with using ultrasound plane waves the resonance condition for the MT treated as a rigid rod cannot be provided, and in order to achieve resonance we should excite a single mode of the MT with a harmonic number larger than a threshold value introduced in this paper. Having a large enough amplitude for the resonant vibration effect is crucial in order to maximize the bending moment of an MT. Attaining a high quality factor for a resonance is crucial to have a better control of the energy transfer to the MT. Finally, single mode excitation not only helps to transfer the minimum amount of energy to the surrounding medium compared with multi-mode excitation but it also allows for a simultaneous high-amplitude and high-quality factor which is impossible when using plane waves.
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Document Type: Research Article
Publication date: 2012-01-01
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