The Shannon entropy dependence on temperature, dipole moment and thermodynamic properties of microtubules (MTs) have been investigated using the Landau–Ginzburg phenomenological theory through continuum Boltzmann distribution function. By minimising the loss in energy, we found that there is a possibility that MTs formed from the heterodimers can process information over a long time at higher temperature. We also found that multiple heterodimers under the influence of dipole moment, has the tendency to process information whenever the amount of information stored or transferred decreases with increasing electronegativity of the system. We analyse the dynamic instability phenomenon that infinitely occurs in polymerisation and depolymerisation processes in MTs. Also, under physiological conditions, temperature dependence of thermodynamic properties was investigated and our results exhibited critical behaviour of heat capacity and chemical potential giving room for phase transitions around 302 K.

We developed and obtained close-form solutions for the buckling growth rate of microtubule (MT) bundles using the Timoshenko beam theory. We took into consideration the surface effects and the Poisson’s ratio of the microtubules surrounded by neighbouring filaments in the viscous cytosol. We developed the motion equation by using the modified couple stress theory (MCST) which will take into account the small-scale effects of the microtubules. We then proceeded by studying the effects of various parameters on the buckling growth rate of microtubule bundles. Our results show that the internal material length scale parameter has a decreasing effect on the buckling growth rate of the microtubule bundle. And as microtubule added in the bundle increases, the buckling growth rate reduces further due to the effects of the surrounding microtubule-associated proteins (MAPs). On the contrary, the Poisson’s ratio has an increasing effect on the value of the buckling growth rate of the microtubule bundle. We also investigated the effects of other parameters such as surface energy on the buckling growth rates of microtubule bundles and showed the validity of our model by comparing our results with those obtained by previous researchers.