The subject of my work are microtubules (MT). MTs are biological structures that are an important part of the cytoskeleton of eukaryotic cells. They participate in cell division, information transfer and transport of materials within the cell, they play a role in changing the shape of the cell and other important cell activities.
MTs are assembled from the molecules of tubulin that have dipole character. Tubulin molecules form protofilaments along the axis of the tubule. In the process of the assembly i.e. attaching a molecule of tubulin to a MT the energy of about 0.43 eV is released through the hydrolysis of GTP into GDP. Our aim is to find what happens to this energy in a biological, hence very efficient system. We conjecture that the energy can be used in the disassembly of the MTs, attaching of microtubule associated proteins (MAPs) or it can be utilized in some other yet unknown way. In my work I used a model proposed by my supervisor Dr. Tuzsynski. In this model a MT protofilament is described as 1-D chain of ordered dipoles that are coupled with elastic forces (polarization and dislocation are coupled linearly). In the continuum approximation the model has an analytical solution a kink like soliton traveling at a constant velocity that is proportional to the electric field produced by the MT when it is in its completely ordered state (ferroelectric). This implies that applying an external electric field to a MT in parallel or opposite direction to the intrinsic MT electric field can result into a faster or slower kink. The kink is a domain wall between two subchains of dipoles oriented in the opposite direction.
The effect of MAPs has been modeled numerically using the same model where an attached MAP was represented by a gaussian potential. The presence of the potential slows the kink down. When the amplitude of the potential reaches a critical value the motion of the kink is stopped completely. For the kinks with smaller velocities this critical value is smaller.