Spindle checkpoint regulated by nonequilibrium collective spindle-chromosome interaction; relationship to single DNA molecule force-extension formula

Nonlinear dynamics of C-terminal tails in cellular microtubules

The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano-electrical waves elicited in the rows of very flexible C-terminal tails which decorate the outer surface of each microtubule. The fact that C-terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule-associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink-waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process.

Chromatin compaction by condensin I, intra-kinetochore stretch and tension, and anaphase onset, in collective spindle assembly checkpoint interaction

The control mechanism in mitosis and meiosis by which cells decide to inhibit or allow segregation, the so-called spindle assembly checkpoint (SAC), increases the fidelity of chromosome segregation. It acts like a clockwork mechanism which measures time in units of stable attachments of microtubules (MTs) to kinetochores (the order parameter). Stable MT-kinetochore attachments mediate poleward forces and 'unstable' attachments, acting alone or together with motor proteins on kinetochores via chromosomes, antipoleward forces. Stable and unstable attachments could be separated, and the non-equilibrium integrated MT mediated force acting on stably attached kinetochores was derived in a collective interaction (Matsson 2009 J. Phys.: Condens. Matter 21 502101), in which kinetochores were treated as rigid protein complexes. As forces and tension in that model became equally distributed in all bioriented sister chromatid (SC) pairs, segregation was inhibited without need of a 'wait-anaphase' signal. In this generalization, the kinetochore is divided into an inner chromatin proximal complex and an outer MT proximal complex, and the integrated MT mediated force is divided into an integrated poleward and an integrated antipoleward force. The model also describes the collective interaction of condensin I with chromatin, which together with the MT mediated dynamics yields the putative in vivo tension in kinetochores and centromeric and pericentromeric chromatin, as a non-linear function of the order parameter. Supported by the compaction force and an increased stiffness in chromatin towards the end of metaphase, the two opposing integrated MT mediated poleward forces, together with metaphase oscillations, induce a swift and synchronized anaphase onset by first increasing the intra-kinetochore stretch. This increase lowers the SAC energy threshold, making a cleavage by separase of all cohesin tethering SC pairs in anaphase energetically possible, thereby reducing the risk for aneuploidy and cancer. It is also shown how this risk might increase in condensin I depleted cells. Moreover, a solution is provided to the fundamental statistical physics problem with a system containing an increasing number of particles (molecular complexes) that become strongly correlated in space.

Nonlinear ionic pulses along microtubules

Microtubules are cylindrically shaped cytoskeletal biopolymers that are essential for cell motility, cell division and intracellular trafficking. Here, we investigate their polyelectrolyte character that plays a very important role in ionic transport throughout the intra-cellular environment. The model we propose demonstrates an essentially nonlinear behavior of ionic currents which are guided by microtubules. These features are primarily due to the dynamics of tubulin C-terminal tails which are extended out of the surface of the microtubule cylinder. We also demonstrate that the origin of nonlinearity stems from the nonlinear capacitance of each tubulin dimer. This brings about conditions required for the creation and propagation of solitonic ionic waves along the microtubule axis. We conclude that a microtubule plays the role of a biological nonlinear transmission line for ionic currents. These currents might be of particular significance in cell division and possibly also in cognitive processes taking place in nerve cells.

DNA-RNA transcription as an impact of viscosity

The impact of viscosity on DNA dynamics is studied both analytically and numerically. It is assumed that the viscosity exists at the segments where DNA molecule is surrounded by RNA polymerase. We demonstrate that the frictional forces destroy the modulation of the incoming solitonic wave. We show that viscosity, crucial for demodulation, is essential for DNA-RNA transcription.