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.

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

The spindle checkpoint, which blocks segregation until all sister chromatid pairs have been stably connected to the two spindle poles, is perhaps the biggest mystery of the cell cycle. The main reason seems to be that the spatial correlations imposed by microtubules between stably attached kinetochores and the nonlinear dependence of the system on the increasing number of such kinetochores have been disregarded in earlier spindle checkpoint studies. From these missing parts a non-equilibrium collective spindle-chromosome interaction is obtained here for budding yeast (Saccharomyces cerevisiae) cells.

Complex movements of motor protein relay helices during the power stroke.

We use the Toda soliton formalism to propose a possible complex movement of alpha helices with a very important role in energy transduction during the power stroke of motor proteins. We find that this approach has advantages in comparison with the Davydov soliton model and its variants. We estimated the model's parameters and calculated corresponding properties of the predicted solitary waves including propagation velocities and energies.

Lyotropic ion channel current model compared with ising model.

Trans-membrane currents in ligand-gated ion channels are calculated in a non-equilibrium, chemically open whole cell system. The model is lyotropic in the sense that dynamics and parameters such as ligand concentration for half-maximal response (scale of response), and threshold for firing in neurons, are nonlinear functions of the reactant concentrations. The derived total current fits recorded data significantly better than those derived from mass action, Ising, and other equilibrium type models, in which the derived response can be displaced from the assessed response by several orders in the ligand concentration.

Model of DNA dynamics and replication.

Before DNA replication can be initiated a definite number of adenosine triphosphate (ATP) containing pre-replication protein complexes (pre-RCs) must be assembled and bound to DNA like in a super-critical mass. A chemically driven dynamics of the Ginzburg-Landau (GL) type is derived, using the non-equilibrium equation for binding of pre-RCs to DNA and a probabilistic conformational distribution of these protein complexes. This dynamics, in which the DNA-protein system behaves like a nonlinear elastically braced string (NEBS), can control the cell cycle via conformational transitions such that G(2) cells contain exactly twice as much DNA as G(1) cells.

Ligand-gated ion channel currents in a nonstationary lyotropic model.

Transmembrane currents in ligand-gated ion channels are calculated in a nonstationary, chemically open whole cell system or patch of a membrane. The model is lyotropic in the sense that dynamics, and parameters such as the ligand concentration for half-maximal response (scale of response), and threshold for firing, such as in neurons, become nonlinear functions of the reactant concentrations. The derived total currents fit recorded data significantly better than those derived from mass action, Ising, and other stationary type models, in which the derived response is often displaced from the assessed response by several orders in the ligand concentration.