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.

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. The interaction, which is based on a non-equilibrium statistical mechanics, can sense and count the number of stably attached kinetochores and sense the threshold for segregation. It blocks segregation until all sister chromatids pairs have been bi-oriented and regulates tension such that segregation becomes synchronized, thus explaining how the cell might decide to segregate replicated chromosomes. The model also predicts kinetochore oscillations at a frequency which agrees well with observation. Finally, a relationship between this spindle-chromosome dynamics and the force-extension formula obtained in a single DNA molecule experiment is obtained.

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. The energies are found to be within the expected range.

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. After adjustment of previously-made derivations, the model is compared with cell growth data from the T lymphocyte MLA-144.

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. A comparison of the model obtained with an Ising-like model provides a methodology to obtain the non-equilibrium scaling dependence of Ising-like models on the reactant concentrations.

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. Also, the derived slope of response is in perfect agreement with the values assessed.