MS11.1: Nonlinear Dynamics in Biological Systems

We study the mammalian whisker-object contact problem by applying the Kirchhoff rod theory. We analyse equilibria of a thin intrinsically curved elastic rod clamped at one end and touching a flat rigid wall, which is arbitrarily positioned and oriented in space. We distinguish four qualitatively different configuration types: 1) tip contact, 2) single point tangential contact, 3) two-point contact (the tip and a tangential point), 4) tip and interval contact. We present a series of diagrams revealing an arrangement of domains of those different contact types in a parameter space.

For process of fertilization to occur both in natural and in IVF conditions certain minimal amount of sperm cells are required. That minimal amount is species specific. Based on previous hypothesis in the oscillatory model of mammalian fertilization the theory of sperm penetration mechanism is proposed trough biomechanical model. In this model each sperm is consider as a material particle with certain mass, with three spherical coordinates, certain oocyte contact surface and velocity. In order to predict the penetration area on the surface of an oocyte an algorithm that calculates the maximum and minimum penetration forces of radial and tangential components of the force generated by the different sperm cells that influence the oocyte surface at the same time interval is generated.

We develop a geometrically exact theory for an elastic rod constrained to deform, under the action of end loads, on the surface of a torus. The theory is used to model the twist-bend instability of toroidal DNA condensates.

Biomolecular condensates formed by liquid-liquid phase separation allow cells to overcome various challenges in a relatively straightforward manner. Here we propose that cells use specialized condensates to reconstruct epigenetic information that is lost during replication. Chromatin itself plays an important role in the formation of these condensates through a mechanism called polymer-assisted condensation. Missing epigenetic tags are then placed back on the nucleosomes via special enzymes located inside the condensates. I present some unpublished computer simulations that show that this mechanism can work near optimally.