1:30 - 2:00 :
(Mathematics, University of Cincinnati)
-Title: Electrostatic effects on the supercoiling DNA
We investigate the effects of electrostatic and steric repulsion on the dynamics of pre-twisted circular DNA in a viscous incompressible fluid. The DNA is modeled as a charged elastic rod represented by a three-dimensional closed axial curve and orthonormal triads embedded in each cross-section. Equations of motion of the rod, which include the fluid-structure interaction, are solved by the generalized immersed boundary method combined with the Cosserrat theory of an elastic rod. We include a modified Debye-Huckel repulsive force in which the electrostatic force depends on the salt concentration and the distance between base pairs, and a close range steric repulsion force to prevent self-penetration. We find that after perturbation a pretwisted DNA circle collapses into a compact supercoiled configuration. The collapse proceeds along a complex trajectory that may pass near several equilibrium configurations of saddle type, before it settles in a locally stable equilibrium. The final configuration is sensitive to the initial excess link, ionic stregth of the solvent, and the initial perturbation.
2:00 - 2:30 :
(Mathematics, University of St. Thomas)
- Authors: Magdalena A. Stolarska
- Title: A model of cellular movement and its effect on substrate traction patterns
Mechanical interactions between a cell and the substrate are vital for cell migration and are involved in various cellular processes, such as wound healing, embryonic development, and metastasis of cancerous tumors. As a result, understanding the nature of force generation by single cells and the mechanical interaction of a cell with the substrate is extremely important, and mathematical models are being used in furthering this understanding. In this talk, we present a continuum model of the mechanics of single cell motility in which the stresses that result from the active deformation of the cell are transmitted to a deformable substrate via adhesion sites that are modeled as either fixed connections or frictional interaction between the cell and the substrate. A finite element implementation of this model is used to numerically examine the nature of the stresses generated by the cell and the resulting traction patterns that occur at the substrate. We use the model to better understand what are the local active deformation profiles and the adhesion types necessary to replicate experimentally observed motion and traction patterns of different cell types.
2:30 - 3:00 :
Liu, Di (Richard)
(Depatment of Mathematics, Michigan State Univeristy)
-Title: Numerical methods for stochastic bio-chemical reacting networks with multiple time scales
Multiscale and stochastic approaches play a crucial role in faithfully capturing the dynamical features and making insightful predictions of cellular reacting systems involving gene expression. Despite their accuracy, the standard stochastic simulation algorithms are necessarily inefficient for most of the realistic problems with a multiscale nature characterized by multiple time scales induced by widely disparate reactions rates. In this talk, I will discuss some recent progress on using asymptotic techniques for probability theory to simplify the complex networks and help to design efficient numerical schemes.
3:00 - 3:30 :
(Mathematics, University of Notre Dame)
-Authors: Eunjung Kim, Zhiliang Xu, and Mark Alber
-Title: Contributions of branching points to fibrin network strength and stability
-Abstract: Blood clots are primarily composed of a network of branched fibrin fibers. These fibrin networks stabilize the primary platelets and enable blood clots to withstand the blood flow during wound healing at sites of vascular injury. The structure of the network is believed to be an essential component to its function. In the present study, a three-dimensional mechanical model of a fibrin network was developed to determine the detailed relationship between the network structure and its mechanical properties. We compare the mechanical responses of the network for two distinct structures; high branching vs. low branching based on image analysis of in situ fibrin network data.