**1:30 - 2:00** :
Lim, Sookkyung
(Mathematics, University of Cincinnati)

-Title: **Electrostatic
effects on the supercoiling DNA**

-Abstract:

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** :
Stolarska, Magdalena
(Mathematics, University of St. Thomas)

- Authors: Magdalena A. Stolarska

- Title: ** A model of cellular movement and its effect on
substrate traction patterns**

- Abstract:

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**

-Abstract:

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** :
Kim, Eunjung
(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.