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Mathematics of Molecular and Cellular Biology
Seminar

September 12, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Marcia Oliveira Fenley
(Department of Physics and Institute of Molecular Biophysics, Florida State University)

**Revisiting the salt dependence of the drug-DNA association
process: A Poisson-Boltzmann analysis**

Abstract: The proper modeling of
salt-mediated electrostatic interactions is essential in order
to correctly account for the energetics of a variety of
biological processes involving nucleic acids since they are
highly charged polyelectrolytes. Due to the high charge density
of nucleic acids, ions in the solution will condense around
them. This “counterion cloud” that surrounds nucleic acids,
which is not captured with structural techniques such as X-ray
crystallography and NMR, is an integral part of their
structure and essential to maintain their stability. Given this
unique highly charged polyelectrolyte nature of nucleic acids
it is not surprising that small changes in salt concentration
can greatly affect its association with charged ligands (e.g.,
cationic drugs). Here, we examine the salt dependence of the
association of more than 40 cationic minor groove antibiotics
to AT-rich DNAs, for many of which thermodynamic binding data
is available, using a novel implicit solvent-based
Poisson-Boltzmann algorithm. We find that the plots of the
electrostatic binding free energy versus the logarithm of salt
concentration are linear, based on both the linear and
nonlinear Poisson-Boltzmann equation. The slopes of these
curves can be directly compared with experimental thermodynamic
data of the observed binding constant at various salt
concentrations. The good agreement between experimental and
Poisson-Boltzmann predictions is only possible if the full
nonlinear Poisson-Boltzmann equation is employed, since the
linear PBE overestimates the slope of the plots of the
electrostatic binding free energies vs. the logarithm of salt
concentration. Thus, our results suggest that one should not
employ the linear Poisson-Boltzmann or Generalized Born
approach in order to assess the salt dependent behavior of
nucleic acids. Further experimental and implicit solvent-based
computational studies should be performed in order to verify if
indeed the linear PBE always overestimates the salt dependence
of the binding energetics of charged ligand-nucleic acid
complexes.

September 26, 2007, 11:15 am-12:15 pm,
Lind Hall
409

F. Javier Arsuaga
(Department of Mathematics, San Francisco State
University)

http://math.sfsu.edu/arsuaga/

**Quantitative analysis of radiation induced chromosome
aberrations **

Abstract:
Chromosome aberrations are large-scale illegitimate
rearrangements of the genome. They are indicative of DNA damage
and of disease and are informative of nuclear architecture and
of DNA damage processing pathways. In this talk I will present
our mathematical approaches to analyze multiplex fluorescent in
situ hybridization (mFISH)assays.

October 3, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Kenneth C. Millett
(Department of Mathematics, University of California, Santa
Barbara)

http://www.math.ucsb.edu/~millett/KM.html

**The shape of knots**

Abstract: What do the knots that occur in natural
macromolecules look like? What about those arising in random
equilateral spatial polygons such as those used to model DNA or
polymers? The asphericity is a number between 1.0 and 0.0 that
measures the degree to which the ellipsoid of inertia is more
like a sausage (near 1.0), a rugby ball (near 0.5) or, a soccer
ball (near 0.0). An analogous measure, the spatial asphericity,
is defined by considering the smallest ellipsoid containing the
knot. Computer simulations and examples of proteins will be
used to illustrate these measures. Via the simulations, we
will consider the influence of constrained topology on these
measures in comparison to the unconstrained averages. In a
continuation of earlier research, we will look at the
equilibrium lengths defined by the asphericity, the lengths at
with the constrained and unconstrained have equal values, and
compare these with those determined earlier. We present
computer simulations to examine the differences between the
average asphericity of polygons with constrained and
unconstrained topology.

October 10, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Christine E. Heitsch
(School of Mathematics, Georgia Institute of Technology)

http://www.math.gatech.edu/~heitsch

**Combinatorics of RNA secondary structures**

Abstract:
Under a suitable abstraction, complex biological problems can
reveal
surprising mathematical structure. For instance, the planar
self-bonding,
or nested "secondary structure," of an RNA molecule is nicely
represented
by a plane tree. Under our plane tree model of RNA folding, we
prove
combinatorial theorems which yield insight into the coding of
structural
and functional information in RNA sequences. One result
demonstrates
the importance of local constraints in specifying a global
structure
while another characterizes the degree of branching in minimal
energy
configurations. Additionally, by transitioning between RNA
configurations
by an appropriate local move, we obtain an isomorphism with the
lattice
of noncrossing partitions. Thus, the interaction between
combinatorics
and molecular biology motivates new combinatorial theorems as
well as
advancing biological applications.

October 17, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Shi-Jie Chen
(Department of Physics, University of Missouri)

http://www.biochem.missouri.edu/schen.php

**RNA Folding Energy Landscapes in mRNA splicing**

Abstract: We develop a
statistical mechanical model for RNA/RNA complexes with both
intramolecular and intermolecular interactions. As an
application of the model, we compute the free energy
landscapes, which give the full distribution for all the
possible conformations for spliceosomal snRNA complexes.
Different snRNA experiments found contrasting structures, our
free energy landscape theory shows why these structures emerge
and how they compete with each other. In addition, the energy
landscapes suggest possible mechanisms for the conformational
switches in splicing. The change of the energy landscape shape
gives information about the conformational changes. We find
multiple (native-like and misfolded) intermediates formed
through base-pairing rearrangements in snRNA complexes.
Furthermore, the energy landscape gives the stabilities of all
the possible (functional) intermediates and such information is
directly related to splicing efficiency.

October 24, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Marcia Oliveira Fenley
(Department of Physics and Institute of Molecular Biophysics, Florida State University)

**The role of anionic residues on
the salt dependence of the binding of aminoacyl-tRNA
synthetases to tRNA: A Poisson-Boltzmann analysis**

Abstract:
October 26, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Mariel Vazquez
(Mathematics Department, San Francisco State University)

http://math.sfsu.edu/vazquez

**Modeling DNA unknotting by type II topoisomerases**

Abstract: Type II topoisomerases simplify DNA knots and links efficiently by performing strand-passage on DNA strands. Experimental studies have shown that these enzymes simplify the topology of DNA below thermodynamical equilibrium, however the key behind their efficiency is yet to be revealed. Motivated by these experimental observations, we study random transitions of knotted polygonal chains of fixed length. We use Monte Carlo computer simulations and computational knot theory methods to model strand-passage, with and without topological biases, on the knotted chains and to identify the resulting knotting probabilities.

This project is funded by NIH MBRS SCORE grant S06 GM052588.

November 7, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Timothy Newman
(Department of Physics, Arizona State University)

http://phy.asu.edu/biodyn/newman.htm

**Strong fluctuations and cycling in biological systems**

Abstract: In this talk I describe
a mechanism for generating cycles in a large
class of "mesoscale" biological populations (meaning
populations
composed of thousands to tens of thousands of units). Cycles
are caused
by a resonant amplification of the system dynamics triggered
by internal
noise. I will discuss this mechanism in the context of two
classes of
simple systems: ecological (e.g. predator-prey, host-
pathogen) and
biochemical (e.g. small gene regulation networks,
modules of metabolic processes).

November 14, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Gilad Lerman
(School of Mathematics, University of Minnesota)

http://www.math.umn.edu/~lerman/

**Defining functional distance using manifold embeddings of
gene ontology annotations**

ppt

Abstract: Although rigorous measures of similarity for sequence and structure are now well established, the problem of defining functional relationships has been particularly daunting. Here, we present several manifold embedding techniques to compute distances between Gene Ontology (GO) functional annotations and consequently estimate functional distances between protein domains. To evaluate accuracy, we correlate the functional distance to the well established measures of sequence, structural, and phylogenetic similarities. Finally, we show that manual classification of structures into folds and superfamilies is mirrored by proximity in the newly defined function space. We show how functional distances place structure-function relationships in biological context resulting in insight into divergent and convergent evolution. Our methods and results can be readily generalized and applied to a wide array of biologically relevant investigations, such as accuracy of annotation transference, the relationship between sequence, structure, and function, or coherence of expression modules.

This work is joint work Boris Shakhnovich and described in
http://www.pnas.org/cgi/reprint/0702965104v1.

November 28, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Debra Knisley
(2007-2008 New Directions Visiting Professor, IMA)

http://www.etsu.edu/math/knisleyd/dknisley.htm

**Graphical invariants and topological indices as biomolecular
descriptors**

Abstract: A number of molecular
descriptors of small molecules are derived from graphical
representations of the molecule. These descriptors, sometimes
called topological indices, are used to identify or relate the
structure of a molecule with expected bioactivity and they are
an essential tool in the drug design industry. It is generally
accepted that these molecular descriptors are not applicable to
macromolecules. However, topological indices are equivalent to
graphical invariants in graph theory. Graph theory offers a
wealth of graphical invariants annotated with structural
implications, primarily for large graphs. Thus we consider
applying known graphical measures to quantify macromolecules,
including secondary RNA structures, amino acids and several
families of proteins.

December 5, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Zhijun Wu
(Department of Mathematics, Iowa State University)

http://orion.math.iastate.edu/wu/

**The solution of the boundary-value problems
for the simulation of transitions of protein conformations**

Abstract: Under certain kinetic
or thermodynamic conditions,
proteins make conformational transitions, resulting in
significant
functional variations. Such dynamic properties can be studied
through molecular dynamics simulation. However, in contrast to
conventional dynamics simulation protocols where an
initial-value
problem is solved, the simulation of transitions of protein
conformations can be done by solving a boundary-value problem,
with the beginning and ending states of the protein as the
boundary
conditions. While a boundary-value problem is more difficult
to solve in general, it provides a more realistic model
for the study of protein conformational transitions and has
certain
computational advantages as well, especially for large scale
simulations. Here we study the solution of the boundary-value
problems
for the simulation of transitions of protein conformations
using a standard class of numerical methods called the multiple
shooting methods. We describe the methods and discuss the
issues
related to their implementations for our specific applications,
including the definition of the boundary conditions, the
formation
of the initial trajectories, and the convergence of the
solutions.
We present the results from using the multiple shooting
methods for the study of conformational transitions of a small
molecular cluster and an alanine dipeptide, and show the
potential
extension of the methods to larger biomolecular systems.

December 12, 2007, 11:15 am-12:15 pm,
Lind Hall
409

Soojeong Kim
(Department of Mathematics, University of Iowa)

http://www.math.uiowa.edu/~soojkim/

**Topological analysis of DNA-protein complexes**

Abstract: Difference topology is a methodology to derive the number of DNA crossings trapped in an unknown protein complex. By this method, Pathania, Jayaram, and Harshey revealed the topological structure within the Mu protein complex which consisted of three DNA segments containing five nodes [1]. In their experiments, they used a member of the site-specific recombinases which is known as Cre. Cre mediates DNA exchange by rearranging target sites of the DNA segments. During this DNA recombination, there are no extra DNA crossings introduced. The initial DNA conformation is unknotted. After Cre recombination, the products are knots or catenanes. Recently, Darcy, Luecke, and Vazquez analyzed these experimental results and proved that the five-noded conformation is the only biologically reasonable structure of the Mu protein DNA complex [2]. We address the possibility of protein complexes that binds four DNA segments. By the useful property of Cre, we can make the assumption that after Cre recombination, the topology of a DNA-protein complex would be a knot or catenane. The latest results of the topological tangle model for this case and very basic biological and mathematical backgrounds will be discussed.

Reference:

[1] S. Pathania, M. Jayaram, and R. Harshey, Path of DNA within the Mu transpososome: Transposase interaction bridging two Mu ends and the enhancer trap five DNA supercoils, Cell 109 (2002), 425-436.

[2] I. K. Darcy, J. Luecke, and M. Vazquez, A tangle analysis
of the Mu transpososome protein complex which binds three DNA
segments, Preprint.

January 9, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Zhijun Wu
(Department of Mathematics,
Program on Bioinformatics and Computational Biology,
Iowa State University)

http://orion.math.iastate.edu/wu/

**The solution of the distance
geometry problem for protein modeling**

Abstract: A well-known problem in
protein modeling is the determination of the structure of a
protein with a given set of inter-atomic or inter-residue
distances obtained from either physical experiments or
theoretical estimates. A general form of the problem is known
as the distance geometry problem in mathematics, the graph
embedding problem in computer science, and the multidimensional
scaling problem in statistics. The problem has applications in
many other scientific and engineering fields as well such as
sensor network localization, image recognition, and protein
classification. We describe the formulations and complexities
of the problem in its various forms, and introduce a geometric
buildup approach to the problem. Central to this approach is
the idea that the coordinates of the atoms in a protein can be
determined one atom at a time, with the distances from the
determined atoms to the undetermined ones. The determination of
each atom requires the solution of a small system of distance
equations, which can usually be obtained in constant time.
Therefore, in ideal cases, the coordinates of n atoms can be
determined by a geometric buildup algorithm with O(n) distances
in O(n) computing time instead of O(n2) distances in O(n2)
computing time as required by a conventional singular-value
decomposition algorithm. We present the general algorithm and
discuss the methods for controlling the propagation of the
numerical errors in the buildup process, for determining rigid
vs. unique structures, and for handling problems with inexact
distances (distances with errors). We show the results from
applying the algorithm to a set of model protein problems with
varying degrees of availability and accuracy of the distances
and justify the potential use of the algorithm in protein
modeling practice.

January 23, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Robert L. Jernigan
(Department of Biochemistry, Biophysics, and Molecular Biology,
Iowa State University)

http://ribosome.bb.iastate.edu/jernigan.html

**Analyzing the protein-protein interaction network**

Abstract: The abundant data available for protein interaction networks have not yet been fully understood. New types of analyses are needed to reveal organizational principles of these networks to investigate the details of functional and regulatory clusters of proteins. In the present work, individual clusters identified by an eigenmode analysis of the connectivity matrix of the protein-protein interaction network in yeast are investigated for possible functional relationships among the members of the cluster. With our functional clustering we have successfully predicted several new protein-protein interactions that indeed have been reported recently. Eigenmode analysis of the entire connectivity matrix yields both a global and a detailed view of the network. We have shown that the eigenmode clustering not only is guided by the number of proteins with which each protein interacts, but also leads to functional clustering that can be applied to predict new protein interactions.

Some other applications of this type of analysis for the
identification of important variable in a simulation will be
considered.

January 30, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Brigitte Servatius
(Department of Mathematics,
Worcester Polytechnic Institute)

http://users.wpi.edu/~bservat/

**Combinatorial rigidity and the molecular conjecture**

pdf

Abstract: Graph theory has
successfully been used by several authors to predict protein
flexibility, in particular, combinatorial rigidity is an
important tool. The most important new result in combinatorial
rigidity is the characterization of global rigidity while one
of the most intriguing open problems is called "the molecular
conjecture". We will explain the state of the art in the
progress toward the conjecture and the implications of recent
progress in rigidity theory, including the concept of
combinatorial allostery, toward understanding the behavior of
molecules.

February 6, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Roger Y. Lui
(Department of Mathematical Sciences,
Worcester Polytechnic Institute)

http://www.wpi.edu/Academics/Depts/Math/People/ryl.html

**Three topics in the mathematics of molecular and cellular
biology**

pdf ppt

Abstract: In this talk, I am
going to talk about protein folding,
biochemical network, and cell motility. I am an analyst by
training so
you are going to see a lot of equations in my talk. But I will
try to
make things easy to understand and enjoyable.

February 13, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Imre M. Janosi
(Department of Physics of Complex Systems,
Lorand Eotvos University,
Budapest, Hungary )

http://karman3.elte.hu/janosi/index.html

**Why is the microtubule lattice helical?
**

pdf ppt

Abstract:
Microtubules polymerize from identical tubulin heterodimers,
which form a helical lattice pattern for each known species.
This pattern always has left-handed chirality, but it is not
known why. Since tubulin, similar to other proteins, evolved
for a purpose, the question of the title of this talk appears
to be meaningful. In a computer simulation that explores the
â€˜counterfactual biologyâ€™ of microtubules without helicity,
we demonstrate that these have the same mechanical properties
as Natureâ€™s microtubules with helicity. Thus only a dynamical
reason for helicity is left as potential explanation. We
propose that helicity solves â€˜the problem of the blind
masonâ€™, i.e. how to correctly build a structure, guided only
by the shape of the bricks. This answer in turn raises some new
questions for researchers to address.

February 20, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Christopher J. Lee
(Department of Biochemistry,
University of California at Los Angeles)

http://www.uclaaccess.ucla.edu/UCLAACCESS/Web/Faculty.aspx?ri=434

**Mapping evolutionary pathways of HIV-1 drug resistance using
conditional selection pressure**

Abstract: Can genomics provide a
new level of strategic intelligence about rapidly evolving
pathogens? We have developed a new approach to measure the
rates of all possible evolutionary pathways in a genome, using
conditional Ka/Ks to estimate their "evolutionary velocity,"
and have applied this to several datasets, including clinical
sequencing of 50,000 HIV-1 samples. Conditional Ka/Ks predicts
the preferred order and relative rates of competing
evolutionary pathways. We recently tested this approach using
independent data generously provided by Shafer and coworkers
(Stanford HIV Database), in which multiple samples collected at
different times from each patient make it possible to track
which mutations occurred first during this time-course. Out of
35 such mutation pairs in protease and RT, conditional Ka/Ks
correctly predicted the experimentally observed order in 28
cases (p=0.00025). Conditional Ka/Ks data reveal specific
accessory mutations that greatly accelerate the evolution of
multi-drug resistance. Our analysis was highly reproducible in
four independent datasets, and can decipher a pathogen’s
evolutionary pathways to multi-drug resistance even while such
mutants are still rare. Analysis of samples from untreated
patients shows that these rapid evolutionary pathways are
specifically associated with drug treatment, and vanish in its
absence.

February 27, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Peter R. Kramer
(Department of Mathematical Sciences,
Rensselaer Polytechnic Institute)

http://www.math.rpi.edu/ms_faculty/profile/kramer_p.html

**Stochastic mathematical
and computational models in microbiology**

pdf

Abstract:
I shall discuss three areas of current research involving the
use of
stochastic methods for the physical modeling for microscopic
processes
in physiology. First, I exhibit a variation of the immersed
boundary
method designed, in joint work with Paul Atzberger (UCSB) and
Charles
Peskin (NYU) for simulating microbiological systems where
thermal
effects play a significant role, such as molecular motors, DNA
and
other polymer dynamics, and gel swelling. Statistical
mechanical
principles indicate that the thermal fluctuations should
manifest
themselves through a random force density in the fluid
component of
the immersed boundary equations. Secondly, I briefly review
the
mathematical procedure, currently being developed with Juan
Latorre
and Grigorios Pavliotis (Imperial), for coarse-graining
stochastic
molecular motor models. Finally, I shall discuss recent
explorations
with Adnan Khan (Lahore) and Shekhar Garde (Rensselaer,
Biochemical
Engineering) concerning the parameterization of a simple
stochastic
model for the behavior of water molecules near a solute surface
which
has the potential for improving substantially upon Brownian
dynamics
models more conventionally used in engineering applications.
We use
exactly solvable mathematical models as a testbed for
addressing some
basic data-driven parameterization issues.

March 19, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Peter R. Kramer
(Department of Mathematical Sciences,
Rensselaer Polytechnic Institute)

http://www.math.rpi.edu/ms_faculty/profile/kramer_p.html

**Stochastic mathematical
and computational models in microbiology (continued)**

pdf

Abstract:
I shall discuss three areas of current research involving the
use of
stochastic methods for the physical modeling for microscopic
processes
in physiology. First, I exhibit a variation of the immersed
boundary
method designed, in joint work with Paul Atzberger (UCSB) and
Charles
Peskin (NYU) for simulating microbiological systems where
thermal
effects play a significant role, such as molecular motors, DNA
and
other polymer dynamics, and gel swelling. Statistical
mechanical
principles indicate that the thermal fluctuations should
manifest
themselves through a random force density in the fluid
component of
the immersed boundary equations. Secondly, I briefly review
the
mathematical procedure, currently being developed with Juan
Latorre
and Grigorios Pavliotis (Imperial), for coarse-graining
stochastic
molecular motor models. Finally, I shall discuss recent
explorations
with Adnan Khan (Lahore) and Shekhar Garde (Rensselaer,
Biochemical
Engineering) concerning the parameterization of a simple
stochastic
model for the behavior of water molecules near a solute surface
which
has the potential for improving substantially upon Brownian
dynamics
models more conventionally used in engineering applications.
We use
exactly solvable mathematical models as a testbed for
addressing some
basic data-driven parameterization issues.

March 26, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Robert Guy
(Department of Mathematics, University of Utah)

http://www.math.utah.edu/~guy/

**Modeling fibrin gel formation:
Continuous to discrete**

pdf

Abstract: Hemostasis is the
normal physiological response to blood
vessel injury and is essential to maintaining the integrity of
the
vascular system. It consists of two interacting processes:
platelet
aggregation and coagulation. The first involves cell-cell
adhesion
resulting in a platelet aggregate, and the second involves an
enzyme
network that leads to the formation of a fibrin gel. Though
both
processes contribute to the formation of blood clots, those
formed at
high shear rates are composed primarily of platelets and clots
formed
at low shear rates are composed predominantly of fibrin gel.
In order
to understand this phenomenon, a simple mathematical model of
chemically-induced monomer production, polymerization, and
gelation
under shear flow is presented. The model is used to explore
how the
shear rate and other parameters control the formation of fibrin
gel.
The results show that the thrombin inhibition rate, the gel
permeability, and the shear rate are key parameters in
regulating the
height of the clot. Experiments show that the gel permeability
depends on the chemical environment in which it was made.
However,
the reasons for these structural differences are unclear.
Discrete,
Monte Carlo simulations of fibrin polymerization are used to
explore
what factors determine the microstructure of the gel.

April 2, 2008, 11:15 am-12:15 pm
Lind Hall
409

Jeff Randall Knisley
(Department of Mathematics, East Tennessee State University)

http://www.etsu.edu/math/jknisley.htm

**From neurons to neural networks**

pdf ppt

Abstract: Artificial Neural
Networks (ANN's) are machine-learning algorithms that are often
used as classifiers in molecular and computational biology.
Originally, ANN's were inspired by in vivo models of axonal and
dendritic neuro-electric activity, especially the classical
models of Hodkgin, Huxley, and others. Much of the successive
development of ANN's, as well as the parallel development of
other approaches such as Support Vector Machines, has been as a
means of addressing issues such as overfitting and hard margins
which arise in machine learning applications. To address these
issues, ANN's have borrowed from a variety of sources in
computer science, physics, and cognitive psychology, but not so
much from the ever-improving neuronal models which provided
their initial inspiration. We will revisit much of the
historical and algorithmic development of ANN's, with the goal
being that of suggesting the types of ANN's that might be
inspired by more recent developments in dendritic electrotonic
models.

April 9, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Christodoulos A. Floudas
(Department of Chemicial Engineering, Princeton University)

http://titan.princeton.edu/

**Recent advances and challenges in deterministic global
optimization**

Abstract: In this presentation,
we will provide an overview of the
research progress in global optimization. The focus will be on
important contributions during the last five years, and will
provide a perspective for future research opportunities. The
overview will cover the areas of (a) twice continuously
differentiable constrained nonlinear optimization, and (b)
mixed-integer nonlinear optimization models. Subsequently, we
will present our recent fundamental advances in (i) convex
envelope results for multi-linear functions, (ii) a piecewise
quadratic convex underestimator for twice continuously
differentiable functions, (iii) the generalized alpha-BB
framework, (iv) our recently improved convex underestimation
techniques for univariate and multivariate functions, and (v)
generalized pooling problems. Computational studies will
illustrate the potential of these advances.

April 16, 2008, 11:45 am-12:45 pm
[note time change],
Lind Hall
409

Eric J. Rawdon
(Department of Mathematics, University of St. Thomas)

http://george.math.stthomas.edu/rawdon/

**Size and shape of polymers**

pdf

Abstract:
We use numerical simulations to investigate how chain length
and
knotting in freely fluctuating knotted polymer rings affect
their size
and shape. In particular, we find smallest containers, such as
rectangular boxes, spheres, and polyhedra, which contain the
simulated
polymers. Ideal knots, and their relationship to the
containers, also
will be discussed.

May 7, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Claudio Altafini
(SISSA-ISAS,
International School for Advanced Studies)

http://people.sissa.it/~altafini/

**Modeling the genome-wide transient response to stimuli in
yeast: adaptation through integral feedback**

Abstract: At the level of gene
expression, the response of yeast to various
types of stresses/perturbations is characterized by a
short-term
transient followed by a return to the basal level (adaptation).
A thorough investigation of the transient response to several
different stimuli shows a common modulation, functionally and
dynamically similar.
The adaptation that follows the transient excursion is modeled
by
means of an integral feedback, with the gene product
representing the
variable that is fed back.
The resulting linear system with input explains sufficiently
well the
different time constants observable in the transient response
while
being in agreement with the known experimental degradation
rates
measurements.

May 14, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Howard A. Levine
(Department of Mathematics, Iowa State University)

http://www.public.iastate.edu/~halevine/

**Some mathematical issues arising in single and
multiple target SELEX**

Abstract:

May 21, 2008, 11:15 am-12:15 pm,
Lind Hall
409

Sergei Fedotov
(School of Mathematics, The University of Manchester)

http://www.maths.manchester.ac.uk/~sf/

**Anomalous diffusion, tumor growth and random walk models**

Abstract: The theory of anomalous
diffusion is well-established and leads to the
integral equations or the alternative fractional diffusion
equations for
number densities.
Despite the progress in understanding the anomalous transport
most work has been concentrated on the passive density of the
particles,
and comparatively little is known about the interaction of non-
standard
transport with reactions. This work is intended to address this
issue by utilising the random walk techniques in order to model
the
anomalous diffusion with reactions. Example is the tumor's
cells migration and
proliferation (Phys. Rev. Lett. 98, 118101 (2007)).

June 4, 2008, 11:15 am-12:15 pm,
Lind Hall 409

Timothy
Newman (IMA and Arizona State University,
http://phy.asu.edu/faculty.php?name=tjnewman and Hans G.
Othmer (School of Mathematics, University of
Minnesota, http://www.math.umn.edu/~othmer/)

**Review and discussion of IMA workshop: Quantitative
approaches to cell motility and chemotaxis**

Abstract:
This Wednesday, we are planning to discuss topics and questions
arising from the recent IMA workshop on Quantitative Approaches
to Cell Motility and Chemotaxis. Everyone is welcome to attend
and take part. There will be no set agenda. Hans Othmer will
lead the discussion. Hans has asked that everyone attending
think over their experience at the workshop and distill
important issues and open questions.
Looking forward to seeing you this Wednesday at 11:15 in the
IMA seminar room.

June 10, 2008, 11:15 am-12:15 pm,
Lind Hall 409 [note Tuesday instead of
Wednesday]

Andrew M. Stein
(IMA postdoctoral associate)

http://www.ima.umn.edu/~astein/

**The micromechanics of 3d collagen gels**

Abstract: Collagen is the most
abundant animal protein and its mechanics have been studied in
great detai. It takes on many morphologies, including skin,
tendons, ligaments, individual fibers, and gels. Of particular
interest is the mechanics of collagen-I gels. These gels
provide a relatively simple structure that can be noninvasively
observed by confocal microscopy and used as a scaffold for
growing artificial tissues, and as a 3d environment for
studying cell motility and tumor invasion. A critical first
step in understanding these systems is to develop a model for
the collagen gel alone. In this paper we give a successful
theoretical model of the micromechanics of realistic networks.

June 18, 2008, 12:30 pm-1:30 pm,
Lind Hall 305 [note different room
and time]

Dirk Hartmann
(Center for Modelling and Simulation in the Biosciences
(BIOMS), Institut für Angewandte Mathematik)

http://www.hartmann.uni-hd.de/

**Single cell mechanics: Mechanics of membranes and
cytoskeletal networks**

Abstract: In this talk, I will first review existing theoretical approaches for mechanics of single cells. These are mainly determined by the membrane and the cytoskeleton. The most popular class of models among physicists are static models given in terms of energy functionals, e.g. the Canham-Helfrich energy modelling membrane mechanics or microscopic pseudo-spring / cable networks modelling cytoskeletal mechanics. On the other hand mathematicians often prefer to work in terms of continuous models based on conservation equations, e.g. the plate equation modelling mechanics of membranes on short length scales, a completely different class of models.

Considering mechanics of red blood cells, one of the most simplest cells, I will show how it is possible to link those different classes of models in a rigorous manner. Simulations of optical tweezers experiments based on finite element methods will be shown.