Complex Systems: Mathematics, Computation & Science
(Leader: Prof. Greg McColm)
Wednesday, April 23, 2003
| Title |
The Usefulness of Simulating DNA Evolution in Understanding
Problems in Phylogeny |
| Speaker |
Professor Jim Garey
Department of Biology |
| Time |
1:00-2:00 p.m. |
| Place |
SCA 202 |
Wednesday, April 9, 2003
| Title |
What do amino acids do when they're at home? Combining bioinformatics
and proteomics to define residue roles in cytochrome b5 reductase: A member
of the FNR superfamily |
| Speaker |
Professor Michael Barber
Department of Biochemistry and Molecular Biology |
| Time |
1:00-2:00 p.m. |
| Place |
SCA 202 |
Abstract
The combination of genomics, proteomics and bioinformatics have resulted in
a rapid expansion of our insight into amino acid sequence motifs that are characteristic
of various protein families and have specific roles in protein structure and
function.
Cytochrome b5 reductase, a vital component enzyme of the microsomal electron
transport system and erythrocyte function, catalyzes the transfer of reducing
equivalents from the reduced pyridine dinucleotide, NADH, to two molecules of
the small heme-containing protein, cytochrome b5. Cytochrome b5 reductase participates
in a diverse array of metabolic transformations that include the desaturation
and elongation of fatty acids, specific P450-mediated hydroxylation reactions,
cholesterol biosynthesis and methemoglobin reduction.
Both sequence and structural analyses have demonstrated cytochrome b5 reductase
to be a member of the ferredoxin:NADP+ reductase family of flavoprotein oxidoreductases.
Members of this family retain four primary sequence motifs that are involved
in either FAD/FMN or NAD(P)H binding and are required for functionality. Using
a recombinant form of R. norvegicus cytochrome b5 reductase as a model system,
bioinformatics, site-directed mutagenesis and structural biology have been combined
to identify the functional roles of specific flavin- or pyridine nucleotide-binding
sequence motifs. In addition, studies of amino acid residues that have been
altered in forms of the enzyme responsible for recessive congenital methemoglobinemia
have provided the first explanation for the cause of this disease at the atomic
level.
Wednesday, March 26, 2003
| Title |
Complexities in the Calculations for and Representation of
Some Simple Properties of the Liquid Phase |
| Speaker |
Professor Venkat R. Bhethanabotla
Department of Chemical Engineering |
| Time |
1:00-2:00 p.m. |
| Place |
SCA 202 |
Abstract
Systematic approximations to the (1) compressibility equation of state for
classical liquids via the virial expansion (2) pair correlation function and
(3) triplet correlation function will be considered in this presentation. The
current status of my calculations for each of these properties will be presented,
and help sought from the mathematicians in the audience for proceeding further.
All these calculations pertain to axially symmetric molecules.
First, a simple hard-body model for axially symmetric molecules, the Hard Gaussian
Overlap (HGO) model, will be introduced. This model allows for representation
of both prolate and oblate bodies and is efficient in calculations. Monte Carlo
estimates of the virial coefficients up to the sixth will be presented for values
of the aspect ratio that ranges from small molecules to liquid crystals. Padé
approximants to the pressure and residual Helmholtz energy will be constructed
in an attempt to achieve a compact equation of state for such axi-symmetric
systems. Unexpected singularities that arise in the attempt at such a representation
will be discussed, which make the desired representation difficult. Comparison
with limited Monte Carlo simulation data for small aspect ratios shows that
the Padé approximants are reasonable. Calculations for the higher, seventh and
eigth virals would allow for better approximations, however, my difficulties
in finding all the unlabelled blocks for 7 and 8 vertices (blocks are simple
graphs with connectivity 2, which arise in the graphical representation of the
contributing integrals to the virial coefficients), are holding up such calculations.
These calculations are useful in careful representations of the properties of
liquids such as in the thermodynamic tables published by NIST. They are also
useful in the representation of the isotropic phase properties of liquid crystals,
which are needed for theories of the liquid crystal phase transitions.
Related Monte Carlo techniques will be presented to estimate the coefficients
of the density expansion of the pair correlation function for the HGO model,
which are in turn represented as expansions in an orthonormal basis set, the
spherical harmonics. Results of these calculations have been used by colleagues
in multiple scattering calculations from random media.
A spherical harmonic expansion of the static triplet correlation function will
be presented along with a representation of this function utilizing spherical
perimetric coordinates. An extended superposition approximation (ESA) will be
presented and evaluated for certain parts of the triplet correlation function,
for the axi-symmetric models of HGO and a much more realistic model for CO2.
Molecular dynamics and Monte Carlo simulated triplet correlation functions for
the dense fluid state will be utilized to evaluate the extended ESA and convergence
of the expansion will be considered, both for the simulated data and for the
ESA. Accurate representation of the triplet correlation function allows for
estimation of three-body energy contributions, and evaluation of the ESA allows
for the validation of the closure of the Born-Green-Yvon hierarchy in theories
of the liquid state. The slow convergence of the spherical harmonic expansion
will be brought up for discussion.
Wednesday, February 19, 2003
| Title |
Black-Scholes Equations and Solutions in Mathematical Finance |
| Speaker |
Professor Yuncheng You |
| Time |
1:00-2:00 p.m. |
| Place |
SCA 202 |
Abstract
The Black-Scholes equation was first drafted by F. Black, M. Scholes, and R.
Merton in 1969 and was officially published in 1973. Later in 1997, M. Scholes
and R. Merton received the Nobel Prize for Economics as an award on this work.
(Fisher Black died in 1995). As the 10/15/97 New York Times commented, it was
a breakthrough and plays a profound role in the explosive growth in financial
markets since the 1970's. In this talk, we shall take the PDE approach to derive
this BSE along with some generalizations and find the explicit solutions. We
shall briefly comment on some applications to the arbitarge-based pricing theory
of derivative securities in finance.
Wednesday, February 5, 2003
| Title |
The Role of Feedbacks in Community Networks |
| Speaker |
Professor Gary Huxel
Department of Biology |
| Time |
1:00-2:00 p.m. |
| Place |
SCA 202 |
Abstract
This talk will be on systems of differential equations and the limitations
of current food web models.
Wednesday, January 22, 2003
| Title |
Crystal Engineering of Nanoscale Structures |
| Speaker |
Professor Mike Zaworotko and Brian Moulton
Department of Chemistry |
| Time |
1:00-2:00 p.m. |
| Place |
SCA 202 |
Abstract
Chemists can use solid-state architecture to design new structures without
developing new molecular structures. We focus on the self-assembly of known
molecules or ions, the geometries of the components and the topologies of the
networks thus generated.
This seminar will meet on alternate Wednesdays at 1:00 p.m. in SCA 202, beginning
January 22nd. A more complete schedule of talks will appear soon.