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Mathematics & Statistics

(Leader: Prof. Greg McColm)

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The Usefulness of Simulating DNA Evolution in Understanding Problems in Phylogeny

Jim Garey

Biology Department, USF

1:00pm-2:00pm

SCA 202

**Abstract**

TBA

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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

Michael Barber

Biochemistry and Molecular Biology Department, USF

1:00pm-2:00pm

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.

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Complexities in the Calculations for and Representation of Some Simple Properties of the Liquid Phase

Venkat R. Bhethanabotla

Chemical Engineering Department, USF

1:00pm-2:00pm

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 PadÃ© 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 axisymmetric models of HGO and a much more realistic model for \(\mathrm{CO}_2\). 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.

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Black-Scholes Equations and Solutions in Mathematical Finance

Yuncheng You

1:00pm-2:00pm

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 has played 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.

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The Role of Feedbacks in Community Networks

Gary Huxel

Biology Department, USF

1:00pm-2:00pm

SCA 202

**Abstract**

This talk will be on systems of differential equations and the limitations of current food web models.

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Crystal Engineering of Nanoscale Structures

Mike Zaworotko and Brian Moulton

Chemistry Department, USF

1:00pm-2:00pm

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.