Seminars 2004-2005

January 25, 2005 3:30 - 4:30PM
Abstract

Having puzzled the scientists for decades, the problem of protein folding still remains a grand challenge of modern science. While it is a fundamental problem in biology, its solution requires knowledge beyond the traditional field of biology and has appealed research across many other disciplines including mathematics, computer science, physics, and chemistry. In this talk, I will discuss some computational approaches to protein folding including the minimum energy principle and the initial and boundary value problems for fold simulation. I will review some most recent results in the field and discuss related mathematical and computational issues.

January 31, 2005 3:30 - 4:30PM
Abstract

No abstract available. 

February 02, 2005 3:30 - 4:30PM
Abstract

A long-standing issue in statistical approaches to X-ray crystallography phase estimation is to solve a set of entropy maximization problems efficiently during the estimation. Each of these entropy maximization problems is a semi-infinite convex program and can be solved in a finite dual space by using a standard Newton method. However, the Newton method is too expensive since it requires O (n3) floating-point operations per iteration, where n corresponds to the number of the phases to be estimated. Other less expensive methods have been used but they cannot guarantee fast convergence. In this talk, I will describe a fast Newton method my colleagues and I have recently developed for solving the entropy maximization problems. The method uses the Sherman-Morrison-Woodbury Formula and the Fast Fourier Transform to compute the Newton step and requires only O (n log n) floating-point operations per iteration. On the other hand, it can converge in the same rate as the standard Newton. I will show how the method works and present some numerical results.

February 08, 2005 3:30 - 4:30PM
Abstract

Age-related slowing hypotheses were evaluated with 305 participants, ranging in age from 4 to 95 years. Various perception and motor tasks, including spontaneous and synchronize-continue tapping were employed to assess different models derived, respectively, from interval time and entrainment theory. Spontaneous motor tapping and judgments of preferred sequence tempi showed different age-related regions of preferred tapping, with younger participants favoring faster tempi than adults. Accuracy and variability of continuation tapping also varied systematically with age in a manner consistent with age-related slowing, especially in children. These findings were in accord with the entrainment hypothesis that people rely on preferred internal periods which change over the lifespan. This approach correctly predicts age-related changes in error and variability and leads to a modification of Weber's Law, the Restricted Weber Function.

February 28, 2005 3:30 - 4:30PM
Abstract

dentifying evolutionarily conserved blocks in orthologous genomic sequences is an effective way to detect regulatory elements. In this study, with the aim of elucidating the architecture of the regulatory network, we systematically estimated the degree of conservation of the upstream sequences of 3,750 human�mouse ortholoogue pairs along 8-kb stretches. We found that the genes with high upstream conservation are predominantly transcription factor (TF) genes. In particular, developmental process-related TF genes showed significantly higher conservation of the upstream sequences than other TF genes. Such extreme upstream conservation of the developmental process-related TF genes suggests that the regulatory networks involved with developmental processes have been evolutionarily well conserved in both human and mouse lineages.


Work done in collaboration with Hisakazu Iwama and Takashi Gojobori.

March 17, 2005 10:30 - 11:30AM
Abstract

Phylogenetic trees are representations of the evolutionary history of groups of organisms. The leaves of these graphs represent biological species (or a higher level taxonomic unit) and the internal nodes are interpreted as hypothetical evolutionary ancestors. Although it was considered relevant only to taxonomic and evolutionary studies, phylogenetics is becoming a critical tool for numerous disciplines in biology and medicine, providing a unique organizing framework for biological variation and predictive analysis.


Several phylogenetic methods aim to find the optimal phylogenetic trees from the space of all possible trees, evaluating the hypotheses with an objective function. Thus, this combinatorial optimization problem (phylogenetic tree search) is compute bound and must be approached through heuristics for large and biologically interesting datasets. Large phylogenetic problems are of interest to biologists because they provide a rich context of phenotypes and genotypes. Here, I will approach the problem of analyzing datasets with large number of species (between several hundreds and several thousands) using recently developed tree search algorithms and diverse parallelization strategies using Beowulf clusters for parallel computing.

April 14, 2005 10:30 - 11:30AM
Abstract

Although in the broadly defined genetic algebra, multiplication suggests a forward direction from parents to progeny, when looking from the reverse direction, it also suggests to us a new algebraic structure - coalgebraic structure, which we call genetic coalgebras. It is not the dual coalgebraic structure and can be used in the construction of phylogenetic trees. Mathematically, to construct phylogenetic trees means we need to solve equations x^[n]=a, or x^(n)=a. It is generally impossible to solve these equations in algebras. However, we can solve them in coalgebras in the sense of tracing back for their ancestors. A thorough exploration of coalgebraic structure in genetics is apparently necessary. Here, we develop a theoretical framework of the coalgebraic structure of genetics. From biological viewpoint, we defined various fundamental concepts and examined their elementary properties that contain genetic significance. Mathematically, by genetic coalgebra, we mean any coalgebra that occurs in genetics. They are generally noncoassociative and without counit; and in the case of non-sex-linked inheritance, they are cocommutative. Each coalgebra with genetic realization has a baric property. We have also discussed the methods to construct new genetic coalgebras, including cocommutative duplication, the tensor product, linear combinations and the skew linear map, which allow us to describe complex genetic traits. We also put forward certain theorems that state the relationship between gametic coalgebra and gametic algebra. By Brower's theorem in topology, we prove the existence of equilibrium state for the in-evolution operator. (The paper is available http://math.asu.edu/~mbe/, Vol.1, 2. pp.243-266)


Note: Joint work with Bai-Lian Li, Department of Botany and Plant Sciences, University of California, Riverside.

April 28, 2005 10:30 - 11:30AM
Abstract

The form of the amino acid (AA) table, and the relationship between genotype and phenotype that it implies, are at the basis of all processes of evolution. We have developed a network view of the AA table in which every codon is a node and every edge is a mutation. We have used the measures this view generates to study the process of affinity maturation in the immune reaction. In this enclosed process of selection, B lymphocytes triggered by a pathogen undergo rapid mutation, proliferation and death over a short period of time. This process leads to the selection of those cells which produce high affinity receptors to the pathogen. Due to the short time scale we expect the process to be dependent on the connectivity of the AA network. We looked at the germline DNA of two light chain types that undergo mutation and selection, and as a control at CD8 - a light chain homologue that does not mutate. Our results suggest three new ideas about selection: First, the chemical properties shared by groups of AA (i.e. "traits") and the potential to change them are a meaningful signal for selection. Second, we found that while all light chains have evolved to generate variable progeny under high rates of mutation. k and l gene families differ in the extent to which they will risk their potential viability. Finally, the existence of a transition bias in mutations means that not all movements on the AA network are equal, dividing it into Transition Neighborhoods, the codons of which tend to mutate into each other. We have found an over expression of codons belonging to a single neighborhood in those regions of the light chain that contact antigen. This is another method to balance viability and variability as it constrains the extent to which mutations will change the structure of the light chain.

December 31, 1969 7:00 - 7:00PM
Abstract

The form of the amino acid (AA) table, and the relationship between genotype and phenotype that it implies, are at the basis of all processes of evolution. We have developed a network view of the AA table in which every codon is a node and every edge is a mutation. We have used the measures this view generates to study the process of affinity maturation in the immune reaction. In this enclosed process of selection, B lymphocytes triggered by a pathogen undergo rapid mutation, proliferation and death over a short period of time. This process leads to the selection of those cells which produce high affinity receptors to the pathogen. Due to the short time scale we expect the process to be dependent on the connectivity of the AA network. We looked at the germline DNA of two light chain types that undergo mutation and selection, and as a control at CD8 - a light chain homologue that does not mutate. Our results suggest three new ideas about selection: First, the chemical properties shared by groups of AA (i.e. "traits") and the potential to change them are a meaningful signal for selection. Second, we found that while all light chains have evolved to generate variable progeny under high rates of mutation. k and l gene families differ in the extent to which they will risk their potential viability. Finally, the existence of a transition bias in mutations means that not all movements on the AA network are equal, dividing it into Transition Neighborhoods, the codons of which tend to mutate into each other. We have found an over expression of codons belonging to a single neighborhood in those regions of the light chain that contact antigen. This is another method to balance viability and variability as it constrains the extent to which mutations will change the structure of the light chain.

May 05, 2005 10:30 - 11:30AM
Abstract

Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that assign different cell fates at different concentrations. One of the central questions in cell and developmental biology is to identify mechanisms by which the morphogen gradient systems might achieve robustness to ensure reproducible embryonic patterns despite genetic or environmental fluctuations.


Recently, through computations and analysis of various bio-chemical models and examination of old and new experimental data, we found a set of of new mechanisms for enhancing robustness of cell-cell signaling through non-signaling cell surface molecules (e.g., HSPG). In addition, we examined the roles of diffusive ligands (e.g., Sog) on the formation and robustness of BMP (Bone Morphogenetic Protein) gradients in the Drosophila embryo. In this talk, I shall also discuss some mathematical and computational challenges associated with such study, and present a new class of numerical algorithms for reaction-diffusion equations arising from biological models.

December 31, 1969 7:00 - 7:00PM
Abstract

Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that assign different cell fates at different concentrations. One of the central questions in cell and developmental biology is to identify mechanisms by which the morphogen gradient systems might achieve robustness to ensure reproducible embryonic patterns despite genetic or environmental fluctuations.


Recently, through computations and analysis of various bio-chemical models and examination of old and new experimental data, we found a set of of new mechanisms for enhancing robustness of cell-cell signaling through non-signaling cell surface molecules (e.g., HSPG). In addition, we examined the roles of diffusive ligands (e.g., Sog) on the formation and robustness of BMP (Bone Morphogenetic Protein) gradients in the Drosophila embryo. In this talk, I shall also discuss some mathematical and computational challenges associated with such study, and present a new class of numerical algorithms for reaction-diffusion equations arising from biological models.

December 31, 1969 7:00 - 7:00PM
Abstract

Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that assign different cell fates at different concentrations. One of the central questions in cell and developmental biology is to identify mechanisms by which the morphogen gradient systems might achieve robustness to ensure reproducible embryonic patterns despite genetic or environmental fluctuations.


Recently, through computations and analysis of various bio-chemical models and examination of old and new experimental data, we found a set of of new mechanisms for enhancing robustness of cell-cell signaling through non-signaling cell surface molecules (e.g., HSPG). In addition, we examined the roles of diffusive ligands (e.g., Sog) on the formation and robustness of BMP (Bone Morphogenetic Protein) gradients in the Drosophila embryo. In this talk, I shall also discuss some mathematical and computational challenges associated with such study, and present a new class of numerical algorithms for reaction-diffusion equations arising from biological models.

May 24, 2005 3:30 - 4:30PM
Abstract

The Weibull distribution is used to model the vertical distribution of insects under the following activities: natural flight without any artificial stimulus, resting behaviour, and response to trapping involving colour attractants and odour baits. Formulae are derived for determining the mean heights at which insect flight, resting and trapping tend to occur. The model is tested on data from three sources: coleoptera in natural flight over Tallulah, Louisiana; Glossina palpalis palpalis at rest during the dry season in Nigeria; and catches of Glossina spp., in Rwanda, by traps placed at varying heights above the ground. Results show that different species of insects tend to fly, rest or be trapped at heights which are characteristic of the species.

December 31, 1969 7:00 - 7:00PM
Abstract

The Weibull distribution is used to model the vertical distribution of insects under the following activities: natural flight without any artificial stimulus, resting behaviour, and response to trapping involving colour attractants and odour baits. Formulae are derived for determining the mean heights at which insect flight, resting and trapping tend to occur. The model is tested on data from three sources: coleoptera in natural flight over Tallulah, Louisiana; Glossina palpalis palpalis at rest during the dry season in Nigeria; and catches of Glossina spp., in Rwanda, by traps placed at varying heights above the ground. Results show that different species of insects tend to fly, rest or be trapped at heights which are characteristic of the species.

May 24, 2005 11:00 - 12:00PM
Abstract

The typical large scale behavior of an asymmetric particle system is described by a Hamilton-Jacobi equation, in the sense that the random evolution converges to a deterministic solution of such an equation in a space-time scaling limit. This talk describes such limits and the fluctuations from the limit.


It turns out that for asymmetric systems dynamical noise occurs at a scale smaller than the diffusive scale that is common in central limit type results. Specific models from the field of interacting particle systems discussed here are the exclusion process, Hammersley's process, independent random walks, and the random average process.

May 26, 2005 10:30 - 11:30AM
Abstract

Cardiovascular medicine has witnessed tremendous advances in last few years thanks to high-resolution, multidimensional noninvasive technology. Subha V. Raman, MD, MS will provide an overview of recent advances in these fields particularly as they relate to novel approaches in the diagnosis and treatment of cardiovascular disease. Her research efforts involve clinical applications as well technology development drawing on her expertise in cardiovascular medicine and electrical engineering. She will dicuss some of her work in image analysis and discuss some of the computational and technical challenges that require interdisciplinary solutions to facilitate transfer of technological advances to better patient care.

December 31, 1969 7:00 - 7:00PM
Abstract

Cardiovascular medicine has witnessed tremendous advances in last few years thanks to high-resolution, multidimensional noninvasive technology. Subha V. Raman, MD, MS will provide an overview of recent advances in these fields particularly as they relate to novel approaches in the diagnosis and treatment of cardiovascular disease. Her research efforts involve clinical applications as well technology development drawing on her expertise in cardiovascular medicine and electrical engineering. She will dicuss some of her work in image analysis and discuss some of the computational and technical challenges that require interdisciplinary solutions to facilitate transfer of technological advances to better patient care.

June 10, 2005 11:00 - 12:00PM
Abstract

We study the role of cross-diffusion in the existence of spatially non-constant periodic solutions for a Lotka-Volterra competition system for three species. We will show that by choosing cross-diffusion coefficients in a cyclic way Hopf-bifurcation may arise. We characterize the stability of these solutions when the cross diffusion coefficients are small or large compared with the competition coefficients.

December 31, 1969 7:00 - 7:00PM
Abstract

We study the role of cross-diffusion in the existence of spatially non-constant periodic solutions for a Lotka-Volterra competition system for three species. We will show that by choosing cross-diffusion coefficients in a cyclic way Hopf-bifurcation may arise. We characterize the stability of these solutions when the cross diffusion coefficients are small or large compared with the competition coefficients.

June 23, 2005 10:00 - 11:00AM
Abstract

Imaging of the heart has proven to be one of the most challenging applications of MRI technology. MR data acquisition typically takes on the order of seconds to minutes to obtain high resolution images. Irregular cardiac and respiratory motion during this period can give rise to significant artifacts and can render images non-diagnostic. A number of different strategies have evolved to synchronize MR image acquistion with physiological motion. More recently, imaging times have been reduced to under 100msec, fast enough to freeze most physiological motion and permit real-time imaging without cardiac or respiratory synchronization. Strategies for physiological synchronization and real-time MRI will be reviewed in the presentation.

June 29, 2005 10:30 - 11:30AM
Abstract

An overview will be given of recent research of the speaker on problems in the theory of DNA elasticity and the regulation of gene expression. A brief outline of the theory of the elastic rod model for DNA will focus on methods for solving the equations of mechanical equilibrium in cases when self-contact is present and on conditions for determining the stability of equilibrium configurations. Majority of the talk will be concerned with applications of a base pair level theory of DNA elasticity that enables one to incorporate the effects of nucleotide composition and negative charge of DNA in mesoscale modeling of complex protein DNA assemblies. Examples include models of the Lac repressor mediated DNA loop and the Class I CAP dependent transcription activation complex, which are well supported by available data and yield experimentally verifiable conclusions about the influence of DNA deformability on the mechanism of regulation of the Lac operon by LacR and CAP. The talk will conclude with a discussion of the implications of obtained results for the role of DNA deformability in regulation of transcription.