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Past MBI Seminars: 2004-2005
Wednesday, June 29, 10:30-11:30am
Thursday, June 23, 10:00-11:00am 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.
Friday,
June 10, 11:00am-12:00pm 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.
Thursday, May 26, 10:30-11:30am 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.
Tuesday, May 24, 3:30-4:30am 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.
Recruitment Talk Author: Qing Nie, Department
of Mathematics, Department of Biomedical Engineering, Center for
Complex Biological Systems, University of California, Irvine 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.
Thursday,
April 28, 10:30-11:30am 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.
MBI/Human Cancer Genetics System Biology Journal
Club The journal club will meet on Monday, 3:30-4:30 pm, MBI Lecture Hall (MA 240) on the following dates:
Thursday, April 14, 10:30-11:30am 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)
Thursday, March 24, 11:00am-12:00pm 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.
Friday, March 25, 11:00am-12:00pm This talk will concentrate on the fluctuation part of the general
picture given by Timo Seppalainen in the preceding talk. A class
of systems will be considered, including the exclusion process,
independent random walks, the zero range process, and a deposition
model. The fluctuation of the current of particles is computable
in the diffusive (i.e. square root of time-) scaling within this
class.
NOTE: We will be having lunch with Timo Seppalainen and Marton Balazs at the Faculty Club at 12:30. We will meet near the elevators of the Math Tower at 12:20. If you are interested in joining us, please email Firas Rassoul-Agha at firas@math.ohio-state.edu, before 10am of March 24th.
Thursday, March 17, 10:30-11:30am 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.
System Biology Journal Club
- February 28, 2005; 3:30-4:30pm Identifying 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 humanmouse 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.
Thursday, February 10, 10:30-11:30am In the last twenty years, coalescent theory has been developed
into a powerful analytical tool for population genetics. This theory
is especially significant with the rapid accumulation of DNA sequence
data. First formulation in the seminal work of Kingman in 1982,
coalescent theory offers various sample-based and highly efficient
statistical methods for analyzing molecular data such as DNA sequence
samples. Mathematically, coalescent theory studies stochastic processes
leading to the most recent common ancestor (MRCA) from a sample
under various coalescent models. If one thinks of the more commonly
studied branching processes as stochastic models of generating random
trees from their roots, coalescent processes can be viewed as the
inverse processes which recover random trees from their leaves.
In more elaborated versions crucial for population genetics, coalescent
processes are usually superimposed with mutation processes. These
mutation processes can be viewed as independent Poisson processes
running over the random trees generated by the coalescent processes
with the edge lengths of the random trees serving as the time scale
for the mutation processes. In our this research, we introduce a
colored coalescent process which recovers random colored genealogical
trees. Here a color genealogical tree has its vertices colored black
or white. Moving backward along the colored genealogical tree, the
color of vertices may change only when two vertice coalesce. The
rule that governs the change of color involves a parameter x. When
this parameter takes value of one half, the colored coalescent process
can be derived from a variant of the Wright-Fisher model for a haploid
population in population genetics. Explicit computations of the
expectation and the cumulative distribution function of the coalescent
time are carried out. For example, our calculation shows that when
x=1/2, for a sample of n colored individuals, the expected time
for the colored coalescent process to reach a black MRAC or a white
MRAC, respectively, is 3 - 2/n. On the other hand, the expected
time for the colored coalescent process to reach a MRAC, either
black or white, is 2 - 2/n, which is the same as that for the standard
Kingman coalescent process. This colored coalescent process with
a color mutation process superimposed is also studied in explicit
details. (The paper is available at arXiv:math.PR/0410514 v1)
Tuesday, February 8, 2005,
3:30-4:30pm 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.
Tuesday, February 1, 2005,
3:30-4:30pm 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.
January 31, 2005; 3:30-4:30pm
Tuesday, January 25, 2005,
3:30-4:30pm 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.
Micro RNA Genes in Normal and Disease State Wednesday,
January 19, 2005, 2:00pm-5:00pm Abstract - George Calin: Micro RNAs (miRNA genes) are a large family of highly conserved non-coding genes thought to be involved in temporal and tissue specific gene regulation. MiRs are transcribed as short hairpin precursors (~70nt) and are processed into active 21-22 nucleotides RNAs by Dicer, a ribonuclease that recognizes target mRNAs via base-pairing interactions. We reported that miR15a and miR16-1 are located at chromosome 13q14, a region deleted in more than half of B cell chronic lymphocytic leukemias (B-CLL), a disorder characterized by increased survival. Detailed deletion and expression analysis shows that miR15 and miR16 are located within a 30 kb region of loss in CLL and that both genes are deleted or down-regulated in the majority (approximately 68%) of CLL cases. To further investigate the possible involvement of miRNAs in human cancers on a genome-wide basis we have mapped 186 miRNAs and compared their location to the location of previous reported non-random genetic alterations. We show that miRNA genes are frequently located at fragile sites, as well as in minimal regions of loss of heterozygosity (minimal LOH), minimal regions of amplification (minimal amplicons), or common breakpoint regions. Overall, 98 of 186 (52.5%) of miR genes are in cancer-associated genomic regions (CAGR) or in fragile sites. Much more, by Northern blotting we have shown that several miRNAs located in deleted regions have low levels of expression in cancer samples. These data provide a catalogue of miRNA genes that may have roles in cancer and argue that the miRNome (defined as the full complement of miRNAs in a genome) may be extensively involved in cancers. Little is known about miRNA expression levels or function in normal and neoplastic cells. We identified, using genome-wide expression profiling of miRNAs with an oligonucleotide microarray, two distinct clusters of human B-CLL samples associated with the presence or the absence of Zap-70 expression, a predictor of early disease progression. Two miRNA signatures were associated with presence or absence of mutations in the expressed immunoglobulin variable-region genes or with deletions at 13q14 respectively. These data suggest that miRNA expression patterns have relevance to the biological and clinical behaviour of this leukemia.
Abstract - Chang-gong Liu: MicroRNAs (miRNAs) are a class of small non-coding RNA genes recently
found to be abnormally expressed in several types of cancer. We
described a novel methodology for miRNA gene expression profiling
based on the development of a microchip containing oligonucleotides
corresponding to 245 miRNAs from human and mouse genomes. Using
these microarrays, we obtained highly reproducible results that
revealed tissue-specific miRNA expression signatures, data confirmed
by assessment of expression by Northern blots, real-time PCR and
literature search. The microchip oligolibrary can be expanded to
include an increasing number of miRNAs discovered in various species,
and is useful for the analysis of normal and disease states.
Thursday, December 9, 10:30-11:30am Behind the phenomena of genetics and stochastic processes, we find there is an intrinsic algebraic structure. We call this algebraic structure --- evolution algebra. Evolution algebras are non-associative (non-power-associative) Banach algebras and have many connections with other mathematical fields including graph theory, group theory, Markov chains, dynamic systems, knot theory, 3-manifold and the study of the Riemann-zeta function. In the present talk, we will give the foundation of the theory of evolution algebras and establish a hierarchical structure theorem for evolution algebras. One of the unusual features of an evolution algebra is that it possesses an evolution operator. This evolution operator reveals the dynamic information of an evolution algebra. However, what makes the theory of evolution algebras different from the classical theory of algebras is that in an evolution algebra, we can have two different kinds of generators: algebraically persistent generators and algebraically transient generators. The basic notions of algebraic persistency and algebraic transiency, and their relative versions, lead to a hierarchical structure on an evolution algebra. Dynamically, this hierarchical structure displays the direction of the flow induced by the evolution operator. Algebraically, this hierarchical structure is given in the form of a sequence of semi-direct-sum decompositions of a general evolution algebra. Thus, this hierarchical structure demonstrates that an evolution algebra is a mixed algebraic and dynamic object. The algebraic nature of this hierarchical structure allows us to have a rough skeleton-shape classification of evolution algebras. On the other hand, the dynamic nature of this hierarchical structure is what makes the notion of an evolution algebra applicable to the study of stochastic processes and many other objects in different fields. For example, when we apply our structure theorem to evolution algebras induced by Markov chains, we see that any general Markov chain has a dynamic hierarchy and the probabilistic flow is moving with invariance on this hierarchy, and that all Markov chains can be classified by the skeleton-shape classification of their evolution algebras. There is a bunch of open problems in this direction.
Tuesday, December 7, 3:30-4:30pm Discovering meaningful patterns in the wealth of data produced by gene expression experiments and genome sequencing projects requires rigorous statistical methods. Multiple testing problems arise whenever one wishes to perform statistical tests for each of many genes or genomic regions. Identifying differently expressed genes from microarray experiments is a typical example. We have derived a general characterization of the null distribution for multiple testing that asymptotically controls type I error rates without conditions such as subset pivotality. This characterization is novel, because it utilizes the distribution of the test statistics rather than a data null distribution. A simple bootstrap estimator of this distribution is presented. With a statistically significant subset in hand, clustering methods assist in the identification of patterns in the data. We have developed a hybrid clustering algorithm called HOPACH, which combines the strengths of both partitioning and agglomerative hierarchical clustering methods. Using this algorithm as an example, I demonstrate how the bootstrap can be employed as a statistical method in cluster analysis to establish the reproducibility of the clusters and the overall variability of the followed procedure. Applications to microarray data and comparative genomics illustrate the methodologies.
Tuesday, November 30, 3:30-4:30
pm
Tuesday, November 23, 3:30-4:30
pm The dopaminergic neuron ordinarily will not fire faster than about 10 Hz when depolarized in slices. In vivo, much higher rates are briefly attained, for example after an unexpected reward. Using a biophysically based model, we suggest a mechanism for the burst generation and show that the mechanism is influenced by dendritic geometry. Our model represents the neuron as a number of electrically coupled oscillators (compartments) with different natural frequencies, corresponding to the soma and parts of the dendrite. We show that the coupled system, but none of the individual compartments, has oscillatory transient dynamics. Moreover, the transient frequency in such a system can be higher than the frequency of the fastest of the oscillators in isolation. We study dynamical mechanisms that lead to a substantial frequency difference between the transient and steady-state oscillations. Finally, we study the role of dendritic geometry for the burst generation, and show that branching and long thin sections help to create the transients. An implication of this is that slicing itself may explain the absence of the burst firing in vitro: slicing cuts off distal dendrites and so reduces the number of fast compartments.
Monday, November 22, 1:30-2:30
pm This seminar is a presentation of a project in progress studying the dynamic properties of the QT interval of the EKG. Lengthening of the QT interval is thought to be a precursor of some types of ventricular arrhythmias. However, from beat to beat in live subjects, the QT interval is highly variable, and results are often averaged in order to produce a single measure of QT length. In this project, we are attempting to construct a model that can account for the mechanism and give a framework for understanding beat to beat QT dynamics. This mathematical model will (at minimum) include the electrical activity of the heart, the baroreceptor reflex, and a component that relates heart activity to blood pressure. Ideally, it is hoped that a better understanding of QT dynamics through this model will lead to a better quantification of QT lengthening and it's relation to ventricular arrhythmias.
Thursday, November 4, 10:30-11:30am Recent work by Drover et al. on a network of Hodgkin-Huxley neurons coupled by excitatory synapses showed significant slowing of the firing rate of the synchronized network. The slowing of the firing rate is accompanied by subthreshold oscillations near the action potential threshold. I will explain these observations using methods from dynamical systems theory. Especially, i show that so called `Canards' (french for `duck') are responsible for the delay and line out the geometric explanation for this phenomenon. General conditions for neuronal models to possess canards are given.
Thursday, October 28, 10:30-11:30am Binary-splitting or bifurcating models are concerned with modeling
tree-indexed time series data, e.g., each individual in one generation
gives rise to two offspring in the next generation. Cell lineage
data (e.g. Powell(1955)) are typically of this kind.
Thursday, October 21, 10:30-11:30am Regression Contour Cluster Analysis could be applied in a wide
variety of scientific fields where the goal is to find the regions
in the input space with relatively high (low) values of the target
variable. Often there are problems where a decision maker can in
a sense choose the values or ranges of the input variables so as
to optimize the values of the target variable. For example, in Clinical
Trials, the goal may be to find variables that describe patients
with an extremely bad or good prognosis, which is useful for detecting
risk potentials or judging new therapies. In medical research, physicians
may be interested in identifying groups of patients with different
prognosis in order to take different treatment. These tasks can
be done using Regression Contour Cluster Analysis.
Thursday, October 7, 10:30-11:30am Stochasticity is often viewed as a nuisance. However, stochastic processes can impart structural features in the dynamics of biological systems that would not exist in a purely deterministic system. When applying inverse modeling techniques to these systems it is essential to be able to reliably sample from a population of stochastic realizations. In this talk, I'll focus on techniques for adaptive numerical solution of stochastic differential equations using a new JAVA-based numerical library.
Tuesday, October 5, 3:30-4:30pm The BIAcore is an ingenious device that allows the measurement of rate constants for binding processes without disturbing the system. The BIAcore is used mainly to analyze biochemical systems, and its geometry and fluid dynamics closely mimic real biological applications. In order to estimate the rate constants, an accurate mathematical model is needed to interpret the raw data correctly. This talk will discuss the latest enhancements to these models, namely flow inside the reacting receptor layer. By using asymptotics and perturbation methods, simple expressions may be obtained which are valid for a wide range of experimental parameters. These solutions, which provide corrections to the rate constants measured in the BIAcore, are interpreted physically.
Monday, September 27, 3:30-4:30am This lecture is a presentation of some of the basic biology and modeling involved in cardiac physiology. Topics will include the structure and function of the heart, ECG interpretation, cardiac arrhythmias, and the heart's neural regulation system.
Tuesday, September 28, 3:30-4:30pm Flows driven by pumping without valves are observed, motivated by biomedical applications: cardiopulmonary resuscitation (CPR) for the thoracic pump model and the human fetus before the development of the heart valves. Although the mechanism of valveless pumping (VP) has been discussed over the centuries, lots of phenomena of VP are still remained mysterious. In this talk, we present the two different mathematical models of VP in order to explain the mechanism of VP: One is a lumped parameter circuit model with time-dependent resistances and compliances governing by an ODE system. The other is a two-dimensional computational model with a full Navier-Stokes system solved by the Immersed Boundary Method. The flow mechanism around a loop of tubing that is composed of the two different compliant sections is investigated when an asymmetric force is applied in the valveless circulatory system. In both models, we present that the direction and magnitude of a net flow around the loop of tubing are dependent on the parameters, such as frequency, amplitude, and compression duration.
Tuesday, September 7, 3:00-4:00pm Gillies et al. [1] have experimentally shown the existence of oscillation in the theta frequency range (8-10 Hz) in slices of the CA1 hippocampal area of the brain when phasic excitation is blocked. In the presence of phasic excitation, the predominant frequency is in the gamma range (~ 40 Hz). Two different types of inhibitory neurons are involved in the mechanism of generating these rhythms: fast spiking interneurons and OLM cells; the latter have a hyperpolarization activated inward current (Ih) in addition to the standard Hodgkin-Huxley currents. They also have longer lasting inhibitory postsynaptic potentials (IPSP) in comparison with the former. We present a biophysically plausible mathematical model that successfully reproduces experimental findings. This model focuses on the activity of O-LM (O), cells producing slow IPSPs, and other inhibitory neurons (I), each modeled as a single compartment. In addition to standard Hodgkin-Huxley currents, we model the Ih current in the O cells; blockade of Ih has been shown to destroy the rhythmicity both experimentally and in simulations. We propose a mechanism by which coherent theta oscillations are created, due to the interaction of the I and O cells via the fast and slow inhibition. Using numerical and analytical techniques we demonstrate the effect that the I cells exert on the O cells due to the presence of Ih. [1] Gillies, M. J., Traub, R. D., Le Bleau, F. E. N, Davis, C. H., Gloveli, T., Buhl, E. H., et al. (2002). A model of atropine-resistant theta oscillations in rat hippocampal area CA1. J Physiol (Lond), 543, 779-793.
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