Applied & Biological Contemporary Mathematics Program |
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Applied & Biological Contemporary Mathematics ProgramThe ABC program is intended to foster and promote interdisciplinary research linking mathematics with the life sciences. It is also intended to be supportive of other College and Institute initiatives - specifically the emerging Integrative Biological Systems thrust. Due to its clear interdisciplinary focus, the success of the ABC program will come from clear and effective communications and research partnerships with our life sciences colleagues. Initially, a broad range of faculty from the School of Mathematics will be affiliated with the ABC program, although this is expected in time to extend to faculty from other units on campus. The ABC program will support:
Activities in 2007-2008
11:00 am Wednesday, April 23, 2008 A significant challenge in bioinformatics is to develop methods for detecting and modeling patterns in variable DNA sequence sites, such as protein-binding sites in regulatory DNA. Current approaches sometimes perform poorly when positions in the site do not independently affect protein binding. We developed a statistical technique for modeling the correlation structure in variable DNA sequence sites. The method places no restrictions on the number of correlated positions or on their spatial relationship within the site. The technique is based on model selection by cross-validation and produces models that allow computation of a score for any sequence of appropriate length. We applied our method to the recombination signal sequences (RS) that direct assembly of B-cell and T-cell antigen-receptor genes via V(D)J recombination. Our model-development procedure produces models that estimate well the recombinogenic potential of RS and discriminate RS from non-RS in genome scans. Our models are, therefore, valuable for studying the regulation of both physiologic and aberrant V(D)J recombination. The approach could be equally powerful for the study of promoter and enhancer elements, splice sites, and other DNA regulatory sites that are highly variable at the level of individual nucleotide positions.
11:00 am Wednesday, April 16, 2008 Niche Construction and the Emergence of Ecosystems. Classical niche theory treats species as passively responding to the environment so that prevailing environmental conditions determine when a population can grow and which species win in competition. However, many species active influence some of the very environmental factors that determine their own fitness and population growth rate. I will briefly review classical niche theory and give examples of how the theory predicts patterns of species diversity in a temporally and spatially heterogeneous environment. I will then give a number of examples of niche construction and show how niche theory can be modified to account for it. I develop a detailed case example for acid acid bacteria that consume sugars and alcohols and produce acetic acid as a waste product, thereby acidifying their own environment. I show that if there are many species of acetic acid bacteria competing for the same resource and similar in all respects except their optimal pH, then the species that wins in competition is the one that creates pH conditions closest to its own optimum. I also explore a time-varying version of the model where temperature cycles and ambient pH is responsive to both temperature and bacterial activity. I show that if there is a large pool of species competing for the resource, those that persist are able to track both temperature and pH cycles and to actively regulate pH at an optimum value for the community of species. Finally, I provide a model and graphical argument to show how niche construction provides a useful framework for exploring the emergence of ecosystem properties.
11:00 am Wednesday, April 2, 2008 An RNA molecule is a linear biochemical chain which folds into a three dimensional structure via a set of 2D base pairings known as a nested secondary structure. Reliably determining a secondary structure for large RNA molecules, such as the genomes of most viruses, is an important open problem in computational molecular biology. We give combinatorial results which yield insights into the interaction of local and global constraints in RNA secondary structures and suggest new directions in understanding the folding of RNA viral genomes.
11:00 am Wednesday, March 26, 2008 Viruses exist at the boundary between living and non-living objects. Some are as small as 50 nm in diameter and have quasi-icosahedral symmetry, but their apparent simplicity hides an amazingly rich set of mechanisms for infecting their hosts and reproducing themselves. This talk will examine the mechanisms of assembling icosahedral viruses, with a description of recent experimental advances (electron microscopy; single-molecule experiments) and a discussion of theoretical and computational approaches to investigating viral assembly.
11:00 am Wednesday, February 13, 2008 Interactions between cells are critical to the development and function of multicellular organisms and are mediated by special proteins. These antenna-like proteins, "receptors", span the cell membrane. Many of them are signaling units and, upon binding with their specific counterpart "ligand" (usually used in the biological jargon) on another cell, "receptors" could relay the information inside the cell. Several state-of-the-art techniques were developed to characterize the binding properties of receptor-ligand interactions. These techniques physically bring the interacting molecules into the vicinity of each other, allow binding to happen, and measure the bond parameters during molecules separation. The recorded parameters, for example, lifetime of a receptor-ligand bond, are inherently stochastic, thereby requiring a large amount of data for statistical analysis. Usually, sequentially repeated tests are used to obtain a data ensemble, implicitly assuming that the test sequence consists of independent and identically-distributed (i.i.d.) random variables, i.e., Bernoulli process. We tested this assumption using data from the micropipette adhesion frequency assay that generates sequences of two random outcomes: adhesion and no-adhesion. Analysis of distributions of consecutive adhesion events revealed violations of the i.i.d. assumption in several receptor-ligand systems. We observed systems with positive feedback (T cell receptor interacting with antigen peptide bound to major histocompatibility complex) or negative feedback (homotypic interaction between C-cadherins), where adhesion probability in the next test was increased or decreased, respectively, by adhesion in the immediate past test. The cell ability to "remember" the past test outcome is reported for the first time and may represent a novel mechanism for the cell to regulate adhesion and signaling. Different mechanisms that could underlie the observed cell "memory" and approaches to reveal them will be discussed.
11:00 am Wednesday, January 30, 2008 Although the equations that describe cardiac mechanics and electrophysiology are different, in both cases a realistic treatment demands the use of methods that account for anisotropy, inhomogeneity, and complex geometries. We employ a unified theoretical framework, the immersed boundary (IB) method, for both aspects of cardiac physiology. This unified approach not only yields methodological overlap but also allows for substantial software reuse.
11:00 am Wednesday, January 9, 2008 When oscillated in a fluid, appendages such as insect wings and fish fins can produce large thrust forces while undergoing considerable bending. We attempt to understand the role of flexibility by formulating two optimization problems. Can we determine the flexibility which produces maximum thrust, or a given thrust at maximum efficiency? We present first a general model for how flexible surfaces produce vorticity and bend passively in a fluid. The model combines a nonlinear ODE for elastic bodies with a singular integral equation for a potential flow with velocity discontinuities. We solve the linearized model and find a series of local thrust optima with power-law dependences on rigidity and driving frequency. These optima are resonant peaks, damped by fluid inertia, and can be predicted with a scaling analysis. We discuss extensions to large-amplitude motions, and motions of actual fish fins.
11:00 am Wednesday, September 12, 2007 To ensure standard initial conditions in recent gene finding competitions, the organizers specified training sets of validated eukaryotic genes, so that these sets were supposed to be used by participants for estimating parameters of statistical models, the key components of ab initio gene finding algorithms. I'll present a gene prediction algorithm that does not require a training set for the model parameter estimation. Nevertheless, this algorithm achieves the same or better level of precision in gene identification as an algorithm trained on a sufficiently large training set. With more than 600 eukaryotic genome sequencing projects currently in progress, ab initio gene finders that estimate model parameters directly from anonymous sequence will accelerate the process of identification of proteins encoded in eukaryotic genomes. Another type of challenge is presented by appeared recently in vast amounts metagenomic sequences, the mixtures of short DNA contigs originated from genomes of mostly non-cultivated organisms. Metagenomes are highly fragmented, diverse in nature, and carry larger fractions of sequence irregularities than known complete prokaryotic genomes. Finding gene starts or identifying short and partial genes in metagenomes become much more difficult than in conventional genomes. Given that the length of a individual metagenomic sequence is not sufficient for estimation of model parameters of a gene finding algorithm I'll describe an approach that allows to circumvent this difficulty and determine parameters of a model for accurate gene finding.
11:00 am Wednesday, September 5, 2007 Activities in 2006-2007Affiliated Faculty
ContactLeonid A. Bunimovich, Regents' ProfessorDirector, ABC Math Georgia Tech Atlanta, GA 30332-0160 phone: (404) 894-4748 fax: (404) 894-4409 email: bunimovh@math.gatech.edu |
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School of Mathematics, Georgia Institute
of Technology, Atlanta, GA 30332-0160
phone: 404-894-2700, fax: 404-894-4409, webmaster@math.gatech.edu
URL:http://www.math.gatech.edu/abc/index.html |