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Mathematics of Molecular and Cellular Biology Seminar

September 12, 2007, 11:15 am-12:15 pm, Lind Hall 409
Marcia Oliveira Fenley (Department of Physics and Institute of Molecular Biophysics, Florida State University)

Revisiting the salt dependence of the drug-DNA association process: A Poisson-Boltzmann analysis

Abstract: The proper modeling of salt-mediated electrostatic interactions is essential in order to correctly account for the energetics of a variety of biological processes involving nucleic acids since they are highly charged polyelectrolytes. Due to the high charge density of nucleic acids, ions in the solution will condense around them. This “counterion cloud” that surrounds nucleic acids, which is not captured with structural techniques such as X-ray crystallography and NMR, is an integral part of their structure and essential to maintain their stability. Given this unique highly charged polyelectrolyte nature of nucleic acids it is not surprising that small changes in salt concentration can greatly affect its association with charged ligands (e.g., cationic drugs). Here, we examine the salt dependence of the association of more than 40 cationic minor groove antibiotics to AT-rich DNAs, for many of which thermodynamic binding data is available, using a novel implicit solvent-based Poisson-Boltzmann algorithm. We find that the plots of the electrostatic binding free energy versus the logarithm of salt concentration are linear, based on both the linear and nonlinear Poisson-Boltzmann equation. The slopes of these curves can be directly compared with experimental thermodynamic data of the observed binding constant at various salt concentrations. The good agreement between experimental and Poisson-Boltzmann predictions is only possible if the full nonlinear Poisson-Boltzmann equation is employed, since the linear PBE overestimates the slope of the plots of the electrostatic binding free energies vs. the logarithm of salt concentration. Thus, our results suggest that one should not employ the linear Poisson-Boltzmann or Generalized Born approach in order to assess the salt dependent behavior of nucleic acids. Further experimental and implicit solvent-based computational studies should be performed in order to verify if indeed the linear PBE always overestimates the salt dependence of the binding energetics of charged ligand-nucleic acid complexes.

September 26, 2007, 11:15 am-12:15 pm, Lind Hall 409
F. Javier Arsuaga (Department of Mathematics, San Francisco State University)
http://math.sfsu.edu/arsuaga/

Quantitative analysis of radiation induced chromosome aberrations

Abstract: Chromosome aberrations are large-scale illegitimate rearrangements of the genome. They are indicative of DNA damage and of disease and are informative of nuclear architecture and of DNA damage processing pathways. In this talk I will present our mathematical approaches to analyze multiplex fluorescent in situ hybridization (mFISH)assays.

October 3, 2007, 11:15 am-12:15 pm, Lind Hall 409
Kenneth C. Millett (Department of Mathematics, University of California, Santa Barbara)
http://www.math.ucsb.edu/~millett/KM.html

The shape of knots

Abstract: What do the knots that occur in natural macromolecules look like? What about those arising in random equilateral spatial polygons such as those used to model DNA or polymers? The asphericity is a number between 1.0 and 0.0 that measures the degree to which the ellipsoid of inertia is more like a sausage (near 1.0), a rugby ball (near 0.5) or, a soccer ball (near 0.0). An analogous measure, the spatial asphericity, is defined by considering the smallest ellipsoid containing the knot. Computer simulations and examples of proteins will be used to illustrate these measures. Via the simulations, we will consider the influence of constrained topology on these measures in comparison to the unconstrained averages. In a continuation of earlier research, we will look at the equilibrium lengths defined by the asphericity, the lengths at with the constrained and unconstrained have equal values, and compare these with those determined earlier. We present computer simulations to examine the differences between the average asphericity of polygons with constrained and unconstrained topology.

October 10, 2007, 11:15 am-12:15 pm, Lind Hall 409
Christine E. Heitsch (School of Mathematics, Georgia Institute of Technology)
http://www.math.gatech.edu/~heitsch

Combinatorics of RNA secondary structures

Abstract: Under a suitable abstraction, complex biological problems can reveal surprising mathematical structure. For instance, the planar self-bonding, or nested "secondary structure," of an RNA molecule is nicely represented by a plane tree. Under our plane tree model of RNA folding, we prove combinatorial theorems which yield insight into the coding of structural and functional information in RNA sequences. One result demonstrates the importance of local constraints in specifying a global structure while another characterizes the degree of branching in minimal energy configurations. Additionally, by transitioning between RNA configurations by an appropriate local move, we obtain an isomorphism with the lattice of noncrossing partitions. Thus, the interaction between combinatorics and molecular biology motivates new combinatorial theorems as well as advancing biological applications.

October 17, 2007, 11:15 am-12:15 pm, Lind Hall 409
Shi-Jie Chen (Department of Physics, University of Missouri)
http://www.biochem.missouri.edu/schen.php

RNA Folding Energy Landscapes in mRNA splicing

Abstract: We develop a statistical mechanical model for RNA/RNA complexes with both intramolecular and intermolecular interactions. As an application of the model, we compute the free energy landscapes, which give the full distribution for all the possible conformations for spliceosomal snRNA complexes. Different snRNA experiments found contrasting structures, our free energy landscape theory shows why these structures emerge and how they compete with each other. In addition, the energy landscapes suggest possible mechanisms for the conformational switches in splicing. The change of the energy landscape shape gives information about the conformational changes. We find multiple (native-like and misfolded) intermediates formed through base-pairing rearrangements in snRNA complexes. Furthermore, the energy landscape gives the stabilities of all the possible (functional) intermediates and such information is directly related to splicing efficiency.

October 24, 2007, 11:15 am-12:15 pm, Lind Hall 409
Marcia Oliveira Fenley (Department of Physics and Institute of Molecular Biophysics, Florida State University)

The role of anionic residues on the salt dependence of the binding of aminoacyl-tRNA synthetases to tRNA: A Poisson-Boltzmann analysis

Abstract: October 26, 2007, 11:15 am-12:15 pm, Lind Hall 409
Mariel Vazquez (Mathematics Department, San Francisco State University)
http://math.sfsu.edu/vazquez

Modeling DNA unknotting by type II topoisomerases

Abstract: Type II topoisomerases simplify DNA knots and links efficiently by performing strand-passage on DNA strands. Experimental studies have shown that these enzymes simplify the topology of DNA below thermodynamical equilibrium, however the key behind their efficiency is yet to be revealed. Motivated by these experimental observations, we study random transitions of knotted polygonal chains of fixed length. We use Monte Carlo computer simulations and computational knot theory methods to model strand-passage, with and without topological biases, on the knotted chains and to identify the resulting knotting probabilities.

This project is funded by NIH MBRS SCORE grant S06 GM052588.

November 7, 2007, 11:15 am-12:15 pm, Lind Hall 409
Timothy Newman (Department of Physics, Arizona State University)
http://phy.asu.edu/biodyn/newman.htm

Strong fluctuations and cycling in biological systems

Abstract: In this talk I describe a mechanism for generating cycles in a large class of "mesoscale" biological populations (meaning populations composed of thousands to tens of thousands of units). Cycles are caused by a resonant amplification of the system dynamics triggered by internal noise. I will discuss this mechanism in the context of two classes of simple systems: ecological (e.g. predator-prey, host- pathogen) and biochemical (e.g. small gene regulation networks, modules of metabolic processes).

November 14, 2007, 11:15 am-12:15 pm, Lind Hall 409
Gilad Lerman (School of Mathematics, University of Minnesota)
http://www.math.umn.edu/~lerman/

Defining functional distance using manifold embeddings of gene ontology annotations
Slides:  ppt

Abstract: Although rigorous measures of similarity for sequence and structure are now well established, the problem of defining functional relationships has been particularly daunting. Here, we present several manifold embedding techniques to compute distances between Gene Ontology (GO) functional annotations and consequently estimate functional distances between protein domains. To evaluate accuracy, we correlate the functional distance to the well established measures of sequence, structural, and phylogenetic similarities. Finally, we show that manual classification of structures into folds and superfamilies is mirrored by proximity in the newly defined function space. We show how functional distances place structure-function relationships in biological context resulting in insight into divergent and convergent evolution. Our methods and results can be readily generalized and applied to a wide array of biologically relevant investigations, such as accuracy of annotation transference, the relationship between sequence, structure, and function, or coherence of expression modules.

This work is joint work Boris Shakhnovich and described in http://www.pnas.org/cgi/reprint/0702965104v1.

November 28, 2007, 11:15 am-12:15 pm, Lind Hall 409
Debra Knisley (2007-2008 New Directions Visiting Professor, IMA)
http://www.etsu.edu/math/knisleyd/dknisley.htm

Graphical invariants and topological indices as biomolecular descriptors

Abstract: A number of molecular descriptors of small molecules are derived from graphical representations of the molecule. These descriptors, sometimes called topological indices, are used to identify or relate the structure of a molecule with expected bioactivity and they are an essential tool in the drug design industry. It is generally accepted that these molecular descriptors are not applicable to macromolecules. However, topological indices are equivalent to graphical invariants in graph theory. Graph theory offers a wealth of graphical invariants annotated with structural implications, primarily for large graphs. Thus we consider applying known graphical measures to quantify macromolecules, including secondary RNA structures, amino acids and several families of proteins.

December 5, 2007, 11:15 am-12:15 pm, Lind Hall 409
Zhijun Wu (Department of Mathematics, Iowa State University)
http://orion.math.iastate.edu/wu/

The solution of the boundary-value problems for the simulation of transitions of protein conformations

Abstract: Under certain kinetic or thermodynamic conditions, proteins make conformational transitions, resulting in significant functional variations. Such dynamic properties can be studied through molecular dynamics simulation. However, in contrast to conventional dynamics simulation protocols where an initial-value problem is solved, the simulation of transitions of protein conformations can be done by solving a boundary-value problem, with the beginning and ending states of the protein as the boundary conditions. While a boundary-value problem is more difficult to solve in general, it provides a more realistic model for the study of protein conformational transitions and has certain computational advantages as well, especially for large scale simulations. Here we study the solution of the boundary-value problems for the simulation of transitions of protein conformations using a standard class of numerical methods called the multiple shooting methods. We describe the methods and discuss the issues related to their implementations for our specific applications, including the definition of the boundary conditions, the formation of the initial trajectories, and the convergence of the solutions. We present the results from using the multiple shooting methods for the study of conformational transitions of a small molecular cluster and an alanine dipeptide, and show the potential extension of the methods to larger biomolecular systems.

December 12, 2007, 11:15 am-12:15 pm, Lind Hall 409
Soojeong Kim (Department of Mathematics, University of Iowa)
http://www.math.uiowa.edu/~soojkim/

Topological analysis of DNA-protein complexes

Abstract: Difference topology is a methodology to derive the number of DNA crossings trapped in an unknown protein complex. By this method, Pathania, Jayaram, and Harshey revealed the topological structure within the Mu protein complex which consisted of three DNA segments containing five nodes [1]. In their experiments, they used a member of the site-specific recombinases which is known as Cre. Cre mediates DNA exchange by rearranging target sites of the DNA segments. During this DNA recombination, there are no extra DNA crossings introduced. The initial DNA conformation is unknotted. After Cre recombination, the products are knots or catenanes. Recently, Darcy, Luecke, and Vazquez analyzed these experimental results and proved that the five-noded conformation is the only biologically reasonable structure of the Mu protein DNA complex [2]. We address the possibility of protein complexes that binds four DNA segments. By the useful property of Cre, we can make the assumption that after Cre recombination, the topology of a DNA-protein complex would be a knot or catenane. The latest results of the topological tangle model for this case and very basic biological and mathematical backgrounds will be discussed.

Reference:

[1] S. Pathania, M. Jayaram, and R. Harshey, Path of DNA within the Mu transpososome: Transposase interaction bridging two Mu ends and the enhancer trap five DNA supercoils, Cell 109 (2002), 425-436.

[2] I. K. Darcy, J. Luecke, and M. Vazquez, A tangle analysis of the Mu transpososome protein complex which binds three DNA segments, Preprint.

January 9, 2008, 11:15 am-12:15 pm, Lind Hall 409
Zhijun Wu (Department of Mathematics, Program on Bioinformatics and Computational Biology, Iowa State University)
http://orion.math.iastate.edu/wu/

The solution of the distance geometry problem for protein modeling

Abstract: A well-known problem in protein modeling is the determination of the structure of a protein with a given set of inter-atomic or inter-residue distances obtained from either physical experiments or theoretical estimates. A general form of the problem is known as the distance geometry problem in mathematics, the graph embedding problem in computer science, and the multidimensional scaling problem in statistics. The problem has applications in many other scientific and engineering fields as well such as sensor network localization, image recognition, and protein classification. We describe the formulations and complexities of the problem in its various forms, and introduce a geometric buildup approach to the problem. Central to this approach is the idea that the coordinates of the atoms in a protein can be determined one atom at a time, with the distances from the determined atoms to the undetermined ones. The determination of each atom requires the solution of a small system of distance equations, which can usually be obtained in constant time. Therefore, in ideal cases, the coordinates of n atoms can be determined by a geometric buildup algorithm with O(n) distances in O(n) computing time instead of O(n2) distances in O(n2) computing time as required by a conventional singular-value decomposition algorithm. We present the general algorithm and discuss the methods for controlling the propagation of the numerical errors in the buildup process, for determining rigid vs. unique structures, and for handling problems with inexact distances (distances with errors). We show the results from applying the algorithm to a set of model protein problems with varying degrees of availability and accuracy of the distances and justify the potential use of the algorithm in protein modeling practice.

January 23, 2008, 11:15 am-12:15 pm, Lind Hall 409
Robert L. Jernigan (Department of Biochemistry, Biophysics, and Molecular Biology, Iowa State University)
http://ribosome.bb.iastate.edu/jernigan.html

Analyzing the protein-protein interaction network

Abstract: The abundant data available for protein interaction networks have not yet been fully understood. New types of analyses are needed to reveal organizational principles of these networks to investigate the details of functional and regulatory clusters of proteins. In the present work, individual clusters identified by an eigenmode analysis of the connectivity matrix of the protein-protein interaction network in yeast are investigated for possible functional relationships among the members of the cluster. With our functional clustering we have successfully predicted several new protein-protein interactions that indeed have been reported recently. Eigenmode analysis of the entire connectivity matrix yields both a global and a detailed view of the network. We have shown that the eigenmode clustering not only is guided by the number of proteins with which each protein interacts, but also leads to functional clustering that can be applied to predict new protein interactions.

Some other applications of this type of analysis for the identification of important variable in a simulation will be considered.

January 30, 2008, 11:15 am-12:15 pm, Lind Hall 409
Brigitte Servatius (Department of Mathematics, Worcester Polytechnic Institute)
http://users.wpi.edu/~bservat/

Combinatorial rigidity and the molecular conjecture
Slides:  pdf

Abstract: Graph theory has successfully been used by several authors to predict protein flexibility, in particular, combinatorial rigidity is an important tool. The most important new result in combinatorial rigidity is the characterization of global rigidity while one of the most intriguing open problems is called "the molecular conjecture". We will explain the state of the art in the progress toward the conjecture and the implications of recent progress in rigidity theory, including the concept of combinatorial allostery, toward understanding the behavior of molecules.

February 6, 2008, 11:15 am-12:15 pm, Lind Hall 409
Roger Y. Lui (Department of Mathematical Sciences, Worcester Polytechnic Institute)
http://www.wpi.edu/Academics/Depts/Math/People/ryl.html

Three topics in the mathematics of molecular and cellular biology
Slides:  pdf   ppt

Abstract: In this talk, I am going to talk about protein folding, biochemical network, and cell motility. I am an analyst by training so you are going to see a lot of equations in my talk. But I will try to make things easy to understand and enjoyable.

February 13, 2008, 11:15 am-12:15 pm, Lind Hall 409
Imre M. Janosi (Department of Physics of Complex Systems, Lorand Eotvos University, Budapest, Hungary )
http://karman3.elte.hu/janosi/index.html

Why is the microtubule lattice helical?
Slides:  pdf   ppt

Abstract: Microtubules polymerize from identical tubulin heterodimers, which form a helical lattice pattern for each known species. This pattern always has left-handed chirality, but it is not known why. Since tubulin, similar to other proteins, evolved for a purpose, the question of the title of this talk appears to be meaningful. In a computer simulation that explores the ‘counterfactual biology’ of microtubules without helicity, we demonstrate that these have the same mechanical properties as Nature’s microtubules with helicity. Thus only a dynamical reason for helicity is left as potential explanation. We propose that helicity solves ‘the problem of the blind mason’, i.e. how to correctly build a structure, guided only by the shape of the bricks. This answer in turn raises some new questions for researchers to address.

February 20, 2008, 11:15 am-12:15 pm, Lind Hall 409
Christopher J. Lee (Department of Biochemistry, University of California at Los Angeles)
http://www.uclaaccess.ucla.edu/UCLAACCESS/Web/Faculty.aspx?ri=434

Mapping evolutionary pathways of HIV-1 drug resistance using conditional selection pressure

Abstract: Can genomics provide a new level of strategic intelligence about rapidly evolving pathogens? We have developed a new approach to measure the rates of all possible evolutionary pathways in a genome, using conditional Ka/Ks to estimate their "evolutionary velocity," and have applied this to several datasets, including clinical sequencing of 50,000 HIV-1 samples. Conditional Ka/Ks predicts the preferred order and relative rates of competing evolutionary pathways. We recently tested this approach using independent data generously provided by Shafer and coworkers (Stanford HIV Database), in which multiple samples collected at different times from each patient make it possible to track which mutations occurred first during this time-course. Out of 35 such mutation pairs in protease and RT, conditional Ka/Ks correctly predicted the experimentally observed order in 28 cases (p=0.00025). Conditional Ka/Ks data reveal specific accessory mutations that greatly accelerate the evolution of multi-drug resistance. Our analysis was highly reproducible in four independent datasets, and can decipher a pathogen’s evolutionary pathways to multi-drug resistance even while such mutants are still rare. Analysis of samples from untreated patients shows that these rapid evolutionary pathways are specifically associated with drug treatment, and vanish in its absence.

February 27, 2008, 11:15 am-12:15 pm, Lind Hall 409
Peter R. Kramer (Department of Mathematical Sciences, Rensselaer Polytechnic Institute)
http://www.math.rpi.edu/ms_faculty/profile/kramer_p.html

Stochastic mathematical and computational models in microbiology
Slides:  pdf

Abstract: I shall discuss three areas of current research involving the use of stochastic methods for the physical modeling for microscopic processes in physiology. First, I exhibit a variation of the immersed boundary method designed, in joint work with Paul Atzberger (UCSB) and Charles Peskin (NYU) for simulating microbiological systems where thermal effects play a significant role, such as molecular motors, DNA and other polymer dynamics, and gel swelling. Statistical mechanical principles indicate that the thermal fluctuations should manifest themselves through a random force density in the fluid component of the immersed boundary equations. Secondly, I briefly review the mathematical procedure, currently being developed with Juan Latorre and Grigorios Pavliotis (Imperial), for coarse-graining stochastic molecular motor models. Finally, I shall discuss recent explorations with Adnan Khan (Lahore) and Shekhar Garde (Rensselaer, Biochemical Engineering) concerning the parameterization of a simple stochastic model for the behavior of water molecules near a solute surface which has the potential for improving substantially upon Brownian dynamics models more conventionally used in engineering applications. We use exactly solvable mathematical models as a testbed for addressing some basic data-driven parameterization issues.

March 19, 2008, 11:15 am-12:15 pm, Lind Hall 409
Peter R. Kramer (Department of Mathematical Sciences, Rensselaer Polytechnic Institute)
http://www.math.rpi.edu/ms_faculty/profile/kramer_p.html

Stochastic mathematical and computational models in microbiology (continued)
Slides:  pdf

Abstract: I shall discuss three areas of current research involving the use of stochastic methods for the physical modeling for microscopic processes in physiology. First, I exhibit a variation of the immersed boundary method designed, in joint work with Paul Atzberger (UCSB) and Charles Peskin (NYU) for simulating microbiological systems where thermal effects play a significant role, such as molecular motors, DNA and other polymer dynamics, and gel swelling. Statistical mechanical principles indicate that the thermal fluctuations should manifest themselves through a random force density in the fluid component of the immersed boundary equations. Secondly, I briefly review the mathematical procedure, currently being developed with Juan Latorre and Grigorios Pavliotis (Imperial), for coarse-graining stochastic molecular motor models. Finally, I shall discuss recent explorations with Adnan Khan (Lahore) and Shekhar Garde (Rensselaer, Biochemical Engineering) concerning the parameterization of a simple stochastic model for the behavior of water molecules near a solute surface which has the potential for improving substantially upon Brownian dynamics models more conventionally used in engineering applications. We use exactly solvable mathematical models as a testbed for addressing some basic data-driven parameterization issues.

March 26, 2008, 11:15 am-12:15 pm, Lind Hall 409
Robert Guy (Department of Mathematics, University of Utah)
http://www.math.utah.edu/~guy/

Modeling fibrin gel formation: Continuous to discrete
Slides:  pdf

Abstract: Hemostasis is the normal physiological response to blood vessel injury and is essential to maintaining the integrity of the vascular system. It consists of two interacting processes: platelet aggregation and coagulation. The first involves cell-cell adhesion resulting in a platelet aggregate, and the second involves an enzyme network that leads to the formation of a fibrin gel. Though both processes contribute to the formation of blood clots, those formed at high shear rates are composed primarily of platelets and clots formed at low shear rates are composed predominantly of fibrin gel. In order to understand this phenomenon, a simple mathematical model of chemically-induced monomer production, polymerization, and gelation under shear flow is presented. The model is used to explore how the shear rate and other parameters control the formation of fibrin gel. The results show that the thrombin inhibition rate, the gel permeability, and the shear rate are key parameters in regulating the height of the clot. Experiments show that the gel permeability depends on the chemical environment in which it was made. However, the reasons for these structural differences are unclear. Discrete, Monte Carlo simulations of fibrin polymerization are used to explore what factors determine the microstructure of the gel.

April 2, 2008, 11:15 am-12:15 pm Lind Hall 409
Jeff Randall Knisley (Department of Mathematics, East Tennessee State University)
http://www.etsu.edu/math/jknisley.htm

From neurons to neural networks
Slides:  pdf    ppt

Abstract: Artificial Neural Networks (ANN's) are machine-learning algorithms that are often used as classifiers in molecular and computational biology. Originally, ANN's were inspired by in vivo models of axonal and dendritic neuro-electric activity, especially the classical models of Hodkgin, Huxley, and others. Much of the successive development of ANN's, as well as the parallel development of other approaches such as Support Vector Machines, has been as a means of addressing issues such as overfitting and hard margins which arise in machine learning applications. To address these issues, ANN's have borrowed from a variety of sources in computer science, physics, and cognitive psychology, but not so much from the ever-improving neuronal models which provided their initial inspiration. We will revisit much of the historical and algorithmic development of ANN's, with the goal being that of suggesting the types of ANN's that might be inspired by more recent developments in dendritic electrotonic models.

April 9, 2008, 11:15 am-12:15 pm, Lind Hall 409
Christodoulos A. Floudas (Department of Chemicial Engineering, Princeton University)
http://titan.princeton.edu/

Recent advances and challenges in deterministic global optimization

Abstract: In this presentation, we will provide an overview of the research progress in global optimization. The focus will be on important contributions during the last five years, and will provide a perspective for future research opportunities. The overview will cover the areas of (a) twice continuously differentiable constrained nonlinear optimization, and (b) mixed-integer nonlinear optimization models. Subsequently, we will present our recent fundamental advances in (i) convex envelope results for multi-linear functions, (ii) a piecewise quadratic convex underestimator for twice continuously differentiable functions, (iii) the generalized alpha-BB framework, (iv) our recently improved convex underestimation techniques for univariate and multivariate functions, and (v) generalized pooling problems. Computational studies will illustrate the potential of these advances.

April 16, 2008, 11:45 am-12:45 pm [note time change], Lind Hall 409
Eric J. Rawdon (Department of Mathematics, University of St. Thomas)
http://george.math.stthomas.edu/rawdon/

Size and shape of polymers
Slides:  pdf

Abstract: We use numerical simulations to investigate how chain length and knotting in freely fluctuating knotted polymer rings affect their size and shape. In particular, we find smallest containers, such as rectangular boxes, spheres, and polyhedra, which contain the simulated polymers. Ideal knots, and their relationship to the containers, also will be discussed.

May 7, 2008, 11:15 am-12:15 pm, Lind Hall 409
Claudio Altafini (SISSA-ISAS, International School for Advanced Studies)
http://people.sissa.it/~altafini/

Modeling the genome-wide transient response to stimuli in yeast: adaptation through integral feedback

Abstract: At the level of gene expression, the response of yeast to various types of stresses/perturbations is characterized by a short-term transient followed by a return to the basal level (adaptation). A thorough investigation of the transient response to several different stimuli shows a common modulation, functionally and dynamically similar. The adaptation that follows the transient excursion is modeled by means of an integral feedback, with the gene product representing the variable that is fed back. The resulting linear system with input explains sufficiently well the different time constants observable in the transient response while being in agreement with the known experimental degradation rates measurements.

May 14, 2008, 11:15 am-12:15 pm, Lind Hall 409
Howard A. Levine (Department of Mathematics, Iowa State University)
http://www.public.iastate.edu/~halevine/

Some mathematical issues arising in single and multiple target SELEX

Abstract:

May 21, 2008, 11:15 am-12:15 pm, Lind Hall 409
Sergei Fedotov (School of Mathematics, The University of Manchester)
http://www.maths.manchester.ac.uk/~sf/

Anomalous diffusion, tumor growth and random walk models

Abstract: The theory of anomalous diffusion is well-established and leads to the integral equations or the alternative fractional diffusion equations for number densities. Despite the progress in understanding the anomalous transport most work has been concentrated on the passive density of the particles, and comparatively little is known about the interaction of non- standard transport with reactions. This work is intended to address this issue by utilising the random walk techniques in order to model the anomalous diffusion with reactions. Example is the tumor's cells migration and proliferation (Phys. Rev. Lett. 98, 118101 (2007)).

June 4, 2008, 11:15 am-12:15 pm, Lind Hall 409
Timothy Newman (IMA and Arizona State University, http://phy.asu.edu/faculty.php?name=tjnewman and Hans G. Othmer (School of Mathematics, University of Minnesota, http://www.math.umn.edu/~othmer/)

Review and discussion of IMA workshop: Quantitative approaches to cell motility and chemotaxis

Abstract: This Wednesday, we are planning to discuss topics and questions arising from the recent IMA workshop on Quantitative Approaches to Cell Motility and Chemotaxis. Everyone is welcome to attend and take part. There will be no set agenda. Hans Othmer will lead the discussion. Hans has asked that everyone attending think over their experience at the workshop and distill important issues and open questions. Looking forward to seeing you this Wednesday at 11:15 in the IMA seminar room.

June 10, 2008, 11:15 am-12:15 pm, Lind Hall 409 [note Tuesday instead of Wednesday]
Andrew M. Stein (IMA postdoctoral associate)
http://www.ima.umn.edu/~astein/

The micromechanics of 3d collagen gels

Abstract: Collagen is the most abundant animal protein and its mechanics have been studied in great detai. It takes on many morphologies, including skin, tendons, ligaments, individual fibers, and gels. Of particular interest is the mechanics of collagen-I gels. These gels provide a relatively simple structure that can be noninvasively observed by confocal microscopy and used as a scaffold for growing artificial tissues, and as a 3d environment for studying cell motility and tumor invasion. A critical first step in understanding these systems is to develop a model for the collagen gel alone. In this paper we give a successful theoretical model of the micromechanics of realistic networks.

June 18, 2008, 12:30 pm-1:30 pm, Lind Hall 305 [note different room and time]
Dirk Hartmann (Center for Modelling and Simulation in the Biosciences (BIOMS), Institut für Angewandte Mathematik)
http://www.hartmann.uni-hd.de/

Single cell mechanics: Mechanics of membranes and cytoskeletal networks

Abstract: In this talk, I will first review existing theoretical approaches for mechanics of single cells. These are mainly determined by the membrane and the cytoskeleton. The most popular class of models among physicists are static models given in terms of energy functionals, e.g. the Canham-Helfrich energy modelling membrane mechanics or microscopic pseudo-spring / cable networks modelling cytoskeletal mechanics. On the other hand mathematicians often prefer to work in terms of continuous models based on conservation equations, e.g. the plate equation modelling mechanics of membranes on short length scales, a completely different class of models.

Considering mechanics of red blood cells, one of the most simplest cells, I will show how it is possible to link those different classes of models in a rigorous manner. Simulations of optical tweezers experiments based on finite element methods will be shown.

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