Mathematics in Molecular Cell Biology

 Speakers

Prof. Dr. Willi Jäger
Institute for Applied Mathematics & Institut für Wissenschaftliches Rechnen
University Heidelberg, Germany
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Abstract:
We consider mathematical models in cells, including interaction of biphysics, biomechanics and biochemistry. Main topics are models based on partial differential equations, stochastic models, bifurcation, limiting behaviour, homogenization and multiple scales.  Also contributions on signalling and transport of substances in cells will be discussed

    
Prof. Dr. Alex Mogilner
Department of Mathematics and Center for Genetics and Development
University of California Davis, USA
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   Abstract:
Living cells maintain their shape and function with the help of the cytoskeleton - dynamic and heterogeneous network of biopolymers, accessory proteins and molecular motors. Cytoskeletal dynamics are at their most spectacular when the cells move and divide. Biophysical and mathematical modeling becomes increasingly important tool of biological discovery, while the cytoskeletal dynamics becomes the source of novel mathematical challenges - from large scale stochastic models to hierarchical and modular dynamic systems to free boundary problems. I will introduce a few cell motility and division phenomena where successful mathematical modeling made biological impact, and will focus on the corresponding models. I will emphasize the art of asking biologically relevant and mathematically interesting questions, choosing appropriate modeling techniques, and making testable conclusions and predictions.

    
Prof. Dr. Wolfgang Nonner
Department of Physiology and Biophysics
University of Miami, USA
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    Abstract:
Lipid membranes of cells and subcellular organelles confine water-soluble molecules and utilize specialized transmembrane proteins to effect and regulate the transport of such molecules. These transmembrane proteins include a large variety of  ion channels, which, among other functions, underlie the electrical signalling in nerve and muscle cells. As transport enzymes, ion channels are remarkable for their high rates of turnover (often many millions of ions per second) that are achieved while maintaining an adequate selectivity for certain physiological ions. For instance, Ca channels prefer Ca ion more than thousandfold over Na ion and thus manage to 'find' their ion among a hundredfold physiological excess of extracellular Na ion. Ionic selectivity and fast conduction are essential for the channels' specific roles in cellular signalling and signal amplification.
Current research is focussed on the physical principles that underlie the selective conduction of ions in ionic channels. The long-term goal is to predict these essential functional properties from the structural information that is now becoming available from molecular-biological and  crystallographic work. Modern concepts of other fields are used (like transport models of statistical mechanics and solid-state physics, or physicochemical models of ionic solutions and ion-surface interactions)  to develop a physical theory, by which structure and transport function of ion channels can be linked.
Our  approach combines theoretical work, development of numerical techniques to compute theoretical models, extensive computer simulations of channel behavior, and electrophysiological measurements to further test our theories.

    
Prof. Dr. Hans Othmer
Department of Mathematics
University of Minnesota, USA
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Abstract:
1. Basic  theory of chemical reaction dynamics,
2. Singular perturbation theory, 
3. An introduction to graph theory and the representation of chemical reactions,
4. Analysis of metabolic and gene control networks,
5. Specific models:  (a) Signal transduction: G-protein coupled receptors, kinase-coupled, (b) Cell cycle, (c) Complex regulatory schemes, (d) Map K switches – Xenopus
6. Stochastic effects and analysis

    

Prof. Dr. Christoph Schütte
Department of Mathematics, Biocomputing Group
Free University of Berlin, Germany
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Abstract:
Biomolecular Conformations, Metastability and Transfer Operators: The chemically interesting function of many important biomolecules, like proteins or enzymes, results from their dynamical properties, particularly from their ability to undergo so-called conformational transitions. The term conformations describes metastable global states of the molecule, in which the large scale geometric structure is understood to be conserved.
Modeling biomolecular systems via Hamiltonian equations of motion, the metastable conformational states show up as metastable sets of the corresponding Hamiltonian system. These metastable sets and the transition probabilities between them can be identified via the dominant eigenmodes of a so-called transfer operator, which describes the overall dynamics of the system under consideration. The algorithmic approach to the identification of metastable sets exploits the intriguing property of the dominant eigenvectors of the transfer operator: They exhibit significant jumps at the boundaries of the metastable sets, while varying only slowly within those.
Uncoupling-Coupling Monte Carlo: Exploring the state space of a biomolecule is a prerequisite for identifying its metastable sets. The Uncoupling-Coupling method is an algorithmic approach addressing this problem by integrating transfer operator techniques in a Markov chain Monte Carlo framework
Essential Degrees of Freedom: The essential degrees of freedom are understood as those degrees of freedom that allow to characterize the metastable sets including the effective dynamics between them. Within the above transfer operator approach to metastability, the essential degrees of freedom are characterized locally by those directions, in which the dominant eigenvectors display significant jumps.
Hidden Markov Models: Hidden Markov Models are used to analyse time series data from molecular dynamics or Monte Carlo simulations. They allow to identify metastable states as information hidden in the sequence of molecular states; interestingly enough, novel HMM techniques allow to solve this identification problem based on some torsion angles only. Recently application of these techniques to B-DNA time series resulted in intriguing novel insights.
Transition Pathways: Computation of transition pathways and related transition probabilities is of utmost interest for the biophysical understanding of the molecular system under consideration. Several novel approaches have been presented recently. In cooperation with other groups we are developing techniques based on pathwise concepts and on interpretations of the discretized transfer operator as a huge graph (shortest path problems).