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Multiscale Dynamics of Bio-Systems: Molecules to Continuum

Multiscale Dynamics of Bio-Systems: Molecules to Continuum. February 2005. Why we need new approaches. Many degrees of freedom: multidimensional surface, local minima Interconnected components: strongly or weakly coupled Hierarchy of scales both in time & space.

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Multiscale Dynamics of Bio-Systems: Molecules to Continuum

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  1. Multiscale Dynamics of Bio-Systems:Molecules to Continuum February 2005

  2. Why we need new approaches • Many degrees of freedom: multidimensional surface, local minima • Interconnected components: strongly or weakly coupled • Hierarchy of scales both in time & space Bridging regimes: time and length scales from atomistic to continuum How can we derive lower dimensional models from submicroscopic dynamics that reflect the physico-chemical properties of the system at different scales? M. Klein

  3. Key question: • How does the molecular fingerprint appear • at different time & length scales

  4. Techniques include • Efficient Numerical Algorithms: Advanced Time-Stepping and Sampling methods • System Reduction: Algebraic Graph theory, Computational Geometry, Convex Optimisation • Continuous Representations: Finite volume, Adaptive meshing

  5. Integrated Multidisciplinary Approach • At the Interface of Science, Engineering, Biology • From Departments of Aeronautics, Bioengineering, Chemistry, Mathematics… • M.A. Robb Ab-initio and QM/MM methodology for chemical Reactivity • I.R. Gould Hybrid QM/MM, Parallel MD, Force-field Development • S.N Yaliraki Coarse graining with Convex Optimisation • M. Barahona Graph theory, Nonlinear System Reduction, Dynamical Systems • K.H. Parker Biomechanics, Physiological Fluid Dynamics, Heamodynamics • J. Peiro´ Automatic generation of unstructured meshes, Biomedical Fluid Dynamics

  6. Identify optimal pathways that connect main structures Global Optimisation (SOS, SDP) Parrilo, Jadbabaie,Yaliraki Multiscale approaches in BioMolecular Modelling A. Efficient Numerical Algorithms for Atomistic Simulations Advanced time-stepping and sampling methods– SDEs, Symplectic methods Improved empirical potentials and Quantum/Classical interface Gould,Robb B. System Reduction C. Continuous Representations Finite volume approaches to mesh generation for biomolecules - Parker, Yaliraki, Peiró Identify Global Conformational motions Neighborhood graphs Geometric graphs Algebraic Graph theory - Barahona, Jadbabaie Reduce the multidimensional space Computational Geometry & Global Optimisation Compatible, geometric-based models that satisfy constraints Yaliraki Nonlinear System Reduction Barahona, Parrilo Discrete Probability Reversible Markov Chains Deduce state-based graphs

  7. A few examples

  8. Self Assembly of Viral Capsids 100 nm Barahona et al.

  9. Amyloid Fibril Formation in Neurodegenerative Diseases mm (length) nm (diameter); hours to ?? (Fig: Soto et al) Yaliraki et al. (e.g., Burke et al, PNAS100, 2003)

  10. Protein-Membrane Interactions: Signalling Gould et al. nm-mm; fs to hours

  11. Connective Tissue: Cartilage mm; hours Parker et al. Ehrlich et al, Biorheology35 (98) Mestel et al, Biorheology35 (98)

  12. V Design of Molecular Circuitry at the Nanoscale Molecular Electronics Bio-sensors

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