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## Multiscale Dynamics of Bio-Systems: Molecules to Continuum

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**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 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**Key question:**• How does the molecular fingerprint appear • at different time & length scales**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**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**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**Self Assembly of Viral Capsids**100 nm Barahona et al.**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)**Protein-Membrane Interactions: Signalling**Gould et al. nm-mm; fs to hours**Connective Tissue: Cartilage**mm; hours Parker et al. Ehrlich et al, Biorheology35 (98) Mestel et al, Biorheology35 (98)**V**Design of Molecular Circuitry at the Nanoscale Molecular Electronics Bio-sensors