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

From atomistic descriptions to dynamical coarse-graining Hierarchy of time and length scales Compatible geometric based models that satisfy constraints Derive model Extract Global Properties at different scales

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

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 Identify optimal pathways that connect main structures Global Optimisation (SOS, SDP) Parrilo, Jadbabaie,Yaliraki Multiscale approaches in BioMolecular Modelling Identify Global Conformational motions Discrete Probability Reversible Markov Chains Deduce state-based graphs C. Continuous Representations Finite volume approaches to mesh generation for biomolecules - Parker, Yaliraki, Peiró Reduce the multidimensional space Computational Geometry & Global Optimisation Compatible, geometric-based models that satisfy constraints Yaliraki Nonlinear System Reduction Barahona, Parrilo Geometric graphs Algebraic Graph theory - Barahona, Jadbabaie Neighborhood graphs B. System Reduction

A few examples

Self Assembly of Viral Capsids Barahona et al. 100 nm

Amyloid Fibril Formation in Neurodegenerative Diseases Yaliraki et al. (e.g., Burke et al, PNAS 100, 2003)  m (length) nm (diameter); hours to ?? (Fig: Soto et al)

Protein-Membrane Interactions: Signalling Gould et al. nm-  m; fs to hours

Connective Tissue: Cartilage Parker et al. mm; hours Ehrlich et al, Biorheology 35 (98) Mestel et al, Biorheology 35 (98)

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