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 appearat 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 ProbabilityReversible 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

Cornell et al, J.Am.Chem.Soc. 117 (95)Hughes et al, BMC Structural Biology, 3 (03)

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

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