10/3/2003 Molecular and Cellular Modeling
10/3/2003 Introduction Objective: to construct a comprehensive simulation software system for the computational modeling of mechanical interactions in proteins and cells. Main idea: civil engineering approach to biology Mathematical model: thin rod theory –Ribbons and groups –Perturbation method –Finite element model
10/3/2003 Ribbons and Groups Ribbons are framed paths: (r,n) central curve director Deformation: The set of deformation forms Lie group under Rotation matrix and rotation rate Rotation matrix Rotation rate
10/3/2003 Perturbation Method Equilibrium configurations: minimum energy state Quadratic approximation Thin rod equations Perturbation equations
10/3/2003 Finite Element Model Strains and strain increments Energy increments
10/3/2003 Molecular Mechanics - Proteinmorphosis Objective: to create a general model for ligand binding and more general protein conformational changes. Microscopic approaches: molecular dynamics Main features of our system –macroscopic formulation –protein backbone as 1-D elasticity thin rod –global parameterization –incremental energy minimization –interactive visualization
10/3/2003 Protein Structure Hierarchy Protein: linear amino acid polymer polypeptide chains Primary: amino acid sequence Secondary: helix, sheet Supersecondary: motif Tertiary: single polypeptide Quaternary: i.e. enzyme complex
10/3/2003 Hierarchical Representation Primary structureSecondary structure Tertiary structureQuaternary structure
10/3/2003 Dynamic Visualization
10/3/2003 Collision Vector Visualization
10/3/2003 Global Parameterization Backbone - rather constrained degrees of freedoms: –Fixed bond length, bond angle –Torsion angles are freedoms –Every third bond is rigid Sidechains - less flexibility. Local coordinate: torsion angles Global coordinate: displacement of nodal atoms. CC CC CC N N H H H C’ O O sidechain
10/3/2003 Potential Energy Force field: torsion, hydrogen bond, van der Waals, distance restraint Stiffness and load
10/3/2003 Variational Approach Total stiffness and load Linear constraint quadratic minimization Multi-scale methods
10/3/2003 Calmodulin Peptide Binding CalmodulinPeptide binding (PDB) Peptide binding (simulation) Animation
10/3/2003 Hemoglobin Oxygen Binding Hemoglobin structure: symmetrically arranged four subunits Allosteric oxygen binding Deoxygenated Hb (T state) Oxygenated Hb (R state)
10/3/2003 Modeling of Allostery Trigger of allosteric transition Loss of cooperativity F helix F8 HIS Fe heme
10/3/2003 Cellular Mechanics - Cellmate From gel volume to civil engineering structure: cytoskeleton network and its three components How mechanics controls biochemistry
10/3/2003 Tensegrity - Architecture of Life Continuous tension and isolated compression. Prestressed tensions Features: - Highly stable - Global response to a local signal
10/3/2003 Cells as Tensegrity Structures Tension elements: microfilaments Compression elements: microtubules and ECM Intermediate filaments as integrators and guy wires
10/3/2003 Image Processing Data acquisition: confocal microscopy Filament extraction
10/3/2003 Create Virtual Cytoskeleton
10/3/2003 Reach-In Interface
10/3/2003 Model of Cell Crawling
10/3/2003 An Integrated System A multi-scale computational model Different virtual environment: CAVE, Reach-In
10/3/2003 Conclusions It is a multi-disciplinary research: - mathematics and physics - biology - computer science - engineering The result can also be used elsewhere