Chapter 1  Modeling and Simulations of the Dynamics of Growing CellClusters  1.1  Introduction  1.2  Single cell geometry and kinematics    1.2.1  The  Chapter 1 Modeling and Simulations of the Dynamics of Growing CellClusters 1.1 Introduction 1.2 Single cell geometry and kinematics 1.2.1 The continuum model 1.2.2 The numerical model for the cell geometry 1.3 Single cell equilibrium and material model 1.3.1 Cell equilibrium 1.3.2 The material model 1.3.3 Determination of material constants 1.4 Modeling cell interactions 1.4.1 Cell-to-cell contact 1.4.2 Cell-to-cell adhesion 1.4.3 Cell-to-cell interaction test 1.5 Modeling the cell life cycle 1.6 Details of the numerical implementation 1.6.1 The finite element model 1.6.2 Contact/adhesion interface detection 1.6.3 Time integration 1.6.4 Parallelization 1.7 Numerical results 1.8 Summary and conclusions ReferencesChapter 2 Multiscale Biomechanical Modeling of StemCell-Extracellular Matrix Interactions 2.1 Introduction 2.2 Cell and ECM modeling 2.2.1 Basic hypothesis and assumptions 2.2.2 Hyperelastic model 2.2.3 Liquid crystal model 2.3 Contact and adhesion models for cell-substrateinteractions 2.3.1 The adhesive body force with continuum mechanics contact 2.3.2 The cohesive contact model 2.4 Meshfree Galerkin formulation and the computationalalgorithm 2.5 Numerical simulations 2.5.1 Validation of the material rhodels 2.5.2 Cell response in four different stiffness substrates 2.5.3 Cell response to a stiffness-varying substrate 2.5.4 Comparison of two different contact algorithms 2.5.5 Three-dimensional simulation of cell spreading 2.6 Discussion and conclusions ReferencesChapter 3 Modeling of Proteins and Their Interactions with Solvent 3.1 Introduction 3.2 Classical molecular dynamics 3.2.1 Coarse-grained model 3.2.2 High performance computing 3.3 Principal component analysis 3.3.1 Three oscillators system analysis with PCA 3.3.2 Quasi-harmonic analysis 3.3.3 Equilibrium conformational analysis 3.4 Methods and procedures 3.4.1 Framework 3.4.2 Overlap coefficients 3.4.3 Correlation analysis 3.4.4 PCA with MD simulation 3.4.5 Kabsch algorithm 3.4.6 Positional correlation matrix 3.4.7 Cluster analysis 3.5 MD simulation with T4 lysozyme 3.5.1 Equilibration measures 3.5.2 Fluctuation analysis 3.5.3 Mode selection and evaluation 3.5.4 Eigenvalue analysis 3.5.5 Overlap evaluation 3.5.6 Identification of slow conformational flexibility 3.5.7 Correlation analysis of T4 lysozyme 3.6 Hemoglobin and sickle cell anemia 3.6.1 Molecular dynamic simulation with NAMD 3.6.2 Conformational change analysis 3.6.3 PCA analysis 3.6.4 Correlation analysis with HbS interaction 3.7 Conclusion ReferencesChapter 4 Structural， Mechanical and Functional Properties ofIntermediate Filaments from the Atomistic to the Cellular Scales 4.1 Introduction 4.1.1 Hierarchical structure of vimentin intermediatefilaments 4.1.2 The structural and physiological character of keratin 4.2 Connecting filaments to cells level function and pathology 4.2.1 Bending and stretching properties of IFs in cells 4.2.2 IFs responding differently to tensile and shear stresses 4.2.3 Mechanotransduction through the intermediate filamentnetwork 4.3 Experimental mechanics 4.3.1 Single filament mechanics 4.3.2 Rheology of IF networks in vitro 4.3.3 IF networks rheology in cells 4.4 Case studies 4.4.1 Single vimentin filament mechanics 4.4.2 Network mechanics 4.4.3 The mechanical role of intermediate filament in cellularsystem 4.5 Conclusion ReferencesChapter 5 Cytoskeletal Mechanics and Rheology 5.1 Introduction 5.2 Modelling semiflexible filament dynamics 5.3 Experimental measurements 5.3.1 Glass microneedles 5.3.2 Cell poking 5.3.3 Atomic force microscopy 5.3.4 Micropipette aspiration 5.3.5 Microplates 5.3.6 Parallel-plate flow chambers 5.3.7 Optical tweezers 5.3.8 Magnetic traps 5.4 Computational models 5.5 Conclusion ReferencesChapter 6 On the Application of Multiphasic Theories to theProblem of Cell-substrate Mechanical Interactions 6.1 Introduction 6.2 The physics of contractile fibroblasts and theirinteractions with an elastic substrate 6.2.1 Cell spreading, contractility and substrate elasticity 6.2.2 Molecular mechanisms of cell contractility 6.3 Multiphasic mixture theory and cell contractility 6.3.1 The cytoplasm as a quadriphasic medium 6.3.2 Mass transport and mass exchange within the cell 6.3.3 Contractility and force balance 6.3.4 Model's prediction for simple cases 6.4 Interaction between contractile cells and compliantsubstrates 6.4.1 Two-dimensional plane stress formulation 6.4.2 Numerical strategy: XFEM-level methods 6.4.3 Analysis of mechanical interactions between acontractile cell and an elastic substrate 6.5 Summary and conclusion 6.5.1 Summary 6.5.2 Limitations of the multiphasic approach 6.5.3 Concluding remark ReferencesChapter 7 Effect of Substrate Rigidity on the Growth of NascentAdhesion Sites 7.1 Introduction 7.2 Model 7.3 Results and Discussion 7.4 Conclusion ReferencesChapter 8 Opto-Hydrodynamic Trapping for Multiaxial Single-CellBiomechanics 8.1 Introduction 8.2 Optical-hydrodynamic trapping. 8.2.1 Optical physics and microfluidics 8.2.2 Theoretical stress analysis 8.2.3 Experimental and computational flow validation 8.2.4 Applied stresses and strain response 8.2.5 Multiaxial single-cell biomechanics 8.3 Discussion ReferencesChapter 9 Application of Nonlocal Shell Models to MicrotubuleBuckling in Living Cells 9.1 Introduction 9.2 Nonlocal shell theories 9.2.1 Constitutive relations 9.2.2 Shear deformable shell model 9.2.3 Thin shell model 9.3 Bending buckling analysis 9.4 Numerical results and discussion 9.5 ConclusionsAppendix AAppendix BAppendix CAppendix DReferences