Post on 20-Apr-2018
Introduction to Cell Mechanics and Mechanobiology
Christopher R. Jacobs
Hayden Huang
Ronald Y. Kwon
GS Garland Science Taylor & Francis Group
NEW YORK AND LONDON
Preface v CHAPTER 2: Fundamentals in Cell Biology 19
PART 1: PRINCIPLES 1 2.1 Fundamentals in cell and molecular
CHAPTER 1: Cell Mechanics as a Framework 3 biology 19
1.1 Cell mechanics and human disease 4 Proteins are polymers of amino acids 20
Specialized cells in the ear allow you to hear 5 DNA and RNA are polymers of
nucleic acids 22 Hemodynamic forces regulate endothelial Polysaccharides are polymers of sugars 24
cells 6
To keep bone healthy, bone cells need Fatty acids store energy but also form
structures 24 mechanical stimulation 6
The cells that line your lungs sense stretch 7 Correspondence between DNA-to-RNA-
to-protein is the central dogma of Pathogens can alter cell mechanical properties 7 modern cell biology 25 Other pathogens can use cell mechanical Phenotype is the manifestation
structures to their advantage 7 of genotype 27 Cancer cells need to crawl to be metastatic 8 Transcriptional regulation is one way Viruses transfer their cargo into cells they that phenotype differs from genotype 28
infect 8 Cell organelles perform a variety 1.2 The cell is an applied mechanics grand of functions 29
challenge 8 2.2 Receptors are cells' primary chemical Computer simulation of cell mechanics sensors 30
requires state-of-the-art approaches 9 Cells communicate by biochemical signals 30 1.3 Model problem: micropipette aspiration 9 Signaling between cells can occur
What is a typical experimental setup for through many different mechanisms 31 micropipette aspiration? 9 Intracellular signaling occurs via small
The liquid-drop model is a simple model molecules known as second messengers 32 that can explain some aspiration results 11 Large molecule signaling cascades
The Law of Laplace can be applied to a have the potential for more specificity 34 spherical cell 12 Receptors use several mechanisms to
Micropipette aspiration experiments can initiate signaling 35 be analyzed with the Law of Laplace 12 2.3 Experimental biology 36
How do we measure surface tension Optical techniques can display cells clearly 37 and areal expansion modulus? 13 Fluorescence visualizes cells with lower
Why do cells "rush in"? 15 background 38 Cells can behave as elastic solids Fluorophores can highlight structures 39
or liquid drops 16 Fluorophores can probe function 40 Key Concepts 16 Atomic force microscopy can elucidate Problems 17 the mechanical behavior of cells 40 Annotated References 17 Gel electrophoresis can separate molecules 41
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Visualizing gel-separated products employs Torsion of a solid cylinder can be a variety of methods 42 modeled as a torsion of a series of
PCR amplifies specific DNA regions shells of increasing radius 61
exponentially 43 Kinematics, equilibrium, and constitutive
2.4 Experimental design in biology 46 equations are the foundation of solid
Reductionist experiments are powerful mechanics 62
but limited 46 Kinematics in a beam are the strain-
Modern genetics has advanced our displacement relationship 62
ability to study in situ 48 Equilibrium in a beam is the stress-
Bioinformatics allows us to use vast moment relationship 64
amounts of genomic data 49 The constitutive equation is the
Systems biology is integration rather stress-strain relationship 65
than reduction 49 The second moment of inertia is a
Biomechanics and mechanobiology are measure of bending resistance 65
integrative 49 The cantilevered beam can be solved
Key Concepts 50 from the general beam equations 66
Problems 50 Buckling loads can be determined from
Annotated References 52 the beam equations 67
Transverse strains occur with axial loading 68
CHAPTER 3: Solid Mechanics Primer 53 The general continuum equations can be
3.1 Rigid-body mechanics and free-body developed from our simple examples 68
diagrams 53 Equilibrium implies conditions on stress 69
What is a "rigid" body? 53 Kinematics relate strain to displacement 71
One of the most powerful, but underused, The constitutive equation or stress-strain
tools is a free-body diagram 53 relation characterizes the material behavior 73
Identifying the forces is the first step in Vector notation is a compact way to express
drawing a free-body diagram 54 equations in continuum mechanics 74
Influences are identified by applying the Stress and strain can be expressed as matrices 76
equations of motion 54 In the principal directions shear stress is zero 76
Free-body diagrams can be drawn for parts 3.3 Large deformation mechanics 78
of objects 55 The deformation gradient tensor
3.2 Mechanics of deformable bodies 55 describes large deformations 78
Rigid-body mechanics is not very Stretch is another geometrical measure
useful for analyzing deformable bodies 55 of deformation 79
Mechanical stress is analogous to pressure 56 Large deformation strain can be defined
Normal stress is perpendicular to the in terms of the deformation gradient 80
area of interest 56 The deformation gradient can be
Strain represents the normalized decomposed into rotation and
change in length of an object to load 57 stretch components 82
The stress-strain plot for a material 3.4 Structural elements are defined by
reveals information about its stiffness 57 their shape and loading mode 83
Stress and pressure are not the same Key Concepts 84
thing, because stress has directionality 58 Problems 84
Shear stress describes stress when forces Annotated References 87
and areas are perpendicular to each other 59
Shear strain measures deformation CHAPTER4: Fluid Mechanics Primer 89 resulting from shear stress 59 4.1 Fluid statics 89
Torsion in the thin-walled cylinder can Hydrostati.c pressure results from be modeled with shear stress relations 60 gravitational forces 89
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Hydrostatic pressure is isotropic 91 5.1 Internal energy 120
Resultant forces arising from hydrostatic Potential energy can be used to make pressure can be calculated through predictions of mechanical behavior 120 integration 92 Strain energy is potential energy stored
4.2 Newtonian fluids 92 in elastic deformations 122
Fluids obey mass conservation 93 Equilibrium in continuum mechanics is
Fluid flows can be laminar or turbulent 94 a problem of strain energy minimization 123
Many laminar flows can be solved analytically 95 Changes in mechanical state alter
Many biological fluids can exhibit internal energy 123
non-Newtonian behavior 97 5.2 Entropy 124
4.3 The Navier-Stokes equations 98 Entropy is directly defined within
Derivation of the Navier-Stokes equations statistical mechanics 124
begins with Newton's second law 99 Microstates, macrostates, and density
Constitutive relations and the continuity of states can be exemplified in a
equation are necessary to make Navier's three-coin system 124
equations solvable 102 Microstates, macrostates, and density
Navier-Stokes equations: putting it all of states provide insight to macroscopic
together 103 system behavior 127
4.4 Rheological analysis 103 Ensembles are collections of microstates
The mechanical behavior of viscoelastic sharing a common property 127
materials can be decomposed into Entropy is related to the number of microstates
elastic and viscous components 104 associated with a given macrostate 127
Complex moduli can be defined for 5.3 Free energy 128
viscoelastic materials 106 Equilibrium behavior for thermodynamic
Power laws can be used to model frequency- systems can be obtained via free energy
dependent changes in storage and minimization 128
loss moduli 108 Temperature-dependence of end-to-end
4.5 Dimensional analysis no length in polymers arises out of
Dimensional analysis requires the competition between energy and entropy 129
determination of base parameters llO 5.4 Microcanonical ensemble 131
The Buckingham Pi Theorem gives the The hairpinned polymer as a non-
number of dimensionless parameters interacting two-level system 132
that can be formed from base parameters ll1 A microcanonical ensemble can be
Dimensionless parameters can be found used to determine
through solving a system of equations 1ll constant energy microstates 132
Similitude is a practical use of Entropy can be calculated via
dimensional analysis 113 combinatorial enumeration of the
Dimensional parameters can be density of states 133
used to check analytical expressions ll4 Entropy is maximal when half the
Key Concepts 115 sites contain hairpins 133
Problems ll6 S(W) can be used to predict equilibrium
behavior 133 Annotated References ll7 The number of hairpins at equilibrium is
dependent on temperature 134 CHAPTER 5: Statistical Mechanics Primer 119 Equilibrium obtained via the
Statistical mechanics relies on the use microcanonical ensemble is identical to
of probabilistic distributions ll9 that obtained via free energy minimization 135
Statistical mechanics can be used to 5.5 Canonical ensemble 136 investigate the influence of random Canonical ensemble starting from the molecular forces on mechanical behavior 119 microcanonical ensemble 136
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Probability distribution from the canonical 6.2 Measurement offorces produced by cells 160 ensemble gives Boltzmann's law 138 Traction force microscopy measures the forces
The free energy at equilibrium can be exerted by a cell on its underlying surface 160 found using the partition function 139 Cross-correlation can be used for
The internal energy at equilibrium can be particle tracking 160 determined using the partition function 141 Determining the forces that produced a
Using the canonical approach may be displacement is an inverse problem 163 preferable for analyzing thermodynamic Microfabricated micropillar arrays can systems 142 be used to measure traction forces directly 165
5.6 Random walks 143 Surface modification can help determine A simple random walk can be how a cell interacts with its surroundings 166
demonstrated using soccer 143 6.3 Applying forces to cells 167
The diffusion equation can be derived Flow chambers are used for studying from the random walk 145 cellular responses to fluid shear stress 167
Key Concepts 147 The transition between laminar and
Problems 148 turbulent flow is governed by the
Annotated References 149 Reynolds number 168
Parallel plate flow devices can be designed for low Reynolds number shear flow 168
CHAPTER 6: Cell Mechanics in the Fully developed flow occurs past the
Laboratory 151 entrance length 169
6.1 Probing the mechanical behavior of cells Cone-and-plate flow can be used to
through cellular micromanipulation 151 study responses to shear 170
Known forces can be applied to cells through Diverse device designs can be used to
the use of cell-bound beads and an study responses to fluid flow 171
electromagnet 152 Flexible substrates are used for
The dependence of force on distance subjecting cells to strain 172
from the magnet tip can be calibrated Confined uniaxial stretching can lead through Stokes' law 152 to multiaxial cellular deformations 172
Magnetic twisting and multiple-pole Cylindrically symmetric deformations micromanipulators can apply stresses generate uniform biaxial stretch 172 to many cells simultaneously 153 6.4 Analysis of deformation 173
Optical traps generate forces on particles Viscoelastic behavior in micromanipulation through transfer of light momentum 153 experiments can be parameterized
Ray tracing elucidates the origin of through spring-dashpot models 173
restoring forces in optical tweezers 154 Combinations of springs and dash pots can
What are the magnitudes of forces in be used to model viscoelastic behavior 174
an optical trap? 155 Microscopy techniques can be adapted
How does optical trapping compare to visualize cells subject to mechanical
with magnetic micromanipulation? 156 loading 177
Atomic force microscopy involves the Cellular deformations can be inferred
direct probing of objects with a small from image sequences through
cantilever 157 image correlation-based approaches 178
Cantilever deflection is detected using Intracellular strains can be computed
a reflected laser beam 157 from displacement fields 179
Scanning and tapping modes can be 6.5 Blinding and controls 181
used to obtain cellular topography 158 Key Concepts 182
A Hertz model can be used to estimate Problems 183
mechanical properties 158 Annotated References 184
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PART II: Practices 187 Force is the gradient of free energy in thermodynamic systems 208
CHAPTER 7: Mechanics of Cellular The behavior of polymers tends Polymers 189 toward that of an ideal chain in
7.1 Biopolymer structure 189 the limit oflong contour length 209 Microfilaments are polymers composed 7.5 Freely jointed chain (FJC) 210
of actin monomers 189 The FJC model places a limit on F-actin polymerization is influenced by polymer extension 210
the molecular characteristics of G-actin 189 The force-displacement relation for the Microtubules are polymers composed FJC can be found by the canonical
of tubulin dimers 191 ensemble 211 MT polymerization is affected by Differences between the ideal chain
polarity and GTP /GDP binding 191 and the FJC emerge at large forces 213 Intermediate filaments are polymers 7.6 Worm-like chain (WLC) 214
with a diverse range in composition 192 The WLC incorporates energetic Intermediate filaments possess a coiled-coil effects of bending 214
structure 192 The force-displacement relation for Intermediate filaments have diverse the WLC can be found by the
functions in cells 192 canonical ensemble 216 7.2 Polymerization kinetics 194 Differences in the WLC and FJC emerge
Actin and MT polymerization can when they are fitted to experimental data be modeled as a bimolecular reaction 195 for DNA 217
The critical concentration is the only Persistence length is related to Kuhn concentration at which the polymer length 218 does not change length 195 Key Concepts 219
Polarity leads to different kinetics on Problems 220 each end 196 Annotated References 221
Polymerization kinetics are affected by ATP/ADP in actin and GTP/GDP binding in tubulin 197 CHAPTER 8: Polymer Networks and
Subunit polarity and ATP hydrolysis lead to the Cytoskeleton 223 polymer treadmilling 197 8.1 Polymer networks 223
7.3 Persistence length 198 Polymer networks have many degrees Persistence length gives a measure of freedom 223
of flexibility in a thermally fluctuating Effective continuums can be used to polymer 198 model polymer networks 223
Persistence length is related to 8.2 Scaling approaches 225 flexural rigidity for an elastic beam 200
Cellular solids theory implies Polymers can be classified as stiff, flexible, scaling relationships between
or semi-flexible by the persistence length 202 effective mechanical properties and 7.4 Ideal chain 203 network volume fraction 225
The ideal chain is a polymer model Bending-dominated deformation results for flexible polymers 203 in a nonlinear scaling of the elastic
The probability for the chain to have different modulus with volume fraction 225 end-to-end lengths can be determined Deformation dominated by axial strain from the random walk 204 results in a linear scaling of the
The free energy of the ideal chain can be elastic modulus with volume fraction 227 computed from its probability The stiffness oftensegrity structures distribution function 207 scales linearly with member prestress 228
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8.3 Affine networks 229 The fluid mosaic model of the cell membrane
Affine deformations assume the describes its physical properties 252
filaments deform as if they are 9.2 Phospholipid self-assembly 252 embedded in a continuum 229 Critical micelle concentration depends
Flexible polymer networks can on amphiphile molecular structure 253 be modeled using rubber elasticity 230 Aggregate shape can be understood
Anisotropic affine networks can be from packing constraints 254 modeled using strain energy approaches 233 9.3 Membrane barrier function 255
Elastic moduli can be computed The diffusion equations relate from strain energy density 233 concentration to flux per unit area 256
Elastic moduli of affine anisotropic networks Pick's second law shows how spatial can be calculated from appropriate concentration changes as a function of time 257 strain energy density and angular
9.4 Membrane mechanics 1: In -plane shear distribution functions 235
and tension 259 8.4 Biomechanical function and
Thin structures such as membranes cytoskeletal structure 236
can be treated as plates or shells 260 Filopodia are cross-linked bundles
Kinematic assumptions help describe of actin filaments involved in cell motility 236 deformations 260
Actin filaments within filopodia can be A constitutive model describes
modeled as elastic beams undergoing material behavior 262
buckling 236
The membrane imparts force on the The equilibrium condition simplifies
ends of filopodia 238 for in-plane tension and shear 262
The maximum filopodium length before Equilibrium simplifies in the case of
buckling in the absence of cross-linking is shear alone 265
shorter than what is observed in vivo 238 Equilibrium simplifies in the case of
Cross-linking extends the maximum equibiaxial tension 266
length before buckling 238 Areal strain can be a measure of
Is the structure of the red blood cell's biaxial deformation 267
cytoskeleton functionally advantageous? 239 9.5 Membrane mechanics II: Bending 267
Thin structures can be analyzed using the In bending the kinematics are
two-dimensional shear modulus and governed by membrane rotation 268
the areal strain energy density 240 Linear elastic behavior is assumed
Sixfold connectivity facilitates resistance for the constitutive model 269
to shear 242 Equilibrium places conditions on
Fourfold connectivity does not resultant forces and moments 269
sustain shear as well as sixfold 245 Which dominates, tension or bending? 272
Key Concepts 246 9.6 Measurement of bending rigidity 272
Problems 246 Membranes undergo thermal
Annotated References 247 undulations similar to polymers 272
Membranes straighten out with tension 273
CHAPTER 9: Mechanics of the Cell Key Concepts 275
Membrane 249 Problems 275
9.1 Membrane biology 249 Annotated References 277
Water is a polar molecule 249
Cellular membranes form by interacting CHAPTER 10: Adhesion, Migration, and with water 250 Contraction 279
The saturation of the lipid tails determines 10.1 Adhesion 279
some properties of the membrane 251 Cells can form adhesions with the substrate 279
The cell membrane distinguishes inside Fluid shear can be used to measure and outside 251 adhesion strength indirectly 281
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ll.4 Alteration of cellular function 330 Mechanical stimulation can induce
Intracellular calcium increases in extracellular matrix remodeling 333
response to mechanical stress 330 Cell viability and apoptosis are altered
Nitric oxide, inositol triphosphate, and by different processes 334
cyclic AMP, like Ca2+, are second Key Concepts 334
messenger molecules implicated in Problems 334 mechanosensation 331 Annotated References 335
Mitogen-activated protein kinase activity is altered after exposure to mechanical stimulation 332 Abbreviations 337
Mechanically stimulated cells exhibit List of variables and units 338 prostanglandin release 332 Index 343
Mechanical forces can induce morphological changes in cells 332