Physical Models of Cell Motility

208 Pages·2016·6.826 MB·English

by  Igor S. Aranson (eds.)

Biological and Medical Physics, Biomedical Engineering
Igor S. Aranson Editor
Physical
Models of
Cell Motility
Physical Models of Cell Motility
BIOLOGICAL AND MEDICAL PHYSICS,
BIOMEDICAL ENGINEERING
The fields of biological and medical physics and biomedical engineering are broad, multidisciplinary and
dynamic. Theylie atthe crossroadsof frontierresearchinphysics, biology, chemistry, andmedicine. The
BiologicalandMedicalPhysics,BiomedicalEngineeringSeriesisintendedtobecomprehensive,coveringa
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engineering.
Editor-in-Chief:
EliasGreenbaum,OakRidgeNationalLaboratory,OakRidge,Tennessee,USA
EditorialBoard:
MasuoAizawa,DepartmentofBioengineering, MarkS.Humayun,DohenyEyeInstitute,
TokyoInstituteofTechnology,Yokohama,Japan LosAngeles,California,USA
OlafS.Andersen,DepartmentofPhysiology, PierreJoliot,InstitutedeBiologie
Biophysics&MolecularMedicine, Physico-Chimique,FondationEdmond
CornellUniversity,NewYork,USA deRothschild,Paris,France
RobertH.Austin,DepartmentofPhysics, LajosKeszthelyi,InstituteofBiophysics,Hungarian
PrincetonUniversity,Princeton,NewJersey,USA AcademyofSciences,Szeged,Hungary
JamesBarber,DepartmentofBiochemistry, RobertS.Knox,DepartmentofPhysics
ImperialCollegeofScience,Technology andAstronomy,UniversityofRochester,Rochester,
andMedicine,London,England NewYork,USA
HowardC.Berg,DepartmentofMolecular AaronLewis,DepartmentofAppliedPhysics,
andCellularBiology,HarvardUniversity, HebrewUniversity,Jerusalem,Israel
Cambridge,Massachusetts,USA
StuartM.Lindsay,DepartmentofPhysics
VictorBloomfield,DepartmentofBiochemistry, andAstronomy,ArizonaStateUniversity,
UniversityofMinnesota,St.Paul,Minnesota,USA Tempe,Arizona,USA
RobertCallender,DepartmentofBiochemistry,
DavidMauzerall,RockefellerUniversity,
AlbertEinsteinCollegeofMedicine,
NewYork,NewYork,USA
Bronx,NewYork,USA
EugenieV.Mielczarek,DepartmentofPhysics
StevenChu,LawrenceBerkeleyNational
andAstronomy,GeorgeMasonUniversity,Fairfax,
Laboratory,Berkeley,California,USA
Virginia,USA
LouisJ.DeFelice,DepartmentofPharmacology,
MarkolfNiemz,MedicalFacultyMannheim,
VanderbiltUniversity,Nashville,Tennessee,USA
UniversityofHeidelberg,Mannheim,Germany
JohannDeisenhofer,HowardHughesMedical
V.AdrianParsegian,PhysicalScienceLaboratory,
Institute,TheUniversityofTexas,Dallas,
NationalInstitutesofHealth,Bethesda,
Texas,USA
Maryland,USA
GeorgeFeher,DepartmentofPhysics,
UniversityofCalifornia,SanDiego,LaJolla, LindaS.Powers,UniversityofArizona,
California,USA Tucson,Arizona,USA
HansFrauenfelder, EarlW.Prohofsky,DepartmentofPhysics,
LosAlamosNationalLaboratory, PurdueUniversity,WestLafayette,Indiana,USA
LosAlamos,NewMexico,USA AndrewRubin,DepartmentofBiophysics,Moscow
IvarGiaever,RensselaerPolytechnicInstitute, StateUniversity,Moscow,Russia
Troy,NewYork,USA MichaelSeibert,NationalRenewableEnergy
SolM.Gruner,CornellUniversity, Laboratory,Golden,Colorado,USA
Ithaca,NewYork,USA DavidThomas,DepartmentofBiochemistry,
JudithHerzfeld,DepartmentofChemistry, UniversityofMinnesotaMedicalSchool,
BrandeisUniversity,Waltham,Massachusetts,USA Minneapolis,Minnesota,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/3740
Igor S. Aranson
Editor
Physical Models of Cell
Motility
123
Editor
IgorS.Aranson
ArgonneNationalLaboratory
Argonne,IL,USA
ISSN1618-7210 ISSN2197-5647 (electronic)
BiologicalandMedicalPhysics,BiomedicalEngineering
ISBN978-3-319-24446-4 ISBN978-3-319-24448-8 (eBook)
DOI10.1007/978-3-319-24448-8
LibraryofCongressControlNumber:2015956180
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Preface
Multicellular organisms are composed of individual cells that form the tissues,
organs,andnervoussystem.Intheseorganisms,thecellsarereplacedroughlyevery
100 days via controlled division and cell death. However, both during organism
developmentandeveninthedevelopedorganism,therearespecializedcells,such
as keratocytes, fibroblasts, neutrophils, and others, that show a high propensity
to move. The motility of these cells is associated with their specific function
withintheorganism.Motileeukaryoticcellsrespondingtochemicalormechanical
stimuli play a fundamental role in tissue growth, wound healing, and immune
response. In addition, cell migration is essential for understanding several life-
threateningpathologiessuchascancer.Beyondtheobviousbiologicalandmedical
relevance, cell motility is also a fascinating example of a self-organizedand self-
propelledsystemwithintherealmofphysics.Themaindifficultyinformulatinga
comprehensivepredictivemodelof cell motility lies in the extremecomplexityof
theunderlyingbiologicalprocessesassociatedwith thedynamicsofmovingcells.
Correspondingly, a number of conceptually different theoretical approaches were
formulatedtotacklethisformidableproblem.Thisbookattemptstogiveasnapshot
of the most recent theoretical and experimental studies in this rapidly developing
field.Thedistinctivefeatureofthisbookisthatthemodelingapproachesarebased
onconceptsinspiredbycontemporarysoftmatterphysics,suchasorderparameters,
phasetransitions,reaction-diffusionsystems,conservationlaws,andforcebalance
conditions.
The structure of the book is as follows. It contains four chapters focused on
various approaches to cell movement. Chapter 1 presents a study of cell motility
basedonthephasefieldmethod.Thismethodisespeciallywellsuitedtotreatthe
movingand deformableboundariesinvolvedin bothindividualandcollective cell
motility.Itstartswithadidacticintroductiontoasimplemodelforthemovementof
an individual cell. Then, it describes how complexity can be added step by step,
such as deformability and adhesiveness of substrate, as well as modulations of
the substrate properties. Finally, it discusses how the modelcan be generalizedto
describetheinteractionsandthecollectivemovementofmany,self-organizedcells.
Chapter2focusesoncrawlingcellmotility drivenbyspontaneouspolymerization
v
vi Preface
waves.Itpresentstheoreticaldescriptionsofactindynamicsanddiscussesindetail
possiblemechanismsforwavegeneration.Then,thecouplingoftheactinnetwork
tothecellmembraneisadded.Theanalysisshowsthatspontaneouspolymerization
wavesofferaunifyingframeworkforexplainingdirectionalanderraticcellmotion
such as amoeboid motility. Chapter 3 features a modular view of the signaling
systemregulatingchemotaxis.Themodeldescribesanexcitablenetworkforsignal
transductionthatintegratesinformationfromvariousinternalandexternalcuesand
signalsto the actin cytoskeleton.Simulationsusingthe levelset methodallow the
testingofthismodelbyrecreatingchangesinmorphologyinducedbythesignaling
network.Finally,Chap.4isfocusedonone-dimensionalmodelsofmovingcellsthat
are amenableto theoreticaltreatment.Despite the unavoidableoversimplifications
associated with such a representation, the one-dimensional models happen to be
usefulforunderstandingtheintricateinterplaybetweencontractionandprotrusion.
This book is written primarily for biophysicists, mathematical biologists, and
biomedicalengineersenteringthefieldofcellmotilityandbiomechanics.We also
hope that experimentalists and theorists already working in the field will find it
usefulforitscomprehensivereviewof experimentalstudiesof cellmovementand
survey of the most recent physics-based modeling approaches. It can also serve
as supplementary reading material for advanced graduate courses on biological
physics and mathematical biology. This book is accompanied by a collection of
computationalonlinevideosillustratingvariousaspectsofcellmotility.
Argonne,IL,USA IgorS.Aranson
June2015
Contents
1 MacroscopicModelofSubstrate-BasedCellMotility ................... 1
FalkoZiebert,JakobLöber,andIgorS.Aranson
1.1 Introduction ............................................................. 1
1.1.1 Basic MechanismsInvolvedinthe Motility
ofEukaryoticCells............................................ 2
1.1.2 SurveyofExperimentalFactsforCellsCrawling
onTwo-DimensionalSubstrates.............................. 4
1.1.3 MainModelingApproaches.................................. 8
1.2 PhaseFieldModelforaSingleCell ................................... 11
1.2.1 PhaseFieldDescriptionoftheInterface ..................... 13
1.2.2 ActinDynamics ............................................... 16
1.2.3 OnForceBalanceVersusExplicitFlow...................... 19
1.2.4 AdhesionandCouplingtoSubstrateDeformation .......... 20
1.3 DynamicsofanIndividualCell ........................................ 22
1.3.1 SteadyMovingCell........................................... 23
1.3.2 SubcriticalOnsetofMotion .................................. 25
1.3.2.1 AnalyticalStudyofCellMovementin
CircularApproximation ............................ 26
1.3.2.2 VelocityBranchesinCircularApproximation..... 27
1.3.3 SteadyMotionvs.Stick-Slip ................................. 28
1.3.3.1 ReducedDescriptionoftheStick-SlipCycle...... 31
1.3.4 MoreComplexMotilityModes............................... 33
1.3.5 MovementonInhomogeneousSubstrates.................... 34
1.3.5.1 ModulationofSubstrateAdhesiveness ............ 36
1.3.5.2 ModulationofSubstrateStiffnessandDurotaxis . 38
1.4 CollectiveMigration.................................................... 39
1.4.1 MultiplePhaseFields ......................................... 40
1.4.1.1 StericInteraction.................................... 40
1.4.1.2 Cell–CellAdhesion................................. 41
1.4.1.3 GeneralizationofActin,Adhesion,and
SubstrateDynamics................................. 42
vii
viii Contents
1.4.2 BinaryInteractionsofCells................................... 43
1.4.3 ManyCells:CollectiveMigration............................ 45
1.4.3.1 TransitionsBetweenSpreadingand
CollectiveMotion................................... 45
1.4.3.2 CollectiveMigrationatModerateDensities....... 46
1.4.3.3 Collective Migration for Strong
Cell–CellAdhesionand/orHighDensity.......... 49
1.5 Conclusions ............................................................. 50
Appendix ...................................................................... 52
References..................................................................... 60
2 CellCrawlingDrivenbySpontaneousActinPolymerizationWaves... 69
KarstenKruse
2.1 Introduction ............................................................. 69
2.2 SpontaneousActinWaves .............................................. 70
2.3 TheoreticalDescriptionsofCellularActinDynamics ................ 73
2.3.1 ActinPolymerization.......................................... 73
2.3.2 MechanismsforGeneratingSpontaneousActinWaves..... 75
2.3.2.1 PolymerizationWavesintheAbsence
ofMotors............................................ 75
2.3.2.2 CytoskeletalWavesinPresenceofMotors ........ 79
2.3.3 CouplingActinDynamicstotheMembrane................. 81
2.3.3.1 SharpBoundaryMethods........................... 82
2.3.3.2 Phase-FieldMethods................................ 83
2.4 Wave-DrivenMigration................................................. 84
2.4.1 PhaseDiagram................................................. 85
2.4.2 PersistentMigrationPatterns ................................. 86
2.4.3 ErraticMigrationPatterns..................................... 88
2.5 Conclusions ............................................................. 89
2.6 SupplementaryMovies ................................................. 90
References..................................................................... 90
3 AModularViewoftheSignalingSystemRegulatingChemotaxis..... 95
PabloA.Iglesias
3.1 Introduction ............................................................. 95
3.2 Motility.................................................................. 97
3.2.1 RandomMotility .............................................. 97
3.2.2 ExcitableBehavior............................................ 98
3.2.3 ModelsofExcitableBehavior................................ 99
3.2.4 CouplingENActivitytoCellularDeformations............. 101
3.2.5 ViscoelasticCellMechanicalModel ......................... 102
3.2.6 SimulationsofRandomMotility ............................. 104
3.3 DirectionalSensingandAdaptation.................................... 104
3.3.1 LocalExcitation,GlobalInhibition........................... 105
3.3.2 ExperimentalSupportfortheLEGIMechanism ............ 106
Contents ix
3.4 CouplingDirectionalSensingtoMotility.............................. 108
3.4.1 ResponseofLEGI-BENtoSpatiallyUniformStimulation. 109
3.4.2 ResponseofLEGI-BENtoSpatiallyGradedStimulation... 111
3.4.3 MorphologicalChangesInducedbyLEGI-BEN............ 112
3.5 PolarizationandDirectionalPersistence............................... 113
3.5.1 SimulationsofLEGI-BEN-POL.............................. 115
3.5.2 ModelingInSilicoMutants................................... 116
3.6 TheCytoskeletalOscillatoryNetwork................................. 119
3.6.1 MathematicalDescriptionofSTEN-CON ................... 120
3.6.2 STEN-CONCoupling......................................... 121
3.6.3 SimulationsofCoupledSTEN-CONSystems............... 122
3.7 DiscussionandConclusions............................................ 124
Appendix ...................................................................... 126
References..................................................................... 128
4 CellLocomotioninOneDimension........................................ 135
PierreRechoandLevTruskinovsky
4.1 Introduction ............................................................. 135
4.2 Contraction.............................................................. 139
4.2.1 AToyModel................................................... 140
4.2.2 ContinuumThermodynamics................................. 145
4.2.3 SpecializationoftheModel................................... 150
4.2.4 Non-LocalReformulation..................................... 152
4.2.5 StaticSolutions................................................ 154
4.2.6 LinearStability................................................ 156
4.2.7 MotileSolutions............................................... 158
4.2.8 PassiveActinTreadmilling ................................... 162
4.2.9 NonlinearActiveStress....................................... 165
4.2.10 Discussion ..................................................... 167
4.3 Protrusion................................................................ 167
4.3.1 TheModel..................................................... 168
4.3.2 ForceVelocityRelation....................................... 171
4.3.3 ElasticRegularization......................................... 173
4.3.4 AlternativeDrivingModes.................................... 176
4.3.5 Discussion ..................................................... 178
4.4 Adhesion................................................................. 179
4.4.1 TheModel..................................................... 180
4.4.2 ContractionDrivenMotility .................................. 182
4.4.3 TheGeneralCase.............................................. 185
4.4.4 Discussion ..................................................... 188
4.5 Conclusions ............................................................. 189
References..................................................................... 190
Index............................................................................... 199