Living Cell Mechanics I. Jelly, glass or prestressed construction?

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18 Ιουλ 2012 (πριν από 5 χρόνια και 2 μήνες)

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Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Living Cell Mechanics I.
Jelly,glass or prestressed construction?
Miroslav Holeˇcek,Petra Kochov´a
Nanosemin´aˇr 2007,Plzeˇn,February
1
Department of Mechanics,West Bohemia University,Pilsen,Faculty of Applied Sciences
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Outline
Cell Mechanics
Cytoskeleton
Approaches for Understanding Mechanical Properties of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement techniques
Microrheology
Atomic Force Microscopy
Micropipette Aspiration
Traction Force Microscopy
Optical Tweezers or Laser Traps
Magnetic Traps
Magnetic Twisting Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Microelectromechanical Systems Devices
Future View
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Biological complexitythe structural basis of cell motility.It is a major challenge to rebuild in vitro such complex heterogeneous
and out-of-equilibrium structures as the filopodia,emerging at the leading edge of crawling melanoma cells,as shown in these
electron microscopy images.a,A tight bundle of actin filaments,splaying apart at its root,becomes an integral part of the
surrounding dendritic network of the lamellipodium.b,Fused filopodia,each having a splayed root.c,Enlargement of the
boxed region in b at the root of the filopodium;branches at which filopodia originate are circled.Scale bars 0.2 µm.
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Semi-flexible Polymers
Description of the mechanical behavior of reconstituted networks (especially
F-actin),usually in vitro experiments.Elasticity of not fully flexible polymer
networks - both entropic and enthalphic elasticity.Strongly non-linear
behavior.
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Semi-flexible Polymers
￿
gels can be formed from a variety of biological filament types
￿
biological gels stiffen when they are strained to a large extent
￿
this property prevents large cell/tissue deformations and thus damage
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Semi-flexible Polymers
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
”Engineering” Approaches
FEM or other computer-generated solutions to constitutive equations.Their
predictive power is ultimately limited by the exact input used to described
components of the cell.
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
”Engineering” Approaches
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Tensegrity Model
Cell as a prestressed ”construction” (tension integrity).They highlights the
role of prestress in determining cell elasticity.
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Soft Glassy Rheology
Cell as a soft glassy material near the glassy transition.At slow time scales
(> 0.01 s),some relaxation processes driven by non-thermal stress
fluctuations,such as those generated by molecular motors.
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Soft Glassy Rheology
Dispersed Medium
Gas
Liquid
Solid
Gas
NONE
Liquid Aerosol
Solid Aerosol
(All gases are
Examples:Fog,
Examples:
soluble)
mist
Smoke,
dust
Conti-
Liquid
Foam
Emulsion
Sol
nuous
Examples:
Examples:Milk,
Examples:Paint,
Medium
Whipped
mayonnaise,hand
pigmented ink,
cream
cream
blood
Solid
Solid Foam
Gel
Solid Sol
Examples:
Examples:Gelatin
Examples:
Aerogel,
jelly,cheese,opal
Cranberry glass,
styrofoam,
ruby glass
pumice
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Living Cells
￿
the biological cell constitutes the basic unit of life and performs a variety
of functions:the synthesis,sorting,storage and transport of molecules;
the expression of genetic information;the recognition,transmission and
transduction of signals;and the powering of molecular motors
￿
cells can sense mechanical forces and convert them into biological
responses
￿
the cell also converts energy from one form to another and responds to
external environments by continually altering its structure
￿
adhesion of cells to extracellular matrix (ECM) through focal adhesion
complexes provides both signalling and structural functions
￿
cells also undergo mechanical deformation when subjected to external
forces and geometric constraints — the human red blood cell with a
diameter of 7.8 −8.0 µm is subjected to about 100% elastic deformation
as blood flows through narrow capillaries with inner diameter smaller than
3 µm
￿
many normal and diseased conditions of cells are dependent on/or
regulated by their mechanical environment,and the deformation
characteristics of cells can provide important information about their
biological and structural functions
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Mechanical Properties
￿
the resistance of single cells to elastic deformation,as quantified by an
effective elastic modulus,ranges from 10
2
to 10
5
Pa,orders of magnitude
smaller than that of metals,ceramics and polymers
￿
the deformability of cells is determined largely by the cytoskeleton,whose
rigidity is influenced by the mechanical and chemical environments
including cell–cell and cell-ECM interactions
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Measurement techniques
￿
the past decade has seen the development of instruments capable of
mechanically probing and manipulating single cells and biomolecules at
forces and displacements smaller than a piconewton (1 pN = 10
−12
N)
and a nanometer (1 nm = 10
−9
m),respectively →for examining the
processes responsible for operation of cellular machinery,the forces
arising from molecular motors and the interactions between cells,proteins
and nucleic acids
￿
experimental techniques developed over the years to study the mechanical
behaviour of cells can be broadly classified into three types
- local probes in which a portion of the cell is deformed (structural
heterogeneity and region-to-region variation of cell properties);
- mechanical loading of an entire cell;
- simultaneous mechanical stressing of a population of cells
￿
all these experiments aim is to explain cellular deformation versus applied
force data and/or the cellular deformation versus datas time,by
investigating how the deformability of the cell is connected to its internal
structure
￿
suitable cell structural models are created to analyze deformation data
and obtain structural parameters,such as elastic modulus E or G,
viscosity µ or frequency-dependent storage modulus E
￿
of G
￿
(elasticity)
and loss modulus E
￿￿
of G
￿￿
(viscosity)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Measurement techniques
￿
many materials have both elastic and viscous properties
￿
the elasticity of biopolymer networks makes them resist deformation like a
simple spring for which the energy of deformation is stored in the material
regardless of time;to quantify this we measure an elastic modulus,G’,
which is analogous to a spring constant.
￿
the viscosity of biopolymer networks allows them to flow as a fluid,
leading to resistance that depends on the rate of deformation like in a
dashpot for which the energy put into deformation is dissipated or lost;a
viscous modulus,G”,characterizes this
￿
isotropic materials:
G =
E
2(1 +ν)
,
where G is shear modulus,E is Young’s modulus and ν is Poisson’s ratio
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Microrheology
￿
rheology is the study of the deformation and flow of a material in
response to applied stress;simple solids store energy and provide a
spring-like,elastic response,whereas simple liquids dissipate energy
through viscous flow;for more complex viscoelastic materials,rheological
measurements reveal both the solid and fluid-like responses and generally
depend on the time scale at which the sample is probed (gardel)
￿
one way to characterize rheological response is to measure the shear
modulus as a function of frequency:mechanical rheometer by applying a
small amplitude oscillatory shear strain:γ(t) = γ
0
sin(ωt),where γ
0
is the
amplitude and ω is the frequency of oscillation,and measuring the
resultant shear stress
￿
time-dependent stress is linearly proportional to the strain,and is given
by:
σ(t) = γ
0
[G
￿
(ω) sin(ωt) +G”(ω) cos(ωt)],
where G
￿
(ω) is the response in phase with the applied strain and is called
the elastic or storage modulus,a measure of the storage of elastic energy
by the sample,and G
￿￿
(ω) is the response out of phase with the applied
strain and in phase with the strain rate,and is called the viscous or loss
modulus (viscous dissipation of energy)
￿
the complex shear modulus is defined as G

= G
￿
+iG
￿￿
￿
alternatively,it is possible to apply stress and measure strain and obtain
equivalent material properties
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Microrheology
￿
the motion of probe particles is measured using either video or laser
tracking techniques
￿
one class of microrheology techniques involves the active manipulation of
small probe particles by external forces,using magnetic fields,electric
fields,or micromechanical forces (AFM,MTC,optical tweezers)
￿
a second class of passive microrheology techniques uses the Brownian
dynamics of embedded colloids to measure the rheology and structure of
a material,passive measurements use only the thermal energy of
embedded colloids,determined by k
B
T,to measure rheological properties
￿
the thermal motion of the probe in a homogeneous elastic medium
depends on the stiffness of the local microenvironment,equating the
thermal energy density of a bead of radius a to the elastic energy needed
to deform a material with an elastic modulus G
￿
a length L (gardel):
k
B
T
a
3
=
G
￿
L
2
a
2
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Atomic Force Microscopy (AFM)
￿
local probes method;normally used for the purpose of imaging,can also
provide structural information about the cell
￿
the probe used in AFM consists of a fine pyramidal tip attached to a
cantilever that flexes as the tip is pushed into the sample surface and
applies stress to the surface,resp.generates a local deformation on the
cell surface
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Atomic Force Microscopy
￿
by measuring the flexure in the cantilever with the reflection of a laser,it
is possible to calculate the upward force acting at the tip (bao2003,
kasza2007,huang2004)
￿
the contours of the surface can be revealed by the vertical motion of the
tip as it traverses horizontally back and forth over the sample →one can
obtain both geometrical information about the surface being probed and
the local stiffness of the surface
￿
AFM typically produced estimates of cell stiffness in the higher ranges of
measured values (hundreds of kilopascals,in contrast to most other
techniques ranging from 0.1 to 10 kPa) but is perhaps the best method
for demonstrating cell heterogeneity
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Atomic Force Microscopy
￿
deformation data from most AFM experiments have been analyzed by the
Hertz model (only for elastic measurement) or a its variation
(ananthakrishnan2006)
￿
the attached cell is modeled as an elastic half space,while the AFM tip is
modeled as a paraboloid of radius R at the contact point;from an
analysis of this elastic half-space model deformed by a hard axisymmetric
indentor,the following relation can be obtained for the indentation δ to
an applied force F (indentation depth δ to be much less than the cell
radius):
F =
4
3
R
0.5
δ
1.5
¯
E,
where
¯
E = E
cell
/(1 −ν
2
cell
) is effective Young’s modulus and ν
cell
is
Poisson’s ratio of the cytoskeleton
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Atomic Force Microscopy (AFM)
￿
Hertz model variation for frequency probing:
F =
4
3
R
0.5
(
¯
E
0
δ
1.5
+
2
3
¯
E

δ
0.5
0
˜
δ),
where
¯
E
0
is the zero frequency value on elastic modulus,
¯
E

=
¯
E
￿
+i
¯
E
￿￿
is
frequency-dependent part of
E
1−ν
2
,the probe deforms the cell by δ
0
with
a small additional oscillating signal to which the cantilever responds with
phase-shifted signal
˜
δ
￿
extraction of both the frequency-dependent elastic modulus (E
￿
or G
￿
)
and the loss modulus (E
￿￿
or G
￿￿
)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Micropipette Aspiration
￿
pipette aspiration uses a subatmospheric pressure to partially aspirate a
entire cell (huang2004,bao2003)
￿
the difference in pressure across the cell membrane is related to its
deformation;by recording geometry changes of the cell,the elastic
response of the cell is inferred,usually by ignoring friction between the
cell membrane and micropipette walls
￿
most commonly used on white blood cells such as neutrophils and
adherent cells
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Micropipette Aspiration
￿
sample boundaries (boudou2006):
(i) a controlled suction pressure ΔP was applied on the tissue section
inside the pipette,
(ii) zero normal displacement conditions were applied along the sample
section belonging to the axis of symmetry,
(iii) two different types of boundary conditions were considered at the
sample/rigid substrate interface:zero displacement conditions when the
sample is fully adherent to the substrate or sliding without friction over
the substrate for non-adherent samples and free boundary conditions were
assumed for all other sample surfaces
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Micropipette Aspiration
￿
model:incompressible (ν = 0.5) and semi-infinite sample (a and h tend
to infinity) (boudou2006)
￿
analytical relationship between the applied pressure ΔP and the resulting
aspirated length d into the micropipette;after rescaling,this relationship
shows that the normalized aspirated length δ = d/R
i
depends not only on
the sample Young’s modulus E but also on a pipette shape factor
function φ(η):
δ =
3ΔP
2πE
φ(η),
where η = (R
e
−R
i
)/R
i
,so apparent elasticity modulus:
E
app
=
3ΔP
2πδ
φ(η),
where φ(η) varies between 2.006 and 2.071,when 0.4 ￿η ￿0.6 and
modified sample stiffness:
E = αE
app
,
where α is correcting factor (incorporation of the influences of the
geometrical parameters h and R
i
,of the adhesion condition and of the
Poissons ratio ν;α = 1 for a semi-infinite and incompressible sample)
￿
to obtain cellular viscosity µ (3-element model,ananthakrishnan2006):
d(t) =
3R
i
ΔP
2π(E
0
+E
1
)
φ(η)
`
1 +(
E
0
E
1
−1)e

tE
0
µ
´
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Traction Force Microscopy
￿
entire cell contraction deform a flexible substrate
￿
force are estimated from bead displacement
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Traction Force Microscopy
￿
fibroblasts,polyacrylamide substrates (Y = 28 kPa) (munevar2001)
￿
the traction magnitude (mag) and shear (shr) are defined as follows:
mag(T) =| T |≡ [T
2
x
+T
2
y
]
1/2
shr(T) ≡ [2(∂
x
T
x
)
2
+(∂
y
T
x
+∂
x
T
y
)
2
+2(∂
y
T
y
)
2
]
1/2
,
where T = [T
x
(x,y),T
y
(x,y)] is the continuous field of traction vectors
underlying the cells
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers or Laser Traps (Optical Traps)
￿
optical traps consist of a laser directed at a micrometer-scale object,such
as beads or organelles,and used to control their position —typical object
sizes (0.5 −10 µm in diameter,very small objects do not trap well
because the trapping force decreases with decreasing object volume)
￿
the force is generated by the refraction of the laser within the bead
coupled with the difference in photon density from the center to the edge
of the beam
￿
optical traps can generate tens to hundreds of piconewtons of force per
bead
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers or Laser Traps (Optical Traps)
￿
main limitation:with one beam path can be controlled only one bead at
a time
￿
typically,optical traps are used to control particle position,but the force
acting on a bead can also be determined on the basis of the distance
between the center of the particle and the laser focal point →high
spatial resolution of particle position,however,and feedback control if
force is to be specified
￿
optical traps have been used to study membrane and cell elasticity and
local responses in a diverse array of cell types,including neurons and red
blood cells
￿
optical traps are also suitable for studying movement or force generation
by structures at the molecular scale,such as kinesin motors
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers or Laser Traps (Optical Traps)
￿
an attractve force is created between a dielectric bead of high refractive
index and a laser beam,pulling the bead towards the focal point of the
trap (bao2003)
￿
in one adaptation of the optical tweezers to deform a single cell,a trap is
used with two microbeads (typically 1 µm to several micrometres in
diameter) attached to the opposite ends of a cell (optical stretcher)
￿
this illustrated techniques can also be suitably modified to probe the
mechanical response of single biomolecules
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Laser Trap
￿
measurement of stiffness of actin filament (dupuis1997)
￿
experimental microsphere-filament system was modelled as a simple
mechanical system;each of the two microspheres (m
1
and m
2
) are
connected to fixed positions by springs (each with stiffness α
trap
)
representing the laser traps
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Laser Trap
￿
the microspheres are connected to each other through a third spring with
stiffness α
actin
representing the effective elasticity of the actin filament
￿
system can be reduced to an equivalent system such that one microsphere
is connected to a fixed position through a single spring (a composite of
the springs representing the traps and actin filament) with stiffness α
sys
α
sys
= α
trap
+
α
trap
α
actin
α
trap

actin
,
α
actin
=
α
trap(α
sys
−α
trap
)

trap
−α
sys
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers
￿
a laser beam is focused by a high-quality microscope objective to a spot
in the specimen plane,this spot creates an ”optical trap” which is able to
hold a small particle at its center;the forces felt by this particle consist of
the light scattering and gradient forces due to the interaction of the
particle with the light
￿
the basic principle behind optical tweezers is the momentum transfer
associated with bending light;light carries momentum that is
proportional to its energy and in the direction of propagation;any change
in the direction of light,by reflection or refraction,will result in a change
of the momentum of the light;if an object bends the light,changing its
momentum,conservation of momentum requires that the object must
undergo an equal and opposite momentum change;this gives rise to a
force acting on the object.
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers
￿
the restoring force of the optical trap works like an optical spring:the
force is proportional to the displacement out of the trap (the bead is
constantly moving with Brownian motion);but whenever it leaves the
center of the optical trap the restoring force pulls it back to the center;if
some external object,like a molecular motor,were to pull the bead away
from the center of the trap,a restoring force would be imparted to the
bead and thus to the motor.An example trace of a single kinesin motor
taking 8 nm steps against a 5 pN force
￿
the optical tweezers set-up used a focused laser light beam to deform
cells;this prohibits the use of very high laser power to avoid heating
damage to the cell (ananthakrishnan2006);the optical tweezers setup is
generally used to deform only soft cells
￿
in contrast,the optical stretcher uses divergent unfocussed laser beams,
which minimize heating effects in the cell and allow the use of higher
powers to deform cells
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers
￿
deforming an epithelial cell via a single silica bead (attached to integrin
receptors on the cell membrane) that is subjected to a radiation force
from a laser (laurent2002)
￿
the rigid spherical bead is assumed to examine the viscoelasticity of the
cellular medium to which it is attached;the cellular medium is modeled
as a linear viscoelastic Voigt solid (an elastic spring in parallel with a
viscous dashpot);the force F applied to the silica bead is approximately
at its center and tangential to the cell membrane and its magnitude is
calculated from the distance between the bead and the trap position;the
displacement u
x
of the attached bead to the exerted force F is obtained
by calculating the elastic response of a rigid spherical bead in contact
with a homogeneous (visco)elastic medium to a force
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Optical Tweezers
￿
for a bead in contact by a small area with a semi-infinite medium,the
expression is given as:
u
x
=
3F
4πER

3
2 sinα
+
cos α
sin
3
α

,
where E is the elasticity of the cell and R is the bead radius,the angle α
is the degree of bead immersion in the medium and is estimated for each
bead from experimental images
￿
from the relaxation time τ is the cell viscosity µ obtain:
τ =

E
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Traps (Magnetic Bead Microrheology)
￿
apply either a linear force or twisting torque to a particle
￿
linear force application:the device is constructed with one or more
electromagnetic poles consisting of a para- or ferromagnetic core wrapped
with wires;when current is passed through the wires,the pole becomes
magnetized,and small para- or ferromagnetic beads are attracted to the
pole
￿
the force can be amplified by designing the pole to converge to a sharp
tip;uniform forces across an area – multiple tips can be arranged with
different current amplitudes and directions to generate a nearly uniform
magnetic force field in any direction;blunt pole – generate a much
smaller force over a larger area
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Traps
￿
magnetic force application can be viewed as the mechanical complement
to optical trapping,its main feature is that it generates a constant force
￿
bead selection is crucial:because the magnetic contents of the particle
influence the applied force
- Ferromagnetic beads can generally exert much more force but retain
some of their magnetization each time they are exposed to the field
- Paramagnetic beads are less susceptible to magnetization but are
limited to smaller forces,generate hundreds of piconewtons per bead for
an area magnetic trap and up to tens of nanonewtons for a single-pole
trap,assuming one works within a distance of 10 −100 µm of the
magnetic trap tip (huang2004)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Traps
￿
adherent cell surface;4-elements mechanical model (bausch1998):spring
of elasticity k
0
in parallel with a series combination of a second spring of
elasticity k
1
and dashpot of viscosity γ
1
,which whole assembly is in series
with a dashpot of viscosity γ
0
￿
the viscoelastic parameters are determined by comparing the response of
the mechanical model to a step stress to the experimental creep response
and relaxation curves
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Traps
￿
effective elastic constant k = k
0
+k
1
,relaxation time τ =
γ
1
(k
0
+k
1
)
k
0
∙k
1
and
viscosity γ
0
are than related to the viscoelastic moduli of the cell by
modeling the cell membrane and actin cortex as a thin elastic plate of 2D
shear modulus G

(coupled to cytoplasm)
￿
2D shear modulus →3D shear modulus of the cortex G:
G = G

/h,
where h is the thickness of the membrane and the actin cortex
￿
the cytoplasmic viscosity is obtain from the mechanical model parameter
γ
0
from the relation:
µ
cytoplasm
=
γ
0
d
c
πR
2
,
where R is the radius of contact area between membrane and bead and
d
c
is the thickness of the viscous cytoplasm
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry (MTC)
￿
second form of magnetic trapping by application of torque
￿
magnetic beads with functionalized surfaces are attached to a cell and a
magnetic field imposes a twisting moment on the beads,thereby
deforming a portion of the cell (bao2003)
￿
the beads are not pulled,but instead,a brief magnetic field is pulsed on
the sample to magnetize the beads with a specific orientation
￿
when a counterpulse is generated at a much higher magnitude and in a
different direction,the beads then experience a rotational force to realign
with the new field;the resulting torque is described by the decay of the
initial magnetization and the decrease in torque as a result of bead
rotation (huang2004)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry
￿
a twisting torque was applied with a weak vertical homogeneous magnetic
field (0 to 30 G);the extent of bead rotation (angular strain) was
measured by an in-line magnetometer that measured the magnitude of
the bead magnetic vector in the horizontal direction;stress was calibrated
in a viscous standard,and angular strain was measured as the beads
rotated in place in response to applied stress (wang1993)
￿
stiffness is defined as the ratio of stress to angular strain;apparent
viscosity was calculated as the product of time constant after stress
release and stiffness;permanent deformation was calculated as the
percent angular strain sustained after stress release
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry
￿
the resultant bead displacement is measured either with video microscopy
or,to even higher precision,with laser particle tracking (bao2003)
￿
an appropriate analysis of deformation provides the elastic or viscoelastic
properties of the cellular component (bao2003,kasza2007)
￿
determining a true magnitude for the elastic and viscous moduli is
difficult (uncertainties in the nature of the bead attachment to the cell)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry
￿
endothelial cells phagocytized magnetic particles (Fe
3
O
4
,diameter 1.9
µm) and formed a monocellular layer in bottles (nemoto2000);the
particles were magnetized by pulse magnetic field
￿
model consists of two viscous elements and one elastic element,the
differential equation governing the model are:

1
dt
=
c
k
2

1
(t) −Θ
1
) +
1
k
2
(
dW(t)
dt
+f (t,Θ))

2
dt
=
1
k
1
(
dW(t)
dt
+f (t,Θ)),
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry
￿
where Θ = Θ
1

2
is a direction of the magnetic moment of the
phagosome measured from that of measurement;Θ
1
is the natural length
of the elastic body from which it is in the resisting state;f (t,Θ) is the
torque (Nm) exerted by the external field designed to achieve a particular
propose in each experiment;c comes from elasticity (Nm);W(t) is the
Brownian motion caused by the intracellular movements such as
cytoplasmic streaming;all the parameters are normalized with respect to
the energy E
r
of randomization caused by W(t)
￿
during the relaxation,the cell field decays according to
B(t) = exp(−
V[Θ(t)]
2
),
where V[Θ(t)] is the variance of Θ(t) at the time t
￿
after pulse magnetization,the variance is given by:
V[Θ(t)] = α

1 −e
−σt
σk
2
2
+
2(1 −e
−σt
)
σk
1
k
2
+
t
k
2
1
!
￿
for twisting experiment is the equation solved by Runge Kutta method for
N sample processes of Brownian motion W(t) and
1
N
P
N
i =1
cos Θ(t,i ),
where Θ(t,i ) is the azimuth of the i -th moment at time t calculated
from the differential equation (N was 2000 −4000 in most cases)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry
￿
beads coated with RGD are attached to integrin transmembrane
mechanoreceptors (laurent2003)
￿
response curves may be divided in three periods:
- Period I ≈ 30s with no loading and no bead rotation,
- Period II ≈ 1min where a magnetic torque (of about 1000 pNµm,in
this case) was applied,generated by a constant perpendicular magnetic
field.In response to this torque,beads initially rotate,to reach a plateau
which suggest a viscoelastic ”solid” behavior,
-Period III ≈ 30s,the magnetic torque is switched off and CSK response
is characterized by a partial recovery of the initial bead position,which
indicates a plastic behavior
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Magnetic Twisting Cytometry
￿
standard rheological methods used for quantification:
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Whole Cell Stretching
￿
squeezing the cell between two flat surfaces;this approach has not been
used extensively
￿
a cell is placed between two parallel plates,which can then be moved
closer together,pulled apart,or twisted,while the cell can be imaged to
evaluate the distortion and subsequent mechanical response to the stimuli
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Whole Cell Stretching
￿
microplate traction experiment:3 element mechanical model
(thoumine1997) to extract two elastic moduli and a viscosity from their
traction experimental data and oscillatory tests,Kelvin model (with one
spring of elasticity k
0
(N/m
2
) in parallel with a series combination of a
second spring of elasticity k
1
and a dashpot of viscosity µ)
￿
slope of the stress-strain curve from traction data gives the sum k
0
+k
1
of the two elastic constants,while the stress relaxation curve gives the
time constant τ =
µ
k
1
and the spring constant k
0
;k
0
,k
1
and µ can also
be extracted from oscillation data:
σ(t) = ε
0
(k
0
+k
1
e
t
τ
)
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Shear-flow Method
￿
methods used to study the mechanical response of an entire population of
10
2
−10
4
cells;the application of shear stress to a monolayer is
accomplished by moving fluid through a flow chamber
￿
are two main designs:a pressure-driven flow chamber that typically
results in a fully developed parabolic laminar flow profile and a
cone-and-plate flow chamber in which the cone is rotated relative to a
fixed plate that results in a linear flow profile and uniform shear stress
(huang2004,bao2003)
￿
many variants on each main design:the pressure-driven flow chamber can
have a rectangular cross section or a circular cross section;flow can be
either steady or unsteady to generate a time-varying shear stress;
investigators have also designed geometric changes within these flow
chambers to create a recirculation region in which to simulate disturbed
flow regions,such as near arterial bifurcations
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Shear-flow Method
￿
care must be taken to keep flow rates sufficiently low to maintain laminar
flow,unless turbulence is being studied as a factor,to maintain a
constant level of uniform shear stress
￿
most commonly used on endothelial cells;typical shear stress levels for
studying endothelial cell effects range from 1 to 20 dyne/cm
2
(0.1−2 Pa)
￿
shear stress applied to cells can be readily quantified;different uniaxial,
biaxial and pressure-controlled elastic-membrane stretching devices have
also been used to deform cells
￿
shear stress can induce changes in endothelial cell proliferation,
membrane fluidity,and cell morphology
￿
in one adaptation,cells are cultured on a thin-sheet polymer substrate,
such as silicone,which is coated with ECM molecules for cell adhesion;
the substrate is then mechanically deformed while maintaining the cell’s
viability in vitro;in this manner,the effects of mechanical loading on cell
morphology,phenotype and injury can be examined
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Shear-flow Method
￿
furthermore,by systematically altering the mechanical properties of the
substrate material through,for example,changing the degree of crosslink
in the polymeric gel,the individual and collective interactions of the cells
with the substrate can be studied (propensity for migration of a group of
cells towards or away from the region of localized tension or compression
in the substrate)
￿
by using elastic micropatterned substrates,the relationship between force
applied by the cell to the substrate and the assembly of focal adhesions
can be investigated;the contractile forces generated by cells during
locomotion and mitosis have also been measured with a
deformable-substrate method
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Microfabricated or Microelectromechanical Systems (MEMS)
Devices
￿
an alternative approach based on a cluster of microneedles or a cantilever
beam
￿
it might also be possible to apply a pointwise mechanical force or
deformation in a controlled fashion by using a MEMS device
￿
it is still difficult to quantify accurately the forces generated by cells or
the distribution of forces between various subcellular structures inside a
cell;the reason is that a significant portion of forces is supported as well
as generated by the cell cytoskeleton;however,cells are active and the
cytoskeletal structures are dynamic they could undergo remodelling or
re-organization in response to mechanical perturbations
Living Cell Mechanics
I.
Jelly,glass or
prestressed
construction?
Miroslav Holeˇcek,
Petra Kochov´a
Cell Mechanics
Cytoskeleton
Approaches for
Understanding
Mechanical Properties
of Cells
Cells
Living Cells
Mechanical Properties
Experimental Methods
Measurement
techniques
Microrheology
Atomic Force
Microscopy
Micropipette
Aspiration
Traction Force
Microscopy
Optical Tweezers or
Laser Traps
Magnetic Traps
Magnetic Twisting
Cytometry
Whole Cell Stretching
Shear-flow Method
Microfabricated or Mi-
croelectromechanical
Systems Devices
Future View
Future View
￿
owing to the dynamic nature and complex geometry of living cells,even
for the same cell type studied under similar conditions,the measurement
of the mechanical behaviour of individual cells can give rise to different
results depending on cell morphology,the stage in the cell cycle and the
response of different subcellular structures to mechanical perturbation
￿
fundamental paradox:how can we measure the mechanical behaviour of
living cells if they react to our measurement tools?
￿
we need to study systematically how such reactions depend on the type,
history and intensity of the associated mechanical forces or deformations,
and how quickly (or slowly) the specific cellular property of interest
changes after mechanical perturbation