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Cytomechanics432/532
• Tuesday, January 18, 2005: Introduction
• WebCT syllabus, book, resources, posting.
• Office : BME 124 Weds, Thurs: 1-4 PM
• Grading: HW + Exams + Project
• Craelius@rci
Learning objectives• 1. To learn the structural/mechanical
components of cells, specifically: biophysics and material properties of the cytoskeleton (CSK), membrane, and matrix.
• 2. To learn about experimental tools for evaluating cell mechanical properties, specifically: mechanical testing, imaging with immunocytochemisty and knock-out methods.
Learning Objectives• 3. To learn kinematics and dynamics of cells,
specifically, interactions among CSK, cytosol, matrix, and nucleus, mechanotransduction, and motility
• 4. To learn statistical mechanics of cell polymers and CSK assembly.
• 5. To learn tools for modelling cell mechanics, specifically simulations with matlab and simulink.
Topics in Cytomechanics
• A cell is a “cytoplasmic structural element.”• Tensegrity holds it together -’centripetally.’• Structural components include lipids, and 3
separate filament systems. • No cell is an island- interactions with others
and the ECM shape and regulate it.• Trans-skeletal molecules regulate the cell.• Rxns in solid-state versus enzyme solution.
Questions
• How do cells – maintain and change shape?– Move?– Grow and maintain a size?– Anchor to substrate or stick together or not?– Transport materials inside?– Form tissues?– Sense force and deformation?
Applications of Cytomechanics?
• Medical• Stress-Growth Hypothesis
• Mechanoelectrical Feedback
• Tumor-Endothelium
• Wound Healing
• Edema
• Bone & Cartilage Control
• Cellular signalling
• Technological• Gas structural elements
• Motility of Gels
• Microtubular nanostructures
• Bioprocess optimization
• Plant Growth & Production
• Microgravity Effects
How are cells put together?
200 different types
Not nice and regularVaried and irregular
The generic cell
Tension + compression hold the cell together
Green fluorescent dye for Actin
Basic Cell Components
• A membrane, skeleton, and internal structures.
• All serve both as structural and functional elements.
• Simplified basic building blocks
Geodesic- Buckminster Fuller A geodesic dome uses a pattern of self-bracing triangles in a pattern that gives maximum structural advantage, thus theoretically using the least material possible. (A "geodesic" line on a sphere is the shortest distance between any two points.)
Stick Geodesic Domes : Ingber
Tensegrity structures
MuscleTension
Mg
• Body stands upright by compression due to gravity counteracted by tension from muscles
• Same for bridges and many other structures.
Bow and Arrow
Tension
Compression
MuscleTension
Mg
Ten
segr
ity
SpectrinIn RBC
100 nM
NeurofilamentsCross-linkedIn frog axon
the CSK: smart design
• orienting along stress lines, filaments size themselves according to strength requirements: a conservative architectural practice.
Thin supportingstruts connectingthick beams
Underneath the hood
• Lipid shell • Actin network• Cytosol• Filaments• Organelles• Nucleus
Lipid vesicles are ghost-like
• pipets suck up the vesicles
• Miscibility allows intermingling
Plasma membrane
• Lipid bilayer 30 A°• Dielectric - capacitor• Amphiphile• Semi-permeable• No tensile but some
shear strength
The cytoskeleton
Cartoon of membrane cross-section
CSKactin microfilamentsmicrotubulesintermediate filaments
lipidIntegrin
ECM
Channels
Polymerized network:Spectrin in RBCsDecorated actin
Malines, Belgium
FibroblastTen
segr
ity
Major Filaments
• Filaments:• Actin : 8 nM• Intermediate 10nM• Microtubules:25
nM
Actin Intermediate Microtubules f……………………..filaments
3 types of filaments
Cellular Rods and Ropes
Filaments have different functions
Spectrin bends
Microtubules are stiff
Cell Crawling
Visualizing actin-myosin motion
Types of motors
How does the CSK provide structure?
Some results are not compatible with tensegrity model
Signals travel at speed of sound.
Structure by light & immunofluorescence
PMT
Fibroblasts are stained with Phallacidin green for F actin,Texas red for microtubules, and DAPI for nucleic acid.
F actin microtubules
F actin is green with Phalloidin, G actin is red with Texasred. Nucleus has fewer stress fibers, but is thicker thanrest of cell, so red is diffuse.
F actin G actin
Fibroblast dividing
Cells are Wiggly and Soft
New ways to describe softness- difference between cookedand uncooked noodles.
thermal fluctuationsOf lipid vesicle:
Types of Loading
Swelling and Lysis to measure membrane strength
• RBCs
Muscle
3%
50%
Frog
10 seconds after hypotonic stressGd3+ present
Iso-osmoticGd3+ present
10 m 10 m
Pipet Aspiration
Neutrophils are WBCs involved in immune response.The source of cortical tension is unknown, but may befrom actin tangential to surface.
Unwinding of rubber
Rubber Elasticity
Collagen
1 mm
Stress-strain varieties
Rubber
J Curve
liquid
unwinding
Tension
Micropipette
QpQp
Qm
Mesangial Cell
C i
Co
Pp
(K )w
Pi
C =constant i
A. Whole Patched Cell
MicropipetteStretch
Mesangial CellC (t)i
Co
Pi
Qm w(K )
Stretch Solutes
B. Isolated Cell
Solutes
Fractional Area Expansion (A/A)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Ten
sion
T
(dyn
/cm
)
0
10
20
30
40
50
60
70
Elasticity and safety at high strains
Mesangial cell area expansivity
Rubber-like
Common Quantities in Cytomechanics
Quantity Units Applications Symbol
Stress, tension Pascals,dynes/cm2
bars, rods,rubber, etc.
F
Pressure same as above,plus mm Hg,psi, millibars
Gases, liquids P F
MembraneTension
dynes/cm thin shells,membranes
T = F/d
Where we are going
• Feedback Regulation: Bioelectricity- eg. Heart, bone, cartilage
• Optics of cytoskeleton; immunofluoresc.
• Micromotors; Gels; piezo- & ferro-electric
• Cell shape regulation, eg. Edema, tumors
• Tissue morphogenesis; osseointegration
• Endothelial regulation
• Wound healing
Common quantities
Strain
Extension
dimensionless any deformablematerial
x-xxx/xo
Young’sModulus
Pascals,dynes/cm2
E=
Viscosity dynes-sec /cm2 Fluids,membranes
Shear stress dynes /cm2 Fluids,membranes
ddt
The cytoskeleton is both internal and external
Fibroblast-myocyte interactions
Fibroblasts Myocytes
Growth patterns vary in myocytes
Wall stress in a thick sphere
• To find equilibrium forces:
Fup = Fdown
.
P
Ri
Ro h
P
Ri
Roh
Membrane Tension
Tm Tm
Tm
Tm
P
P
R
Tm dyTm dy
P
1. Hemisphere
2. Patch
3. Patch in x-z plane
R
dx
d
Tdy
Tdy
Tdy d
4. Vertical Resultant
dxdy
T
T
• Cells will adhere to specific islands, properly coated.
• The traction force can be seen by the bending of the substrate.
• Microfabricated culture wells allow cell to make many E connections.
Shape Determined by Stress
“Knock-out” methods
• Spectrin• Actin• Microtubules• Intermediate
Filaments
• Heat• Cytochalasin• Nocodazole• Acyrlamide
Pulling Chromosomes out
CartilageDeformations of gel-cartilage
Swelling pressure = osmotic pressure- elastic (compressive) pressure
H20
Polymer-polymerIntra-polymerosmosis
FactorsCa++, pH
pKa=pH +log[HA] [A-]
Polymer charge determinesSwelling
Tensegrity Industry
Designer foam
Zero Mean curvature
Percolation: theory of the CSK assembly
• Rule: network evolves by random connections between 2 “active” sites, each with some site occupation probability, p. A cluster is a set of occupied sites all of which are connected either horizontally or vertically, i.e. an occupied site belongs to a cluster if a member of the cluster is either above, below, left, or right of it. A spanning cluster has an element in both the top and bottom rows of the site matrix.
LA NY
Hypothetical telephone network in the U.S.
Proteins• Primary, secondary,
tertiary, quaternary structures
• Make filaments: rods, tubes,
• Flexural Stiffness
4RI
IYK f
Polymer bendingassuming it is a thin rod
Lbend
R
R
L
p
fp
f
farc
LwhenkT
YIR
LE
22
At finite temperature, an otherwisestraight rod bends as it exchangesenergy with its environment. It bendsmore as T rises, like a noodle.
Landau & Lifshitz,Theory of Elasticity, 1986.
?
What persistence length meansWhen L = p , what happens at Earc= kT?
2
2
2 2
2
R
R
kTkTR
E
p
p
farc
Thus a rod of the persistence length is curved at 81 degrees when the thermal energy scale reaches kT.
If L << p then rod is relatively straight, otherwise not. Persistence length sets the scale of thermal fluctuations. Filaments with countour length >> p are highly convoluted and can assume many configurations.2
Entropic springs
Large reeFew Configurations
Small reeMany Config-urations
4-segment chain configurations
24
Applying a tension to the zero ree statereduces possible configurations to 10.S drops from ln(16) to ln (10). Hence tension translates to loss of entropy.
tension
psp L
kTk
2
3
Effective spring constant for a convoluted chain near equilibrium:
Have you seen a model of this?
Tissue
• Aggregate cells are more complicated. Many different types of connections, each with their own biochemical traffic patterns
Methods of cell regulation• Signalling by mechanotransducers: current• Molecular CSK regulators: Integrin• Nuclear transcription: protein
Exercise
• Prove that a hollow design is advantageous for a microtubule. Assume an outer and inner radii of 14 and 11.5 nM, respectively, and compare this with a solid MT of the same outer radius. What is the most efficient way for proteins to gain rigidity, ie. on a per unit mass basis?
• Review Questions
• The cytoskeleton is made of (Select one)
a. Filamentous protein
b. Lipid
c. Actin, microtubules and microfilaments
d. Extracellular matrix (ECM)
e. (a, b and c)
f. (a and c)
g. (all of the above)
2. Integrin is a transmembrane peptide (True or False)
3. State a specific method or technique to "knock out" or remove a component of the cytoskeleton
•
4. Immunofluorescence is a procedure to visualize specific molecules in a cell. The technique involves shining long wavelength light on the specimen, and seeing or detecting shorter wavelength light fluoresce. (True or false).
