Tuesday, March 01, 2005
-
Upload
galena-ferguson -
Category
Documents
-
view
38 -
download
1
description
Transcript of Tuesday, March 01, 2005
![Page 1: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/1.jpg)
Tuesday, March 01, 2005
• Geometric and Mechanical Properties
• Mechanical Statics
• Review-
![Page 2: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/2.jpg)
Thick walled sphere
• Equilibrium• Pressure inside• Average stress in wall
• Pressure from outside
• Pressurized both sidesh
pr
h
pr
rrh
rp
rrh
rp
rr
rp
prrr
oi
PP
io
ooP
io
ii
io
iiP
iiPio
outin
out
in
in
22
)(
)()(
)(
2
2
22
2
222
![Page 3: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/3.jpg)
Charged polymers: Electromechanical Chemistry
I.e. Alanine charge+H3N-CH-COO-
CH3
pKa =9.9 pKa =2.7
pH pKalog A
HA( )
- = fractional charge = A
A
AH 1
11
alog pH pKa( )
- =
Aqueous charge
![Page 4: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/4.jpg)
X Y Z
Meridions
Latitudes
Losing volume, not gainingarea;
21
11
RRC
Curvature
Shape : Oblate sphere
![Page 5: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/5.jpg)
Slow cell squishing
![Page 6: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/6.jpg)
b 0FRAME
5
a 3FRAME
10
Curvature
![Page 7: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/7.jpg)
![Page 8: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/8.jpg)
Membrane Tension
T m T m
T m
T m
P
P
R
T m dyT m 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
![Page 9: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/9.jpg)
Tension on membrane patch
Ri
Rc
T
FT = 2 Ri T sin()
Tension force pulling down:
Fappl + FT = P Ri 2
Force Balance
Fappl
![Page 10: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/10.jpg)
Tangent-Curvature
2
2
;)(
s
rC
s
rst
Cs
t
R(s)= position
t1
t2
![Page 11: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/11.jpg)
Forces on Rods
• Does compressive force play a role?• Failure mode is buckling-To analyze must
consider geometry when it buckles-• (1) get m.o.I; • (2) general formula for moment in the rod.
(3) moment as a fxn of applied F.• (4) relation between R of curvature and x,
(5) simplify eqn.
![Page 12: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/12.jpg)
Step (1) Moment of Inertia of c.s.
4
)(4
)(2
2
2/122
0
2
2/122
2
R
dyyRyI
dyyRdA
dAyI
R
For hollow cylinder,subtract the hollow portion.
![Page 13: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/13.jpg)
Step (2) Bending a rod
y
s
s+s
dA
)1.......(..........
1
........
0....0
dAR
yEdF
dA
dF
EER
y
s
s
ctrcommonhavearcsR
yR
s
ss
ywhens
l
R (at neutral surface) is assumed constant onthe small segment.
![Page 14: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/14.jpg)
Step (2) reiteration(Landau & Lifschitz, 1986 , Theory of Elasticity)
R
Ey
dA
dFR
y
s
sstrain
strainE
yatdA
dF
}{
}{
![Page 15: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/15.jpg)
)2(..........)(
)(
2
sec
xR
EIxM
R
EI
dAyR
EydFM
ydFdMnowfinddAR
EydF
tioncross
Step (2) continued: Integrate
dAyI 2
![Page 16: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/16.jpg)
Step (3) Moment due to appl F
)2.......()(
..........
)3)......(()(
xR
EI
xPhxM
P
h(x)
x
P
P P
![Page 17: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/17.jpg)
)sin()(
......
)4.........()(
/1
max
22
2
2
2
2
2
2
2
cL
xhxh
xdt
xdasformsame
EI
xPh
dx
hdso
dx
hd
ds
rdcurvatureR
Note similarity to harmonicMotion :
Minus sign because Curvature is negative.
From before:
(5)
Step (4)
.......... curvesgentlefor
)()()(
xR
EIxPhxM
Hmax occurs at Lc/2 and h(0) = h(Lc)= 0.
![Page 18: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/18.jpg)
22
2
2
2max
22
2
)()(
.....
)4.......()(
.............................
)5)...(()()sin()(
cc
cc
LEI
Lf
fPSoEI
xPh
dx
hdand
xhLL
xh
Ldx
hd
fbuckle
buckle
c
Step (5) Differentiate h twice
![Page 19: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/19.jpg)
• Use spring equation. Hmax occurs at Lc/2. h(0) = h(Lc)= 0. We can relate F to Lc by double differentiating h, and then comparing it to the previous formula for the moment.
• Buckle force is independent of hmax . Rod will buckle when P> Pbuckle
• Can a microtubule withstand typical forces in a cell?
![Page 20: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/20.jpg)
22
2
2
2
2
max2
2
2
)/()/(
)/(
)(
)()/(
)/sin()/(
LcLcEIP
LcEI
P
xhEI
P
dx
hd
xhLc
LcxhLcdx
hd
f
![Page 21: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/21.jpg)
2
2
1 L
EIP
2
2
2 4L
EIP
2
2
3 4L
EIP
Buckling ofRods withDifferentFixations
![Page 22: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/22.jpg)
Buckling of cell without reinforcement
))1(3
(2
2
2
2
h
L
Ecrit
![Page 23: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/23.jpg)
Tissue Mechanical Environment Normal Range Cell Types
Bone,Cartilage
Weight bearing forces Continuous: 1X -4X Body weight
Osteocytes,Osteoblasts,Chondrocytes
ArterialEndothelium
Fluid pressure and shear Pulsatile: 60-140mm Hg;
Endothelial
Tendon Tension Up to 560 +- 9Kg/cm2
Nerve
Skin Compression and shear NerveOrgan ofCorti
Fluid shear Hair
Muscle(Intrafusal)
Tension Nerve/specializedmuscle
Muscle(Extrafusal)
Tension; active contraction Smooth, cardiac,and skeletalmyocytes
Mesangium Fluid pressure and shear Pulsatile: 60-140mm Hg
Mesangial
![Page 24: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/24.jpg)
• Living cells are both affected by and dependent upon mechanical forces in their environment. Cells are specialized for life in their own particular environments, whose physical stress patterns become necessary for normal functioning of the cells. If the forces go outside the normal range, then the cells are likely to malfunction, possibly manifesting as a disease or disability.
![Page 25: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/25.jpg)
Material efficiencyStrength/weight
RodSquareBar
![Page 26: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/26.jpg)
Fiber orientation for strength
A: Actin fibers in two C2C12 cells. B,C: C2C12 cell with a schematic representation of the actin cytoskeleton, whichis predominantly orientated along the first principal axis of the cell. As a result of the actin fibers, deformation of the cell and itsnucleus is restricted in this direction.
![Page 27: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/27.jpg)
Cell Walls for strengthHow thick does wall need to be to withstand normal pressures inside a bacterium, I.e. 30-60 atm. ?Lets say lysis occurs @ 50% strain. We can approximate KA By KVd, and for isotropic wall material, Kv ~ E, so,failure= 0.5 KA= RP= 0.5 E d. So to not fail,d> 2RP/E . So for R = 0.5 M, P= 1 atm,
nM
x
xd
3
10103
10105.027
56
![Page 28: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/28.jpg)
Homogeneous rigid sheet: Biomembrane
Bilayer compression resistance, KA = 4 J/M2
Stretching membrane thins itexposing hydrophobic core toWater. Rupture at 2-10% areaExpansion, so say lysis tension~ 0.2 J/M2. For a 5 m cell ,
P= ~ 8000 J/M3 ~ 0.08 atm. at rupture.
![Page 29: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/29.jpg)
Comparative Forces
• To pull a 5 m cell at a speed of 1 /sec:
• F= 6Rv = 0.1 pN
• Compare this with force to bend or buckle hair, 10 cm length, R = 0.05 mm:
• 5 x 10 4 pN
• or to move it 1 cm:
• F = 3 f z/L3 = 1.5 x 10 6 pN
bucklefF
![Page 30: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/30.jpg)
Comparative Forces
• Adhesion force between proteins on cell and on matrix: tens of pN.
• Spectrin spring constant = 1-2 x 10 –5 J/m2
so to stretch by 0.1 um takes 1 pN.
![Page 31: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/31.jpg)
Properties of the CSK
• A dynamic structure that changes both its properties and composition in response to mechanical perturbations.
![Page 32: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/32.jpg)
Pulling on CSK
![Page 33: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/33.jpg)
![Page 34: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/34.jpg)
![Page 35: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/35.jpg)
![Page 36: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/36.jpg)
y
y
y
y
y
Uni- and Bi-axial Stress and Strain
Take the case of unconstrained isotropic object compressed in the y direction:
Before strain After strain
x
![Page 37: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/37.jpg)
• Note that for an elastic material the strain occurs almost instantaneously upon application of the stress. Also note that to maintain constant stress, y , the applied force must be reduced if the face area increases, but this would be a negligible change for all
practical situations.
• The strain in the y direction is:
•
Ey
y
![Page 38: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/38.jpg)
• Because the transverse direction is unconstrained:
•
• and,
•
![Page 39: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/39.jpg)
xyy E 2'
yxy 2'
Thus the new stress in the y direction is the original unconstrained stress plus the stress caused by transverse constraint:
xyy E
Now, Consider the case where the x direction is constrained from movement. I.e. transverse
movement is resisted, making y
y
xx
![Page 40: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/40.jpg)
Solving for y we have the biaxial strain equation:
)(1
xyy E
![Page 41: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/41.jpg)
Z
Y
X
xx
yx
zx
xy
yy
zy
xz
yz
zz
3-Dimensional stresses (stress tensor)
![Page 42: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/42.jpg)
Stress components @ Equilibrium
0
0
0
3
33
2
32
1
31
3
13
2
22
1
21
3
13
2
12
1
11
xxx
xxx
xxx
![Page 43: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/43.jpg)
Blood Forces
Y.C. Fung
![Page 44: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/44.jpg)
Analyze a Small element of upper EC membrane : (Also a mult-part solution)
x
y
z
Cell 1 cell 2 cell 3
Flow
![Page 45: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/45.jpg)
Analysis of EC upper membrane
0
,,
zyyzxzzx
xzzxzyyzyxxy
xx
yx
zx
xy
yy
zy
xz
yz
zz
Symmetrical
(Fluid Mosaic)
x
y
z
![Page 46: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/46.jpg)
0
,
yxxy
yxxy
On surface facingblood
On surface facingcytosol
x
y
z
![Page 47: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/47.jpg)
h
xx
xzxyxx
dyT
zyx
0
0
x
y
z
![Page 48: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/48.jpg)
h
xxx
yxxy
yxxy
dyT0
0
,
On surface facing
blood
We need membrane tension as f()x
y
z
Define
![Page 49: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/49.jpg)
LTdxx
T
x
T
dyT
ce
dyy
dyx
egrateanddymultbyzyx
x
Lxx
h
xxx
hxy
hxx
xzxyxx
0
0
00
0
sin
0
int0
(if Tx= 0 @ x=0)
x
y
z
![Page 50: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/50.jpg)
Stress on cell from flow
h
L
h
T
so
hT
xxx
xxx
@ x = -L
For = 1 N/m2 , L= 10 m, h = 10 nm
2310m
Nxx m
NTx
610
![Page 51: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/51.jpg)
Shear stress from flow in a pipe
rL
P
raL
PrU
dl
dU
2
)(4
)( 22
P1 P2
![Page 52: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/52.jpg)
Fluid Pressure is omnidirectional
>
A
dZ
dx
dy
P1
P2
P3
P4q
P5
Rotate by 90, and see also:
P4 = p5
P1 dy dz = P2 sin(q) dz dy/sin(q)
P1= P2
Fx = 0
P3 dx dz = P2 cos(q) dz dx/cos(q)
P2=P3
Fy = 0
Fz = 0
Hence P1=P2=P3=P4=P5 =P
![Page 53: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/53.jpg)
Two State Transitions
2121212
2121211
XKXKdt
dX
and
XKXKdt
dX
2
1
2
12221
1211
X
X
X
Xaa
aa
XAX
1221
1221
kk
kkA
![Page 54: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/54.jpg)
Entropic springs
Large reeFew Configurations
Small reeMany Config-urations
4-segment chain configurations RNA
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
Sudden extensions of 22 nM (unfolding) when forces above 14 pN are applied
22 nM
![Page 55: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/55.jpg)
Rate Constants
Kopen = 7 sec-1
Kfold = 1.5 sec-1
Kopen = 0.9 sec-1
Kfold = 8.5 sec-1
![Page 56: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/56.jpg)
RNA unfolding
Sudden extensions of 22 nM (unfolding) when forces above 14 pN are applied
22 nM
![Page 57: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/57.jpg)
Coding of Probability
1
))(1(i
i
t
t
dttnKT
Integral pulse frequency modulation
Probability Pulse frequency and width Modulation
![Page 58: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/58.jpg)
Pulse Width Modulator
2
1
)(t
t
dttu
Leaky integrator
Thresholder
Pulsesout
Inputs
Reset
![Page 59: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/59.jpg)
Mechanical Models
![Page 60: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/60.jpg)
Voigt solution1
Z
1
Rs C Z
1
C
s1
Laplace domain V s( ) I s( ) Z s( )I o
s
1
C 1
s 0( ) s1
taat eeaa
21
12
1 = bi-exponential decay
Time domainV t( ) I o R 1 e
t
E o
E1 e
t
![Page 61: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/61.jpg)
Classwork
• Make a simulink model of the RNA unfolding kinetics. Your model should be well documented, according to the following guidelines:
• All parameter boxes should be labeled
• Document boxes should be included to describe operations
• Internal parameters, such as initial conditions, should be specified
• Sub-systems should be used so that the entire model can be fit onto 1 page and each sub-system can be printed separately, with documentation.
• A separate description of the system and all formulae should be made.
• Outputs should be the predicted, as well as measured probabilities
• A reasonable noise level should be placed in the model
![Page 62: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/62.jpg)
Control System, I.e. climate control
Sensor Plant-
--
-
Output
Error
Perturbation
Feedback
Set Point
![Page 63: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/63.jpg)
Temperature Control
![Page 64: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/64.jpg)
BAsIC
su
sysG
CXY
BUAXX
T 1)(
)(
)()(
0
1
1
0
03
10
C
B
A
G(s)Y(s)U(s)
![Page 65: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/65.jpg)
1/s 1/s+
-1
3
X2 X1
0
1
1
0
03
10
C
B
A
)()(
)()()(
tCXty
tBUtAXtX
![Page 66: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/66.jpg)
• Patterns on silicon with fibronectin.
• Cells grown on small pattern : Apoptosis
• On a line they differentiate
• On a large surface, they grow.
![Page 67: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/67.jpg)
Mechanical Terms Review
• Statics and dynamics
• Kinematics and kinetics
• Vector and scalars
• Forces, resultants
• Deformation
![Page 68: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/68.jpg)
Homework
Using the data shown in Figure previous, and the ground free energy, Fo = 79 kT, graph the unfolding and folding probabilities, using Excel or other program. Put actual data points for the selected forces on your theoretical curve.
![Page 69: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/69.jpg)
Tensiometry
Balance
)(12
12
32 RR
RR
R
FT
TCP
Plates coated with poly-HEMA
Compression of cells reduces theload measured by the balanceby an equivalent amount
![Page 70: Tuesday, March 01, 2005](https://reader035.fdocuments.us/reader035/viewer/2022062314/56812d5c550346895d9269b1/html5/thumbnails/70.jpg)
Liquid behaviour: Surface tensions of embryonic tissue
0
5
10
15
20
25
Neu
ral
reti
na
hear
t
mes
oder
mdynes/cm
NRLHEpM
120/12/13/14/15/1 P
Liquid Properties