![Page 1: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/1.jpg)
NeurofilamentsCross-linkedIn frog axon
Isotropic: same in all directions
![Page 2: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/2.jpg)
Linker proteins for actin
![Page 3: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/3.jpg)
Particle Tracking in fibroblastsLecture 5
![Page 4: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/4.jpg)
Tracking particles: Regional stiffness
![Page 5: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/5.jpg)
• #3- Think of a balloon with stiff meridional bands- networks can stretch more easily along the axis with less stiff ropes.
• #4 hoop stress versus axial stress
![Page 6: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/6.jpg)
Cylindrical Stresses
shx
sh
d
rP
d
rP
2
![Page 7: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/7.jpg)
X Y Z
![Page 8: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/8.jpg)
Buckling & Bending
2
2
1 L
EIP
10 cm
20 cm
![Page 9: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/9.jpg)
Tension Field Theory
Cell 1 cell 2 cell 3
Flow
h
L
h
T
so
hT
xxx
xxx
Membrane
![Page 10: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/10.jpg)
Coupling: Mechano-/Biochemical-/Cellular-
![Page 11: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/11.jpg)
Inside a Blood VesselEndothelial cells withNucleus bulging out
Blood flow
10 microns
![Page 12: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/12.jpg)
Cells- fluid or solid?
• Micropipet aspiration comparison between ECs and chondrocytes
• Comparison between EC cell & nucleus
• Stiffness following spreading or adapting to flow.
• ECs in flow will minimize force on nucleus
• Enucleus = 9 Ecytoplasm
![Page 13: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/13.jpg)
Applying global strains to Nucleus1
rigiditydeflectionF *Round
Spread
Nucleus
Compression & relaxation donequickly to measure passive propswhile avoiding adaptation. No hysteresis or plastic behaviour seen in spread cells and nuclei.
1. Caille, N: J. Biomech, 2002
![Page 14: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/14.jpg)
• Material properties, not inhomogeneity, explains
The non-linear behaviour
![Page 15: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/15.jpg)
![Page 16: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/16.jpg)
Slow cell squishing
![Page 17: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/17.jpg)
FEM of compression
![Page 18: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/18.jpg)
Bone Adaptation
• Most bones experience 1000’s of loads daily• Bone cells must detect mech signals in situ
and adjust bone architecture appropriately. • Sensor cells: Osteocytes; Effector cells:
Osteoblasts, osteoclasts• Signalling molecules: PGs, NO• Responses: bone formation/resorption
![Page 19: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/19.jpg)
• Bending forces not only cause deformation of osteocytes, but generate pressure gradients that drive fluid flow through the canalicular spaces. Bending causes compressive stress on one side of the bone and tensile stresses on the other. This leads to a pressure gradient in the interstitial fluids that drives fluid flow from regions of compression to tension. Fluid flows through the canaliculae and across the osteocytes, providing nutrients and causing flow-related shear stresses on the cell membranes. The fluid flow also creates an electric potential called a streaming potential
![Page 20: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/20.jpg)
• Strain detected by mechanoreceptors or by CAMs. G protein in membrane causes Ca and other 2nd messengers.
![Page 21: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/21.jpg)
• osteocytes (Oc) and bone lining cells (BLC) detect mechanical signals and communicate those signals to the bone surface. Soluble mediators, which include
• prostaglandins (PGs) and nitric oxide (NO), are released and cause the recruitment and/or differentiation of osteoblasts (Ob) from proliferating and nonproliferating osteoprogenitor cells.
![Page 22: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/22.jpg)
• The error function, i.e., the daily loading stimulus (S)• minus the normal loading pattern (F; So), drives bone
adaptation. Abnormally low values of the error function cause increased osteoclast activity on bone remodeling surfaces, while abnormally high values cause increased osteoblast activity on bone modeling surfaces
![Page 23: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/23.jpg)
• Rats jumping various of numbers of times per day showed that five jumps per day were sufficient to increase bone mass, but increasing numbers of jumps gave diminishing returns with respect to bone mass. These data very closely fit the mathematical relationship proposed in Eq. 1
jj
k
j
ENS )1log(1
![Page 24: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/24.jpg)
• G proteind mechanochemical signal transducer
![Page 25: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/25.jpg)
• Focal adhesions by Integrin and associated proteins.
![Page 26: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/26.jpg)
Load type affects adaptation
• Long bones are loaded mostly in bending
• Strain @ neutral axis is small, and increases away from axis
• Loading that changes the neutral axis, changes bone formation 1
• 1. Turner, CH: J. Orthop. Sci, 1998.
![Page 27: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/27.jpg)
• MC3T3-E1 osteoblasts subjected to fluid shear (12dynes/cm2) for 60min undergo dramatic reorganization of the actin
• cytoskeleton. A Control cells not subjected to flow have poorly organized stress fibers labeled with Texas red-phalloidin.
• B Cells subjected to fluid flow for 60 min develop prominent stress fibers labeled with Texas red-phalloidin that are aligned roughly parallel to each other. C and D Control cells not subjected to fluid shear which have poorly organized stress fibers
![Page 28: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/28.jpg)
Adaptation Cascade• Transduction … Biochemical…
transmission….effector cell…..tissue• Ion channels….Ca++,NOS, COX, PGs, G
protein….Obs, Ocs…..trabeculae• It is an error driven feedback system• Driven more by infrequent abnormal strains than by
normal strains encountered during predominant activity1
• 1. Layton, LE: The success and failure of the adaptive response to functional loading-bearing in averting bone fracture; Bone:13:1992
![Page 29: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/29.jpg)
Quantifying bone adaptation
componentfourierf
strainprincipalpeakstimulusstrainE
typeloadingeachfor
cyclesloadingdailyNstimulusS
fE
ENS
i
n
ii
k
jjj
.
..;.
)...(
..#;
)1log(
1
1
![Page 30: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/30.jpg)
Bone Loading Waveforms
![Page 31: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/31.jpg)
Resonant Stimuli for Bone
• Loading frequencies near 20 Hz• Vibration 1
• Error Driven
• 1. Rubin, C.
)( 0SSKdt
dmL
![Page 32: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/32.jpg)
![Page 33: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/33.jpg)
Mechano - regulation
• Growth, proliferation, protein synthesis, gene expression, homeostasis.
• Transduction process- how?• Single cells do not provide enough material. • MTC can perturb ~ 30,000 cells and is
limited.• MTS is more versatile- more cells, longer
periods, varied waveforms..
![Page 34: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/34.jpg)
![Page 35: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/35.jpg)
![Page 36: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/36.jpg)
![Page 37: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/37.jpg)
![Page 38: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/38.jpg)
Markov Chains
• A dynamic model describing random movement over time of some activity
• Future state can be predicted based on current probability and the transition matrix
![Page 39: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/39.jpg)
Sliding filamentds
![Page 40: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/40.jpg)
Dynamic equilibrium
)(''
')('
'
2
)()(2
2
2
2
2
0
02
2
tCukxdt
xdm
kxtCudt
xdm
xxx
PAC
xxktPAudt
xdm
![Page 41: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/41.jpg)
Sliding Filament Model
xvu
uFkxxm
0
)(
For A-M, vo = 0.5 um/s
Ratchet
![Page 42: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/42.jpg)
Harmonic motion (undamped)
0
)(
)()(2
2
0
xx
xkmx
xxktPAuxm
Gel motion follows simple rulesModel will predict dynamic and Static equilibrium.
Natural Frequency
![Page 43: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/43.jpg)
![Page 44: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/44.jpg)
Transition Probabilities
Win Lose
Win 3/4 1/2
Lose 1/4 1/2
Sum 1 1
Today’s Game Outcome
Tom
orro
w’s
Gam
e O
utco
me
Need a P forToday’s game
![Page 45: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/45.jpg)
Grades Transition Matrix
11Sum
1/21/4Bad
1/23/4Good
BadGood
This Semester
Nex
t S
emes
ter
Grade Tendencies To predict future:
Start with now:What are the gradeprobabilities for thissemester?
![Page 46: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/46.jpg)
WinLose
1/4
1/2
1/23/4
16/54/32/14/34/1
16/114/12/14/34/3
4/1
4/3
2/14/1
2/14/3
1,
1,
2221
1211
1
ilose
iwin
i
ii
P
P
P
aa
aaA
APP
Markov Chain
Intial ProbabilitySet independently
![Page 47: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/47.jpg)
Computing Markov Chains
% A is the transition probability
A= [.75 .5
.25 .5]
% P is starting Probability
P=[.1
.9]
for i = 1:20
P(:,i+1)=A*P(:,i)
end
![Page 48: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/48.jpg)
Control System, I.e. climate control
Sensor Plant-
--
-
Output
Error
Perturbation
Feedback
Set Point
![Page 49: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/49.jpg)
Finding G
BAsIcsG
BAsICsG
sBuAsICsy
sBuAsIsx
sBusxAsI
sBusAxssx
tCxty
tButAxtx
su
sysG
T 1
1
1
1
)()(
)()(
)()()(
)()()(
)()()(
)()()(
)()(
)()()(
;)(
)()(
![Page 50: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/50.jpg)
Temperature Control
![Page 51: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/51.jpg)
Example Control System
1/s 1/s+
-1
2
X2 X1
0
1
1
0
32
10
C
B
A
)()(
)()()(
tCXty
tBUtAXtX
-
3
u
![Page 52: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/52.jpg)
Homework• 1. Assuming the buckling force calculated in #6,
compare the energy required to bend the microtubule as in #5. (State assumptions).
• 2. Find evidence (for or against) that the tension field theory applies to endothelial cell regulation.
• 3. Make a model of bone adaptation. What kind of function fits the data?
• 4. Make a model of A-M sliding filaments.
• 5. Based on bending forces of microtubules, calculate how many would be present in the EC, in the experiments shown (make simplifying assumptions).
![Page 53: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/53.jpg)
Bibliography
• 1. Hamill OP, Martinac B. Molecular basis of mechanotransduction in living cells. Physiol Rev 81 2001; (2):685-740.
• 2. Lang F, Busch, GL, Ritter M, Volkl H, Waldegger S, Gulbins E, Haussinger D. Functional significance of cell volume regulatory mechanisms. Physiol. Rev 1998; 78:247-273.
• 3. Zhu C, Bao G, Wang N. Cell mechanics: Mechanical response, cell adhesion, and molecular deformation. Annu Rev Biomed Eng 2000; 2:189-226.
• 4. Turner CH. Mechanical transduction mechanisms in bone. J Bone Miner Res 2000; 15 (4):105.
5. Tavi P, Laine M, Weckstrom M, Ruskoaho H. Cardiac mechanotransduction: from sensing to disease and treatment. Trends in Pharmacological Sciences 2001; 22 (5):254-260.
![Page 54: Neurofilaments Cross-linked In frog axon Isotropic: same in all directions](https://reader035.vdocuments.net/reader035/viewer/2022062321/56649e2b5503460f94b197fe/html5/thumbnails/54.jpg)
Bibliography
• 6. Craelius W. Stretch activation of rat cardiac myocytes. Experimental Physiology 1993; 78 (3):411-423.
• 7. Ingber DE and Folkman J. How does extracellular matrix control capillary morphogenesis? Cell 1989; 58:803-805.
• 8. Craelius, W, Huang, CJ, Palant, CE, Guber H: “Mechanotransduction of swelling by rat mesangial cells,” Mechanotransduction 2000, Engineering and Biological Materials and Structures, ENPC, France, 13-20, 2000.
• 9. Craelius, W, Huang, CJ, Guber, H, Palant, CE: “Rheological behaviour of rat mesangial cells during swelling in vitro,” Biorheology 35:397-405, 1998.
• 10. Pedersen SF, Hoffmann EK, Mills JW. The cytoskeleton and cell volume regulation. Comp Biochem Phys A 2001; 130 (3):385-399, Sp Iss SI.
• 11. Lange K. Regulation of cell volume via microvillar ion channels. J Cell Phys 2000; 185 (1): 21-35.