NeurofilamentsCross-linkedIn frog axon
Isotropic: same in all directions
Linker proteins for actin
Particle Tracking in fibroblastsLecture 5
Tracking particles: Regional stiffness
• #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
Cylindrical Stresses
shx
sh
d
rP
d
rP
2
X Y Z
Buckling & Bending
2
2
1 L
EIP
10 cm
20 cm
Tension Field Theory
Cell 1 cell 2 cell 3
Flow
h
L
h
T
so
hT
xxx
xxx
Membrane
Coupling: Mechano-/Biochemical-/Cellular-
Inside a Blood VesselEndothelial cells withNucleus bulging out
Blood flow
10 microns
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
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
• Material properties, not inhomogeneity, explains
The non-linear behaviour
Slow cell squishing
FEM of compression
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
• 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
• Strain detected by mechanoreceptors or by CAMs. G protein in membrane causes Ca and other 2nd messengers.
• 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.
• 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
• 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
• G proteind mechanochemical signal transducer
• Focal adhesions by Integrin and associated proteins.
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.
• 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
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
Quantifying bone adaptation
componentfourierf
strainprincipalpeakstimulusstrainE
typeloadingeachfor
cyclesloadingdailyNstimulusS
fE
ENS
i
n
ii
k
jjj
.
..;.
)...(
..#;
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1
1
Bone Loading Waveforms
Resonant Stimuli for Bone
• Loading frequencies near 20 Hz• Vibration 1
• Error Driven
• 1. Rubin, C.
)( 0SSKdt
dmL
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..
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
Sliding filamentds
Dynamic equilibrium
)(''
')('
'
2
)()(2
2
2
2
2
0
02
2
tCukxdt
xdm
kxtCudt
xdm
xxx
PAC
xxktPAudt
xdm
Sliding Filament Model
xvu
uFkxxm
0
)(
For A-M, vo = 0.5 um/s
Ratchet
Harmonic motion (undamped)
0
)(
)()(2
2
0
xx
xkmx
xxktPAuxm
Gel motion follows simple rulesModel will predict dynamic and Static equilibrium.
Natural Frequency
Transition Probabilities
Win Lose
Win 3/4 1/2
Lose 1/4 1/2
Sum 1 1
Today’s Game Outcome
Tom
orro
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utco
me
Need a P forToday’s game
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?
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
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
Control System, I.e. climate control
Sensor Plant-
--
-
Output
Error
Perturbation
Feedback
Set Point
Finding G
BAsIcsG
BAsICsG
sBuAsICsy
sBuAsIsx
sBusxAsI
sBusAxssx
tCxty
tButAxtx
su
sysG
T 1
1
1
1
)()(
)()(
)()()(
)()()(
)()()(
)()()(
)()(
)()()(
;)(
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Temperature Control
Example Control System
1/s 1/s+
-1
2
X2 X1
0
1
1
0
32
10
C
B
A
)()(
)()()(
tCXty
tBUtAXtX
-
3
u
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).
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.
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.