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

.

..;.

)...(

..#;

)1log(

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

w’s

Gam

e O

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

)()(

)()(

)()()(

)()()(

)()()(

)()()(

)()(

)()()(

;)(

)()(

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.