lecture 08:lecture 08: review: basics of the diffusion ......bme 42-620 engineering molecular cell...

BME 42-620 Engineering Molecular Cell Biology

Lecture 08:Lecture 08:

Review: Basics of the Diffusion Theory

The Cytoskeleton (I)

1BME42-620 Lecture 08, September 22, 2011

Outline

• Background: FRAP & SPT

• Review: microscopic diffusion theory

• Review: macroscopic diffusion theoryp y

• An overview of the cytoskeleton• An overview of the cytoskeleton

• Actin and its associated proteins

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Outline






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Fluorescence Microscopy of Cell Dynamics

http://lippincottschwartzlab.nichd.nih.gov/video/classic/VSVGrelease.mov

Two Frequently Used Methods to Determine Diffusion CoefficientDiffusion Coefficient

• Method 1: Fluorescence recovery after photobleaching

• Method 2: Single particle trackingg p g

5

Fluorescence Recovery After Photobleaching (FRAP)

• FRAP provides a convenientapproach to visualize diffusion.pp

• Diffusion coefficient can beestimated from FRAP.

2wD 1/24D

t

1/2

: radius of a Gaussian profile bleaching beamh lf ti f fl

wt

1) D. Axelrod, D.E. Koppel, J. Schlessinger, E. Elson, and W.W. Webb. MobilityMeasurement by Analysis of Fluorescence Photobleaching Recovery Kinetics.Biophys. J. 1976; 16(9):1055-1069.

1/2: half time of fluorescence recoveryt

6

2) J. Lippincott-Schwartz, N. Altan-Bonnet, G. H. Patterson,Photobleaching and photoactivation: following protein dynamics in living cells.Nature Cell Biology, 2003 Sep;Suppl:S7-14.

Single Particle Tracking (SPT)

D Wi t P ti l t ki i h l f li i ll A RD. Wirtz, Particle-tracking microrheology of living cells, Ann. Rev. Biophys. 38:301-326, 2009.

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http://web.mit.edu/savin/Public/.Tutorial_v1.2/Introduction.html

Outline






8

1D Random Walk in Solution (I)

• Assumptions:(1) A particle i has equal probabilities to walk to the left and to the right.

(2) Particle movement at consecutive time points are independent.

(3) M t f diff t ti l i d d t(3) Movement of different particles are independent.

(4) Each particle moves at a average step size of δ=vx·τ

1i ix n x n i i

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1D Random Walk in Solution (II)

• Property 1: The mean position of an ensemble of particles undergoing random walk remains at the origin.

• The same holds for a single particle over a sufficiently long period of time (ergodicity). ( g y)

1i ix n x n

1 1 1N N

x n x n x n

1 1

1

1

1 1 1

i ii iN

ii

x n x n x nN N

x n x nN

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1D Random Walk in Solution (III)

• Property 2: The mean square displacement of an ensemble of particles undergoing random walk increases linearly w r t timeparticles undergoing random walk increases linearly w.r.t. time.

• Again, the same holds for a single particle. g g p

2 2 2 2

1 12 2

1 1 1 2 1N N

i i ii i

x n x n x n x nN N

2 21x n

2 2 2 2tx n n Dt

2 2 2 4r n x n y n Dt

2 2 2 2 6r n x n y n z n Dt

22 V

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22

2 2xVD

1D Random Walk in Solution (IV)

• Property 3: The displacement of a particle follows a normal distributiondistribution.

! 1 1

! ! 2 2k n k

np k;nk n k

2

2

2 222

1 where and 4 22

k n np k e

2x n k n k k n

2 2 2 2 2 2 2 2 24 4 2k k

2 0x n k n

2 2 2 2 2 2 2 2 24 4 2x n k k n n n n n n n

2

241 where 2xDtp x e n Dt

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where 24

p x e n DtDt

Application of the Microscopic Theory (I)

Object Distance diffused

1 μm 100 μm 1 mm 1 m1 μm 100 μm 1 mm 1 m

K+ 0.25ms 2.5s 2.5104s(7 hrs)

2.5108s (8 yrs)(7 hrs) (8 yrs)

Protein 5ms 50s 5.0105s (6 days)

5.0109s (150 yrs)

Organelle 1s 104s 108s 1012sg(3 hrs) (3 yrs) (31710 yers)

K+: Radius = 0 1nm viscosity = 1mPa·s-1; T = 25°C; D=2000 μm2/secK+: Radius = 0.1nm, viscosity = 1mPa s ; T = 25 C; D=2000 μm /secProtein: Radius = 3nm, viscosity = 0.6915mPa·s-1; T = 37; D = 100 μm2/secOrganelle: Radis = 500nm, viscosity = 0.8904mPa·s-1; T = 25°C; D = 0.5 μm2/sec

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Application of the Microscopic Theory (II)

Pure diffusionx2 >

Diffusion with external flow

Pure diffusionac

emen

t <ua

re d

ispl

aM

ean

squ Diffusion in a cage

H. Qian, M. P. Sheetz, E. L. Elson, Single particle tracking: analysis of diffusion and flow in two-dimensional systems, Biophysical Journal 60(4):910 921 1991

t

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Biophysical Journal, 60(4):910-921, 1991.

Outline






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Macroscopic Theory of Diffusion (I)

• Fick's first equation: net flux is proportional to the spatial gradient of the concentration function.

12N x N x

1

0

2

0

12

12

xF N x N x / A

N x N xA A

lim

lim

CF D

0

1D C x C x

CDx

lim

xF Dx

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Macroscopic Theory of Diffusion (II)

• Fick's second equation

1x xC t C t F x F x A

A

1 1 1

1x xC t C t F x F x A

AF x F x

x xF x F x

2xFC CD

Ch i Ch2x D

t x x

The time rate of change in concentration is proportional to th t f th t ti f ti

Change over time Change over space

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the curvature of the concentration function.

Diffusion Coefficient of a Particle

2

2 • Einstein-Smoluchowski Relation

1 12 2

xd

Fv am

22

2

22x x

d

mF mvm kTfv D D

kTDf

f: viscous drag coefficient

• Stokes' relation: the viscous drag coefficient of a sphere moving in an unbounded fluid

6f r : viscousityr: radius

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An example of D calculation

• Calculation of diffusion coefficient

6kTDr

• k=1.38110-23J/k=1.381 10-17 N·m/k

• T = 273.15 + 25• =0.8904mPa·s=0.8904 10-3 10-12N·m-2·s• r= 500nm=0 5μmr 500nm 0.5μm• D=0.5 m2/s

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References

• Howard Berg, Random Walks in Biology, Princeton University Press, 1993.

• Jonathon Howard, Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associated, 2001.

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Outline






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The Cytoskeleton is Highly Dynamic and Regulated

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The Cytoskeleton (I)• Three classes of filaments

- actin: stress fiber; cell cortex; filopodiumi b l- microtubule: centrosome

- intermediate filaments

Red: actinGreen: microtubule

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The Cytoskeleton (II)• Intermediate filaments

• Spatial organization of cytoskeletal filaments is dependent on many factors, e.g.

Green: vimentin IFRed: microtubule- cell type

- cell states (cycle)- cell activities

Orange: keratin IFG dGreen: desmosome

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The Cytoskeleton (III)• The cytoskeleton plays a

critical role in many basic ll l f ticellular functions, e.g.

- structural organization & supportshape control- shape control

- intracellular transport- force and motion generation- signaling integrationg g g

• Highly dynamic and adaptive

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Overview of Cytoskeletal Filaments

Shape Diameter Subunits Polarized

i bl iactin cable ~6 nm actinmonomer

yes

microtubule tube ~25nm tubulin heterodimer

yes

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intermediate filament

rope ~10nm Various dimers

no

Organization of Actin with a Cell

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Actin Structure and Function• Each actin subunit is a

globular monomerglobular monomer.

• One ATP binding site per monomer.

• FunctionsFunctions- Cell migration- Cell shape- Used as tracks for myosin Used as t ac s o yosfor short distance transport

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Pollard & Cooper, Science,326-1208, 2009

Basics Terms of Chemical Reaction Kinetics

• A reversible bimolecular binding reaction

A + B AB

• Rate of association = k+[A][B]

• Rate of disassociation = k-[AB]

• At equilibrium k+[A][B] = k-[AB]

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Actin Nucleation and Nucleotide Hydrolysis

• Actin polymerizes and depolymerizes substantially faster t th l d (b b d d) that the plus end (barbed end) than

at the minus end (pointed end).

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Outline






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Actin Accessory Proteins (I)

• More than 60 families identified so far.

• Functions- Monomer binding- Nucleation- Filament capping- Filament severing

Filament side binding and supporting- Filament side-binding and supporting- Filament crosslinking

- Signaling adapterg g p

• Functional overlap and collaboration between actin-binding proteins

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binding proteins

Actin Accessory Proteins (II)

• Monomer binding proteins- profilin: to bind actin monomer and accelerate elongationprofilin: to bind actin monomer and accelerate elongation- thymosin: to bind and lock actin monomer - ADF/cofilin: to bind and destabilize ADP-actin filaments

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Actin Accessory Proteins (III)

• Actin nucleation- Formins: to initiate unbranched actin filamentsFormins: to initiate unbranched actin filaments- Arp2/3: to bind the side of actin and initiate branching

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Actin Accessory Proteins (IV)

• Actin capping protein- Blocks subunit addition and disassociationBlocks subunit addition and disassociation

• Actin severing protein

• Three families of proteins perform both functions

- Gelsolin- Fragmin-severin- ADF/cofilin

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Actin Accessory Proteins (V)

• Actin side-binding proteinstropomyosin nebulin caldesmontropomyosin, nebulin, caldesmon

• Actin crosslinking proteing p- -actinin- filamin- spectrin- ERM

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Actin Adapter Protein

• Adaptor proteins such as WASP (a branchingas WASP (a branching mediating factor) & VASP (a polymerization mediating factor) servermediating factor) server as connectors between signaling pathways and actin assemblyactin assembly.

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Actin Regulation

• GTPase: Molecule switch; Family of proteins that areFamily of proteins that are activated by GTP binding and inactivated by GTP hydrolysis and phosphate dissociation.

• Rho GTPase:Rho GTPase: cdc42: its activation triggers actinpolymerization and bundling at filopodia.

Rho: its activation promotes actinbundling.

Rac: its activation promotes

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Rac: its activation promotes polymerization at the cell periphery.

Rac on Actin Organization

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Summary: actin

• Relatively soft (quantification in following lectures).y (q g )

• Often form bundles; mechanical strength comes mostly from bundling and crosslinking.

• Mostly function to withstand tension rather than• Mostly function to withstand tension rather than compression.

• Relatively stable and easy to work with (biochemically).

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Summary: actin accessory proteins

• Different proteins have distinct functions.p

• Proteins with multiple functional domains can have lti l f timultiple functions.

• Some of them are essential• Some of them are essential.

• Most of the proteins have functional overlap. p p

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Required Reading

• Chapter 16p

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Questions ?

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