BME Engineering Molecular Cell Biology. Review: Basics of the Diffusion Theory. The Cytoskeleton (I)

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1 BME Engineering Molecular Cell Biology Lecture 08: Review: Basics of the Diffusion Theory The Cytoskeleton (I) BME Lecture 08, September 22,

2 Outline Background: FRAP & SPT Review: microscopic diffusion theory Review: macroscopic diffusion theory An overview of the cytoskeleton Actin and its associated proteins 2

3 Outline Background: FRAP & SPT Review: microscopic diffusion theory Review: macroscopic diffusion theory An overview of the cytoskeleton Actin and its associated proteins 3

4 Fluorescence Microscopy of Cell Dynamics

5 Two Frequently Used Methods to Determine Diffusion Coefficient Method 1: Fluorescence recovery after photobleaching Method 2: Single particle tracking 5

6 Fluorescence Recovery After Photobleaching (FRAP) FRAP provides a convenient approach to visualize diffusion. Diffusion coefficient can be estimated from FRAP. 2 w D 1/2 4t w: radius of a Gaussian profile bleaching beam t 1/2 : hlfti half time of ffluorescence recovery 1) D. Axelrod, D.E. Koppel, J. Schlessinger, E. Elson, and W.W. Webb. Mobility Measurement by Analysis of Fluorescence Photobleaching Recovery Kinetics. Biophys. J. 1976; 16(9): ) J. Lippincott-Schwartz, N. Altan-Bonnet, G. H. Patterson, Photobleaching and photoactivation: following protein dynamics in living cells. Nature Cell Biology, 2003 Sep;Suppl:S

7 Single Particle Tracking (SPT) D. Wirtz, Particle-tracking t microrheology of fliving i cells, Ann. Rev. Biophys. 38: ,

8 Outline Background: FRAP & SPT Review: microscopic diffusion theory Review: macroscopic diffusion theory An overview of the cytoskeleton Actin and its associated proteins 8

9 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) Movement of different particles are independent. d (4) Each particle moves at a average step size of δ=v x τ i 1 x n x n i 9

10 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). i 1 x n x n i N N 1 1 x n xi n xi n 1 N i 1 N i1 N 1 xi n1 xn1 N i1 10

11 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. time. Again, the same holds for a single particle. 1 1 x n x n x n x n N N i i 12 i 1 N i1 N i1 2 2 x n1 t x n n 2Dt r n x n y n 4Dt r n x n y n z n 6Dt D 2 2 V x

12 1D Random Walk in Solution (IV) Property 3: The displacement of a particle follows a normal distribution. p k;n n! 1 1 k k! n k!2 2 nk p k 1 e 2 2 k 2 n n where and x n k n k k n x n 2 k n x n k k nn n n n n n x 1 4Dt 2 p x e where n 2 Dt 4 Dt 12

13 Application of the Microscopic Theory (I) Object Distance diffused 1 μm 100 μm 1mm 1m K ms 2.5s s s (7 hrs) (8 yrs) Protein 5ms 50s s (6 days) s (150 yrs) Organelle 1s 10 4 s 10 8 s s (3 hrs) (3 yrs) (31710 yers) K+: Radius = 0.1nm, viscosity = 1mPa s -1 ;T=25 C; D=2000 μm 2 /sec Protein: Radius = 3nm, viscosity = mPa s -1 ; T = 37; D = 100 μm 2 /sec Organelle: Radis = 500nm, viscosity = mPa s -1 ; T = 25 C; D = 0.5 μm 2 /sec 13

14 Application of the Microscopic Theory (II) Diffusion with external flow x 2 > acement < uare displa Mean squ H. Qian, M. P. Sheetz, E. L. Elson, Single particle tracking: analysis of diffusion and flow in two-dimensional systems, Biophysical Journal, 60(4): , Pure diffusion Diffusion in a cage t 14

15 Outline Background: FRAP & SPT Review: microscopic diffusion theory Review: macroscopic diffusion theory An overview of the cytoskeleton Actin and its associated proteins 15

16 Macroscopic Theory of Diffusion (I) Fick's first equation: net flux is proportional to the spatial gradient of the concentration function. 1 2 N x N x 1 Fx lim 0 2 N x N x / A 2 1 Nx Nx lim 0 2 A A 1 lim D Cx Cx 0 C D x F C x D x 16

17 Macroscopic Theory of Diffusion (II) Fick's second equation 1 Ct Ct FxxFxxA A Ct Ct Fxx Fxx A A 1 Fx x Fx x 2 C F x C D 2 t x x Change over time Change over space The time rate of change in concentration is proportional to the curvature of the concentration ti function. 17

18 Diffusion Coefficient of a Particle Einstein-Smoluchowski Relation v d 1 1 Fx a 2 2 m 2 2m 2 2 Fx 2m mvx kt f 2 vd D D kt D f: viscous drag coefficient f Stokes' relation: the viscous drag coefficient of a sphere moving in an unbounded fluid f 6 r : viscousity r: radius 18

19 An example of D calculation Calculation of diffusion coefficient D kt 6r k= J/k= N m/k T = =0.8904mPa s= N m -2 s r= 500nm=0 0.5μm D=0.5 m 2 /s 19

20 References Howard Berg, Random Walks in Biology, Princeton University Press, Jonathon Howard, Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associated,

21 Outline Background: FRAP & SPT Review: microscopic diffusion theory Review: macroscopic diffusion theory An overview of the cytoskeleton Actin and its associated proteins 21

22 The Cytoskeleton is Highly Dynamic and Regulated 22

23 The Cytoskeleton (I) Three classes of filaments - actin: stress fiber; cell cortex; filopodium - microtubule: centrosome - intermediate filaments Red: actin Green: microtubule 23

24 The Cytoskeleton (II) Intermediate filaments Spatial organization of cytoskeletal filaments is dependent on many factors, e.g. - cell type - cell states (cycle) - cell activities Green: vimentin IF Red: microtubule Orange: keratin IF Green: desmosome 24

25 The cytoskeleton plays a critical role in many basic cellular l functions, e.g. The Cytoskeleton (III) - structural organization & support - shape control - intracellular transport - force and motion generation -signaling g integration Highly dynamic and adaptive 25

26 Overview of Cytoskeletal Filaments Shape Diameter Subunits Polarized actin cable ~6 nm actin monomer microtubule tube ~25nm tubulin heterodimer intermediate filament rope ~10nm Various dimers yes yes no 26

27 Organization of Actin with a Cell 27

28 Actin Structure and Function Each actin subunit is a globular monomer. One ATP binding site per monomer. Functions - Cell migration - Cell shape - Used as tracks for myosin for short distance transport Pollard & Cooper, Science, ,

29 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] 29

30 Actin Nucleation and Nucleotide Hydrolysis Actin polymerizes and depolymerizes substantially faster at tthe plus end d(barbed b end) d)than at the minus end (pointed end). 30

31 Outline Background: FRAP & SPT Review: microscopic diffusion theory Review: macroscopic diffusion theory An overview of the cytoskeleton Actin and its associated proteins 31

32 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 crosslinking -Signaling g adapter Functional overlap and collaboration between actin- binding proteins 32

33 Actin Accessory Proteins (II) Monomer binding proteins - profilin: to bind actin monomer and accelerate elongation - thymosin: to bind and lock actin monomer - ADF/cofilin: to bind and destabilize ADP-actin filaments 33

34 Actin Accessory Proteins (III) Actin nucleation - Formins: to initiate unbranched actin filaments - Arp2/3: to bind the side of actin and initiate branching 34

35 Actin Accessory Proteins (IV) Actin capping protein - Blocks subunit addition and disassociation Actin severing protein Three families of proteins perform both functions - Gelsolin - Fragmin-severin - ADF/cofilin 35

36 Actin Accessory Proteins (V) Actin side-binding proteins tropomyosin, nebulin, caldesmon Actin crosslinking protein - -actinin - filamin - spectrin -ERM 36

37 Actin Adapter Protein Adaptor proteins such as WASP (a branching mediating factor) & VASP (a polymerization mediating factor) server as connectors between signaling pathways and actin assembly. 37

38 Actin Regulation GTPase: Molecule switch; Family of proteins that are activated by GTP binding and inactivated by GTP hydrolysis and phosphate dissociation. Rho GTPase: cdc42: its activation triggers actin polymerization and bundling at filopodia. Rho: its activation promotes actin bundling. Rac: its activation promotes polymerization at the cell periphery. 38

39 Rac on Actin Organization 39

40 Summary: actin Relatively soft (quantification in following lectures). Often form bundles; mechanical strength comes mostly from bundling and crosslinking. Mostly function to withstand tension rather than compression. Relatively stable and easy to work with (biochemically). 40

41 Summary: actin accessory proteins Different proteins have distinct functions. Proteins with multiple functional domains can have multiple l functions. Some of them are essential. Most of the proteins have functional overlap. 41

42 Required Reading Chapter 16 42

43 Questions? 43