Lectures 18: Biological Membranes: Life in Two Dimensions (contd.)

Transcription

1 Lectures 18: Biological Membranes: Life in Two Dimensions (contd.) Lecturer: Brigita Urbanc Office: ( Course website: 1

2 Structure, Energetics, and Function of Vesicles Energetics assessed by micropipette aspiration experiment suction pressure Key measurements: Rv,R1,l

3 Micropipette aspiration experiment (fluorescent images) Membrane doped with a small fluorescent molecule rhodamine. Measured tensions: 1.1mN /m top 3.mN /m middle 7.4 mn/m bottom 3

4 By measuring the pressure difference and geometric parameters, membrane tension, bending and area stretch moduli can be found:,kb, Ka The pressure difference between the interior of the vesicle and the surrounding medium (Laplace-Young relation): p = outside Rv The pressure difference between the interior of the vesicle and the inside of the micropipette: pinside = R1 The pressure difference between the inside of the micropipette and the surrounding media, which is controlled experimentally, is: p = p inside poutside so that finally the tension can be expressed as: R1 p = 1 R1 /R v 4

5 Determining the area stretch modulus: K a a = Ka a0 a... the change of membrane area a 0... the area of the reference state Calculate the change in the are due to micropipette suction: a = R1 l R1 a R 1 1 l/r1 = a0 R v R1 1 l/r1 versus gives K a as a slope R v 5

6 A series of tensions applied by controlling the pipette pressure; areas were measured for each pressure 6

7 Measured values of the area stretch modulus for different lipids. 7

8 In vivo membranes include: endoplasmic reticulum trans-golgi network tubular and recticular structure Biological tubules are hypothesized to form by membrane-attached motor proteins: Tubules are pulled out of a membrane (right). 8

9 Groups of motor proteins can help pull membrane tubes out of a spherical vesicles 9

10 Differential interference contrast microscopy on an in vitro experiment: microtubules with Xenopus egg cytosolic proteins helps form an elaborate web of rat liver ER membrane 10

11 A single tubule pulled out and switches microtubule tracks: 11 second experiment 11

12 Measuring the force associated with a tether formation Using optical trap with a bead attached to a vesicle and pulled out 1

13 When a tether is formed, the force on the bead increases abruptly 13

14 Calculation of a force needed to pull out a tether Free energy associated with bending and stretching of the vesicle + tether system Gbend = Kb 4 R K b R r r L 1 1 Kb 4 r r L Gbend = 1 Kb K b r 14

15 Ka a a 0 Gstretch = a0 a 0 =4 R a = a 0 r L r L,R Two additional terms contribute to the free energy: work against the pressure difference between the inside and outside of the vesicle: 4 GpV = p R3 r L 3 work done by the pulling force: Gload = f L The total free energy of the vesicle + tether system is: L 4 3 G tot = 1 Kb K b Gstretch p R r L fl 3 r 15

16 The equilibrium shape of a vesicle and a tether is the one that minimizes the total free energy with respect to R, r, & L: G tot =0 R Gstretch R Gstretch r G tot =0 G tot =0 r L a a 0 a = Ka = 8 R a0 R Gstretch = L = r L Eq. 1 : 8 R 4 p R = 0 L Eq. : K b L p r L = 0 r 1 Eq. 3 : K b r p r f = 0 r 16

17 Solution: Eq. 1 p = R the Laplace Young relation Kb L r Eq : K b L 4 L =0 r R r Eq 3 : f K b force tension relation Measured forces for pulling tethers from the ER and Golgi are ~ 10 pn, so tension can be estimated to be: f = pn/nm 8 Kb r 50 nm K b 0 k B T 0 4 pn nm =80 pn nm 17

18 Vesicles in Cells A) clathrin coated pits on a cell membrane before endocytosis B) membrane wrapping around a large particle (phagocytosis) C) a transport vesicle within the axon of a neuron D) thin section through a synapse of a junction between a muscle cell and nerve cell packed with synaptic vesicles E) goblet cell in intestine dumping giant mucus-containing vesicles F) thin section of a Golgi apparatus with small transport vesicles that contain proteins to be transported 18

19 Function of vesicles in the cell: (1) uptake of the matter from extracellular space into the cell: endocytosis () delivering matter to the outside: exocytosis (3) moving matter (proteins, lipids) inside the cell: intracellular transport Example of endocytosis: A) -uptake of cholesterol containing particles (LDL) from the bloodstream; cholesterol from diet is packaged in liver; LDL particles about 0 nm long -LDL bind to the receptor on the cell membrane -bound receptors cluster together because the clathrin molecules attached to the receptor on the intracellular side self-assemble into pits 19

20 Example of exocytosis: synaptic vesicles deliver neurotransmitter molecules into extracellular space to be taken up by a muscle cell diameter : 40 60nm 0

21 Free energy needed to form a vesicle is independent of the vesicle size: G vesicle = Kb R da Kb G vesicle = 4 R = 8 K b R K b 10 0 k B T k B T energy for a vesicle How can this energy be provided? - incorporate proteins that favor curved state - incorporate curvature-inducing lipids Lipid census for synaptic vesicles: 5 3 diameter D 60 nm volume V 10 nm each acetylcholine molecule 450 Da takes : 1nm3 volume 1

22 each vesicle contains : 105 neurotransmitter molecules A rule of thumb for a cell such as fibroblast: The flux of vesicles is such that the area taken up by vesicle in 1 hour is equal to the entire plasma membrane area. a fibroblast 000 nm a vesicle nm 60,000 vesicles per hour 1,000 vesicles per minute 500 k B T 1,000 per minute 5,000 ATP /min