October 30, 2007October 30, 2007

Lustyik

Diffussion, thermodiffusion.Diffussion, thermodiffusion.

Biological role of diffusionBiological role of diffusionOsmosis, chemiosmosisOsmosis, chemiosmosis

The microscopic transport of material

Examples for the biological Examples for the biological role of diffusionrole of diffusion

Motion of small molecules:

Diffusion of water in water: D = 2 x 10-9 m2/s

R2

= 6D

R = 1 cm: 8300 s (2 h 18 m)

R = 3 m (E. coli): 7.5 x 10-5 s

Movement of K+ ions through the plasma membrane

Diffusion of K+ ions in water: D = 10-16 m2/s

100 nm x 100 nm

3 x 104 K+ ion /sec

x = 10 nm

C = 500 mM n/t = -D *A/x * c

O2

CO2

Cells and tissues

Blood flow

Diffusion

Diffusion

Légzés

Convective transport

Convective transport

Oxygen and CO2 exchange in the lung

R2

= 6D

CO2

OO22

~1 m

Alveolus of the lung

Kapillary vessel

Alveolar epithelium

Kapillary endothelium

oxigen ~500 s

CO2 ~80 s Doxigen = 10-9 m2/s

DCO2 = 6 x 10-9 m2/s

Diffusion limited rections

A + B AB PkD

k-D

k 1

2kA + B P

Racting molecules Reaction complex

Product

Reaction constants

Ha k-D k 1<<

k 2 kD=

FRAP (Fluorescence Recovery After Photobleaching)

D

Cell

Nucleus

Flu

ores

cen

ce in

ten

sity

Time

FRAP recovery curve

Recovery

Bleaching

Myoblast, expressing a compound that contains GFP (Green Fluorescence Protein)

FRAP

dndt

dd= - Drot

Rotational diffusion, Florescence anisotropy

fR

kTDrot

fR = 8r3

8rkT

Drot= 3

= 2DrotMeasurement with

fluorescence anisotropy

Diffusion potencial

+ +

+++

+++

+

U

Cell membrane

+ +

+++

+++

+

dU =u+ - u-

u+ + u-RTzF

d(lnc)

Diffusion potential:

„ion mobility”

Integration of this equation provides the

Goldman-Hodgkin-Katz equation

October 30, 2007October 30, 2007

Lustyik

Biological role of diffusionBiological role of diffusion

Osmosis, chemiosmosisOsmosis, chemiosmosis

The microscopic transport of material

Solvent

Solute

Semipermeable wall or membrane

Osmosis

AlcoholAlcohol

Este Reggel

Nollet Abbe, 1748

Dutrochet, 1830

Sucrose solution

Water

Models of osmosis:

Vant’Hoff law

Thermodynamic theory

vant’Hoff’s law

= RTc

= p

Solution

h

p = h g

Pure water

Jacobus Hendricus van’t Hoff (1852-1911)

Thermodynamic theory

o1 = o + RT ln xo1

Chemical potential of the solvent:

o1 o2

p1 p2

+ Vpmp1

Vpm: parcial molar volume

o1 = o + RT ln xo1 + Vpmp1

Equilibrium:

o2 = o + RT ln xo2 + Vpmp2

o1 o2

p1 p2

o1 = o2

p2 – p1 = RTVpm

lnxo2xo1

o1 = o + RT ln xo1 + Vpmp1

o2 = o + RT ln xo2 + Vpmp2

o1 = o2

RT

Vpm

lnxo2

xo1

One compartment is pure solvent (xo1=1)The solution is incompressible (Vpm=konstans)

Solvent concentration is low

Vant’Hoff’s law: = RTc

= c (concentration of the solute)

= RTc

Molality: The number of moles of solute in 1 kg of solvent

Molarity: The number of moles of solute in 1 kg of solution

0,3 M glicerin:

0,3 M NaCl (Na+, Cl-):

0,3 Osmol

0,6 Osmol

Ozmolarity =

= molarity x number of dissociated ions

Isotonic solutions:

If their ospmotic pressure is equal

Isotonic solutions with blood and cytoplasm:

0,15 M-os (0,87%) NaCl solution

5,5%-os glucose solution

3,8%-os Na-citrate solution

Isotonic solution

Hypotonic solution

Hypertonic solution

Human and animal cells

Plant cells

Thermoosmosis

Cold Warm

Equal concentrations (at start)

Solvent transport fom the warmer to the cooler side

Dilution concentration

Biological, medical importance and application:

•Lysing red blood cells for clinical laboratory

•Development of oedemas

•Oedema treatment with hypertonic solution

•Mg-szulfát: causing diarrhea

•Hemodialisis of patients suffering from kidney insufficiency

•Dialisis of laboratory specimens

Isotonic solution = isoosmotic solution

• Colloid osmotic pressure

• Membrane is permeable to the solvent

= RTc„reflection” coefficient 0 < < 1

Szemipermeable membrane

„Leaky” membrane

Time

Hid

rost

ati c

pre

ssu

re d

iffe

ren

cep

„leaky”: permeable to the solvent

Volume regulation of living animal cells

Time

Ch

ange

of

cell

vol

um

e

V Shrinking (water uptake)

Volume regulation

Ion transport, release of isotonic solution

Flow maintained by thermodynamic forces:

Jk = Lk1 X1 + Lk2 X2 + … + Lkn Xn

k = 1, 2, 3, …n

Jv = Lpp p + Lpd Jd = Lpd p + Ldd

Onsager equations:

Jv: „volume” flow Jd: diffussion (osmotic) flow

JQ

Je Jm

Jv

T

U

c

p

Heat flow Volume flow

Electric current

Mass transport

Elektric potencial difference

Pressure difference

Concentration difference

Temperature difference

Diffusion

Thermoosmosis

ChemiosmosisChemiosmosis

Q

CyCNADH

I

II

III

NAD+

OH-

OH-

++

O2

Cytochrom system

ADP

ADP ATP

ATP

ATP Synthase

Chemiosmosis

Q

CyCNADH

I

II

III

NAD+

OH-

OH-

++

O2

Citokróm rendszer

ADP

ADP ATP

ATP

ATP Synthase

Ca2+ +Cy A

No “Mitochondrial Permeability Transition Pore”

Membrare potencial in mitochondria

Intact Damaged

Limited and Facilitated Limited and Facilitated DiffusionDiffusion

Additional cellular transport mechanismsAdditional cellular transport mechanisms

Passive transport (simple diffusion)

Facilitated diffusion

Cell membrane

Lipid bilayer

Membrane proteins

www.whfreeman.com

Special, diffusion associated cellular mechanisms

The ability of an organism or cell to move towards or against concentration gradient of a specific chemical compound

Inflamatory response: Migration towards the inflamatory center

Bacterial migration for finding regions that it deems favorable

Sporulation of amebas

Chemotaxis:

Running: flagella turn counterclockwise

„Tumbling”: flagella turn clockwise

Random walking on organelle scale.