4 diffusion peluffo2010

8/9/2019 4 Diffusion Peluffo2010

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ObjectivesAt the end of this lecture you should be able to:

define diffusion in terms of Ficks First Law recognize the variables involved in the diffusion

process

membranes

distin uish between substances that do and do notpermeate biological membranes

predict the permeation of weak acids and bases summarize the concept of membrane potential


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Ion Gradients in Cells and Or anelles

[Na+]o = 145 mM [Na+]i = ~12 mM

= -30 to -80 mV

[K+]o = 4 [K+]i = 140

[Cl-]o = 116 [Cl-]i = 4

carriers

g +o

= . g +i

= .

pHo = 7.4 pHi = 7.1

Ca2+ = 1.8 Ca2+ = ~10-4channels

pH = 4.5-6 [Ca] ~ 1 mM

Lysosomes, ER,

,endosomes


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average displacement in time =

relation to Diffusion Coefficient, D

21Diffusion of a single particle

2

Ficks First Law of Diffusion

x

CD

dx

dCDJ

Diffusion across a membrane

)( cytext CCPJ

Diffusion through a channelDiffusion of many particles

http://nerve.bsd.uchicago.edu/memb.htmhttp://nerve.bsd.uchicago.edu/diffusion.html

Simulations courtesy of Dr. F. Bezanilla, Univ. Chicago


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Diffusion is rapid over small distances,

slow over large distances The rate of diffusion is directly proportional to the temperature (oK),

2

nverse y propor ona o e me um v scos y an e mo ecu arradius (~ )3 WeightMolec

2D D2or

Diffusin substance D cm2/s 1 s 24 hr

O2 (air) 0.178 0.6 cm 175 cm

Glucose (H2O) 6.7 x 10-6 37 m 1.1 cm

Cu (solid) 1.9 x 10-10 1.9 nm 57 m

On a cellular (m) scale, diffusion is a rapid process


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CdC

xdx

e ux , , s e num er o mo es cross ng a p ane o un area perunit time (moles/cm2s)

D is the Diffusion Coefficient cm2/s

dC/dx ~ C/x (moles/cm3/cm = moles/cm4) is the concentrationgradient

therefore, the rate of diffusion is directly proportional to the magnitudeof the concentration gradient


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Diffusion Across Biological Membranes

Permeability Equation Permeability Coefficient

cytext

x

Ppm

m = us on coe c en n mem rane

Kp = Oil/water partition coefficient

x = membrane thickness ~ 5 nm

oilp

CK

water

high lipid solubility = high permeability

Kp measured by determining distributionof substance between oil and water

water


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permeability increases with lipidsolubility and decreases with molecularsize


9/12

Weak Acids and Bases Cross Membranes Rapidly

H+ + A- HA

. ea c s H+ and A- are impermeable

HA Non-ionized form (HA) is

H+ + A-

permeable

HA rapidly crossesmembrane, dissociates inside

B. Weak BasesH+ + B BH+

B Non-ionized form (B) is permeable

B ra idl crosses membrane, + H+

H+ and BH+ are impermeable

BH+

becomes protonated inside

C. These considerations are very important in understanding how thebody absorbs and handles drugs - Pharmacokinetics


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-

Electrical Potential (): the amount of work required to bring a unitpositive charge from an infinite distance to a particular location

Electric Field: a spatial gradient of electrical potential, i.e. d/dx~ .field, not when the potential is constant.

Electroneutralit Princi le: There must alwa s be e ual numbers

of positive and negative charges in any macroscopic volume. Chargeseparation produces an electric field and occurs only over moleculardistances in biology.


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+ Positive ion In this example, the positive ion diffuses more

- Negative ionrap y an e nega ve on

The dotted line separates a solution

containing lots of ions (left) from a solution

--

- +-

+-

+

+

containing no ions (right)

When diffusion begins, positive ions diffuse

+

-

+

++

+

-

+

+-

+-

-

,

interface (dotted line), and a diffusion potentialdevelops (positive on right side).

-

(+) The diffusion potential accelerates the rate ofdiffusion of the negative ion, and slows thediffusion of the positive ion.

+

(-) Both ions then diffuse down their concentrationgradient at equal rates, i.e. electroneutrality is

preserve except at t e nter ace


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Membrane Potentials

+ Positive ion Membrane potentials are diffusion potentials generatedacross membranes due to ion concentration gradients andunequal membrane permeabilities to the different ions

- egat ve on In this example, the solution on the left is moreconcentrated and the membrane is selectively

permeable to positive ions +-- -

The positive ions diffuse across the membrane from left toright, leaving behind the negative ions. This generates amembrane potential which prevents any further net

-

-

-

+

+

+

-

++

-+

-

``

The excess charges remain very close to themembrane surfaces because of the electrical fieldacross the membrane.

--

+

+

+

In this situation, both the membrane potential and the ionconcentrations on either side of the membrane will be

constant with time (-)(+)

Membrane potentials may be designated as , Vm orEm

For an excellent simulation, see http://nerve.bsd.uchicago.edu/memb.htm (courtesy of Dr. F.

Bezanilla, Univ. Chicago)

4 diffusion peluffo2010

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