Diffusion:

Cs

X- Ds Js =

difference in concentration

distance

diffusion coefficient

flux of a solute in solution

=

(mass/surface area/time)

1. Diffusion

Fick (1855) discovered that the rate of solute transport is directly proportional to the concentration gradient and inversely proportional to distance traveled.

Fick’s Law describes passive movement of molecules down a concentration gradient. Substances move from high [ ] to low [ ].

Diffusion:

Cs

X- Ds Js =

difference in concentration

distance

diffusion coefficient

flux of a solute in solution

=

(mass/surface area/time)

Diffusion:

From Fick’s Law, can predict the time it takes for a substance to diffuse a particular distance

X)2

Dt ½ =

diffusion in a cell:

small molecule

. ...

. .

.. . .

....

X = 50 m

X)2

Dt ½ =

(0.00005 m)2

10-9 m2 s-1=

= 2.5 sec

Conclude: diffusion is rapid across small distances (i.e., within a cell).

Diffusion:

X)2

Dt ½ =

But … replace 50 m with 1 m and t½ becomes 24 years!

So … diffusion important only over very short distances. It can not possibly explain long distance movement within the plant.

Diffusion: describes water evaporation from stomata

.

Cwv high

Cwv low

Cwv

X- Dwv Jwv =

the driving force

the resistance

2. Bulk flow (mass flow):

movement along pressure gradients (e.g., flow in a garden hose, flow in xylem or phloem)

long distance transport in plants

volume rate of flow

driving force

~

(cm3 cm-2 s-1)

Bulk flow (mass flow):

relationship determined experimentally by Jean-Louis Poiseuille in 1840

used glass capillary tubes (d = 0.01 – 0.3 mm)

Bulk flow (mass flow): Poiseuille Equation

P

X

r2

8.Jv =

Jv volume rate of flow per unit area

r radius

viscosity

P change in hydrostatic pressure

X path length

Bulk flow (mass flow): Poiseuille Equation

P

X r2

8 Jv =

What is the pressure gradient necessary to cause flow in xylem vessels?

rearranging:

Bulk flow (mass flow): Poiseuille Equation

P

X r2

8 Jv =

picking some “reasonable” values:

r = 20 m = 0.01 g cm-1 s-1

Jv = ?

Bulk flow (mass flow): estimating sap velocity

thermocouple

voltage applied

hardwoods (large diameter vessels) like oak, ash

20-25

conifers (narrow tracheids) 2-4

m/hr

heatpulse

use 3.6 m/hr = 0.1cm/sec

Bulk flow (mass flow): Poiseuille Equation

P

X r2

8 Jv =

picking some “reasonable” values:

r = 20 m = 0.01 g cm-1 s-1

Jv = 0.1 cm s-1

Bulk flow (mass flow): Poiseuille Equation

P

X r2

8 Jv =

What is the pressure gradient necessary to cause flow in xylem vessels?

(0.1 cm s-1)(0.08 g cm-1 s-1)

(2 x 10-5)2=

= 0.2 bar m-1

0.2 bar m-1

This is the hydrostatic pressure gradient necessary to obtain flow in a horizontal tube of 20 m radius.

P = 1 bar P = 3 bar

10 m

P = -2 bar P = -4 bar

0.2 bar m-1 overcomes the frictional resistances in the tube.

Water transport in plants:

1. diffusion: within a cell or tightly localized

2. bulk flow (mass flow): long distance; no membranes crossed

3. osmosis: cell to cell, crossing membranes

0.2 bar m-1

This is the hydrostatic pressure gradient necessary to obtain flow in a horizontal tube of 20 m radius.

P = 1 bar P = 3 bar

10 m

P = -2 bar P = -4 bar

0.2 bar m-1 overcomes the frictional resistances in the tube.

10 m

Gravity effect

- 5 bars

- 8 bars

H2O at 10 m will move downward unless the force of gravity is opposed.

So … not only need 0.2 bar m-1

but also need: 0.1 bar m-1

0.3 bar m-1

to move H2O against the force of gravity and through the frictional resistance of the xylem

100 m !!

in giant Sequoia:

30 bars more negative up here

than here

(in order to move water at rates similar to that observed in transpiring plants)

i.e., 3 bars for every 10 m

Partial summary:

1. Diffusion H2O (or any substance) flows along concentration gradients from high [ ] low [ ]

Relatively rapid across short distances but can’t explain long-distance transport

Partial summary:

2. Mass flow (bulk flow)

long-distance transport in plants

flow is along pressure gradients (Poiseuille)

supports rapid movement

e.g., a transpiring sunflower leaf loses the equivalent of its entire leaf H2O content every 20 min

Water transport in plants:

3. Osmosis (van’t Hoff, 1887)

movement of a solvent (e.g., H2O) across a semi-permeable membrane

H2O will flow across membrane into solution where the chemical potential (free energy) of the H2O is lower

Water transport in plants:

3. Osmosis

flow is spontaneous in response to a driving force

high wlow w

A B

solute less concentrated

solute more concentrated

an osmotic pressure will develop in “B” = = RTCs

water

van’t Hoff1887

osmotic pressure = = RTCs

R = universal gas constantT = ° KCs = osmolality = moles of solute kg-1 H2O

plant cell sap contains ~ 0.5 2.5 mol kg-1

= RTCs

= R(293)(0.75 mol kg-1)= 18.3 bars !! (this is ~ 260 psi)

(sea water is ~ 28 bars)

VAC

CYT

i.e, the pressure on the internal wall can easily be 18 to 20 bars

This illustrates that plant cells have very substantial capacity to draw in and retain water.

Osmosis is critical in cell enlargement - expansion

role of elastic cell walls

they have sufficient structural rigidity to allow P to build up

Summary: H2O movement can be affected by:

• pressure• concentration• gravity

f (concentration)

pure water

Does this raise or lower the free energy content of the H2O molecules?

add solute (e.g., sucrose)

. ...

.. ...

. .. .

.

Solutes decrease the free energy of the H2O molecules. Therefore vapor pressure is decreased.

The contribution of solutes to w is always negative (always lowers w ).

f (pressure)

VAC

CYT

+ P (i.e., turgor) on inner walls of living cells

p

w = 0

then: w = + p

w = - 12 + 4

= - 8

e.g., = -12 p = +4

f (pressure)

-P (i.e., tension or negative hydrostatic pressure) in xylem cavity and cell walls

p

w = 0

xylem

small radiisurface tension of H2Oadhesion and cohesion

give rise to negative pressures

and because the column of H2O is continuous, the -P is transmitted all the way to the roots

95% RH(-69 bars)

60% RH(-700 bars)

50% RH(-950 bars)

soil surface

.

.

.

.

water-filled pore in the soil. AA - 2 bars

- 4 bars

- 6 bars

- 8 bars

- 12 bars

- 18 bars

BB.

H2O is continuous from A B

The lowered in the transpiration pathway provides the driving force for the movement of H2O out of adjacent tissues such as:

leaf mesophyllphloemroot cortical cells

The consequent loss of H2O from these tissues is what constitutes a water deficit.

Key concept: