Biophysics seminar 2. November 2011.

♦ Diffusion

♦ Osmosis

♦ Properties of water

♦ Exercises

Biological importance:

♦ Transport of substances in biological systems

♦ Transport processes through cell membrane metabolism

gas exchange between blood and the lungs

♦ Stimuli

♦ Absorbtion of medicines

♦ Chemical reactions

♦ Thermodiffusion

Brownian motion

Onsager’s equation

(linear, irreversible processes )

J=XL

The flow density of the extensive quantity (J) is linearly

proportional to the gradient of the intensive quantity (X)

Diffusion is a time-dependent process,

constituted by random motion of given

entities and causing the statistical

distribution of these entities to spread in

space.

Matter flow rate

[mol/s]

Matter flow density

[mol/m2s]

A

n

A

IJ v

v

Jv which given the number of moles of substance „A”

travelling through a unit surface during a time interval

of unity.

After few days The beginning state

Fick’s experiment:

Adolf Eugen Fick (1829-1901)

German anatomist and physiologist

A

n

A

IJ v

v

Onsager’ s equation

J≈X

Gradient of concentration

intensive quantity

Matter flow density

extensive quantity

x

c

A

n

x

cDJ

Fick’s 1th law:

matter flow density is linearly proportional to the drop in concentration

negative sign: diffusion current is in the direction where the concentration drops

D – diffusion coefficient

The amount of substance that diffuses through a surface unit during a

time unit if the concentration drop was unity.

depends on both the diffusing particle and the medium in which the

particle diffuses

Unit: m2/s

For spherical particles (r) in a viscous medium (η) at T temperature:

Stokes-Einstein equation:

r

kTD

6

temperature (T)

the higher the temperature, the stronger the thermal motion

geometry of the particle

globular proteins diffuse more easily than fibres

molar mass of the particle (M) heavier particles diffuse more slowly

viscosity of the medium (η)

diffusion is faster in gases than in liquids

What is the problem?

We quantitated diffusion in 1D (along the x axis) assuming spatial

variations in the concentration (c(x)), but…

…we did not consider that c is not constant in time: c (x, t)!

We have to connect the variation of

concentration in time to those in space:

FICK’S 2ND LAW

space + time-dependence of diffusion

OUT IN particles diffusing IN

matter flow density

particles diffusing OUT

matter flow density

We quantitate diffusion in 1D (along the x axis)

Let’s assume a tiny volume (∆V), where the concentration (c) is constant

in space, so we only have to consider the time dependence: c(t)

Calculated from concentration = Calculated from matter flow density

= (Jx-Jx+ Δx) A Δt (ct+Δt-ct)AΔx

Δc Δx = - ΔJ Δt

t

c

x

J

Fick’s II. law

x

cDJ

From Fick’s I.

Law

Δn = Δnin - Δnout

The heatflow causes the flow of particles.

The beginning concentration is homogen

The temperature is inhomogen →flow of particles

The heat flows from warm place to the cold place.

The lighter particles diffuse faster in the direction of

the warmer regions

In the warmer regions the lighter, in the colder

regions the heavier particles dominate

The Soret effect

The Dufour effect

The mater flow causes the heatflow.

Osmosis

Special case of diffusion.There is a filter (semipermeable membrane).

Semipermeable Membrane

The semipermeable membrane functions similar to a fine sieve, only molecules that are small enough can pass.

Bacteria

Medium sized Molecules, e.g. b2-Microglobulin

Water Flow is Easily Possible

Erythrocyte, Red Blood Cell

Albumin, as Example of a Big Protein Molecule

Electrolytes

Allows smaller slovent molecules to

pass through, but not the larger

solute molecules →”filter”

pl: animal skin pellicles, walls of living

cells, ceramic plate with holes,

cellophane

Osmosis

Unidirectional matter flow,

which takes place by means

of diffusion.

Water in

Water out

Water in

Water out

Water out

Water in

CLASSIFYING SOLUTIONS ON THE BASIS OF OSMOTIC PRESSURE

♦ Same osmotic pressure: ISOTONIC

Extra- and intracellular solutions with the same osmotic

pressure

The osmotic pressure of the solutions in the cells of

human body = osmotic pressure of a 0,87 % (n/n)

(0.15 M) NaCl solution→physiologic saline solution

♦ Lower osmotic pressure: HYPOTONIC

Extracellullar solution has lower osmotic pressure than

the intracellular solution→water influx

♦Higher osmotic pressure: HYPERTONIC

Extracellular solution has higher osmotic pressure than

the intracellular solution→water efflux

water

Sugar solution Semipermeable

membrane

t

Solvent IN

Solvent flows in The pressure grow in

membrane

Solvent flow out

♦ The pressure can increase until dynamic equilibrium

♦ The amount of solvent flowing out is same as the amount of solvent

flowing in. Reason: Pressure difference

♦ Osmotic equilibrium

♦ The pressure difference is the osmotic pressure

t0

Pressure that has to be exerted on the solution connected to pure

solvent by a semipermeable membrane to reach dynamic equilibrium,

to counteract osmosis.

ghposmotic ρ- density

h- height of the liquid column

g- 9,81 m/s2

Van’t Hoff’s-law

cRTposmotic c- concentration of solution

R-universal gas constant

T-temperature

The osmotic pressure exerted by any substance in dilute solution is the same

as that it would exert if present as gas in the same volume.

pozmózis V=nRT

ozmózis

np RT

V

For diluted solutions and perfect semipermeable membranes using the

equation of state of the ideal gas:

The roles of diffusion and osmosis 1. Dialysis

The process in which different molecules or macromolecules are sorted

by semipermeable membrane.

Remove soluble chemical toxic from body instead of kidneys.

Dialysis

FRAP denotes an optical technique capable of quantifying the

two dimensional lateral diffusion of a molecularly thin film

containing fluorescently labeled probes, or to examine single

cells. This technique is very useful in biological studies of cell

membrane diffusion and protein binding.

Specific heat of water Surface tension of water

Specific melting heat of water Evaporation heat of water

Density of water

Density anomaly density of

water is the greatest at 4 °C.

The phase diagram of water

1atm

100 C

0 C

Pre

ssure

Temperature

The unusually high specific heat, surface tension, specific melting heat, evaporation

heat, melting and boiling point, are all explained by the large number of hydrogen

bonds that stabilize the structure of water. The density of ice is lower than that of liquid

water because of the hexagonal crystal structure and the “holes” within.

Explaining the properties of water

Biological relevance of water Density anomaly: seas and lakes freeze at the surface, enableing fish

and other animals to survive.

Large specific heat: helps maintaining a constant temperature, living

organisms will not grow cold easily.

Large evaporation heat: organisms can release heat easily.

Large dipole moment: makes it an excellent solvent for nutrients and

other biologically important molecules, form hydrate shell around

macromolecules (DNA, proteins).

The water that contains 33 gram / liter of sodium

chloride (NaCl), typical of seawater, has an ionic

concentration of c = 1.128 mol / liter. The ambient

temperature T = 300 K. Calculate the osmotic

pressure. (R=0.082 liter*bar)

p=2*27.8 bar

Calculate the concentration if solution in water

(300K) has osmotic pressure of 3.00 atm.

c=P/RT

c=0,122 M

Thank you for your

attention!