Biophysics I. DIFFUSION
Experiment add a droplet of ink to a glass of water Observation: the stain spreads and eventually colours the entire fluid add a droplet of ink to HOT and COLD water Observation: the stain spreads faster in hot water than in cold water
BIOLOGICAL IMPORTANCE OF DIFFUSION microscopic matter transport processes transport through the cell membrane metabolism gas exchange between blood and the lungs stimuli absorption of medicines chemical reactions (inter- and intracellular molecular movements)
EVERYDAY EXAMPLES OF DIFFUSION
MOLECULAR MOTION most of the particles of biological systems are in constant motion in fluid phase aqueous medium (55 60 % of the human body consists of water) in lipid phase cell membrane (exhibit higher order organisation) Brownian motion Robert Brown (scottish botanist, 1827) o experiment: microscopic investigation of pollen in water o observation: random, zig-zag motion of pollen particles, similar to gas particles o explanation?
Brownian motion Brownian motion of a particle in 3D
MACROSCOPIC VIEW BROWNIAN MOTION - basis of the diffusion zig-zag motion of pollen particles MICROSCOPIC VIEW Brownian motion the basis of diffusion - random motion of particles - as a consequence of the repeated collisions with surronding particles (continuous collision between the particles) - depends on the temperature (T): thermal motion kinetic theory of gases model of the perfect/ideal gas e kinetic = 1 2 mv 2 = 3 2 kt~t
Essentials of diffusion due to the non-uniform (inhomogeneous) distribution of particles net transport* of the particles occurs from regions of higher concentration to regions of lower concentration which continues until the distribution of the particles is uniform (homogeneous) * Brownian motion inhomogeneous DIFFUSION homogeneous
t (time) What does the strength of diffusion depend on? FICK S 1 ST LAW QUANTIFYING DIFFUSION IN SPACE For simplicity, let s investigate diffusion in 1D (along the x axis) t = 0 s inhomogeneous distribution t D I F F U S I O N t = homogeneous distribution X (distance)
QUANTIFYING DIFUSSION IN SPACE FICK S 1 ST LAW t = 0s A CONCENTRATION GRADIENT - spatial variation of the concentration (c) along the x axis - ratio of the change in the concentration (Δc) and the distance (Δx) between two points for simplicity: the concentration changes linearly c(x) c x = constant x c max 0 x
QUANTIFYING DIFUSSION IN SPACE FICK S 1 ST LAW t A n Due to diffusion through a surface of A (perpendicular to the direction of matter flow) during t time N number of particles ->-> n amount of particles (mole fraction) travels through c x c c c x
QUANTIFYING DIFUSSION IN SPACE FICK S 1 ST LAW MATTER FLOW RATE: I v (unit: mol/s) depends on the surface (A) PARTICLE FLUX (I N ) MATTER FLOW DENSITY: J (unit:mol/m 2 s) independent from the surface (A) MATTER FLOW DENSITY number of moles of substance travelling through a unit surface during a time interval of unity STRENGTH OF DIFFUSION
QUANTIFYING DIFUSSION IN SPACE FICK S 1 ST LAW General description of transport processes: Onsanger s linear equation the matter flow density of the extensive quantity (amount of particles) is linearly proportional to the gradient of the intensive quantity (concentration)
Diffusion coefficient characterises the mobility of a diffusing particle - tells us how fast a given substance diffuses symbol: D unit: m 2 s -1 gives 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
Diffusion coefficient For shperical particles (r: radius) in a viscous medium (η) at T temperature: STOKES-EINSTEIN EQUATION - temperature (T) the higher the temperature, the stronger the thermal motion - geometry/shape of the particle (r) small/globular particle diffuse more easily than big/fibrillar particle - (molecular weight of the particle (M)) (heavier particles diffuse more slowly than the lighter ones) - viscosity of the medium (η) diffusion is faster in low viscosity media than in high viscosity media; gases>liquids k: Boltzmann constant, k = 1.38 10 23 joule/kelvin
diffusing particle medium [D] = m 2 s -1 T = 20 o C H 2 (2) air 6.4 10-5 O 2 (32) air 2 10-5 O 2 (32) water 1.9 10-9 amino acid: glicine MW: 75 Da globular protein: serum albumin MW: 69 000 Da 60 x 96 x 60 Å fibrilar protein: tropomyosin MW: 93 000 Da l = 40 Å tobacco mosaic virus MW: 40 000 000 Da l = 300 Å d = 150 Å Diffusion coefficient water 0.9 10-9 water 6 10-11 water 2.2 10-11 water 4.6 10-12 x3 x10000 x100 x3 FASTER DIFFUSION
WHAT ELSE? something is missing concentration gradient (force) diffusion (matter flow) homogeneous distribution (equilibrium) We quantitated diffusion considering the spatial variations in the concentration FICK S 1st LAW (spatial description) but we have not considered that the concentration changes with time, too: c (x, t) FICK S 2 nd LAW (spatial & temporal description)
Quantifying diffusion in space & time Fick s II. law for simplicity: we still examine the one-dimensional situation Fick s II. law Graphical illustration of the concentration (c(x)) at time point t 1 and t 2 (t 1 <t 2 ) according to the simplified Fick experiment
Fick s II. law Free diffusion in 1D (the random-walk problem) How far does a particle get from its initial position during t? R(t) =? y x spherical spreading and distribution of potassium permanganate the migration of particles (R(t)) can be described with a distribution function (Gaussian function) R(t) ~ 2Dt concentration distribution as a function of time the average value of R(t) is linearly proportional to the square-root of time
time (t) Notice the diffusion time (t) is proportional to the square of the diffusion distance (R) t ~ R 2 distance (R) Diffusion relatively fast (< seconds) over a short distance (100 μm) exeptionally slow (> days) over a long distance (1 cm)
Diffusion through the cell membrane EXTRACELLULAR SPACE MATTER TRANSPORT LIPID BILAYER MEMBRANE PROTEINS INTRACELLULAR SPACE cytoplasm water apolar molecules ions monosaccharides amino acids metabolites different mechanism: exocytosis and endocytosis
Diffusion through the cell membrane TRANSPORT PROCESSES ACROSS BIOLOGICAL MEMBRANES I. TRANSPORT MECHANISM WITHOUT MEDIATOR WITH MEDIATOR PASSIVE DIFFUSION FACILITATED DIFFUSION ion channels carrier proteins carrier proteins 1. 2. 3. 4. PASSIVE TRANSPORT II. ENERGETIC REQUIREMENTS ACTIVE TRANSPORT
Diffusion through the cell membrane; TRANSPORT PROCESSES ACROSS BIOLOGICAL MEMBRANES 1. PASSIVE DIFFUSION Passive transport Without mediator direction of transport:electro-chemical POTENTIAL GRADIENT o chemical potential gradient (concentration) o electric potential gradient (charge) rate of diffusion: Fick s laws mediator: no energetic requirement: no examples: o hydrophobic molecules: O 2, N 2 o small polar molecules: CO 2, water, alcohol, urea, glycerol o glucose, sacharose
Diffusion through the cell membrane; TRANSPORT PROCESSES ACROSS BIOLOGICAL MEMBRANES 2. FACILITATED DIFFUSION ion channels Passive transport With mediator: ION-CHANNEL direction of transport: chemical or electro-chemical potential gradient rate of diffusion: faster than that expected from Fick s laws mediator: ION-CHANNEL PROTEIN o transmembrane proteins o closed / open state: no transport / transport o regulation: mechanically-gated (mechanical tension) voltage-gated (potential difference) ligand-gated (ligand-binding) o selectivity: size & charge of the ions energetic requirement: no
Diffusion through the cell membrane; TRANSPORT PROCESSES ACROSS BIOLOGICAL MEMBRANES 3. FACILITATED DIFFUSION carrier proteins Passive transport With mediator: CARRIER PROTEINS direction of transport: chemical or electro-chemical potential gradient rate of diffusion: faster than that expected from Fick s laws mediator: CARRIER PROTEIN o specifically binds the ions or molecules and promotes their transport energetic requirement: no
Diffusion through the cell membrane; TRANSPORT PROCESSES ACROSS BIOLOGICAL MEMBRANES 4. FACILITATED DIFFUSION carrier proteins Active transport With mediator: CARRIER PROTEINS direction of transport: AGAINST the chemical or electro-chemical potential gradient! ENERGY IS REQUIRED mediator: CARRIER PROTEIN o uniporter o symporter/antiporter energetic requirement: yes o ATPase transporter (ATP hydrolysis) o photo transporter (light energy) o coupled transporter (energy from an other transport) example: Na+-K+ pump More about it: Lecture 3: The cell membrane. Resting potential.
GAS EXCHANGE BETWEEN BLOOD AND THE LUNGS obstacles diffusional distance: R 1 mm LUNGS O 2 uptake CO 2 discharge BLOOD CIRCULATION diffusional gas exchange Simplified scheme. time spent by the red blood cell t 0.5 s
GAS EXCHANGE BETWEEN BLOOD AND THE LUNGS molecule diffusion distance [R] diffusion coefficient [D], m 2 s -1 time needed [t], s O 2 1 μm = 10-6 m 10-9 m 2 s -1 500 10-6 s = 500 μs << 0.5 s CO 2 1 μm = 10-6 m 6 10-9 m 2 s -1 83 10-6 s = 83 μs << 0.5 s R(t) ~ 2Dt Effectivity of gas exchange: short diffusional distance (µm), large diffusion speed (µs).
OVERVIEW the most important things Exam questions: Brownian motion Diffusion Fick s 1st law (spatial description) Diffusion coefficient, Einstein-Stokes equation Diffusion through the cell membrane: passive, facilitated, active transport You should know about it: Fick s 2nd law (spatial & temporal description)