Physics of biological membranes, diffusion, osmosis Dr. László Nagy

Physics of biological membranes, diffusion, osmosis Dr. László Nagy

-Metabolic processes and transport processes. - Macrotransport : transport of large amount of material : through vessel systems : in large distance - Microtransport : small amount of material : by diffusion : in small distance

Name of the transport process Transport of liquids and gases What is transported macroscopic material Potential pressure difference(dp) Diffusion molecules concentration difference(dc) Temperature heat temperature difference (DT) Electric current ions, electrons electric potential (DU) J DU Dx

Current intensity: I dm dt dm amount of material transported in dt time across the A cross section area - characteristic to the A surface - m is: mass, volume, electric charge, energy, etc. Current density: Unit can be: kg/s; m 3 /s; C/s (A); J/s J di da di is the transport intensity perpendicular to da surface - vector quantity (direction = direction of the transport) - it is defined at the point of the transport area -differential quantity Unit can be: kg/s/m ; m 3 /s/m ; C/s/m (A/m ); J/s/m

Specific conductivity: J g du dx potential gradient specific conductivity current density U: - potential : - negative gradient of U gives the driving force at any point of the transport (potential energy, electric potential, temperature difference, concentration gradient) g: - generalized (specific) conductivity Eg.: in the case of the diffusion the potential gradient is the gradient of the concentration (dc/dx).

Diffusion

c 1 c c 1 > c dc a) Macroscopic approach: J g dx m c(a v t) Unit c and A: J D dc dx, D m s

b) Molecular approach: Chemical potential of a single particle: m = m 0 + ktlnc. The gradient of the chemical potential: f m( x, t) x k T ln c( x, t) x k T c c( x, t) x dn moles are transported across the A surface in dt time: dn = caū dt. dn c Au dt D c( x, t) A x dt Fick s I. law: J dn Adt c( x, t) D x The amount of transported material across a unit area and unit time (the rate of the diffusion) is proportional to the gradient of the concentration. D is the diffusion constant. Dc Dx is constant at a given place and time.

D depends on: 1) temperature 1 mv 3 k T v 3 k T m D T m 1 1 ) viscosity D kbt 6r Einstein-Stokes 3) mass k B = Boltzmann constant T = absolute temperature = viscosity coefficient r = radius of the particle 4) geometry

Fick s II nd law ), ( ), ( ), ( x t x c D x x t x c D t t x c The change of the concentration in time at a given place is proportional with the change of the concentration gradient with the place at a given time. Concentration gradient x t x c ), ( x x x 0 dc/dx

The solution of Fick s nd law and some consequences of it: c(x, t) M D t e x 4Dt M is the amount of material at t=0 and x=0 D = diffusion coefficient x = distance t = time In a special case: x 4Dt 1 c( x, t) M e 1 M e x(t) D t

capillary tissues tissues capillary distance

x( t) Dt t x 4D Pl.: D 10-9 m s -1 ; x = 5 nm =510-9 m; 9 18 5 10 m 510 s t 9 9 410 410 m s = 6.5 ns. D 10-9 m s -1 ; x = 50 mm =510-5 m; = 0.65 s. D 10-9 m s -1 ; x = 1 m = 7.9 év. Diffusion is effective at small distances! Gas exchange across the alveocapillary membrane: D oxigén 110-9 m s -1 ; D CO 610-9 m s -1 ; x = 1 mm =110-6 m; t oxigén = 50 ms; t CO = 40 ms; In the air: D oxigén 10-5 m s -1 ; D CO 1.610-5 m s -1

Swimming of E. coli: friction F s =6πμrv velocity F=m a=m(dv/dt) m dv v dv dt v( t) 6rv 6rv m v 0 e 10 dt t 7 s d 0 v( t) d( t) v d=4 10-10 cm = 0.04Å diameter of H-atom! Distance travelled by the oxygen: x(t) D t 0 9 1 7 8 x( t) 10 m s 10 s,8 10 m 8nm

The membrane equilibrium of electrically neutral particles osmosis

Definition of osmosis p hydr = rgh = RTc= p osm V=1/c (dilution) pv = RT van t Hoff s law: p osm = RTc For diluted solutions. The chemical potential of water: m m 0 RT ln x V p Semipermeable membrane. Distilled water. Sugar in water. In equilibrium: m1 m The difference in two pressure values: p ozm p RT x1 p1 ln V x

For non diluted solutions: p osm RT c sugar c sugar v water v water : molar volume of water When c sugar v water than p osm RTc

Osmotic pressure is additive: RT 1 osmolal is the osmotic pressure of 1 molal material. p osm c i 0.1 molal NaCl 0. osmolal 0.1 molal CaCl 0.3 osmolal Estimation of the magnitude: RT 0 o C.44 MPa M -1 if c = 0.3 molal than mole solute Molality 1000g solvent Rault concentration ; unit : mole kg p osm =.44 MPaM -1 0.3 M -1 0.73 MPa (7.3 bar) in see water:.6 MPa 60 m high water column! in tyres: 0. MPa

How to measure it? 1. By using the van t Hoff s law: Pfeffer osmometer p hydr = rgh = RTc= p osm. By using the Rault s law increase in boiling point: DT G' M D T m G : g solute in 1000g solvent M: molar mass DT m : molal boiling point increase depends on the solvent

Isoosmotic Isotonic??? Calculated Measured Rejection coefficient: 0 < s < 1 s = 1: solute is completely excluded osmolality = tonicity s = 0: solute is not excluded osmolality tonicity (e.g. in biological membranes rather tonicity)

Importance of osmosis in biology - Epsom salt ( bath salt, MgSO 4 ) - iso-, hyper-, hypotonic solutions hemolysis physiological saline:0.9 m/m% (~300 mosm) NaCl (sea water: 3.5%) - dialysis, haemodialysis, peritoneal dialysis -reverse osmosis

-Starling effect: the equilibrium between the blood plasma and the intersticium unbalance oedema Arterial end 5 Hgmm (3,33 kpa) Colloid osmotic pressure 8 Hgmm (1,07 kpa) 35 Hgmm (4,67 kpa) Plasm hydrostatic pressure Resulting pressure Hgmm (0,7 kpa) 0 Hgmm Interstitium hydrostatic pressure Interstitium colloid osmotic pressure Interstitium colloid osmotic pressure 3 Hgmm (0,7 kpa) Interstitium hydrostatic pressure 1 Hgmm (0,7 kpa) Plasm hydrostatic pressure 8 Hgmm (1,07 kpa) 15 Hgmm (,00 kpa) 5 Hgmm (3,33 kpa) Resulting pressure Vein end

Transport across biological membranes

Comparison of transport processes across the mambrane Comparison Passive diffusion Facilitated diffusion Mediator Membrane lipids Ionofores, proteins (permeases) Active transport Membrane proteins Direction of the flux Connection to cell energy supply In the concentration gradient. In the concentration gradient. Against the concentration gradient as well. None None, or indirect Direct connection Specificity None Large Large Saturation None Possible Possible Specific inhibition None Possible Possible Reversibility Reversible Reversible Irreversible Fick s laws are valid Yes No, Michaelis- Menten kinetics No, Michaelis-Menten kinetics Transzported materials Lipid soluble, small molecular mass neutral molecules. Ions, polar compound Large variety of compounds, ions, proteins, etc.

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