Plate 1.9 Transport In, Through and Between Cells Il 19 Cell membranes E5 lons, ATP. CAMP amino acids, etc. 00 Connexin Channel ope Channel closed D. Apical functional complex Microvilli Ce 2 Claudin C thelial cells E-cadherin Actin
191 Fundamentals and Cell Physiology Plate 1.9 Transport In, Through and Between Cells II +/ C # " # . # " . / &&! &" &# 2 1$2 $2 2 ! - #- 1 % 3, - - ' # $ ( )001 + 7" + + $ % @= ( % % C $ < 8 % % * ( B, + G, -551 2 * # &# &" + + &!0 ) !
20 Passive Transport by Means of Diffusion Diffusion is movement of a substance owing to lan=A-D &)Imol-s'I[1.21 where Cis the molar concentration and x is the directions throughout a solvent. Net diffusion distance traveled during diffusion. Since the selective transport can occur only when the driving force"-ie, the concentration gradient olute concentration at the starting point is (dc/dx)-decreases with distance, d higher than at the target site.( Note: uni directional fluxes also occur in absence of a increases exponentially with the distance concentration gradient-i.e, at equilibrium raveled (t-x). If, for example, a molecule y but net diffusion is zero because there is equal travels the first um in 0. 5ms, it will require 5s force "not to be taken in a physical sense, of rming to the previous example (A2). diffusion is, therefore, a concentration gra- if the above-water partial pressure of free o dient. Hence, diffusion equalizes concentra- diffusion constant, the Poz in the tion differences and requires a driving force: water and overlying gas layer will eventually passive transport(-downhill transport). Example: When a layer of O2 gas is placed equalize and net diffusion will equilibrium). This process takes place within on water, the O2 quickly diffuses into the water the body. for example, when O2 diffuses from along the initially high gas pressure gradient the alveoli of the lungs into the bloodstream COz diffuses in the opposite di (Po2)rises, and Oz can diffuse further tion(p. 120). downward into the next Orpoor layer of water Let us imagine two spaces, a and b(B1) (Al)(Note: with gases, partial pressure is supposedly containing different concentra- sed in lieu of concentration.)However, the tions (C> Cb)of an uncharged solute. The deepness of the Po2 profile or gradient( dPoz/ membrane separating t the solutions has quent layer situated at distance x from the area of A. Since the pores are permeable to the of the so-called diffusion rate(- diffusing molecules will diffuse from a to b with ca-cb nount of substance per unit of time). There- Ac representing the concentration gradient as fore, diffusion is only feasible for transport the driving "force". If we consider only the cross short distances within the body. Diffu- sion in liquids is slower than in gases. dC/dx in the pore, as shown in B2, for the sake The diffusion rate, Jaif(mol.5") is also pro- of simplicity), Ficks first law of and the absolute temperature()and is in. (Eq 1. 2)can be modified as folly of diffusion versely proportional to the viscosity (n)of the Jaff=A.D. 4(mols"1l .3 olvent and the radius(r)of the diffused parti- other words the rate of diffusion increases as A, D, and AC increase and decreases as the the coefficient of diffusion(D)is derived from T, thickness of the membrane(Ax)increases. When diffusion occurs through the membrane of a cell, one must consider that hy- N4·6x-· n1. drophilic substances in the membrane are sparingly soluble (compare intramembral gradient in C1 to C2)and, accordingly, hav (8.3144].K-1.mol-')and NA Avogadros con- hard time penetrating the membrane by tant(P. 380). In Ficks first law of diffusion (Adolf Fick, 1855), the diffusion rate is means of " simple"diffusion. The oil-and-water pressed as rtition coefficient(k)is a measure of the lipid solubility of a substance (-C)
201 Fundamentals and Cell Physiology Diffusion is movement of a substance owing to the random thermal motion (brownian movement) of its molecules or ions ( A1) in all directions throughout a solvent. Net diffusion or selective transport can occur only when the solute concentration at the starting point is higher than at the target site. (Note: unidirectional fluxes also occur in absence of a concentration gradient—i.e., at equilibrium— but net diffusion is zero because there is equal flux in both directions.) The driving force, “force” not to be taken in a physical sense, of diffusion is, therefore, a concentration gradient. Hence, diffusion equalizes concentration differences and requires a driving force: passive transport (= downhill transport). Example: When a layer of O2 gas is placed on water, the O2 quickly diffuses into the water along the initially high gas pressure gradient ( A2). As a result, the partial pressure of O2 (Po2) rises, and O2 can diffuse further downward into the next O2-poor layer of water ( A1). (Note: with gases, partial pressure is used in lieu of concentration.) However, the steepness of the Po2 profile or gradient (dPo2/ dx) decreases (exponentially) in each subsequent layer situated at distance x from the O2 source ( A3), which indicates a decrease of the so-called diffusion rate (= diffusing amount of substance per unit of time). Therefore, diffusion is only feasible for transport across short distances within the body. Diffusion in liquids is slower than in gases. The diffusion rate, Jdiff (mol · s–1), is also proportional to the area available for diffusion (A) and the absolute temperature (T) and is inversely proportional to the viscosity (η) of the solvent and the radius (r) of the diffused particles. According to the Stokes–Einstein equation, the coefficient of diffusion (D) is derived from T, η, and r as D R ⋅ T NA · 6π ⋅ r ⋅ η [m2 ⋅ s–1], [1.1] where R is the general gas constant (8.3144 J ·K–1 · mol–1) and NA Avogadro’s constant ( p. 380). In Fick’s first law of diffusion (Adolf Fick, 1855), the diffusion rate is expressed as Jdiff A ⋅ D ⋅ dC dx [mol ⋅ s–1] [1.2] where C is the molar concentration and x is the distance traveled during diffusion. Since the driving “force”—i.e., the concentration gradient (dC/dx)—decreases with distance, as was explained above, the time required for diffusion increases exponentially with the distance traveled (t x2). If, for example, a molecule travels the first µm in 0.5 ms, it will require 5 s to travel 100 µm and a whopping 14 h for 1 cm. Returning to the previous example ( A2), if the above-water partial pressure of free O2 diffusion ( A2) is kept constant, the Po2 in the water and overlying gas layer will eventually equalize and net diffusion will cease (diffusion equilibrium). This process takes place within the body, for example, when O2 diffuses from the alveoli of the lungs into the bloodstream and when CO2 diffuses in the opposite direction ( p. 120). Let us imagine two spaces, a and b ( B1) supposedly containing different concentrations (Ca Cb) of an uncharged solute. The membrane separating the solutions has pores ∆x in length and with total cross-sectional area of A. Since the pores are permeable to the molecules of the dissolved substance, the molecules will diffuse from a to b, with Ca– Cb = ∆C representing the concentration gradient as the driving “force”. If we consider only the spaces a and b (while ignoring the gradients dC/dx in the pore, as shown in B2, for the sake of simplicity), Fick’s first law of diffusion (Eq. 1.2) can be modified as follows: Jdiff A ⋅ D ⋅ ∆C ∆x [mol ⋅ s–1]. [1.3] In other words, the rate of diffusion increases as A, D, and ∆C increase, and decreases as the thickness of the membrane (∆x) increases. When diffusion occurs through the lipid membrane of a cell, one must consider that hydrophilic substances in the membrane are sparingly soluble (compare intramembrane gradient in C1 to C2) and, accordingly, have a hard time penetrating the membrane by means of “simple” diffusion. The oil-and-water partition coefficient (k) is a measure of the lipid solubility of a substance (C). Passive Transport by Means of Diffusion Edema and ascites formation, consequences of hypoxia and ischemia
Plate 1.10 Passive Transport by Means of Diffusion I 21 A Diffusion in homogeneous media 1 Brownian particle movement(-n) 2 Passive transport 990 Distance from O source(x) B Diffusion through porous membranes Porous membrane Space b Gradient C-C C. Diffusion through lipid membranes substance x Gx Water ane Water Water membrane Water Equilibrium concentration in olive oil Equilibrium concentration in water (Partly after S.. Schultz
211 Fundamentals and Cell Physiology Plate 1.10 Passive Transport by Means of Diffusion I " # " # . 6# 6# 6# H 6# . " * * F @I & ! J @I & 5 7 +8", 5 9 +:", &&! &&! 1 H H& G G& *% *% & & & & & 0 7 & & #&J *% *% & * % J J E $6# # ! % .% "B % ! K6 ! ! &!
22 Passive Transport by Means of Diffusion(continued) b The higher the k value, the more quickly the hether these substances ubstance will diffuse through a pure phospholipid charged or not(pk value; -p. 384). the diffu- layer membrane Substitution into Eq 1.3 gives sion of weak acids and bases is clearly depend- =k.A. D=mol"1 ent on the ph [1. 4] The previous equations have not made al- wances for the diffusion of electrical a Whereas the molecular radius r (Eq- 1.1)still charged particles(ions). In their case, the ele must also be taken into account. the electrical onstant(cf urea with ethanol in D)and can potential difference can be an additional driv- erefore have a decisive effect on the permeability ing force of diffusion(electrodiffusion).In that of the membrane tively charged ions(cations) will Since the value of the variables k. D and Ax hen migrate to the negatively charged side of within the body generally cannot be deter. the membrane, and negatively charged ions (anions)will migrate to the positively charged mined, they are usually summarized as the side. The prerequisite for this type of transport permeability coefficient P, where of course that the membrane contain ion m 115) channels(-p. 32 ft that make it permeable If the diffusion rate, Ji mol."1) is related to diffusing along a concentration gradient car- rea A, Eq 1.4 is transformed to yield ries a charge and thus creates an electric diffu- sion potential(→p.32f P·△ cImo.m2sl [1.6 As a result of the electrical charge of an ion, the per- The quantity of substance(net)diffused per formed into the electrical conductance of the unit area and time is therefore proportiona membrane for this ion, g(p. 32): △ C and P(→E, blue line with slope P) When considering the diffusion of gases, AC placed by at. AP (solubility coeffi- cient times partial pressure difference. where R and T have their usual p 126)and Diff [ mol Vai[m.s""I. the Faraday constant(9,65.104 aD is then summarized as diffusion con- equals the mean ionic activity in the membrane. equation yields 10 a=K AxIm." [1.7 where index 1-one side and index 2- the other side Since A and Ax of alveolar gas exchang (p. 120)cannot be determined in living or- tion remains constant at 160 mn ganisms, K-F/Ax for O2 is often expressed as therefore. g will increase by 20go/kg H O).C and. the o2 diffusion capacity of the lung, D Since most of the biologically Vo2a=D·△PoIm3 [1.8 substances k value)that simple diffusion of the substances Nonionic diffusion occurs when the uncharg rough the membrane would proceed much orm of a weak base(e. g, ammonia- Nh3)or acid (e.g, formic acid, HCOOH)passes through called carriers rters exist in addition a membrane more readily than the charged to ion channels. Carriers bind the target form(F) In this case, the membrane would molecule (e.g. glucose)on one side of the be more permeable to NH than to NHA' membrane and detach from it on the other side (p. 176 ff. ) Since the pH of a solution deter- (after a conformational change)(+G).As in
221 Fundamentals and Cell Physiology The higher the k value, the more quickly the substance will diffuse through a pure phospholipid bilayer membrane. Substitution into Eq. 1.3 gives Jdiff k ⋅ A ⋅ D ⋅ ∆C ∆x [mol ⋅ s–1]; [1.4] Whereas the molecular radius r ( Eq. 1.1) still largely determines the magnitude of D when k remains constant (cf. diethylmalonamide with ethylurea in D), k can vary by many powers of ten when r remains constant (cf. urea with ethanol in D) and can therefore have a decisive effect on the permeability of the membrane. Since the value of the variables k, D, and ∆x within the body generally cannot be determined, they are usually summarized as the permeability coefficient P, where P k ⋅ D ∆x [m ⋅ s–1]. [1.5] If the diffusion rate, Jdiff [mol⋅s– 1], is related to area A, Eq. 1.4 is transformed to yield Jdiff A P ⋅ ∆C [mol ⋅ m–2 ⋅ s–1]. [1.6] The quantity of substance (net) diffused per unit area and time is therefore proportional to ∆C and P ( E, blue line with slope P). When considering the diffusion of gases, ∆C in Eq. 1.4 is replaced by α· ∆P (solubility coefficient times partial pressure difference; p. 126) and Jdiff [mol ⋅ s–1] by V. diff [m3⋅ s–1]. k ·α· D is then summarized as diffusion conductance, or Krogh’s diffusion coefficient K [m2 ⋅ s–1 ⋅ Pa–1]. Substitution into Fick’s first diffusion equation yields V . diff A K ⋅ ∆P ∆x [m ⋅ s–1]. [1.7] Since A and ∆x of alveolar gas exchange ( p. 120) cannot be determined in living organisms, K · F/∆x for O2 is often expressed as the O2 diffusion capacity of the lung, DL: V . O2 diff DL ⋅ ∆PO2 [m3 ⋅ s–1]. [1.8] Nonionic diffusion occurs when the uncharged form of a weak base (e.g., ammonia = NH3) or acid (e.g., formic acid, HCOOH) passes through a membrane more readily than the charged form ( F). In this case, the membrane would be more permeable to NH3 than to NH4 + ( p. 176 ff.). Since the pH of a solution determines whether these substances will be charged or not (pK value; p. 384), the diffusion of weak acids and bases is clearly dependent on the pH. The previous equations have not made allowances for the diffusion of electrically charged particles (ions). In their case, the electrical potential difference at cell membranes must also be taken into account. The electrical potential difference can be an additional driving force of diffusion (electrodiffusion). In that case, positively charged ions (cations) will then migrate to the negatively charged side of the membrane, and negatively charged ions (anions) will migrate to the positively charged side. The prerequisite for this type of transport is, of course, that the membrane contain ion channels ( p. 32 ff.) that make it permeable to the transported ions. Inversely, every ion diffusing along a concentration gradient carries a charge and thus creates an electric diffusion potential ( p. 32 ff.). As a result of the electrical charge of an ion, the permeability coefficient of the ion x (= Px) can be transformed into the electrical conductance of the membrane for this ion, gx ( p. 32): gx Px ⋅ zx 2 ⋅ F2 R ⋅ T ⋅ cx [S ⋅ m–2], [1.9] where R and T have their usual meaning (explained above) and zx equals the charge of the ion, F equals the Faraday constant (9,65 ⋅ 104 A ⋅ s ⋅ mol–1), and cx equals the mean ionic activity in the membrane. Furthermore, c c1– c2 lnc1– lnc2 [1.10] where index 1 = one side and index 2 = the other side of the membrane. Unlike P, g is concentration-dependent. If, for example, the extracellular K+ concentration rises from 4 to 8 mmol/kg H2O (cytosolic concentration remains constant at 160 mmol/kg H2O), c and, therefore, gx will increase by 20%. Since most of the biologically important substances are so polar or lipophobic (small k value) that simple diffusion of the substances through the membrane would proceed much too slowly, other membrane transport proteins called carriers or transporters exist in addition to ion channels. Carriers bind the target molecule (e.g., glucose) on one side of the membrane and detach from it on the other side (after a conformational change) ( G). As in Passive Transport by Means of Diffusion (continued) Pulmonary edema consequences, diarrhea, cystic fibrosis, ointment therapy, dialysis
Plate 1.11 Passive Transport by Means of Diffusion Il 23 D. Permeability of lipid membranes E. Facilitated diffusion Facilitated diffusion ● Diethrylmalonamide EE四tcs 10410310-210-1 △ CImo.m-3 Distribution coefficient k for olive oil /water F Nonionic diffusion G. Passive carrier transport Carrier NH 1 HCOOH mple diffus is ratio (passive transport), e.g. with GL porters another. The carriers in botl for glucose (p. 158). On the his transport have the latter features in common
231 Fundamentals and Cell Physiology simple diffusion, a concentration gradient is necessary for such carrier-mediated transport (passive transport), e.g., with GLUT uniporters for glucose (p. 158). On the other hand, this type of “facilitated diffusion” is subject to saturation and is specific for structurally similar substances that may competitively inhibit one another. The carriers in both passive and active transport have the latter features in common ( p. 26). Plate 1.11 Passive Transport by Means of Diffusion II CC +0 C /L-.#2 -.#0 -.#/ -.# -.#- /L-.#1 /L-.#3 /L-.#4 - +0 CCC +/ +/ # CC CC # % 7 @ " ( @" " 7 " = ? " 6 " 6 " (%" ) B " " * " @" " *% J & " L #- & ! E 6 % M L#L #-N M L#/N * A 0! *% !$ (!/ !( 0!$