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Osmotic pressure and volume maintenance
Objectives
- Understand the definition of osmotic pressure and the derivation of van’t Hoffs law.
- Understand the meaning of the reflection coefficient and the osmotic coefficient in characterizing non-ideal solutions.
- Know the starling equation and how it describes volume flow across biological membranes
- Know the major factors responsible for maintenance of cell volume.
- Understand the effects of Vm on steady-state cell volume.
- Understand the key role of Cl-^ transport in regulating cell volume.
- Understand the role of the Na-K ATPase in regulation of cell volume.
- Understand regulatory compensations (RVI, RVD) to anisosmotic conditions involving membrane transport mechanisms.
- Understand the mechanisms involved in AVD and eryptosis
- Understand the interactions between Cl-^ and K+^ channel activities as a means of sustaining driving forces for KCl efflux for RVD or AVD.
Readings
- Hoffmann, E. K., I. H. Lambert, and S. F. Pedersen. Physiology of cell volume regulation in vertebrates. Physiol Rev 89: 193-277, 2009.
- Armstrong, C.M., The Na-K pump, Cl ion, and osmotic stabilization of cells. Proc. Nat. Acad. Sci. 100:6257-6262, 2003.
A. Osmotic pressure and the van’t Hoff relationship
Imagine two aqueous compartments, “o” and i that are separated by a semi-permeable membrane. Initially, compartment “i” contains pure H 2 O whereas compartment “o” contains a solute dissolved in water. The membrane is permeable to H 2 O but not to the solute (s).
Figure 1: Movement of solvent across a solute-impermeable membrane
One way to think about the movement of H 2 O in this situation is to consider the fact that the total concentration of water in compartment “i” is greater than compartment “o” since some of the H 2 O molecules were displaced by the presence of solute. Said another way, the mole fraction of water in compartment “i” is greater than in compartment “o” such that a concentration gradient exists for H 2 O across the membrane. The result is net movement of water across the membrane from the compartment with the higher H 2 O concentration into the compartment with lower H 2 O concentration.
Using some basic principles of thermodynamics and our understanding of chemical potentials, it is possible for us to derive an equation for calculating the osmotic pressure produced by H 2 O movement across the membrane.
- Definition of osmotic pressure We define osmotic pressure as the hydrostatic pressure necessary to stop osmotic flow across the membrane. Osmotic pressure is a colligative property of the solution and is therefore dependent on the solute concentration and the properties of the membrane. Osmotic pressure is determined at equilibrium when the pressure-driven flow balances the osmotic flow of solvent. We can write the chemical potential for H 2 O as the sum of the standard chemical potential (o) and RT ln ao/i, where “a” represents the activity of water (note that activity refers to the free water concentration present within either compartment (o or i).
Eq. 1 i w i o w o
o RT ln a V P RT ln a V P
Also note that a work term is also included that defines the volume/mole ( w
w (^) n
cm V
3 (^) ) and
pressure ( Po/i ) in each compartment ( mole
J
n
g cm cm
g cm n
cm w w
2 2 2
3
sec sec
). This expression
describes the equilibrium state for solvent in our system.
Solute
solvent gradient
Eq. 7 RT Cs
Osmotic pressure and hydrostatic pressure are functionally equivalent in their ability to drive water movement across a membrane. The Starling equation is often used to describe the volume flow (Jv) across a membrane in response to hydrostatic and osmotic pressures.
Eq. 8 Jv = Kf ( P ( ) = Kf ( P RT Cs)
Where Kf is known as the filtration constant and is analogous to hydraulic conductivity (a measure of the ease with which solvent flows across the membrane). The filtration constant reflects the contributions of both hydrostatic and osmotic pressures in the movement of water across the membrane.
- Reverse osmosis Reverse osmosis is a term that refers to the application of high hydrostatic pressure to solutions of high solute content as a means to drive water from the solution against the osmotic gradient through a membrane that is impermeable to the solute. The process can be used for desalination and other commercial purposes and demonstrates that the balance of hydrostatic and osmotic forces determines the direction of water movement.
- Osmotic Pressure of Non-ideal solutions As previously mentioned, the van’t Hoff equation is an approximation that adequately describes osmotic pressure for dilute, ideal solutions, so what corrections are necessary when non-ideal conditions exist? The term “ideal” refers to the condition where Raoult’s law (vapor pressure is proportional to mole fraction of the solvent) is valid for the solution.
Eq. 9 p Xw Pwo
Where: p = vapor pressure, Xw = mole fraction of water and Pwo = vapor pressure of pure water at temperature. Since most solutions are non-ideal, a correction (called the osmotic coefficient: φ ) must be applied such that:
Eq. 10 RT Cs
At physiological concentrations, osmotic coefficients for NaCl and CaCl 2 are 0.93 and 0. respectively. Thus the osmolarity of a 150 mM NaCl solution would be calculated as (0.93 x 2 x 150 mM) = 279 mOsm. For most electrolytes in dilute solution, φ < 1 because a weak attraction exists between ions. When more than one solute is present, it can be difficult to determine the osmotic pressure because of unpredictable interactions between the solutes.
B. Volume maintenance
Human cells vary in volume from approximately 10 fl (platelets) through 90 fl (RBCs) to over 100 nl for skeletal muscle fibers, a range of more than 10^6 -fold! Although different cell types
maintain a wide range of steady-state volumes, common determining factors and transport mechanisms are involved in volume maintenance and in their response to osmotic challenge.
- Factors involved in maintenance of cell volume include: a. The total impermeant anion concentration [ X- ] and mean valency ( zx ). b. The steady-state membrane potential ( Vm ). c. Intracellular [Cl-] and the activity of cation-Cl-^ transport mechanisms that control the distribution of Cl-. d. Activity of the Na-K ATPase which controls the steady-state distribution of the major cations within the cell. e. Concentrations of organic osmolytes within the cell including sugars like sorbitol and free amino acids such as taurine Thus it is clear that impermeable anions, their mean valency, the distribution of Cl-^ and membrane potential represent the key factors affecting steady-state volume. In addition, cation transport mechanisms such as the Na-K ATPase are also important, since this enzyme is critical in setting the steady-state [Na+] and [K+] gradients.
- Effects of membrane depolarization: Changes in Em will affect the distribution of Cl-^ across the plasma membrane especially in cells like skeletal muscle that have high Cl-^ permeability relative to PK. Figure 3 : Electrogenic pathways Depolarization to voltages above ECl produces uptake of Cl-^ and an increase in cell volume. Thus for skeletal muscle cells under conditions of exercise, increases in action potential frequency increases [Na+]i, and decreases [K+]i. This effect coupled with extracellular accumulation of K+ produces depolarization above ECl, Cl-^ uptake and an increase in cell volume. Some compensation for this effect occurs as Cl permeability decreases with intracellular acidification and K+ conductance increases as ATP levels fall during exercise (a result of increased KATP activity).
- Effects of Na-K ATPase inhibition Inhibition of Na-K ATPase activity by treatment with cardiac glycosides (e.g. ouabain) or exposure to low temperatures results in an increase in intracellular [Na+] and decrease in intracellular [K+].
Figure 4 : Effects of PCl on volume and voltage after shifting extracellular [K+] from 5 to 20 mM.
This change in cation distribution generally results in significant membrane depolarization
ENa
EK
ECl
Vm = 0 mV
Vm = 72 mV
Vm = -84 mV
Vm = -60 mV Vm
In some cases regulatory volume responses may be more complete following cell swelling than cell shrinkage depending on the cell type.
Figure 7: Transport pathways and RVD
- Ion transport processes for RVD & RVI Figure 8: RVI transport pathways A variety of electrogenic and electroneutral transport proteins are involved in regulatory volume changes that include various ion channels, exchangers and cotransporters shown in figure 7. In addition, organic osmolytes and their transporters are also critical for some cells, especially renal tubular epithelial cells located in the inner medulla.
- RVD:
Electrogenic transport pathways include K+^ and Cl-^ channels that often act in parallel to produce simultaneous efflux of both ions, so that the net effect is little change in membrane potential. Electroneutral efflux of KCl is also mediated by KCC cotransport proteins of which some isoforms are known to exhibit volume-sensitive activation. In some cells (e.g. epithelial cells) bicarbonate can also play a role through its coupling to Na+^ via Na-(HCO 3 ) 3 cotransport.
- RVI: Electrogenic transport pathways involved in RVI can include Cl-^ channels (as in skeletal muscle) Na+^ channels (e.g. epithelial cells) or transporters such as Na-Ca2+^ exchange which increase Na+^ accumulation within the cell. Electroneutral transport mechanisms include the parallel operation of Na-H and Cl-HCO 3 exchangers that can increase intracellular NaCl and replenish any loss of HCO 3 or H+^ through the activity of carbonic anhydrase. Perhaps the best studied electroneutral pathway contributing to RVI is the Na-K-2Cl cotransporter which is found in a wide variety of cell types and is known to be regulated by changes in cell volume.
Exchangers Na+
H+^
Cotransporters
Increased Cell Volume
H 2 O H 2 O (Na+) 3
Ca2+
Exchangers K+
2Cl- Na+
Na+ HCO 3 -
Cl-
HCO 3 + H+^ →^ H^2 CO^3 →^ CO^2 + H^2 O
H 2 O
RVI
RVD K+
Cl- H 2 O
Cotransporters
Cl- K+
Na+ (HCO 3 - ) 3
Reduced Cell
Volume
H 2 O
2K+^ H^2 O
3Na+
Na-K-ATPase
Channels
- AVD: Loss of cell volume is a morphological characteristic of apoptosis. This isotonic loss of volume is known as apoptotic volume decrease (AVD) and is distinct from volume regulatory responses that occur in cells under anisosmotic conditions. Efflux of K+^ has been shown to be an essential aspect of AVD since preventing its loss protects cells from apoptosis. Pathways responsible for K+ efflux vary depending on cell type and the stimulus used to induce apoptosis, suggesting multiple mechanisms for accomplishing AVD. Additionally, chloride channels have also been shown to play a vital role during apoptosis in mediating anion (Cl-^ or HCO 3 - ) efflux or for transport of large organic osmolytes (such as taurine) out of the cell.
Figure 9: AVD mechanisms Figure 10: Eryptosis
- Eryptosis: RBC death:
In erythrocytes, increased [Ca2+]i stimulates Ca2+- activated K+^ channels. This leads to hyperpolarization and a parallel efflux of Cl−. KCl exit is followed by a loss of water leading to cell shrinkage and enhanced scrambling of the cell membrane, a common feature of erythrocyte death or eryptosis. Inhibition of the Ca2+- activated K+^ channels or increasing of extracellular [K+^ ] not only inhibits cell shrinkage but produces a moderate decrease in phosphatidylserine exposure following treatment of erythrocytes with the apoptosis inducing Ca2+^ ionophore, ionomycin. Cell shrinkage leads to formation of platelet activating factor PAF, which in turn activates a sphingomyelinase leading to formation of ceramide. Ceramide then contributes to the activation of membrane scrambling. Figure 11: Effects of gK and gCl on Vm
- Dynamic interactions between K+^ and Cl-^ channels in the regulation of cell volume In cells where solute efflux under conditions of RVD or AVD is primarily mediated by K and Cl channels, it is important to understand the degree of interdependence between these pathways for sustaining the electrochemical driving force. This can be directly appreciated through an analysis of Fig. 8. As indicated in the figure, increasing either GK or GCl relative to the other conductance will shift Vm towards either EK or ECl. The effect will
AQP
CaCC? VSOR?
K+ KCa3.
Cl-
H 2 O
[Ca2+]i
osmolytes (taurine)
AQP
CFTR?
K+^ KCa3.
Cl-
H 2 O
RBC [Ca2+]i
K+ Cl-
0
50
100
150
200
250
300
350
-100 -80 -60 -40 -20 0 20
pA
mV
Cl-
K+
Vm
EK ECl
K = gK (Vm- EK)
Increasing Cl Cl = gCl (Vm- ECl)
conductance -
0
50
100
150
200
250
300
350
-100 -80 -60 -40 -20 0 20
pA
mV
Cl-
K+
Vm
EEKK EEClCl
K = gK (Vm- EK)
Increasing Cl Cl = gCl (Vm- ECl)
conductance
