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The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium.

Cheng X, Pinsky PM - PLoS ONE (2015)

Bottom Line: In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments.The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges.The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Stanford University, Stanford, California, United States of America.

ABSTRACT
The movement of fluid and solutes across biological membranes facilitates the transport of nutrients for living organisms and maintains the fluid and osmotic pressures in biological systems. Understanding the pressure balances across membranes is crucial for studying fluid and electrolyte homeostasis in living systems, and is an area of active research. In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments. The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges. The steady-state analysis on active membranes suggests a new pressure mechanism which balances the fluid pressure together with the osmotic pressure. The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport. We apply the proposed theory to study the transendothelial fluid pressure in the in vivo cornea, which is a crucial factor maintaining the hydration and transparency of the tissue. The results show the importance of the proposed pressure mechanism in mediating stromal fluid pressure and provide a new interpretation of the pressure modulation mechanism in the in vivo cornea.

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Illustration of a biological membrane that separates two electrolyte solutions, with the one designated as “inside” containing fixed charges that are associated with large molecules.
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pone.0145422.g001: Illustration of a biological membrane that separates two electrolyte solutions, with the one designated as “inside” containing fixed charges that are associated with large molecules.

Mentions: In this section we describe a limitation of existing KK theories [12, 16] which are unable to recover the Donnan equilibrium when fixed charges exist on one side of the membrane. Consider a biological membrane that separates two polyelectrolyte solutions with fluid pressure P and P0, solute concentrations Ci and , where N denotes the number of species, and electrostatic potential φ and φ0. We denote one side of the membrane as “inside” and the other as “outside” (see Fig 1) and assume the inside electrolyte solution contains large molecules that carry fixed charges with concentration Cf and valence value zf. The fixed charges are assumed to be “trapped” in the inside solution and the biological membrane is assumed to be impermeable to large molecules [3]. Both solvent and solutes are considered to have finite permeabilities through the membrane (i.e. the membrane is leaky). The classical KK equations [12] describe the volume flux JV and solute flux Ji(i = 1, …, N) between the two solutions as follows:JV=LpΔP-∑kσkRTΔCk(1)Ji=(1-σi)JVC¯i+ωiRTΔCi(2)where Lp is the hydraulic conductivity, σi and ωi are the reflection coefficient and permeability for species i, respectively, and ΔP and ΔCi are the fluid pressure difference and ionic concentration difference across the membrane, respectively. denotes the mean ionic concentration, and can be simplified as the arithmetic mean between Ci and (i.e. ). Consider the equilibrium condition in which no fluid flow and no ionic fluxes exist across the membrane, i.e. JV = Ji = 0, Eqs (1, 2) immediately giveΔCi=0(3)ΔP=0(4)which suggests that at equilibrium, ionic concentrations will be balanced and there will be no fluid pressure difference across the membrane. This conclusion is apparently contradicted by the well-known Donnan equilibrium where fixed charges induce imbalance of ionic concentrations and develop an osmotic pressure gradient between the inside and outside environments [17]. This limitation of Eqs (1, 2) is attributed to the fact that they were developed for transport of non-ionic species [12]. Li [16] derived an extended set of KK equations which incorporate the electrostatic potential difference between separated electrolyte solutions,JV=LpΔP-∑kσkRTΔCk+zkFC¯kΔφ(5)Ji=(1-σi)JVC¯i+ωiRTΔCi+ziC¯iFΔφ(6)


The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium.

Cheng X, Pinsky PM - PLoS ONE (2015)

Illustration of a biological membrane that separates two electrolyte solutions, with the one designated as “inside” containing fixed charges that are associated with large molecules.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4697791&req=5

pone.0145422.g001: Illustration of a biological membrane that separates two electrolyte solutions, with the one designated as “inside” containing fixed charges that are associated with large molecules.
Mentions: In this section we describe a limitation of existing KK theories [12, 16] which are unable to recover the Donnan equilibrium when fixed charges exist on one side of the membrane. Consider a biological membrane that separates two polyelectrolyte solutions with fluid pressure P and P0, solute concentrations Ci and , where N denotes the number of species, and electrostatic potential φ and φ0. We denote one side of the membrane as “inside” and the other as “outside” (see Fig 1) and assume the inside electrolyte solution contains large molecules that carry fixed charges with concentration Cf and valence value zf. The fixed charges are assumed to be “trapped” in the inside solution and the biological membrane is assumed to be impermeable to large molecules [3]. Both solvent and solutes are considered to have finite permeabilities through the membrane (i.e. the membrane is leaky). The classical KK equations [12] describe the volume flux JV and solute flux Ji(i = 1, …, N) between the two solutions as follows:JV=LpΔP-∑kσkRTΔCk(1)Ji=(1-σi)JVC¯i+ωiRTΔCi(2)where Lp is the hydraulic conductivity, σi and ωi are the reflection coefficient and permeability for species i, respectively, and ΔP and ΔCi are the fluid pressure difference and ionic concentration difference across the membrane, respectively. denotes the mean ionic concentration, and can be simplified as the arithmetic mean between Ci and (i.e. ). Consider the equilibrium condition in which no fluid flow and no ionic fluxes exist across the membrane, i.e. JV = Ji = 0, Eqs (1, 2) immediately giveΔCi=0(3)ΔP=0(4)which suggests that at equilibrium, ionic concentrations will be balanced and there will be no fluid pressure difference across the membrane. This conclusion is apparently contradicted by the well-known Donnan equilibrium where fixed charges induce imbalance of ionic concentrations and develop an osmotic pressure gradient between the inside and outside environments [17]. This limitation of Eqs (1, 2) is attributed to the fact that they were developed for transport of non-ionic species [12]. Li [16] derived an extended set of KK equations which incorporate the electrostatic potential difference between separated electrolyte solutions,JV=LpΔP-∑kσkRTΔCk+zkFC¯kΔφ(5)Ji=(1-σi)JVC¯i+ωiRTΔCi+ziC¯iFΔφ(6)

Bottom Line: In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments.The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges.The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Stanford University, Stanford, California, United States of America.

ABSTRACT
The movement of fluid and solutes across biological membranes facilitates the transport of nutrients for living organisms and maintains the fluid and osmotic pressures in biological systems. Understanding the pressure balances across membranes is crucial for studying fluid and electrolyte homeostasis in living systems, and is an area of active research. In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments. The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges. The steady-state analysis on active membranes suggests a new pressure mechanism which balances the fluid pressure together with the osmotic pressure. The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport. We apply the proposed theory to study the transendothelial fluid pressure in the in vivo cornea, which is a crucial factor maintaining the hydration and transparency of the tissue. The results show the importance of the proposed pressure mechanism in mediating stromal fluid pressure and provide a new interpretation of the pressure modulation mechanism in the in vivo cornea.

Show MeSH
Related in: MedlinePlus