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

Xi Cheng,Peter M Pinsky,Paul J Atzberger

doi:10.1371/journal.pone.0145422

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.

Highlights

The exchange of fluid and solutes across biological membranes facilitates the transport of substances needed for living organisms to maintain their metabolic activities, and regulates pressure balances across bounding membranes to maintain the structural integrity of biological systems
A quantitative understanding of fluid and osmotic pressures in living organisms is crucial for studying biological mechanisms such as cell volume regulation and interstitial fluid homeostasis, and is under investigation for various biological systems, e.g. [2, 3, 6, 7]
This pressure force competes with the osmotic pressure on balancing the fluid pressure, and the new pressure balance condition implies that the values of the water potential on the two sides of separating membranes will not be equal in order to maintain the steady state of biological systems

Summary

Introduction

The exchange of fluid and solutes across biological membranes facilitates the transport of substances needed for living organisms to maintain their metabolic activities, and regulates pressure balances across bounding membranes to maintain the structural integrity of biological systems. Our analysis identifies an additional pressure mechanism that originates from active fluxes and from interactions between water and solutes in membrane transport processes This pressure force competes with the osmotic pressure on balancing the fluid pressure, and the new pressure balance condition implies that the values of the water potential on the two sides of separating membranes will not be equal in order to maintain the steady state of biological systems. As active transport mechanisms are presented and consume energy, the zero flux conditions correspond to a non-equilibrium steady state [26] In this case, the fluid pressure difference ΔP across the membrane is derived by first observing from Eq (31) with JV = 0 and Eq (32) with Ji = 0, that oi RTDCi þ ziCiFDφ þ Jai 1⁄4 0 which implies

RT DCi i

RT Ck0 k

Discussion