Approximate analysis of transport processes in a biological cell

Example 11.11 Approximate analysis of transport processes in a biological cell A typical biological cell and its surroundings are characterized by the following concentrations (Garby and Larsen, 1995) 

In this table, P represents anions of protein and organic phosphate. The membrane is permeable to the group represented by P. The mean values of the charge on P are -6.7 and -1.08 for the interior and the exterior of the cell, respectively. An electrical potential difference of At// = i/t, t// = 90 mV is measured, i and o denote the intracellular and extracellular, respectively. The activity coefficients of components inside and outside the cell are assumed to be the same, and pressure and temperature are 1 atm and 310 K. Assume that the diffusion flows in from the surroundings are positive and the diffusion flows out are negative. Using tracers, the unidirectional flows are determined as follows  

Using these approximate flows, we may estimate permeabilities using 

The permeability coefficient depends on the characteristics of the membrane and solute, and can vary considerably for various solutes. For example,/) = 10-21 m/s for sucrose and 10 4 m/s for water in the human red blood cell membrane. Equation (1) may be generalized by including the effect of pressure gradient APm = P(0) - P(L), and we have 

To use this relation, we need to relate pressure difference in the membrane, APm = P(0) - P(L), and over the membrane, A P = Pi- P0. This requires the introduction of the concept of osmotic pressure in a nonequilibrium membrane system. 

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