Question

In 1925, E. Gorter and F. Grendel, studied erythrocytes from a dog and obtained data similar to the following: volume of packed cells (38 mL); number of cells (7.98 x 106 per mm3); Total surface area of lipid monolayer from cells (62 m2); Total surface area of one cell (98 μm2). Calculate the total surface area (in terms of μm2 to the nearest ones) of lipid monolayer per cell. Think about whether the figure you calculated supports the claim that cell membranes are composed of a bilayer.

Answer 1

Ans. Given,

            Total packed volume of cells = 38 mL

            Cell density = 7.98 x 10⁶ cells/ mm³                                  ; [1 mm³ = 0.001 mL]

= 7.98 x 10⁹ cells/ mL

            Total surface area of lipid monolayer = 62 m²                ; [1 m = 10⁶ um]

                                    = 62 x (10⁶ um)²

                                    = 6.2 x 10¹³ um²

Now,

Total number of cells in 38 mL sample = Cell density x packed volume

                                    = (7.98 x 10⁹ cells/ mL) x 38 mL

                                    = 3.0324 x 10¹¹ cells

Now,

Surface area of lipid monolayer per cell = Total area of lipid monolayer / Number of cells

                                                            = (6.2 x 10¹³ um²) / (3.0324 x 10¹¹ cells)

                                                            = 204.46 um² / cell

                                                            = 204 um² / cell

# Each cell is made up of lipid bilayer. A bilayer consists of two times the monolayer.

So,

Total surface area of lipid bilayer per cell = (Surface area of lipid monolayer per cell) / 2

                                                            = (204 um² / cell) / 2

                                                            = 102 um² / cell

Therefore, total surface area of a cell (enclosed by lipid bilayer) = 102 um² / cell

# Comparison: The calculated value of lipid bilayer surface area per cell of 102 um²/ cell is in close agreement with the given value of 98 um²/ cell.