A resting red blood cell has volume and a membrane area
PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Molecular machines, transport and bioenergetics
Life at Thermal Energy, Ch The membrane: barrier, capacitor and pump
Problem
A resting red blood cell has volume V0=90fL and a membrane area A=135μm2, fixed because the membrane itself cannot stretch, so the largest volume any shape of that area can enclose, a sphere, is 147fL, as this chapter found. Its internal osmolarity, entirely in impermeant solute, is 300mOsm. At t=0 the cell is placed in a very large bath of saline at 200mOsm, so large that its own concentration stays fixed, at body temperature, T=310K, where kBT=4.28×10−21J. Take the red cell membrane's hydraulic permeability as Lp=1.0×10−12ms−1Pa−1.
((a)) Treating the cell as a perfect osmometer holding a fixed amount of trapped solute, find its new equilibrium volume V1, and check whether the cell reaches it without first hitting its shape-limited maximum of 147fL.
((b)) The flow Jv=LpΔΠ that drives the swelling falls as the cell swells, because its internal concentration approaches the bath's and ΔΠ shrinks. Using the largest value ΔΠ ever takes, its value at t=0, estimate the largest possible rate of volume gain, and hence a lower bound on the time the cell needs to reach V1. Explain why this is a lower, not an upper, bound.
((c)) A stopped-flow measurement of a red cell under this same osmotic step finds its volume change essentially complete after about 4.0s. Is the bound from part (b) consistent with that measurement?