A spherical liposome of radius has lysis tension and sits in a bath at body…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch The fluid membrane: bending, flicker and shape

Problem

A spherical liposome of radius

R = 3.0\,\mathrm{\mu m}

has lysis tension

\sigma_{\rm lys} = 5.0\,\mathrm{mN\,m^{-1}}

and sits in a bath at body temperature,

37^\circ\mathrm{C}

(

310\,\mathrm{K}

). ((a)) Using Laplace's law

\Delta p = 2\sigma/R

, find the largest internal excess pressure the membrane can sustain before it lyses. ((b)) Treat this pressure as an osmotic pressure,

\Pi = cR_{\rm gas}T

(van 't Hoff's law), with gas constant

R_{\rm gas} = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}

, and find the concentration difference

c

, in mOsm (mmol per litre), that would just reach this pressure. ((c)) Express

c

as a percentage of the roughly

300\,\mathrm{mOsm}

total solute concentration of the cytoplasm.

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