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Chapter
Physics of the Cell Membrane
DOI link for Physics of the Cell Membrane
Physics of the Cell Membrane book
Physics of the Cell Membrane
DOI link for Physics of the Cell Membrane
Physics of the Cell Membrane book
ABSTRACT
Within a drop of uid t hat i s not su rrounded b y a c ellular membrane, t he relationship between su rface tension a nd pressure is described by the law of Laplace. Given a uniform surface
tension (σ), internal pressure (P), and radius (R) of the drop, the law states that
P = 2σ___ R
. (1.1)
When mo deling t his rel ationship i n a c ell, one m ight t hink that the density of the membrane reacts to pressure di erences between the external and internal environments. However, density, w hich de scribes t he c ompressibility o f l ipids w ithin t he bilayer, rem ains c onstant u nder ph ysiologically rele vant p ressures (100 atm).1 Surface area displays somewhat weaker resistance a nd do es u ndergo s ome c hange, b ut o nly 2 –4% b efore rupturing. e tensile force (Ft) on the membrane is expressed in Equation 1.2 for this situation:
Ft = KA ΔA___ A0
, (1.2)
where ΔA is the increase in bilayer surface area from the original area A0, KA is the area expansion constant (between 102 and 103 mN/m), a nd Ft i s ten sion ( between 3 a nd 3 0 mN/m). A nd while surface area expands, membrane t hickness changes proportionally so that
ΔA___ A0
= Δh___ h0
, (1.3)
where h0 represents original membrane thickness. But the membrane response to s hear stress is what clearly describes it as an elastic s olid. U sing t wo si lica b eads a nd opt ical t raps to e xert shear st ress across a n R BC2 (Figure 1.1), elasticity c an be seen
as this membrane elongates in the direction of applied force F. It can be shown that the diameter of the RBC obeys Equation 1.4:
D = D0 − F____2πμ , (1.4)
where D is the diameter of the RBC, D0 is the original diameter, and μ is the shear stress applied by the optical trap.