## 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.