membranes An improved method for studying the

From bloodjournal.hematologylibrary.org by guest on December 31, 2011. For personal use only.

1979 54: 1069-1079

An improved method for studying the elastic properties of erythrocyte membranes YF Missirlis and MC Brain

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An

Improved

Method

Properties

improved

recently

Yannis

variation

published

determine rocytes the

use

0.7

im

tm

pores/sq

cm),

aspirated

by

static

and

(pore

pore

density,

related

to

the

erythrocytes

protruding region

of

or

ranged

a

discoid The

200

from

M

near

the

argued

that

tongue were

hydrostatic

pressure

800

cm,

to

dyne/sq

ICROPIPETTE

properties

of the

to be calculated, analysis.”2 The membrane

species.3

However,

consequence,

the

obtaining

erythrocytes

limits

cells/day.

This

micropipette

technique number

the

number

that

their

under

It

is

behavior

filter

Brails-

technique

experimental

because

of the the

tension

extension

membrane

erythrocytes

the

is a serious

is

forma-

whole and

theory

cell

the

is not

of individual

oneappli-

erythrocytes

of

various

and

of the

is difficult of serial

erythrocytes

limitation

have been used to study

from

erythrocytes,

requisite

elastic

tongues,

and the data obtained technique has also been

of normal

on

in which,

the

al.

the material properties of the membrane. results, permitted the shear elastic modulus

of human

modification

depended multiple

from et

cable.

ASPIRATION

of the

experimental

have

dimensional and

has been widely used to measure method has provided reproducible

of the membrane sound theoretical

may

membrane

differ

the

i0

agreement

Brailsford

using

the

x

micropipette

membrane

et al.6 found

of

in

the

nonlinear

erythrocyte

ford

tion

are and

with

10.4

=

using by

the

conditions,

dimpled

erythrocyte

the

results

tension

linear

i

technique

of

of

was

obtained

obtained

pressure.

center

those

deformation

dimensionless

modulus.

results

SEM

a x R/t)

hydro-

deter-

dimensionless

These

aspiration

a single

a

shear

dyne/cm.

the

Brain

(P

elastic

partially

by

applied

of

parameter

with

were

with

at

measured.

observed

C.

against

2 x 10

positive

fixation,

plot

(D/R)

diameter,

dimensions as

to

Elastic

Membranes

the

al.6

of erythinvolves

being of

The

“tongue,”

Selected

et

the

and Michael

technique

filters

action

glutaraldehyde

mined

a

Brailsford

erythrocytes

pressure.

aspirated

The

and

the

F. Missirlis

properties The method

of Nuclepore or 1.0

after

of

by

the elastic is presented.

Studying

of Erythrocyte By

An

for

if one

diseases erythrocytes

and

time

can

to compare

and

after

of other

consuming.

measurements that

wants

subjected to the material

In

on individual

be

studied

to

the

elastic

moduli

5-10

of

erythrocytes of two or more blood samples. Many of the sampling and statistical problems would be overcome by methods that enable measurements to be made on many individual cells, each of which had to be subjected to a standard process of deformation. Brailsford thousands

et al.6

bonate

filters

pores/sq

with

cm.

From

the

Ontario,

described

of erythrocytes

a method

that

permitted

to be studied.

The

method

an average

pore

Erythrocytes

Departments

that

of

Engineering

Supported

in part

by the Muscular

February

27, / 979;

Address University,

Blood,

settled

Physics

of 0.6 tm on the

and

deformation

and

a pore

filters

Medicine,

the

were

use

density

subjected

McMaster

University,

of many of polycarof 3 x 10 to positive

Hamilton,

Canada.

Submitted

©

diameter

had

the involved

1979

reprint Hamilton, by Grune

requests

to

Ontario, & Stratton,

Vol. 54, No. 5 (November),

Dystrophy

accepted Dr.

July

Y. F.

Canada, Inc.

1979

Association 1/.

Missirlis,

L8S

of Canada.

/ 979. Department

of

Engineering

Physics.

McMaster

4M/.

0006-497//79/5405-00/2$02.00/0

1069


1070

MISSIRLIS

hydrostatic partially

pressures penetrate

“tongues” the tongues the

of erythrocyte measured

tongues

static

of 20-40 the filter. from

Although the serious

were

applied,

BRAIN

H2O, which forced tongues of membranes fixation and dissolving away the filter,

to the

membrane so formed could be visualized and the length a stereoscan electron microscopic image. The lengths

of membrane

pressure

mm After

AND

then

enabling

correlated

an elastic

with

the

“modulus”

magnitude

of the

of of

hydro-

to be calculated.

the method described by Brailsford et al.6 appeared to have overcome limitations of the micropipette technique, it has the serious disadvantage

that, owing to the high formed from individual the

pore density erythrocytes.

believe

that

elastic between

shear modulus to the results reported

formation

micropipette

technique.

pore

(2 x

density

Furthermore,

filter used, many tongues of membrane were For reasons that we will discuss later, we

of multiple be

However,

l06/sq

if one

cm),

it is possible

tongues

of membrane

does

calculated and thus accounts by these authors and those reported the

uses

Nuclepore

majority

to select

filters

of erythrocytes

for measurement

not

with

have

those

permit

the

for the discrepancy by others using the a much

only

lower

one

erythrocytes

tongue.

from

which

the tongue protrudes at or near the center dimpled region of a discoid erythrocyte, the region that is selected for micropipette aspiration. Under these conditions, the only differences between the measurements made after Nuclepore filtration and micropipette aspiration are that in the former a positive hydrostatic pressure is applied, that the cells have been subjected to fixation and dehydration, and that measurement of the applied pressure cannot be determined as accurately as can negative hydrostatic pressure applied to an individual erythrocyte. However,

the the the

method

the

has

the

length of hydrostatic

major

tongues pressures

being obtained. We now report many

normal

after

Nuclepore

cytes

from

advantage

of enabling

formed from on a single the use of our

human

with

have

Polycarbonate filters

filters, 2 x

were

sealed

25 mm

10’ pores/sq onto

subjected

to forced

was

fluid

through

flow

the glass

apparatus The

the

tube

tube

serum

was

same

the

of erythrocytes capillary

erythrocyte

suspension

and

the erythrocytes

hydrostatic fluid

into

the

buffer

until

the

was

prepared

into

5 ml

tube were

added

pores

fluid of

filled

with

levels

inside

the

and

in the tube

the

achieved

the beaker

filter and two

under

the Pasteur

there

a The

wax that

was

and there

no leak

placed

an

ir

I.

7.4) containing

(pH

the

lowered

tube

obtained

were

into equal.

by finger

Then, above

250 gravity. the

attached

A

zl of

level

dilute using

the of the

The

2%

a beaker

prick

the surface

of

by reducing pipettes

parrafin

was then

carefully

influence

and

Calif.).

verified

that

(PBS)

1 cm

diameter

with

and

saline.

maintained glass

or I m

attached

outside blood

about

of erythro-

process

in Fig.

then

phosphate-buffered

buffer on

and

20 MI of

This

water,

saline

Mo)

modulus

(Pleasanton,

diameter

filter

et al.’ as shown

Louis,

0.7 m

pump.

with

et al. on

shear

aspiration

external

vacuum

were

by adding

to the

into

of 25-mm

A glass tube

St.

elastic

Corporation

phosphate-buffered

Co.,

to settle and

tubes

by Brailsford

across the filter was the tube

size of either

by a water

on

methods.

a pore

by Nuclepore

filter.

isotonic

(Sigma

allowed

gradient

by lowering

with

(BSA)

suspension heparinized

described

filled

containing

that

glass

different

METHODS

with

water

the attached

to that

albumin

with

pores,

and

very similar glass

bovine

filtration

two

made

of Brailsford

the

AND

supplied

the ends of short

then

between

were

technique

by micropipette

by the

in diameter cm,

to be

at the selected positive a few hours of the sample

compared

obtained

studied

MATERIALS pore density

of the

We that

subjects

measurements

40 erythrocytes of blood within

modification

erythrocytes.

filtration

the same

10 to sample

dilute filter

requisite

of the

to vacuum

outer lines;

a


ERYTHROCYTE

MEMBRANE

ELASTICITY

1071

wmi

SUCTION FLUID

TRAP

ERYTHROCYTE SUSPENSION

Fig. 1 . Diagram of the apparatus used to aspirate erythrocytes into a Nucleopore filter under positive hydrostatic pressure.

the height

of the tip of the inner

micrometer

regulating

had been applied

pipette

the inner

relative

pipette.

to the sedimented

was aspirated

fixation.

After

fluid

aspirated

filter

with

as the

hyde

in phosphate

adherent

dehydrated cover

from

coated

attached

erythrocytes Phillips

510)

of

enlargements

by as much

as

Furthermore, observed

the pores

erythrocytes

with

the

true

of the

tongue

was

in one

conditions,

plane

would

at 0#{176} from

and the true

0#{176}; R is the radius

for

450

length

of tongue,

examined

fluid

and

tube,

postfixed

the

in 0,04

lowermost

The

to the glass

by stereoscan

the

I % glutaralde-

was

glass.

of

and the inner

surface

to the

added

the excess

the process

containing filter

adherent

on a

filter

was

then

cover

slip.

The

electron

the

axis cases)

as shown

microscopy

necessary

used

of membrane

screen

was not constant,

diameter

of

every

and

or

from

and it varied

single

the relatively

to take

passing

through

at least

“tongue.”

small

two

number

pictures

was found

its center.

and

another

photograph

was

uniform,

since

it

I -cotan0

Thus,

such

Then

of

was

taken.

is invariant

the following

of each that

the

the stage

2, where H is the observed

of tongue.

+

microscope

stage, a position

in Fig.

length

tongue

of the membrane

of the cell.

H/R-l sin0

the

this explains

the center

it was

is the true

R

and

diameter

was calculated

D

measure

a single

of the tongue

from

of the microscopic

the vertical

with

length

size of the filters to

or near

the tongue

and D

erythrocytes The directly

evenly,

(or 60#{176} in some

test whether

the

to adhere

20-30

pore

tongues

at different angles. By manipulation

photographs

The

from

tongue rotated

the erythrocyte

either

not distributed

length

fixation,

region.

necessary

one tongue

photographed

to find

measured

it was

were

mm with

and

during

of the dish

30-60

the erythrocytes

of the dimpled

was

Thus,

removal

placed

carbon

was slowly

the rate at which

gradient

to a Petri

set by a the filter

of x 12,000.

of the image.

20%.

±

In computing

with

possible

it was

tongue

photographic

was

leaving

coated

After

the erythrocytes

chloroform,

the center

the

a further

a portion

at a magnification

or near

beaker.

hydrostatic

being across

the fluid levels were equalized

and transferred

to enable

then

by SEM,

from

diameter

with

the same

from

After

and

pipette

gradient

10 ml of 1% glutaraldehyde

fixation,

the

pressure

cells nor exceeded

adequate

was detached saline.

were

for 2 mm,

maintaining

removed

collodium

away

On examination protruding

was

alcohols,

with

dissolved

the

tube

buffered

carefully (SEM:

thus

erythrocytes

in graded

slip

the tube,

of the tip of the outer hydrostatic

the sedimented

10 mm to ensure

a further

the desired

erythrocytes

to the tube at a rate that neither disturbed fluid

to the height

After

ratio

was

The

under

two these

length of angle

is obtained:


MISSIRLIS

1072

AND

BRAIN

H-Rp

.

SlflE)

(Dp-Rp) H

+Rp/tane

Rp+(Dp-Rp)sino+Rpcoso

=

Dp

H/Rp-1 +1-cotano

-=

Rp Fig. 2. Schematic the true length.

o©,and

of “tongue.” Relationship D. of a tongue of radius.

RESULTS

From and

the

analysis

formed, it was

many

cells

that

only

those

that

the tongue cylindrical

were

the observed

tongue

length

H, at an angle

R.

AND

visible

satisfied

was almost in shape,

between

sino

DISCUSSION

under the

SEM

we selected

following

criteria:

for measurement

there

was

one

perpendicular (within I 5#{176}) to the surface of the cell, ending in a hemispherical cap, and there was no

evidence of buckling of the tongue or of the rest of the cell. The shape of the tip of the tongue inside the pore is not well defined. shown that the tip of a tongue under these conditions cannot be spherical large

pressures,

assumption theoretical

and

he assumes

for their analysis models in terms

it to be spheroidal.

Chien

that the tip is hemispherical. of plots of the dimensionless

function of dimensionless membrane In calculating the length of the a hemispherical pressures, the

cap, although pictures of the

et al.7

we recognize tongues could

that this may be interpreted and

approximations

have

tal conditions

at constant

area. slides

(2) There is no friction between the freely at the pore mouth and along

developed pore

occurs

on the

mouth,

shear

and

modulus,

experiments. and Chien7 of an infinite The first modulus

cell

membrane

they

are

z, is constant

cell the

outside

negligible for

the

at the the

range

pore

are

of the

of deformations

two as a in

been

made

in

membrane experimen-

membrane

surface

so that the membrane pore. (3) The tensions

diminishing cell.

the

At the lower a spheroidal

erythrocyte under the

material

and the filter length of the

rim

made of these D/R,

not be true. as having

( I ) The

the deformation

has for

in good agreement.7 that the tongue ends

analyzing and interpreting the experimental results: is essentially a two-dimensional and incompressible and

Evans’ except

have

Comparison deformation,

tension, P x Re/i are tongue, we have assumed

rather than hemispherical cap. In addition, the following assumptions

employed

tongue

(4)

away The

from

surface

encountered

the

elastic in these

These assumptions are essentially the same as those made by Evans”' for analyzing data obtained by micropipette aspiration (i.e., aspiration plane membrane into a cylindrical tube of radius Rn). assumption is satisfied, since it has been shown that the area dilation

of the

erythrocyte

membrane

elastic modulus for shear rigidity.9 continuity in the membrane tensions is a consequence of the membrane

is about

4 x

l0

times

greater

than

the

The second assumption implies that there is at the mouth of the pore. The third assumption being modeled as an infinite flat plane being


MEMBRANE

ERYTHROCYTE

Fig. filters

3. (2

Typical x

photographed

10

1073

SEM

pores/sq

at two

ELASTICITY

photomicrographs of erythrocytes after partial aspiration into Nuclepore cm. nominal pore diameter of either 1.0 m or 0.6-0.8 Mm). Each cell was different angles with respect to an imaginary axis passing through the center of

the tongue. (A) Pressure 3 mm H20. angle 0’. magnification 6400. (B) Pressure 3 mm H20. angle 45’, magnification 6000. (C) Pressure 4 mm H20, angle 10’. magnification 5000. (D) Pressure 4 mm H20, angle 45’, magnification 4000. (E) Pressure 6 mm H20. angle 8’, magnification. 5500. (F) Pressure 6 mm H20. angle 50’. magnification 5500.


MISSIRLIS

1074

drawn

into

tension

a cylinder

in the

pipette

axis.

with

flat

plane

Thus,

that the rim of the dimple region. This the rim of the cell,

of say

cell is under approximation and it would

of entering the pore. validity of the fourth constant

subject derived

to verification by the theoretical

Finally,

over

we assume

and

SEM

the

of 3,4 and

plot

of the

4R,

radius

D/R

has

by

whether analysis.

that

the

or

stating not

process

does

shown

by Evans’

distance

away

that

the

from

the

I / 16 of its value

is about

determined plotted

that

the

data

fit the

of glutaraldehyde

not alter

6 mm

the

with

single

is shown

from against

constant, experiments

predicted

at

tongues in Fig.

4. Each

of the

hydrostatic

formed

illustrated

in Fig.

point

diameter

pressure

of the and

of deformation and others after

of membrane are

is

of the tongue

the magnitude by ourselves

pressure

.t,

relationship

dissolution

dimensions

of more than 45 cells of the tongue has been

measurements the

elastic in our

fixation,

relative

1-1,0 hydrostatic data

the

encountered

can be tested by comparing with those previously observed

experimental

been

been of the

tension

of deformations

mean and the bars the standard deviation different filters. In this plot, the length pore

the

assumption,

micropipette aspiration. The appearance of 3 erythrocytes A

It has square

negligible tension if the tongue is formed in the would be less valid if the tongue was formed at not be valid if the cell buckled or folded in the

range

preparation

the cell. This assumption under these conditions

applications

the

BRAIN

Since the radius of the pores of the Nuclepore filters in these sm and the cell radius is 4 sm, it is reasonable to assume

remains

filter,

cap. as

at a distance

the edge of the pipette. experiments is 0.3-0.5

process The

a spheroidal decreases

AND

represents

obtained normalized of the

P. This

after 3. the

from 4-6 by the

tongue,

and

relationship

is

5

4-

3 a.

2

(521

I

0

100

I

200

3)0

400

500

m

lao

000

p (dyn/cm2) Fig. 4. The dimensionless deformation parameter D/R of normal human erythrocyte plotted against the hydrostatic pressure, P. Each point represents the mean value numbers in parentheses represent the number of cells measured at each pressure.

±

membrane 1 SD. The


MEMBRANE

ERYTHROCYTE

evidently

linear.

function

of the

The

that

law ofa

shape,

by SEM.

At lower

Furthermore, variation in D/R

normalized these

is constant of Evans’ and

breaks At these

spheroidal

the

producing

two-dimensional

down when pressures,

as can

length

tongues

the

it is evident than that

our

tongues

basic

incompressible

hydrostatic erythrocytes

be seen

pressures,

of the

justifies

is a linear

assumption

that

over this range of deformations. Furthermore Chien et al., “ especially the linear approximation

t,

to the stress-strain relationship were used.

fact

pressure

the elastic constant, justifies the analysis

1075

ELASTICITY

membrane.

pressures greater than were no longer discoid

by the

appearance

normal

discoid

was

linear

8-10 mm H2O but assumed a

of the erythrocytes shape

This

it

on the

filter

maintained.

from Fig. 4 that at each pressure obtained in micropipette aspiration

there is a greater of individual cells.

This difference reflects the fact that whereas in the micropipette technique measurements are made of the linear elastic deformation of a single cell in response to an accurately determined pressure (±0.01 mm 1-120) range, in the filter experiments, may vary

D/R by ±0.1

pressure. erythrocytes

Thus, the variations due and between experiments

deviation

of measurements

In order from the quantity

made

to calculate the filter experiments, (P

measured,

is derived from mm H2O among

x as

R)t, is the

ofcells experiments

to small differences are cumulative

at selected

and

and

the pressure for the same

with

i

pressures.

is constant the

applied nominal

both among individual increase the standard

elastic shear modulus, t, of the erythrocyte D/R must be plotted against the

where case

a population the different

over

the

micropipette

range

of

experiments.

membrane dimensionless

extension

Chien

ratios

et al.7

have

(P x Rp)/p 5

0

1

2

3

1

1

4

4.

3. a. a. 0 2 #{163}

+ 1

P

Rp. 5 EXPERIMENTS

*

PxRp -

p 1)

o

_oo1

I

0.02

0.03

1.

Dp -

a 10’

dyn

cm

-0.57

Rp I

0.04

0.05

P x Rp (dyn/cm) Fig. 5. The dimensionless deformation parameter D/R of normal human erythrocyte membrance plotted against P(R) (bottom abscissa) and the dimensional membrane tension P x (top abscissa) with IL - 10.4 x i0 dyne/cm. The straight line is the approximate theoretical relationship according to Evans’ and Chien et al.7


1076

MISSIRLIS

shown

that

for I

D/R