Fisher JL and Margulies SS. Modeling the Effect of Stretch and Plasma Membrane Tension on Na+/K+-ATPase in Alveolar Epithelial Cells. Am J Physiol -Cell 2007:292:L40-L53.

Fisher JL and Margulies SS. Modeling the Effect of Stretch and Plasma Membrane Tension on Na+/K+-ATPase in Alveolar Epithelial Cells. Am J Physiol -Cell 2007:292:L40-L53.
Jacob L. Fisher and Susan S. Margulies
Am J Physiol Lung Cell Mol Physiol 292:40-53, 2007. First published Aug 4, 2006;
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Am J Physiol Lung Cell Mol Physiol 292: L40 –L53, 2007.
First published August 4, 2006; doi:10.1152/ajplung.00425.2005.
Modeling the effect of stretch and plasma membrane tension on
Na⫹-K⫹-ATPase activity in alveolar epithelial cells
Jacob L. Fisher1 and Susan S. Margulies1,2
Department of Bioengineering, and 2Institute for Medicine and
Engineering, University of Pennsylvania, Philadelphia, Pennsylvania
Submitted 4 October 2005; accepted in final form 24 July 2006
INVESTIGATORS HAVE FOUND alveolar epithelial stretch magnitude
to be related to cell injury in vitro (55, 56) and tidal volume to
be related to ventilator-induced lung injury (VILI) in animal
models (12–15). Studies have revealed that the frequency of
epithelial stretch or ventilation can also be an important factor
in cell injury (56, 60). The model developed in this study
examines how combinations of amplitude and frequency in
ventilation procedures affect Na⫹-K⫹-ATPase activity via hypothesized pathways including alveolar epithelial cell plasma
membrane tension and stretch-activated channel (SAC) stimulation.
To date, numerous models have been proposed to describe
cellular mechanical behavior, from early continuum viscoelastic representations for erythrocytes and leukocytes (11, 27, 65)
to more sophisticated variations that modeled cell membrane
and the cortical cytoskeleton as a cortical shell with prestress
(9, 11, 37), membrane viscosity (63), and/or a bending rigidity
(64), and the cytoplasm as a Newtonian (63), Maxwell (10, 11),
or power-law (51, 52) fluid. Other investigators have proposed
models that focus on mechanical contributions of discrete
cellular elements, such as tensegrity (4, 28, 47), percolation
(20), and the cellular solid (42) models. None of these models,
however, has focused on the plasma membrane as a separate
cellular component. Generally, the overall deformation of a
cell is determined by the cytoskeleton, cortical cytoskeleton, or
the cytoplasm rather than mechanical deformation of the
plasma membrane (26, 27, 65). Thus plasma membrane tension
is usually considered secondary to mechanical responses of
other cellular components. In most models, the plasma membrane is lumped with the cortical cytoskeleton. But unlike the
cortical cytoskeleton, which is often assumed to be an elastic
shell, the plasma membrane is flaccid and can respond to
deformation by unfolding a ruffled surface (31, 57, 58) or by
inserting lipids from a reservoir of additional plasma membrane material (39). In this study, we develop a model for the
unique tension-area relationship of the plasma membrane to
gain insight into the etiology of stretch-induced functional
responses we have measured previously (18, 19). Namely, we
have demonstrated that mechanogated channels in the plasma
membrane transduce signals for stimulating cell responses,
such as trafficking of Na⫹-K⫹-ATPase to the cell membrane
and consequently enhancing Na⫹-K⫹-ATPase activity (19).
However, high membrane tension can rupture a cell membrane,
leading to cell death. For these reasons, a model specifically
predicting alveolar epithelial cell plasma membrane tension in
response to cell stretch could be a helpful tool in evaluating and
selecting ventilation strategies that promote positive cell responses.
Research over the past decade has generated fundamental
data on plasma membrane mechanical behavior that inform the
plasma membrane model developed here. Investigators have
reported lipid insertion as a protective mechanism against high
membrane tension (7, 34, 61), similar to behavior we have
previously reported for alveolar epithelial cells undergoing
tonic stretch (18). Investigators have also pointed to ruffled
plasma membranes as protection against membrane lysis in
case of rapid deformation (31, 57). Because alveolar epithelial
cells tolerate cyclic stretch in vivo and in vitro at much faster
rates than lipid recruitment occurs, we hypothesize that alveolar epithelial cell plasma membrane expansion probably occurs as a combination of two phenomena, rapid cell surface
unfolding and slower lipid insertion.
Address for reprint requests and other correspondence: S. Margulies, Dept.
of Bioengineering, Univ. of Pennsylvania, 3320 Smith Walk, Philadelphia, PA
19104-6392 (e-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
ventilator-induced lung injury; lipid trafficking; edema recovery
1040-0605/07 $8.00 Copyright © 2007 the American Physiological Society
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Fisher, Jacob L., and Susan S. Margulies. Modeling the effect of stretch
and plasma membrane tension on Na⫹-K⫹-ATPase activity in alveolar
epithelial cells. Am J Physiol Lung Cell Mol Physiol 292: L40–L53, 2007.
First published August 4, 2006; doi:10.1152/ajplung.00425.2005.—While a
number of whole cell mechanical models have been proposed, few, if any,
have focused on the relationship among plasma membrane tension, plasma
membrane unfolding, and plasma membrane expansion and relaxation via
lipid insertion. The goal of this communication is to develop such a model to
better understand how plasma membrane tension, which we propose stimulates Na⫹-K⫹-ATPase activity but possibly also causes cell injury, may be
generated in alveolar epithelial cells during mechanical ventilation. Assuming
basic relationships between plasma membrane unfolding and tension and
lipid insertion as the result of tension, we have captured plasma membrane
mechanical responses observed in alveolar epithelial cells: fast deformation
during fast cyclic stretch, slower, time-dependent deformation via lipid
insertion during tonic stretch, and cell recovery after release from stretch. The
model estimates plasma membrane tension and predicts Na⫹-K⫹-ATPase
activation for a specified cell deformation time course. Model parameters
were fit to plasma membrane tension, whole cell capacitance, and plasma
membrane area data collected from the literature for osmotically swollen and
shrunken cells. Predictions of membrane tension and stretch-stimulated
Na⫹-K⫹-ATPase activity were validated with measurements from previous
studies. As a proof of concept, we demonstrate experimentally that tonic
stretch and consequent plasma membrane recruitment can be exploited to
condition cells against subsequent cyclic stretch and hence mitigate stretchinduced responses, including stretch-induced cell death and stretch-induced
modulation of Na⫹-K⫹-ATPase activity. Finally, the model was exercised to
evaluate plasma membrane tension and potential Na⫹-K⫹-ATPase stimulation for an assortment of traditional and novel ventilation techniques.
Fig. 1. Model flowchart. The goal of this study is to combine several previously reported cellular responses to stretch and combine them into a comprehensive model that predicts Na⫹-K⫹-ATPase stimulation for any stretch
pattern according to the relationships shown above. Black arrows represent
previously reported alveolar epithelial cell behavior. The gray arrow represents
biophysics theory of stretch-activated channel opening in response to tension,
discussed in this study. Finally, white arrows represent the interrelationship
between stretch, plasma membrane tension, and lipid trafficking, which is not
only influenced by tension, but also serves as negative feedback by reducing
tension. These relationships, in white text, will be provided by the mathematical model developed here. Also, solid arrows show direct relationships,
whereas broken arrows indicate indirect but reported relationships between
stimuli and responses. SAC, stretch-activated channel.
AJP-Lung Cell Mol Physiol • VOL
represent relationships between stretch and plasma membrane
tension, including a negative feedback mechanism created by
tension-reducing lipid insertion, all of which we wish to predict
with a mathematical model fit to data derived from the appropriate literature. Finally, white arrows in Fig. 1 represent the
interrelationship between stretch, plasma membrane tension,
and lipid trafficking, which is not only influenced by tension
but also serves as negative feedback by reducing tension.
These white arrow relationships will be provided by the model
developed here. Also, solid arrows show direct relationships,
whereas broken arrows indicate indirect but observed relationships between stimuli and responses. The following subsections describe model conceptualization and fundamental assumptions, model formulation, and parameter fitting.
Model conceptualization. The first premise behind our mathematical model is that equibiaxially stretched alveolar epithelial cells initially respond by unfolding their cell surface.
Because the undisturbed plasma membrane generally has a
ruffled shape provided by an underlying cytoskeletal scaffolding, this unfolding requires work and results in a corresponding
tension and elastic strain energy in the plasma membrane. Our
second premise posits that this membrane tension stimulates
SACs and lipid insertion in the plasma membrane, as suggested
by SAC stimulation (19) and lipid insertion (17). Specifically,
we assume that SACs respond instantly to tension, whereas we
require that lipid insertion occur more slowly, as shown by
lipid insertion observed during tonic stretch (18, 23). Based on
observations of lipid resorption in flaccid cells (7, 18, 33, 61),
we also propose that lipid resorption occurs when the cell
shrinks or is released after stretch and an excess of flaccid
membrane exists. This insertion and resorption of lipid will
reduce and restore membrane tension, respectively.
The paucity of quantitative empirical knowledge regarding
the relationship between plasma membrane stretch and tension,
or between tension and either lipid insertion or resorption,
necessitates several assumptions. First, we have assumed a
simple Hookian elastic relationship between plasma membrane
unfolding (area deformation) and plasma membrane tension.
Second, we have assumed that the rate of lipid insertion is
proportional to plasma membrane tension; that is, the higher
membrane tension, the faster additional lipid inserts into the
membrane. Finally, we have assumed that if the cell shrinks or
is forcibly shrunken by imposed deformation, the cell resorbs
excess membrane at a rate proportional to the amount of
These assumptions can be formulated into mathematical
relationships. The assumed Hookian relationship between
plasma membrane surface area increase due to unfolding,
A ⫺A0, and tension, TBI, is similar to that of a spring. However,
unlike a typical spring, under tension the plasma membrane has
the capacity to add more “spring material” via lipid insertion,
increasing its neutral (zero tension) area and reducing tension.
Hence we use A* to represent a variable neutral or gauge area,
which expands via lipid insertion. Plasma membrane tension,
TBI, is governed by the relationship:
A ⫺ A*
⫽ KBI共␣ ⫺ ␣*兲
where KBI is an area elastic modulus, A is cell surface area, A0
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In this study, we have created a theoretical model that
incorporates the contributions of membrane unfolding and lipid
insertion to relieve plasma membrane tension. We predict
Na⫹-K⫹-ATPase activity in response to modeled membrane
tension output based on biophysical channel opening theory,
and we compare predictions with Na⫹-K⫹-ATPase activity
measurements we have reported previously (19). As a proof of
concept experiment, alveolar epithelial cells were stretched
statically to allow plasma membrane expansion and then
stretched cyclically. A “conditioning” effect, predicted by the
model, was measured through changes in Na⫹-K⫹-ATPase
activity. Conditioning was also observed in cell mortality and
basolateral membrane (BLM) content of Na⫹-K⫹-ATPase ␣1subunit. Finally, the model was exercised to predict alveolar
epithelial membrane tension and relative Na⫹-K⫹-ATPase
stimulation in cells subjected to conventional and innovative
ventilation strategies.
Model development. The objective of this modeling effort is
to predict increases in Na⫹-K⫹-ATPase activity for given
alveolar epithelial deformation patterns derived from clinically
relevant mechanical ventilation maneuvers. With these predictions we will evaluate different ventilation strategies in terms
of their effectiveness in stimulating a desirable increase in
Na⫹-K⫹-ATPase activity. A flowchart of this overall scheme is
shown in Fig. 1. Black arrows indicate previously established
discoveries, namely that cyclic stretch acts through SACs to
induce greater Na⫹-K⫹-ATPase activity and does so by increasing the number of Na⫹-K⫹-ATPases in the BLM (19),
and that tonic stretch stimulates lipid insertion into the plasma
membrane (18). The gray arrow in Fig. 1 represents a biophysics theory, which states that SAC opening probability is described by a Boltzmann distribution dependent on tension over
the SAC (22, 24, 29, 30, 32, 41). The dashed black arrows
is initial cell surface area, ␣ is a relative area strain, and ␣* is
defined as
A* ⫺ A 0
the proportional increase in the neutral area or neutral strain.
We also assumed stretch stimulates lipid insertion at a rate
proportional to the stretch-induced tension so that the neutral
strain, ␣*, can increase as follows:
␩ i␣˙ * ⫽ TBI,
where ␩i is a lipid insertion modulus and
␣˙ * ⫽
Combining Eqs. 1 and 2 yields
冉 冊
A ⫺ A0
where the reference area for determining the amount of deformation is initial surface area A0 instead of neutral area A*. The
total plasma membrane tension, T, is the sum of TBI ⫹ TBII.
In sum we represent the plasma membrane as a two-branch
elastic solid (Fig. 2). The elastic element in Branch I can take
on additional material when it is under tension, resulting in
tension relaxation as A* increases beyond A0. In contrast, the
␤␣˙ * ⫽ 共␣ ⫺ ␣*兲
where ␤ is a strictly positive absorption modulus. Hence, when
␣ ⬍ ␣* and excess lipid exists during imposed shrinking, ␣˙ * ⬍
0, indicating plasma membrane resorption.
Model constitutive equations. The overall constitutive equations for the model proposed above are derived from the
individual properties of its component elements. Total tension,
T, is the sum of tensions in Branch I and Branch II. Differentiating over the total deformation and substituting Eqs. 1 and 2
yield the governing equation during cell expansion:
T ⫹ aṪ ⫽ b␣⫹c␣˙
b ⫽ KBII,
冉 冊
c⫽␩i 1⫹
When the cell shrinks (␣ ⬍ ␣*), tension disappears in Branch
I. Unlike lipid insertion rate, which is defined as proportional
to tension, lipid resorption rate is assumed proportional to the
amount of excess membrane, ␣* ⫺ ␣, so we combine Eqs. 4
and 5 to derive the governing equation during cell shrinkage:
P ⫹ âṖ ⫽ b̂␣ ⫹ ĉ␣˙
P ⫽ T ⫹ ␥共␣ ⫺ ␣*兲
where ␥ is simply a dimensional conversion scalar with units of
tension, and the coefficients â, b̂, and ĉ are combinations of the
moduli KBII, ␤, and ␥.
â ⫽ ␤,
Fig. 2. Three-element mechanical model. The plasma membrane model is
composed of a 2 Hookian springs with elastic moduli KBI and KBII, representing plasma membrane resistance to unfolding. Unlike a standard spring, the
upper arm, Branch I, has the capacity to supplement itself with additional
material at a rate, ␩i, proportional to tension. This lipid insertion increases the
neutral area of Branch I, relaxing tension, T.
AJP-Lung Cell Mol Physiol • VOL
b̂ ⫽ K BII,
ĉ ⫽ ␤共␥ ⫹ KBII兲.
Importantly, we note that at the point where lipid insertion
stops and lipid resorption begins and vice versa, there is
no excess plasma membrane, tension in Branch I is zero, and
P ⫽ T. A full derivation of this model with greater detail has
been published elsewhere (16).
Parameter fitting. Because plasma membrane tension, cell
capacitance, and cell size measurements all require probing or
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The model described by Eq. 3, however, is incomplete because
it predicts that lipid insertion can produce complete membrane
relaxation, allowing tension to diminish to zero under constant
deformation. Contrary to this prediction, investigators have
found that tension did relax partially after increasing with
deformation in osmotically swollen cells, but it did not disappear completely (7, 8). Furthermore, they found that a released
cell, even after lipids have been added, still recovered its initial
shape and size (6, 7). To incorporate these additional characteristics we add a second elastic unfolding element, which we
will designate Branch II, in parallel with the existing model in
Eq. 3, which we will call Branch I. Like Branch I, which was
just derived, Branch II represents a spring-like Hookian relationship between tension and the cell surface area deformation
produced by unfolding, but, unlike Branch I, Branch II is not
affected by lipid insertion. Thus the deformation for the second
elastic element is:
elastic solid in Branch II does not relax but instead maintains
a tension proportional to area deformation relative to the initial
neutral state, A0. This reference to A0 as a baseline in Branch
II supplies a persistent tension in the whole model, even if lipid
insertion and complete tension relaxation occur in Branch I,
and thus provides the recoil required for the released cell to
recover its initial shape.
Released from stretch, the cell shrinks naturally or is forced
to shrink by elastic contraction of adjacent materials (in vitro)
or tissue (in vivo). As the cell shrinks, tension in Branch II
remains positive as long as surface area A remains larger than
the initial area, A0. In contrast, due to the lipid inserted to the
plasma membrane, Branch I possesses an excess of plasma
membrane when the imposed shrunken area A is less than A*.
Because the plasma membrane has a negligible bending stiffness (25), it bears almost no compression before buckling and
bunching into ruffles. Thus tension in Branch I becomes zero
when A ⫽ A* and remains zero as long as A ⬍ A*. The
buckling of excess membrane beyond “normal” membrane
folding is energetically unfavorable and leads to membrane
resorption, as observed experimentally (5–7, 34). Earlier, our
third assumption proposed that the rate of this lipid resorption
is proportional to the amount of excess membrane; mathematically stated:
F ⫽ 2␲ 冑2 BT,
where B, the membrane bending stiffness, is
2.7 ⫻ 10⫺19 N ⫻ m (25).
We acknowledge at this point that the data used for model
parameter fitting were collected from neuronal cells rather than
alveolar epithelial cells. Nevertheless, many basic characteristics such as overall change in cell capacitance and cell size
under a given load and relaxation constants were similar
between the neuronal cells used for parameter fitting and data
obtained by our lab and others for alveolar epithelial cells (6,
7, 57, 58).
Parameter values found to produce a least squares fit between model-generated output and observed data are listed in
Table 1.
For use in proof-of-concept conditioning experiments, alveolar
type 2 (AT2) cells were isolated from male, Sprague-Dawley rats
(Charles River, Wilmington, MA) (55) and cultured using established,
previously described methods (18, 19, 55). AT2 cells were then
Table 1. Model parameters determined by data fitting
3.79 s
0.0289 dyn/cm
0.570 dyn-s/cm
0.0289 dyn/cm
0.121 dyn/cm
0.460 dyn-s/cm
3.58 s
0.0289 dyn/cm
3.68 dyn-s/cm
0.0289 dyn/cm
3.58 s
KBI and KBII, area elastic moduli; ␩i, lipid insertion modulus; ␤, strictly
positive absorption modulus; coefficients a, b, and c, combinations of the
moduli KBI and KBII and ␩i, for membrane swelling; coefficients â, b̂, and ĉ,
combinations of the modulus KBII, ␤, and ␥.
AJP-Lung Cell Mol Physiol • VOL
seeded for confluence at 1 ⫻ 106 cells/cm2. To determine whether
lipid trafficking during static stretch has any conditioning effect on
cells, 2-day cells were tonically prestretched before being stretched
cyclically in a custom-made stretching device capable of imposing
uniform, equibiaxial two-dimensional strain (16, 55). Preconditioning
was performed by stretching cells tonically for 10 min to a prescribed
change in substrate surface area (⌬SA). At the end of this period, any
preconditioned control wells not slated for stretch would be quickly
removed from the device (while others remained statically stretched).
Then the motor of the stretching device was switched on, beginning
cyclic stretch with a falling wave from the peak stretched position.
Within the first minute of cyclic stretch, stretched but unconditioned
wells would be fastened into place while the device was in operation.
Thus preconditioned wells were held in the stretch position until
cyclic stretch began to eliminate the possibility of excess membrane
endocytosis during well changes. Cyclic stretch was carried out at
either 25% or 37% ⌬SA for 60 min at 15 cycles/min. After stretch,
cell viability, Na⫹-K⫹-ATPase activity as measured by 86Rb⫹ uptake,
or Na⫹-K⫹-ATPase ␣1-subunit content in the AT2 BLM were measured using published techniques (19).
Viability, Na⫹-K⫹-ATPase activity, and Na⫹-K⫹-ATPase trafficking data from were analyzed using previously described methods
(16, 19). Differences in viability were assessed using two-way
ANOVA over treatment (preconditioned and unconditioned) and over
three isolations at each stretch magnitude. Na⫹-K⫹-ATPase activity
in conditioned cells was assessed relative to unstretched controls. To
compare conditioned cell results and previous results for stretch
without conditioning, data were normalized by internal controls and
compared by two-way ANOVA over treatment (conditioned and
unconditioned) and over four isolations in each treatment. Na⫹-K⫹ATPase ␣1-subunit blot densities were compared using paired t-tests
(P ⱕ 0.01 for significance) among cells stretched without conditioning, cells stretched with conditioning, and unstretched cells. Tukey’s
procedure for honestly significant differences was used to correct for
multiple comparisons.
Tonic-stretch preconditioning attenuates cyclic stretch responses. Preconditioning alveolar epithelial cells with tonic
stretch significantly reduced their response to subsequent cyclic stretch. In viability studies, cells stretched at 25% ⌬SA
saw a significant decrease in cell death from 15.3 ⫾ 4.2% to
5.6 ⫾ 1.9% with 10 min of tonic prestretch. Results were
similar at 37% ⌬SA, at which the mortality rate decreased from
14.2 ⫾ 1.1% in unconditioned cells to 6.4 ⫾ 0.8% in preconditioned cells (Fig. 3). At both magnitudes, analysis of variance
detected significant differences between conditioned and unconditioned treatments (P ⬍ 0.001). It should be noted that
preconditioning had no negative effect on cell adherence or cell
Similarly, tonic-stretch conditioning resulted in attenuated
Na⫹-K⫹-ATPase activity. Cells tonically prestretched for 10
min at 25% ⌬SA and then cyclically stretched at 15 cycles/min
for 1 h at the same magnitude increased Na⫹-K⫹-ATPase
activity by only 53% (1.53 ⫾ 0.10) over unstretched controls
(1.00 ⫾ 0.06) in contrast to 136% increase for cyclically
stretched cells (2.36 ⫾ 0.25 for stretched cells vs. 1.00 ⫾ 0.20
for separate, unstretched controls; Fig. 4). Western blot density
of BLM Na⫹-K⫹-ATPase ␣1-subunit in preconditioned cells
also rose significantly (1.79 ⫾ 0.19 intensity units, normalized by
controls) over unstretched controls (1.00 ⫾ 0.11), but significantly
less than in stretched cells that had not been conditioned with
tonic stretch beforehand (2.44 ⫾ 0.21; Fig. 5).
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imaging at a microscopic level, it is presently impossible to
stretch cells physically via conventional techniques and simultaneously make microscopic measurements. Thus we relied on
data from two similar osmotic cell-swelling and -shrinking
studies from Dai et al. (7, 8) to fit the relevant model parameters. In these experiments using custom-made apparatus, the
medium surrounding a continuously probed cell was carefully
changed, first to a 50% hypotonic solution to cause osmotic
swelling, which increased plasma membrane tension and promoted creep, and then to an isotonic medium to relieve osmotic
pressure and membrane tension and to allow the cell to shrink.
In the more recent communication (7) the investigators swelled
and shrunk cells osmotically and recorded the following:
plasma membrane tension measured via force in a plasma
membrane tether pulled from the cell using a bead and optical
trap; whole cell capacitance measured via a micropipetteperforated patch technique; and total cell volume, calculated
through a cell diameter measurement, roughly assuming the
cell to be spherical. In the earlier communication (8), the
investigators had only swelled the cells and had only recorded
plasma membrane tension and cell volume, but with greater
temporal resolution than in the recent study. We have used data
from both studies to fit the parameters in Eqs. 8A and 11. In
cases where plasma membrane tension was reported as tether
force, F, force was converted to cell membrane tension, T,
using a relationship derived by the authors (45):
Fig. 3. Effect of tonic-stretch conditioning on cell viability. Stretching cells
tonically for 10 min before stretching them cyclically for 1 h at the same
magnitude significantly reduced cell viability relative to cells stretched cyclically without conditioning. Bars represent means ⫾ SE; n ⫽ 18. An asterisk
(*) over a bar represents significant difference from control. Significance (P ⬍
0.05) was determined by 2-way ANOVA between conditioned and unconditioned cells over 3 isolations at each stretch magnitude. Viability in all controls
was ⬎99% and is not shown. ⌬SA, change in surface area.
Fig. 4. Effect of tonic-stretch conditioning on Na⫹-K⫹-ATPase activity.
Stretching cells tonically for 10 min before stretching them cyclically for 1 h
at 25% ⌬SA significantly lessened stretch-induced increases in Na⫹-K⫹ATPase activity relative to activity in cells that were not conditioned before
stretch. Bars represent means ⫾ SE. Open bars indicate unstretched controls
corresponding to each condition. Significance (P ⬍ 0.05) was determined by
2-way ANOVA between conditioned and unconditioned cells over 4 isolations
at each stretch magnitude. An asterisk (*) over a bar represents significant
difference from control; an asterisk spanning groups shows significant difference between groups.
AJP-Lung Cell Mol Physiol • VOL
shown by the negative Branch I deformation (Fig. 6D). At this
point, ␣* ⬎ ␣, forcing lipid resorption, as indicated by the
decreasing baseline area strain, ␣* (Fig. 6D). As the cell
resorbed excess lipid, ␣* became zero, indicating no further
excess membrane, reflected by the Branch I elastic deformation
ascending from negative values (excess). Relaxation via lipid
insertion during tonic stretch occurred more rapidly than resorption of additional lipid after release from tonic stretch (Fig. 6D).
This same rate differential is illustrated in the fast rise and slow
fall of capacitance in osmotically swollen and shrunken cells (7).
In response to a cyclic stretch deformation (Fig. 7A), tension
rose and fell cyclically (Fig. 7B), suggesting that lipid insertion
did not take place as fast as deformations were imposed.
However, the maximum and average tension imposed by a
deformation did decrease over the first few cycles, implying
that some relaxation occurred even during cyclic stretch. Comparing ␣* between the first stretch cycle (Fig. 7C) and another
later cycle after the tension wave achieved steady state (Fig.
7D) confirmed that lipid insertion had occurred. In the initial
cycle ␣* increased, but only to ⬇9% ⌬SA, not the full
deformation of 25% ⌬SA (Fig. 7C) because the rate of lipid
insertion was slow relative to the deformation rate imposed by
cyclic stretch. Thus the remainder of the deformation, ␣ ⫺ ␣*,
took place elastically in Branch I, which added to the elastic
tension of Branch II to generate the high tension predicted in
the initial cycle. However, in a steady-state cycle, we find that
the increased baseline ␣* accounted for 15–20% ⌬SA in a 25%
⌬SA stretch (Fig. 7D). At this point, deformation in Branch I
was largely negative, indicating an excess of plasma membrane
through most of the cycle. Only at the peak of deformation did
Branch I stretch elastically and contribute to membrane tension. However, because Branch I has a greater elastic modulus
than Branch II, this small elastic Branch I deformation contributes significantly to overall membrane tension.
After 10 min of tonic-stretch preconditioning, the plasma
membrane steady-state response to 25% ⌬SA cyclic stretch
was generally similar in form to the response to 25% ⌬SA
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Model behavior. As a basic confirmation that the model can
predict plasma membrane responses in agreement with our
initial hypotheses, we inspected model predictions of plasma
membrane tension, elastic deformation, and lipid insertion/
resorption for a 25% ⌬SA tonic-stretch input (Fig. 6), a 25%
⌬SA cyclic stretch input (Fig. 7), and 25% ⌬SA cyclic stretch
after 10 min of tonic-stretch preconditioning (Fig. 8). In response to tonic deformation, the model predicted a peak
membrane tension coinciding with the end of the initial stretch
and associated with elastic deformation in both Branches I and
II. As cell deformation was maintained, tension relaxed as lipid
insertion occurred. Within 40 s, Branch I neutral area strain,
␣*, increased to 25% ⌬SA, the magnitude of the entire deformation, ␣ (Fig. 6C). This baseline increase completely relaxed
tension in Branch I so that the only tension in the total
membrane was the tension in Branch II. At the end of the
tonic-stretch experiment, stretch was released, and plasma
membrane tension and total cell deformation both fell to zero,
but excess plasma membrane accumulated at the cell surface as
Fig. 5. Effect of tonic-stretch conditioning on Na⫹-K⫹-ATPase trafficking.
Stretching cells tonically for 10 min before stretching them cyclically for 1 h
at 25% ⌬SA significantly reduced Na⫹-K⫹-ATPase ␣1-subunit levels in the
BLM (1.79 ⫾ 0.19) compared with ␣1-subunit content in cells stretched
without conditioning (2.44 ⫾ 0.21). However, even in conditioned cells, ␣1
content was significantly greater than in wholly unstretched control (1.00 ⫾
0.11). Bars represent means ⫾ SE of Western blot intensity for Na⫹-K⫹ATPase ␣1-subunit, normalized to control values. Significance (P ⬍ 0.01) was
determined by t-tests among the 3 groups using Tukey’s procedure for honestly
significant differences to correct for multiple comparisons. An asterisk (*) over
a bar represents significant difference from control; an asterisk spanning
groups shows significant difference between groups.
cyclic stretch without preconditioning, but with slightly shifted
magnitudes. As shown in Fig. 8B, cells began cyclic stretch
with fully expanded Branch I neutral area, that is ␣* was 25%
⌬SA. Thus during the initial stretch cycles, Branch I deformation exploited the excess “slack” created by expanded ␣* so
that there was almost no elastic Branch I deformation. As
cyclic stretch continued, plasma membrane resorption gradually occurred during the shrinking phase of each cycle until a
steady state was reached. However, we note that steady-state
cyclic plasma membrane deformation in preconditioned cells
was different from that in unconditioned cells. Presumably due
to faster lipid insertion relative to lipid resorption, the lipid
inserted during tonic-stretch conditioning is never fully
resorbed, creating a greater reserve of material and thus a
greater neutral area strain, ␣*, even after steady state is
achieved. The result of this greater neutral area is less elastic
deformation and thus lower tension in preconditioned cells.
In addition to the 25% ⌬SA cyclic and 25% ⌬SA tonic
waves analyzed in detail above, tension output was generated
for two additional deformation patterns: 12% ⌬SA cyclic
stretch and 12–25% ⌬SA cyclic stretch (Fig. 9). In these
additional tension oscillations, we observe the same pattern
noted in cyclic stretch before: high tension peaks in the first
few deformation cycles, but the wave diminishes and stabilizes
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in less than a minute, and continues with that form for the
remainder of the 1-h stretch. On the whole, we find that the
model produces quantitative results in agreement with previous
qualitative observations: cyclic stretch produces higher tensions than tonic stretch; tonic stretch allows for lipid insertion
and partial relaxation of tension, reducing a potential tensioninduced stretch stimulus; and lipid resorption from a flaccid
membrane occurs more rapidly than lipid insertion into a tense
membrane. Making dynamic measurements of quantities such
as plasma membrane tension or lipid insertion in a stretching
cell is impossible with current techniques. Thus until dynamic
measurement techniques are developed, this model provides
estimates of plasma membrane tension and lipid insertion by
extrapolating measurements made in slow osmotic swelling
into the domain of fast dynamic deformation.
As a comparison of predicted model response to experimental
measurements, we consider whether lipid turnover rates projected
by the model are realistic. It is well known that a cell at rest
regularly recycles plasma membrane to regulate surface protein
expression, absorb nutrients, and secrete waste and physiologically important substances, such as surfactant in the case of
alveolar epithelial type 2 cells. Previously, investigators have
demonstrated that tonically stretched alveolar epithelial cells increase both exocytosis (59) and endocytosis (2), although overall
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Fig. 6. Analysis of model output for tonic deformation. A: 25% ⌬SA tonic input deformation, internal Branch I elastic deformation, and change in Branch I
neutral area as a result of lipid insertion or resorption. B: the corresponding tension output, which initially rises and then relaxes. C: the mechanism of that
relaxation, namely enlargement of the neutral area strain, ␣*, via lipid insertion. As lipid inserts, the elastic deformation in Branch I wanes along with its
corresponding tension. D: release from tonic stretch. Although deformation and tension both drop to zero at the end of stretch, the Branch I deformation actually
becomes negative, representing an excess of inserted lipid. At this point, the relative baseline area strain (␣*) exceeds the area strain. As lipid is reabsorbed, ␣*
decreases, and the excess, shown as negative deformation, disappears. We note that lipid insertion in a tense membrane occurs faster than lipid reabsorption in
a flaccid membrane.
turnover rates were not reported. In terms of mass balance, one
can consider normal and stretch-induced lipid insertion as follows:
␣˙ * ⫽ stretch-induced insertion rate ⫺ stretch-induced resorption
rate ⫹ normal insertion rate ⫺ normal resorption rate.
In a resting cell, normal exocytosis and endocytosis rates are
dynamically balanced so that plasma membrane surface area remains
constant. With tonic stretch, insertion and resorption have both been
shown to increase, although the rate of insertion clearly outpaces
resorption as manifest in net plasma membrane expansion. In cell
shrinking, the balance is reversed so that resorption dominates, resulting in net plasma membrane decrease. Whether insertion and
resorption rates are both higher or both lower during tonic-stretch
equilibrium is unknown, although investigators have demonstrated
that pharmacologically induced endocytosis is hindered by increased
plasma membrane tension in some cell types (6, 8), suggesting that
normal exocytosis and endocytosis might both decrease. This could
have important implications for AT2 cells, which regularly exocytose
pulmonary surfactant. However, some studies suggest surfactant
release employs so-called “kiss and run” exocytosis, in which a
vesicle merges with plasma membrane, releases its contents from the
cell, and closes again without fully integrating into the plasma
membrane (43). In terms of whole cell lipid turnover, stretch-induced
lipid insertion certainly calls on a cell’s fullest lipid trafficking
capacity. Hao and Maxfield (23) found that the half-time, t1/2, for
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membrane turnover in resting CHO cells could be as short as 5–10
min. In previous studies, we found lipid trafficking to take place
within 5 min (18); other investigators found deformation-induced
lipid trafficking to occur within 90 s (59); and our model predicts a
25% ⌬SA in 40 s. Thus in an extreme case, stretch-induced trafficking could be occurring at rates 7–8 times that of normal recycling of
a resting cell. Although a potentially great demand on the cell, studies
of lipid trafficking to repair plasma membrane stress failure suggest
that such rates are not unreasonable (21, 48, 58).
Predicting Na⫹-K⫹-ATPase stimulation using tension to
estimate SAC opening. Previously we demonstrated that
stretch-induced SAC activation augments Na⫹-K⫹-ATPase
activity (19). To relate plasma membrane tension to SAC
activation, we employed a prevalent theory (29, 41, 49, 50) that
the probability, Po, of a SAC being open to ion traffic is
determined by a Boltzmann probability distribution dependent
on plasma membrane tension, T:
PO ⫽
1 ⫹ e␨共T⫺T ⁄ 兲
1 2
where T1/2 is the tension at which the probability of SAC
opening is 50% and ␨, sensitivity to tension, represents the
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Fig. 7. Analysis of model output for cyclic deformation. A shows a 25% ⌬SA cyclic deformation input, and B shows the similarly cyclic tension output. Initial
tensions are high but, within 40 s, the tension output reaches a steady-state oscillation. The decrease in tension during the first 10 cycles is explained by the
contrast in internal deformations between the first deformation cycle (C) and a deformation cycle after tension has stabilized (D). C shows that ␣* enlarges via
lipid insertion during the initial cycle but not nearly enough to relax Branch I sufficiently, leaving most of the deformation to tension-generating membrane
unfolding. However, D indicates that after tension stabilizes, the baseline area (␣*) has expanded to between 15 and 20% ⌬SA in a 25% ⌬SA deformation. The
negative values for Branch I deformation indicate an excess of membrane area during much of the cycle with elastic unfolding occurring only at the peak
tension change required to cause an e-fold increase in relative
channel activity.
For our purposes, we performed parametric simulations over
a range of values for ␨, and T1/2 corresponding to a range of
parameter values reported in the SAC classification literature
(24, 29, 30, 41, 49, 50). Model-generated membrane tension
was used to calculate a Po “wave” via Eq. 11 for five stretch
patterns: 25% ⌬SA tonic stretch, 12% ⌬SA cyclic stretch, 25%
⌬SA cyclic stretch, 12–25% ⌬SA cyclic stretch, and 25% ⌬SA
tonic-stretch preconditioning followed by cyclic stretch. A
cumulative SAC activity (CCA) was calculated by integrating
Po over 4 s, the duration of a typical deformation cycle at 15
cycles/min, in a part of the wave where steady-state tension
output had been achieved:
Ultimately, parameters T1/2 and ␨ were adjusted to T1/2 ⫽ 1.4
dyn/cm and ␨ ⫽ 8 cm2/erg to achieve the best linear correlation
(R2 ⫽ 0.96; Fig. 10) between previously published values of
Na⫹-K⫹-ATPase activity increase (19) and CCA (based on an
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implicit assumption that Na⫹-K⫹-ATPase increases are directly proportional to SAC stimulation).
Matrix of model simulations. Once fit with data, the model
was exercised to examine CCA and plasma membrane tension
for several traditional and relatively novel mechanical ventilation strategies. Maneuvers selected for testing included ventilation with various tidal volumes, ventilation with several
constant positive end-expiratory pressure (PEEP) magnitudes
but the same peak tidal volume, ventilation with several constant PEEP magnitudes and the same tidal volume amplitude,
ventilation with PEEP varying at 0.2 cycles/min, ventilation
with tonic volume, and high frequency ventilation (HFV)
(Fig. 11). Using clinically relevant values for ventilator tidal
volume, PEEP, and frequency, deformation waves were created for each maneuver using, as necessary, a pressure-to-total
lung capacity (TLC) conversion from West (62) and a
TLC-to-% ⌬SA conversion from Tschumperlin (53, 54). Deformation curves were used as inputs to the model to simulate
plasma membrane tension curves, from which we extracted
predicted tension and calculated CCA.
Deformation input categories. The first category contains
cyclic oscillations at 15 cycles/min between an undeformed
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Fig. 8. Analysis of model output for 25% ⌬SA cyclic deformation after tonic-stretch preconditioning. A shows a 25% ⌬SA cyclic deformation input, and B shows
the corresponding tension output after 10 min of tonic-stretch preconditioning. Initial cyclic tensions are low, but they gradually rise to steady-state oscillation.
However, plasma membrane tension after preconditioning never achieves tension magnitude observed in unconditioned cyclic stretch (Fig. 7B). Internal
deformations showing elastic deformation and changing neutral area are shown for the first deformation cycle after preconditioning in C and after tension has
stabilized in D. C shows that the baseline area strain (␣*) starts fully expanded at 25% ⌬SA. Thus in early cycles, elastic deformations are small, since the
expanded neutral area material is not quickly resorbed and this slack is utilized for the initial cyclic deformations. However, D indicates that after the tension
response stabilizes, the neutral area strain ␣* has been resorbed somewhat. Comparing D with Fig. 6D, cyclic stretch without preconditioning, we notice that
elastic deformations in Branch I are smaller in preconditioned membrane than in unconditioned membrane, accounting for the lower tensions. A lipid insertion
rate faster than a resorption rate accounts for the persistent preconditioning effect.
state (functional residual capacity) (53) and peak deformations
of 12%, 25%, 37%, and 50% ⌬SA. These peak deformations
roughly correspond to ventilation of intact lungs to 70%, 90%,
100%, and ⬎100% TLC, respectively (53), with no PEEP.
The second category includes ventilation with constant
PEEP. PEEP is often used in mechanical ventilation to prevent
derecruitment or collapse of alveoli when the lung is completely deflated; by maintaining a positive pressure at full
expiration, the lungs remain open and partially inflated. PEEP
Fig. 10. Na⫹-K⫹-ATPase vs. cumulative stretch-activated channel activity
(CCA). Increased Na⫹-K⫹-ATPase activity reported in previous studies (19)
was plotted against a cumulative channel activity calculated by integrating
SAC open probability of a stabilized tension cycle. From left to right, data
points represent 25% ⌬SA tonic stretch, 12% ⌬SA cyclic stretch, 12–25%
⌬SA cyclic stretch (PEEP), 25% ⌬SA preconditioning, and 25% ⌬SA cyclic
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values in clinical trials can range from 5 to 30 cmH2O (3). In
these studies, we have used three subcategories of PEEP. In the
first subcategory, all waveforms had a maximum deformation
of 25% ⌬SA and a baseline deformation of 0%, 5%, 12%,
15%, or 20% ⌬SA, corresponding roughly to 0, 5, 10, 12, and
15 cmH2O PEEP. In the second PEEP subcategory, all deformation waves had an amplitude of 25% ⌬SA with different
PEEP and maximum deformation. The 15-cycle/min oscilla-
Fig. 11. Tested input wave forms. Shown here are examples of waveforms or
sets of waveforms used as deformation inputs to the model.
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Fig. 9. Model tension output for a sampling of 2 additional deformation inputs. Deformation input waves and model-generated tension waves for 12% ⌬SA cyclic
stretch and 12–25% ⌬SA cyclic stretch. For clarity, only the first few cycles are shown.
Fig. 12. Varying PEEP deformation input
and tension output. The graph on the left
depicts a 5-min varying PEEP wave with a
fast frequency of 15 cycles/min and amplitude of 25% ⌬SA superposed upon a shifting
PEEP with a 0.2-cycle/min frequency and
amplitude of 25% ⌬SA. The graph on the
right depicts tension generated by the model
for the input on the left.
50% ⌬SA (Fig. 13). In the cyclic stretch category, only stretch
at 50% ⌬SA generated tensions reaching the plasma membrane
lytic range of 3– 4 dyn/cm (34) during steady-state deformation. However, considering the entire time course rather than
just the steady-state response, stretch at 25% ⌬SA and 37%
⌬SA did generate lytic global maximum tensions, Tgmax, of
3.19 dyn/cm (Fig. 7B) and 4.72 dyn/cm, respectively, in their
first cycle before steady state was reached. In this category,
only cyclic stretch at 12% ⌬SA maintained sublytic tensions
throughout its time history, with Tgmax of 1.92 dyn/cm in the
first cycle (Fig. 9A). For this group of ventilation forms,
Na⫹-K⫹-ATPase activity (based on model-predicted CCA and
its linear relationship to Na⫹-K⫹-ATPase activity, shown in
Fig. 10) increased with a broader dynamic range from 25%
increase at 12% ⌬SA to a 327% increase at 50% ⌬SA (Fig.
13). This broader range of Na⫹-K⫹-ATPase activity increase
relative to Tpeak results from the shape of the Po function: while
Tpeak rose evenly with increasing deformation amplitude, Po,
and, in turn, Na⫹-K⫹-ATPase activity rose precipitously as
tension approached or exceeded T1/2 value of 1.4 dyn/cm.
PEEP ventilation. In the first subcategory of PEEP (waves
with the same peak deformation of 25% ⌬SA) steady-state
Tpeak was reduced as PEEP increased and tidal volumes decreased from 1.68 dyn/cm for 25% ⌬SA cyclic stretch (0
PEEP) to 0.725 dyn/cm for 25% ⌬SA PEEP, a tonic-stretch
wave (Fig. 13). In contrast, Na⫹-K⫹-ATPase dropped steeply
Simulation Results
Fig. 13. Comparison of all ventilation maneuvers. From the perspective of
stimulating Na⫹-K⫹-ATPase activity via plasma membrane tension and SAC
activity while keeping tensions from becoming high enough to cause stress
failure (shown as the shaded area to the right), high volume ventilation with
PEEP and high frequency ventilation at 37% ⌬SA yielded the highest return of
Na⫹-K⫹-ATPase stimulation for tension risk (the distance of a point from the
solid line representing an average group fit). Tonic stretch at 37% ⌬SA also
yielded a good result, but patients cannot be ventilated using tonic stretch.
Cyclic ventilation (15 cycles/min). Standard cyclic ventilation was tested with peak deformations of 12%, 25%, 37%, and
50% ⌬SA at a rate of 15 cycles/min. With increasing deformation, the peak tension of the steady-state response, Tpeak,
increased from 1.10 dyn/cm at 12% ⌬SA to 3.35 dyn/cm with
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tions included 5–30%, 10 –35%, and 20 – 45% ⌬SA, corresponding to pressure ranges of 5–20, 8 –29, and 15 to ⬎40
cmH2O. [In healthy lungs pressures greater than ⬇30 cmH2O
generally correspond to inflation beyond 100% TLC; however,
such pressures are not uncommon in critical care patients
whose lungs are less compliant than normal, healthy lungs (53,
A third PEEP subcategory used sinusoidally varying PEEP
at 0.2 cycles/min under a standard cyclic ventilation of 15
cycles/min (Fig. 12). One varying PEEP deformation wave had
a PEEP range between 0 and 10 cmH2O (0 –12.5% ⌬SA) and
constant amplitude tidal volume wave of 12.5% ⌬SA (peak
deformation ranged between 12.5 and 25% ⌬SA as PEEP
varied). A second varying PEEP wave had a varying PEEP of
0 –12 cmH2O (0 –10% ⌬SA) under a 15-cycle/min deformation
of 15% ⌬SA (peak deformation ranged between 15 and 25%
⌬SA as PEEP varied). Although shifting PEEP is not a standard clinical procedure, the idea was to test a ventilation
pattern with low, noninjurious tidal volume but still substantially inflate the lungs on a 5-min cycle to prevent derecruitment or to recruit potential collapsed regions of the lung. In
clinical ventilation an occasional deep breath or ventilator
“sigh” is sometimes used for the same purpose, which benefits
gas exchange and lung mechanics by recruiting additional,
collapsed acini (1, 36). The varying PEEP ventilation proposed
here aims to achieve the same lung recruitment volume but, by
rising to it gradually, allow the alveolar epithelial cells to
remodel their plasma membranes, decreasing plasma membrane tension and avoiding potential injury.
The third ventilation maneuvers category includes tonic
deformation and HFV. As described in the introduction, in
HFV the patient’s lungs are maintained at a high PEEP and
ventilated or “oscillated” at very low tidal volume at frequencies of 6 –15 Hz. The lung essentially remains continuously
inflated, and oxygenated air travels into the lungs through
central channel in the airways while oxygen-poor air returns
along the airway walls (38, 40, 46). Tonic deformation and
HFV are grouped together because the large baseline deformation and comparatively small amplitude of HFV yield an input
and an output very similar to tonic deformation.
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large contrast arises for Na⫹-K⫹-ATPase activity between
25% and 37% ⌬SA tonic stretch because the 1.07-dyn/cm tonic
tension of the latter is in the steep portion of the Po curve,
whereas the lower 0.73-dyn/cm tension of the former remains
in the essentially flat portion of the curve, corresponding to
almost no SAC opening.
Two HFV simulations were performed using low-amplitude
waves with high PEEP, 24.5–25% ⌬SA (25% ⌬SA HFV) and
37–37.5% ⌬SA (37% ⌬SA HFV), at 10 Hz. The resultant
tension and predicted SAC stimulation were similar to responses of similar magnitude 25% and 37% ⌬SA tonic stretch.
The extremely low amplitude kept Tpeak at a low 0.82 dyn/cm
for 25% ⌬SA HFV and 1.18 dyn/cm for 37% ⌬SA HFV.
However, the extremely high frequency translates to high
strain rate, which permitted very little relaxation within cycles
and did, therefore, produce slightly higher tensions than those
predicted for a pure tonic stretch (Fig. 13). Na⫹-K⫹-ATPase
activity levels for HFV were also slightly higher than those for
similar magnitude tonic stretch and showed the same contrast
relative to the Po curve (Fig. 13). For 25% ⌬SA HFV, Na⫹K⫹-ATPase activity increased only 11%, whereas for 37%
⌬SA HFV, Na⫹-K⫹-ATPase jumped to 111%.
Tgmax values remained low in all tonic stretch and HFV
because a slow 30-s rise was used for the first deformation.
This slow rise was originally employed in tonic-stretch simulations to emulate experimental tonic-stretch protocols and was
used in HFV as well to preserve the analogy between HFV and
tonic ventilation.
Animal and in vitro studies have demonstrated that lung
cells respond to stretch in ways both helpful and harmful to
lung cell, whole lung, and whole organism health. They have
also shown that the magnitude and frequency of cell deformation are critical determinants of how lung cells respond to
stretch. The overall goal of this study was to develop a
mathematical model linking stretch magnitude and frequency
to tension in the plasma membrane, which we propose produces positive responses, such as Na⫹-K⫹-ATPase stimulation, and negative responses, such as plasma membrane rupture
and cell death.
Traditionally, selection of ventilation volume and frequency
has been based on providing adequate gas exchange and blood
oxygenation, but as technical sophistication and understanding
of pulmonary mechanics have increased, additional clinical
objectives, including recruitment of collapsed lung regions,
improving lung compliance, and preventing ventilator-induced
injury, have been taken into consideration. Thus the medical
community, including biomedical engineers, is posed with an
optimization problem of maximizing ventilation benefits like
gas exchange and oxygenation while minimizing injury responses, including increased epithelial permeability and alveolar edema, immune and inflammatory response, and cell death
and high shear stresses associated with alveolar collapse and
reopening. To truly optimize mechanical ventilation, one has to
understand the synergistic and additive influences of the various components of a ventilation pattern, not just on the lungs
as a whole but in the acini, lung cells, and, ultimately, even
subcellular components. In this study, we have focused on the
plasma membrane, which research has shown to be an impor292 • JANUARY 2007 •
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as PEEP increased from 5% to 12% ⌬SA baseline and tension
fell below T1/2 (Fig. 13). Thus, although increasing PEEP
while decreasing tidal volume avoided lysis, Na⫹-K⫹-ATPase
activity is predicted to decrease as well. Over the entire time
course, Tgmax, always encountered in the first deformation
cycle, was 3.19 dyn/cm for every wave with a peak deformation of 25% ⌬SA, the same Tgmax for 25% ⌬SA stretch.
Because the first deformation wave is the same for all the PEEP
waves in this category, the first tension waves are also alike.
In the second PEEP subcategory, deformations had constant
amplitude (tidal volume), but peak deformation increased with
greater PEEP. Expectably, Tpeak rose as the entire deformation
wave shifted upward to higher magnitudes. Even 20 – 45%
⌬SA deformation, the greatest magnitude deformation in the
category, maintained steady-state Tpeak below the lytic tension
range with a value 2.3 dyn/cm (Fig. 13). Here, Na⫹-K⫹ATPase activity increased dynamically over the tested range
(Fig. 13) due to a greater portion of the tension wave approaching or exceeding T1/2. Of greatest concern in these simulations
was Tgmax encountered during the first deformation from an
undeformed state: 3.69 dyn/cm for 5–30% ⌬SA, 4.68 dyn/cm
for 10 –35% ⌬SA, and 6.21 dyn/cm for 10 – 45% ⌬SA.
In the varying PEEP subcategory, the steady-state output
had the same 5-min oscillatory period as the varying PEEP
input. For this subcategory Tpeak was defined as the highest
peak tension over an entire 5-min steady-state wave. Similarly,
CCA and thus Na⫹-K⫹-ATPase activity were calculated as an
average over a 5-min period rather than over a single deformation wave. For the 15% ⌬SA over 10% ⌬SA varying PEEP
simulation, Tpeak was 1.21 dyn/cm, slightly higher than the
1.04 dyn/cm Tpeak found for a similar 15–25% ⌬SA constant
PEEP simulation (Fig. 13). For the 12.5% ⌬SA over 12.5%
⌬SA PEEP simulation, Tpeak was 1.26 dyn/cm, again slightly
higher than the 1.15 dyn/cm Tpeak found for a similar 12–25%
⌬SA constant PEEP input. In contrast, average Na⫹-K⫹ATPase activity was much lower for varying PEEP (⬍1% in
both trials) due to long ranges of low tensions during the ebb
of the PEEP wave. Tgmax values were safely sublytic: 1.72
dyn/cm for the first varying PEEP wave and 1.92 dyn/cm for
the second wave, the same global peak tension found for a 12%
⌬SA cyclic wave.
In sum, the PEEP waves generally produced lower steadystate Tpeak than cyclic counterparts of the same peak deformation. However, constant amplitude (25% ⌬SA) PEEP produced
clearly higher Na⫹-K⫹-ATPase activity levels than constant
deformation (25% ⌬SA) and thus is likely to have a greater
Na⫹-K⫹-ATPase activity “return” relative to the Tpeak “risk.”
Tgmax for constant amplitude PEEP, however, was dangerously
the same, suggesting that a slow initial climb to the high tidal
volume should probably be used. The varying PEEP subcategory returned relatively low Tpeak and low Na⫹-K⫹-ATPase
activity, making it “safe” but not very effective in terms of
stimulating SACs and ultimately the Na⫹-K⫹-ATPase edema
clearance mechanism. These simulations concur with clinical
use of moderate PEEP with reduced tidal volumes.
Tonic stretch and high frequency ventilation. Tonic stretch,
analogous to a prolonged breath-hold, generally produced
relatively low Tpeak because relaxation occurred after the first
deformation and tension was not perturbed afterward. As
shown in Fig. 13, Tpeak for 25% and 37% ⌬SA tonic stretch
remained well below the lytic threshold. We also note that a
AJP-Lung Cell Mol Physiol • VOL
In all simulated waveforms, plasma membrane tensions
were high in the initial deformations before the tension response settled into a repeating steady-state response with lower
peak magnitude. This high transient tension during the first
cycles arises because no lipid insertion has occurred, leaving
tension-generating elastic unfolding to accommodate the entire
deformation. Later, after additional lipid material has inserted
into the plasma membrane, the neutral area has increased,
decreasing elastic deformations of the plasma membrane as
seen by lower peak tension in the steady-state response. To
avoid the risk of dangerously high plasma membrane tension
and cell lysis in the clinical setting, it would be unwise to
initiate ventilation in a lung that had been at rest for a
prolonged period of time with the full desired tidal volume.
Instead, one might start with a lower tidal volume and gradually increase volume of a period of the first 5–10 ventilation
cycles to allow for an accumulation of additional plasma
membrane before the full deformations of the target tidal
volume are imposed.
The theoretical model developed here reveals some interesting phenomena about the response of the alveolar epithelial
cell plasma membrane, SACs, and Na⫹-K⫹-ATPase to stretch
and suggests potential strategies for improving epithelial cell
survival and maximum, safe Na⫹-K⫹-ATPase stimulation.
Nevertheless, there is certainly room for model refinement as
better data and techniques for collecting better data become
available. Most importantly, if it becomes possible to probe
alveolar epithelial cell plasma membrane tension directly in
real time during dynamic stretch, model predictions of membrane tension can be validated directly rather than through
downstream increases in Na⫹-K⫹-ATPase activity. Fundamental assumptions of the model may also be refined as we develop
a better understanding of how tension develops in the plasma
membrane and how lipid insertion and resorption are stimulated at a molecular level. For now we have assumed that
tension in an unfolding membrane increases linearly with the
unfolding area strain. We have also assumed that lipid insertion
rate is proportional to membrane tension. Although these are
reasonable assumptions given the absence of better empirical
knowledge, with the advent of better techniques for direct
measurement of plasma membrane tension and dynamic lipid
insertion, such assumptions might be refined. Inclusion of other
mechanical factors, such as cytoskeletal influence, as they are
better understood, could contribute to model improvement as
Also important is that the model predictions made in this
communication are based on data for healthy lungs. Conversions from PEEP to TLC and from TLC to percent change in
alveolar epithelial ⌬SA were all based on normal lung models.
In previous studies, Tschumperlin (53) modeled regional deformation in diseased or injured lungs by introducing a regional heterogeneity and found that large, injurious local alveolar epithelial deformations are likely even when using safe
ventilation volumes and pressures. However, if the overall lung
compliance is decreased by disease, actual epithelial deformations would be smaller for a given PEEP than predicted. To
model diseased or injured lungs, the model input would have to
be adjusted accordingly, as data become available.
In sum, this model is a valuable first step in demonstrating
how plasma membrane unfolding and lipid insertion can work
together to determine plasma membrane tension and Na⫹-K⫹292 • JANUARY 2007 •
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tant factor in a cellular stretch response. Previously, we described how stimulation of SACs located in the plasma membrane improved Na⫹-K⫹-ATPase activity, a function that directly enhances edema clearance (19). On the other hand,
Vlahakis et al. (58, 60) have shown that stretch, especially at
high rates, can lead to alveolar epithelial cell plasma membrane
stress failure. The goal of this research was to combine and
extend limited experimental data regarding epithelial cell response to stretch by developing a predictive, mathematical
The results of these model simulations indicate that mechanical ventilation frequency, peak deformation, baseline or endexpiratory deformation, and ventilation history, as in the case
of preconditioning, can play a critical role in plasma membrane
tension, SAC opening, and Na⫹-K⫹-ATPase stimulation. They
also demonstrate that waveforms can possibly be tailored to
avoid lytic membrane tension while still achieving relatively
high lung volumes required for adequate gas exchange and
collapsed lung recruitment and maintaining a sublytic degree
of membrane tension needed for maximal Na⫹-K⫹-ATPase
Of clinical significance, constant PEEP ventilation, especially with constant amplitude and relatively high volume,
appeared to produce the highest Na⫹-K⫹-ATPase stimulation
relative to Tpeak (Fig. 13). While Tpeak and Tgmax remained
sublytic, PEEP ventilation generated relatively high predictions of Na⫹-K⫹-ATPase stimulation relative to similar magnitude deformation without PEEP. This is because the baseline
deformation forced a higher mean tension closer to T1/2,
maintaining a high probability of SAC opening and implying
greater Na⫹-K⫹-ATPase stimulation. But, because relaxation
had occurred over the static PEEP baseline, Tpeak remained
lower than in non-PEEP simulations. Three categories of PEEP
ventilation were investigated: same peak deformation, same
deformation amplitude, and slowly varying PEEP sinusoidally
at 0.2 cycles/min. Slowly varying PEEP provided benefits
similar to constant PEEP ventilation modes but to a lesser
degree. Tpeak with varying PEEP was slightly higher than
similar amplitude constant PEEP ventilation (once every 5
min) because full relaxation was not able to occur as it could
with constant PEEP. However, Na⫹-K⫹-ATPase stimulation
was much lower in the former because tensions only rose every
5 min and the higher average tension of constant PEEP was not
maintained. From the perspective of the whole lung, slowly
varying PEEP might be valuable as a recruitment maneuver,
but from the perspective of maintaining Na⫹-K⫹-ATPase
while avoiding dangerous peak tension, constant PEEP appears
to be a better option.
High frequency ventilation also appears to provide potential
clinical benefit by increasing Na⫹-K⫹-ATPase activity with
relatively low Tpeak (Fig. 13). Because it almost mimics tonic
stretch, tension remains nearly constant. At that level, Na⫹K⫹-ATPase activity can be stimulated and lysis avoided by
choosing high PEEP and smaller tidal volume. Therefore,
despite other difficulties associated with high frequency ventilation, such as patient discomfort and recent doubts of the
efficacy of HFV improving the risk of chronic lung disease
(44), HFV does appear to be a useful strategy from the
perspective of optimal Na⫹-K⫹-ATPase stimulation while
avoiding plasma membrane injury.
Support was provided by National Heart, Lung, and Blood Institute Grant
1. Baldwin DN, Suki B, Pillow JJ, Roiha HL, Minocchieri S, and Frey U.
Effect of sighs on breathing memory and dynamics in healthy infants.
J Appl Physiol 97: 1830 –1839, 2004.
2. Berrios JC and Hubmayr RD. Deforming stress triggers endocytosis in
alveolar epithelial cells (Abstract). Am J Respir Crit Care Med 167: A57,
3. Brower RG, Lanken PN, MacIntyre N, Matthay MA, Morris A,
Ancukiewicz M, Schoenfeld D, and Thompson BT. Higher versus lower
positive end-expiratory pressures in patients with the acute respiratory
distress syndrome. N Engl J Med 351: 327–336, 2004.
4. Chen CS and Ingber DE. Tensegrity and mechanoregulation: from
skeleton to cytoskeleton. Osteoarthritis Cartilage 7: 81–94, 1999.
5. Dai J and Sheetz MP. Cell membrane mechanics. Methods Cell Biol 55:
157–171, 1998.
6. Dai J and Sheetz MP. Regulation of endocytosis, exocytosis, and shape
by membrane tension. Cold Spring Harb Symp Quant Biol 60: 567–571,
7. Dai J, Sheetz MP, Wan X, and Morris CE. Membrane tension in
swelling and shrinking molluscan neurons. J Neurosci 18: 6681– 6692,
8. Dai J, Ting-Beall HP, and Sheetz MP. The secretion-coupled endocytosis correlates with membrane tension changes. J Gen Physiol 110: 1–10,
9. Dong C and Skalak R. Leukocyte deformability: finite element modeling
of large viscoelastic deformation. J Theor Biol 158: 173–193, 1992.
10. Dong C, Skalak R, and Sung KL. Cytoplasmic rheology of passive
neutrophils. Biorheology 28: 557–567, 1991.
11. Dong C, Skalak R, Sung KL, Schmid-Schonbein GW, and Chien S.
Passive deformation analysis of human leukocytes. J Biomech Eng 110:
27–36, 1988.
12. Dos Santos CC and Slutsky AS. Mechanisms of ventilator-induced lung
injury: a perspective. Invited Review. J Appl Physiol 89: 1645–1655,
13. Dreyfuss D and Saumon G. Role of tidal volume, FRC, and endinspiratory volume in the development of pulmonary edema following
mechanical ventilation. Am Rev Respir Dis 148: 1194 –1203, 1993.
14. Dreyfuss D and Saumon G. Ventilator-induced lung injury: lessons from
experimental studies. Am J Respir Crit Care Med 157: 294 –323, 1998.
15. Dreyfuss D, Soler P, Basset G, and Saumon G. High inflation pressure
pulmonary edema. Respective effects of high airway pressure, high tidal
AJP-Lung Cell Mol Physiol • VOL
volume, and positive end-expiratory pressure. Am Rev Respir Dis 137:
1159 –1164, 1988.
Fisher JL. Mechanisms and means of Na⫹-K⫹-ATPase activation during
alveolar epithelial stretch (Doctoral Thesis). Philadelphia, PA: University
of Pennsylvania, 2004.
Fisher JL, Levitan I, and Margulies SS. Changes in alveolar epithelial
cell plasma membrane surface area with static stretch. 2003 Summer
Bioengineering Conference of the ASME Bioengineering Division, Key
Biscayne, Florida, 2003.
Fisher JL, Levitan I, and Margulies SS. Plasma membrane surface
increases with tonic stretch of alveolar epithelial cells. Am J Respir Cell
Mol Biol 31: 200 –208, 2004.
Fisher JL and Margulies SS. Na⫹-K⫹-ATPase activity in alveolar
epithelial cells increases with cyclic stretch. Am J Physiol Lung Cell Mol
Physiol 283: L737–L746, 2002.
Forgacs G. On the possible role of cytoskeletal filamentous networks in
intracellular signaling: an approach based on percolation. J Cell Sci 108:
2131–2143, 1995.
Gajic O, Lee J, Doerr CH, Berrios JC, Myers JL, and Hubmayr RD.
Ventilator-induced cell wounding and repair in the intact lung. Am J
Respir Crit Care Med 167: 1057–1063, 2003.
Hamill OP and Martinac B. Molecular basis of mechanotransduction in
living cells. Physiol Rev 81: 685–740, 2001.
Hao M and Maxfield FR. Characterization of rapid membrane internalization and recycling. J Biol Chem 275: 15279 –15286, 2000.
Hase CC, Le Dain AC, and Martinac B. Purification and functional
reconstitution of the recombinant large mechanosensitive ion channel
(MscL) of Escherichia coli. J Biol Chem 270: 18329 –18334, 1995.
Hochmuth FM, Shao JY, Dai J, and Sheetz MP. Deformation and flow
of membrane into tethers extracted from neuronal growth cones. Biophys
J 70: 358 –369, 1996.
Hochmuth RM. Cell biomechanics: a brief overview. J Biomech Eng 112:
233–234, 1990.
Hochmuth RM. Micropipette aspiration of living cells. J Biomech 33:
15–22, 2000.
Ingber DE, Dike L, Hansen L, Karp S, Liley H, Maniotis A, McNamee
H, Mooney D, Plopper G, Sims J, and et al. Cellular tensegrity:
exploring how mechanical changes in the cytoskeleton regulate cell
growth, migration, and tissue pattern during morphogenesis. Int Rev Cytol
150: 173–224, 1994.
Kloda A and Martinac B. Structural and functional differences between
two homologous mechanosensitive channels of Methanococcus jannaschii. EMBO J 20: 1888 –1896, 2001.
Le Dain AC, Saint N, Kloda A, Ghazi A, and Martinac B. Mechanosensitive ion channels of the archaeon Haloferax volcanii. J Biol Chem
273: 12116 –12119, 1998.
Lewis SA and de Moura JL. Incorporation of cytoplasmic vesicles into
apical membrane of mammalian urinary bladder epithelium. Nature 297:
685– 688, 1982.
Markin VS and Martinac B. Mechanosensitive ion channels as reporters
of bilayer expansion. A theoretical model. Biophys J 60: 1120 –1127,
Mills LR and Morris CE. Neuronal plasma membrane dynamics evoked
by osmomechanical perturbations. J Membr Biol 166: 223–235, 1998.
Morris CE and Homann U. Cell surface area regulation and membrane
tension. J Membr Biol 179: 79 –102, 2001.
Morris CE, Lesiuk H, and Mills LR. How do neurons monitor their
mechanical status? Biol Bull 192: 118 –120, 1997.
Mutch WA, Harms S, Ruth Graham M, Kowalski SE, Girling LG,
and Lefevre GR. Biologically variable or naturally noisy mechanical
ventilation recruits atelectatic lung. Am J Respir Crit Care Med 162:
319 –323, 2000.
Needham D and Hochmuth RM. A sensitive measure of surface stress in
the resting neutrophil. Biophys J 61: 1664 –1670, 1992.
Priebe GP and Arnold JH. High-frequency oscillatory ventilation in
pediatric patients. Respir Care Clin N Am 7: 633– 645, 2001.
Raucher D and Sheetz MP. Characteristics of a membrane reservoir
buffering membrane tension. Biophys J 77: 1992–2002, 1999.
Ritacca FV and Stewart TE. Clinical review: high-frequency oscillatory
ventilation in adults–a review of the literature and practical applications.
Crit Care 7: 385–390, 2003.
Sachs F and Morris CE. Mechanosensitive ion channels in nonspecialized cells. Rev Physiol Biochem Pharmacol 132: 1–77, 1998.
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ATPase stimulation in alveolar epithelial cells. The model
provides a means of testing and comparing ventilation strategies from the perspective of plasma membrane tension and
SAC stimulation, which are important elements in overall
VILI. Using the model, we have identified constant PEEP
ventilation, especially with constant amplitude and relatively
high volume, and high frequency ventilation as leading mechanical ventilator maneuvers for stimulating moderate stretchinduced responses while preventing dangerously high plasma
membrane tension. As shown in Fig. 13, these maneuvers
predicted the highest Na⫹-K⫹-ATPase stimulation relative to
peak membrane tension. It should also be noted that Na⫹-K⫹ATPase stimulation is only one of many stretch-stimulated
responses that clinicians might want to optimize, and optimal
ventilation maneuvers may differ among desired responses.
Ultimately, with the development of better methods for collecting more complete and more specific data for mechanically
stretched alveolar epithelial cells and with better modeling of
the cytoskeleton and cytoskeletal plasma membrane interactions, refined versions of this model and more sophisticated
models for other responses can be built on the theoretical and
empirical foundation developed here.
AJP-Lung Cell Mol Physiol • VOL
54. Tschumperlin DJ and Margulies SS. Alveolar epithelial surface areavolume relationship in isolated rat lungs. J Appl Physiol 86: 2026 –2033,
55. Tschumperlin DJ and Margulies SS. Equibiaxial deformation-induced
injury of alveolar epithelial cells in vitro. Am J Physiol Lung Cell Mol
Physiol 275: L1173–L1183, 1998.
56. Tschumperlin DJ, Oswari J, and Margulies SS. Deformation-induced
injury of alveolar epithelial cells. Effect of frequency, duration, and
amplitude. Am J Respir Crit Care Med 162: 357–362, 2000.
57. Vlahakis NE and Hubmayr RD. Invited review: plasma membrane stress
failure in alveolar epithelial cells. J Appl Physiol 89: 2490 –2496; discussion 2497, 2000.
58. Vlahakis NE and Hubmayr RD. Response of alveolar cells to mechanical stress. Curr Opin Crit Care 9: 2– 8, 2003.
59. Vlahakis NE, Schroeder MA, Pagano RE, and Hubmayr RD. Deformation-induced lipid trafficking in alveolar epithelial cells. Am J Physiol
Lung Cell Mol Physiol 280: L938 –L946, 2001.
60. Vlahakis NE, Schroeder MA, Pagano RE, and Hubmayr RD. Role of
deformation-induced lipid trafficking in the prevention of plasma membrane stress failure. Am J Respir Crit Care Med 166: 1282–1289, 2002.
61. Wan X, Harris JA, and Morris CE. Responses of neurons to extreme
osmomechanical stress. J Membr Biol 145: 21–31, 1995.
62. West JB. Respiratory physiology: the essentials. Baltimore, MD: Williams & Wilkins, 1990.
63. Yeung A and Evans E. Cortical shell-liquid core model for passive flow
of liquid-like spherical cells into micropipets. Biophys J 56: 139 –149,
64. Zhelev DV, Needham D, and Hochmuth RM. Role of the membrane
cortex in neutrophil deformation in small pipets. Biophys J 67: 696 –705,
65. Zhu C, Bao G, and Wang N. Cell mechanics: mechanical response, cell
adhesion, and molecular deformation. Annu Rev Biomed Eng 2: 189 –226,
292 • JANUARY 2007 •
Downloaded from on May 6, 2010
42. Satcher RL Jr and Dewey CF Jr. Theoretical estimates of mechanical
properties of the endothelial cell cytoskeleton. Biophys J 71: 109 –118,
43. Schneider SW. Kiss and run mechanism in exocytosis. J Membr Biol 181:
67–76, 2000.
44. Schreiber MD, Gin-Mestan K, Marks JD, Huo D, Lee G, and Srisuparp P. Inhaled nitric oxide in premature infants with the respiratory
distress syndrome. N Engl J Med 349: 2099 –2107, 2003.
45. Sheetz MP and Dai JW. Modulation of membrane dynamics and cell
motility by membrane tension. Trends Cell Biol 6: 85– 89, 1996.
46. Singh JM and Stewart TE. High-frequency oscillatory ventilation in
adults with acute respiratory distress syndrome. Curr Opin Crit Care 9:
28 –32, 2003.
47. Stamenovic D and Coughlin MF. The role of prestress and architecture
of the cytoskeleton and deformability of cytoskeletal filaments in mechanics of adherent cells: a quantitative analysis. J Theor Biol 201: 63–74,
48. Stroetz RW, Vlahakis NE, Walters BJ, Schroeder MA, and Hubmayr
RD. Validation of a new live cell strain system: characterization of plasma
membrane stress failure. J Appl Physiol 90: 2361–2370., 2001.
49. Sukharev S. Purification of the small mechanosensitive channel of Escherichia coli (MscS): the subunit structure, conduction, and gating characteristics in liposomes. Biophys J 83: 290 –298, 2002.
50. Tabarean IV and Morris CE. Membrane stretch accelerates activation
and slow inactivation in Shaker channels with S3–S4 linker deletions.
Biophys J 82: 2982–2994, 2002.
51. Tsai MA, Frank RS, and Waugh RE. Passive mechanical behavior of
human neutrophils: effect of cytochalasin B. Biophys J 66: 2166 –2172,
52. Tsai MA, Frank RS, and Waugh RE. Passive mechanical behavior of
human neutrophils: power-law fluid. Biophys J 65: 2078 –2088, 1993.
53. Tschumperlin DJ. Deformation and injury of the alveolar epithelium
(Doctoral Thesis). Philadelphia: University of Pennsylvania, 1998.
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