R•out Tdð T−1 out − T−1 in Þ, where R•out is the outgoing
long-wave radiation and Tin, Tout, and Td are the
mean temperature of atmospheric heat input,
output, and dissipation, respectively. Observations
of recent tropospheric warming [figures 2.26 and
2.27 in (32)] show that temperature trends are
somewhat uniform in the vertical, which suggests that the difference T −1 out − T −1 in might increase
more slowly than either Tin or Tout. This slower
increase may explain why d Q• total does not follow a
surface Clausius-Clapeyron scaling and why one
would expect moist processes to limit the work
output in simulations with anthropogenic forcing.
Simulations over a wider range of climates would
help verify this hypothesis.
Our comparison of thermodynamic cycles in
CESM and MERRA show many similarities; however, we find that CESM requires less power to
maintain its hydrological cycle than the reanalysis, due to the smaller amplitude of its moistening inefficiencies. We suggest that this difference
might be a consequence of the idealized nature
of parameterized convection schemes, and it is
likely that it might also influence the response of
CESM to anthropogenic forcing. Typically, convection schemes artificially transport moisture
along a moist adiabat without accounting for the
work needed to lift this moisture, but in the real
world, this work is necessary to sustain precipitation. Any increase in global precipitation therefore requires an increase in work output; otherwise,
precipitation would have to become more efficient, for example, by reducing the frictional dissipation of falling hydrometeors (11, 12). This is
one reason we should interpret the constraint in
work output in CESM as a constraint on the large-scale motions and not on the unresolved subgrid-scale convective events.
Our work illustrates a major constraint on the
large-scale global atmospheric engine: As the climate warms, the system may be unable to increase its total entropy production enough to
offset the moistening inefficiencies associated
with phase transitions. This suggests that in a
future climate, the global atmospheric circulation
might comprise highly energetic storms due to
explosive latent heat release, but in such a case,
the constraint on work output identified here
will result in fewer numbers of such events.
Earth’s atmospheric circulation thus suffers from
the “water in gas problem” observed in simulations of tropical convection (6), where its ability
to produce work is constrained by the need to
convert liquid water into water vapor and back
again to tap its fuel.
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Materials and Methods
Figs. S1 to S5
9 June 2014; accepted 3 December 2014
Fei Chen,1 Paul W. Tillberg,2 Edward S. Boyden1,3,4,5,6†
In optical microscopy, fine structural details are resolved by using refraction to magnify
images of a specimen. We discovered that by synthesizing a swellable polymer network
within a specimen, it can be physically expanded, resulting in physical magnification.
By covalently anchoring specific labels located within the specimen directly to the polymer
network, labels spaced closer than the optical diffraction limit can be isotropically
separated and optically resolved, a process we call expansion microscopy (ExM). Thus,
this process can be used to perform scalable superresolution microscopy with
diffraction-limited microscopes. We demonstrate ExM with apparent ~70-nanometer
lateral resolution in both cultured cells and brain tissue, performing three-color
superresolution imaging of ~107 cubic micrometers of the mouse hippocampus with a
conventional confocal microscope.
Microscopy has facilitated the discovery of many biological insights by optically magnifying images of structures in fixed cells and tissues. We here report that physical magnification of the specimen
itself is also possible.
We first set out to see whether a well-known
property of polyelectrolyte gels—namely, that
dialyzing them in water causes expansion of
the polymer network into extended conforma-
tions (Fig. 1A) (1)—could be performed in a bi-
ological sample. We infused into chemically
fixed and permeabilized brain tissue (Fig. 1B)
sodium acrylate, a monomer used to produce
superabsorbent materials (2, 3), along with the
comonomer acrylamide and the cross-linker
N-N′-methylenebisacrylamide. After triggering
free radical polymerization with ammonium
persulfate (APS) initiator and tetramethylethy-
lenediamine (TEMED) accelerator, we treated
the tissue-polymer composite with protease to
homogenize its mechanical characteristics. After
proteolysis, dialysis in water resulted in a 4.5-fold
linear expansion, without distortion at the level
of gross anatomy (Fig. 1C). Digestion was uniform
throughout the slice (fig. S1). Expanded speci-
mens were transparent (fig. S2) because they
consist largely of water. Thus, polyelectrolyte gel
expansion is possible when the polymer is em-
bedded throughout a biological sample.
We developed a fluorescent labeling strategy
compatible with the proteolytic treatment and
subsequent tissue expansion described above,
SCIENCE sciencemag.org 30 JANUARY 2015 • VOL 347 ISSUE 6221 543
1Department of Biological Engineering, Massachussetts
Institute of Technology (MIT), Cambridge, MA, USA.
2Department of Electrical Engineering and Computer
Science, MIT, Cambridge, MA, USA. 3Media Lab, MIT,
Cambridge, MA, USA. 4McGovern Institute, MIT, Cambridge,
MA, USA. 5Department of Brain and Cognitive Sciences,
MIT, Cambridge, MA, USA. 6Center for Neurobiological
Engineering, MIT, Cambridge, MA, USA.
*These authors contributed equally to this work. †Corresponding
author. E-mail: firstname.lastname@example.org
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