Optimal vein density in artificial and real leaves

The long evolution of vascular plants has resulted in a tremendous
variety of natural networks responsible for the evaporatively
driven transport of water. Nevertheless, little is known about the
physical principles that constrain vascular architecture. Inspired by
plant leaves, we used microfluidic devices consisting of simple
parallel channel networks in a polymeric material layer, permeable
to water, to study the mechanisms of and the limits to evaporationdriven flow. We show that the flow rate through our biomimetic
leaves increases linearly with channel density (1/d) until the distance between channels (d) is comparable with the thickness of the
polymer layer (
), above which the flow rate saturates. A comparison with the plant vascular networks shows that the same optimization criterion can be used to describe the placement of veins
in leaves. These scaling relations for evaporatively driven flow
through simple networks reveal basic design principles for the
engineering of evaporation–permeation-driven devices, and highlight the role of physical constraints on the biological design of
leaves.

Limbless undulatory propulsion on land

We analyze the lateral undulatory motion of a natural or artificial
snake or other slender organism that ‘‘swims’’ on land by propagating retrograde flexural waves. The governing equations for the
planar lateral undulation of a thin filament that interacts frictionally with its environment lead to an incomplete system. Closures
accounting for the forces generated by the internal muscles and
the interaction of the filament with its environment lead to a
nonlinear boundary value problem, which we solve using a combination of analytical and numerical methods. We find that the
primary determinant of the shape of the organism is its interaction
with the external environment, whereas the speed of the organism
is determined primarily by the internal muscular forces, consistent
with prior qualitative observations. Our model also allows us to
pose and solve a variety of optimization problems such as those
associated with maximum speed and mechanical efficiency, thus
defining the performance envelope of this mode of locomotion.

Life and times of a cellular bleb

Blebs are spherical cellular protrusions that occur in many physiological situations. Two distinct phases make up
the life of a bleb, each of which have their own biology and physics: expansion, which lasts ;30 s, and retraction, which lasts
;2 min. We investigate these phases using optical microscopy and simple theoretical concepts, seeking information on
blebbing itself, and on cytomechanics in general. We show that bleb nucleation depends on pressure, membrane-cortex
adhesion energy, and membrane tension, and test this experimentally. Bleb growth occurs through a combination of bulk flow of
lipids and delamination from the cell cortex via the formation and propagation of tears. In extreme cases, this can give rise to a
traveling wave around the cell periphery, known as ‘‘circus movement.’’ When growth stalls, an actin cortex reforms under the
bleb membrane, and retraction starts, driven by myosin-II. Using flicker spectroscopy, we find that retracting blebs are fivefold
more rigid than expanding blebs, an increase entirely explained by the properties of the newly formed cortical actin mesh.
Finally, using artificially nucleated blebs as pressure sensors, we show that cells rounded up in mitosis possess a substantial
intracellular pressure.

Settling and swimming of flexible fluid lubricated foils

We study the dynamics of a flexible foil immersed in a fluid and moving close to a rigid wall.
Lubrication theory allows us to derive equations of motion for the foil and thus examine the passive
settling and the active swimming of a foil. This also allows us to partly answer the long-standing question
in cartoon physics—can carpets fly? Our analysis suggests a region in parameter space where one may
realize this dream and move the virtual towards reality.

Force of an actin spring

Cellular movements are produced by forces. Typically, cytoskeletal proteins such as microtubules and actin
filaments generate forces via polymerization or in conjunction with molecular motors. However, the fertilization of a Limulus
polyphemus egg involves a third type of actin-based cellular engine—a biological spring. During the acrosome reaction, a
60-mm long coiled and twisted bundle of actin filaments straightens and extends from a sperm cell, penetrating the vitelline layer
surrounding the egg. A subtle overtwist of 0.2/subunit underlies the mechanochemical basis for the extension of this actin
spring. Upon calcium activation, this conformational strain energy is converted to mechanical work, generating the force required to extend the bundle through the vitelline layer. In this article, we stall the extension of the acrosome bundle in agarose
gels of different concentrations. From the stall forces, we estimate a maximum force of 2 nN and a puncturing pressure of 1.6
MPa. We show the maximum force of extension is three times larger than the force required to puncture the vitelline layer. Thus,
the elastic strain energy stored in the acrosome bundle is more than sufficient to power the acrosome reaction through the
egg envelope.