Life sciences · the experiment
Beat Einstein's ceiling
DNA droplets in a tangle of actin, a rule that carries Einstein's name, a measurement that beats it by far. Four questions, from beginner to expert, on a theoretical ceiling and how to break through it.
1 · Say what the droplets do
Beginner
What did the DNA droplets, filling under 10% of the volume, do to the actin mesh?
2 · Compute Einstein's ceiling
Einstein's rule: stiffening factor = 1 + 5ϕ/2, where ϕ is the fraction of the volume filled by perfectly rigid inclusions.
With 10 µM of nanostars, the droplets fill 2.5% of the volume. Measured factor: 2.2 ± 0.3.
Intermediate
What factor does Einstein's rule allow at most for these droplets on their own?
3 · Find the threshold for bare droplets
The dragged zone extends one droplet radius beyond the surface: each inclusion's effective volume is multiplied by 8.
The enlarged inclusions link into a continuous web above about 30% of the volume.
Expert
What fraction of the volume must the droplets themselves fill, at least, to reach that threshold?
4 · Explain the finite stiffness
At 38 µM and 10 °C, the enlarged inclusions are linked into a continuous web. With perfectly rigid inclusions, such a web would make the stiffness grow without limit.
Expert
Why does the stiffening stay finite here?
Ceiling beaten
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