Physicists investigate egg cells to study the properties of flows interacting with cellular matter.
BY DEBDUTTTA PAUL
When we leave sugar in a cup of tea (or coffee, if you prefer), it takes a long time for the sugar to dissolve. So, we stir the sugar by generating a flow in the tea which interacts with the sugar and dissolves it. Similarly, egg cells generate storms within the ‘cytoplasm’, the fluid inside them, to transport and mix cellular matter.
Humans are born from their mother’s eggs. Fertilised egg cells have a lot to achieve in their relatively short lives. They have to organise cellular matter and transport it in a clockwork-like factory to grow into embryos, which look very different from the egg’s primary stages. The development would be impossible if the cellular matter simply diffused from one site to another — taking hours instead of seconds. “Diffusion is an extremely slow process,” said ICTS’s Brato Chakrabarti, who studies cytoplasmic flow along with his colleagues. The group has tallied unprecedented details of flows in fruit flies’ egg cells with predictions from computer simulations, revealing a perfect match.
Biologists’ favourite model
Fruit flies or Drosophila are biologists’ model organisms, and over the years, the community has figured out many details of the fruit fly’s growth and reproduction. So, they conduct experiments on Drosophila to study processes that are common across organisms. Physicists have been using the biology knowledge to their advantage in studying cellular flows.
Cellular flow in egg cells is quite different from other flows, like winds in the atmosphere. Instead, cellular flows are similar to glacial flows. The cytoplasm is quite dense and viscous and stuck in an enclosed environment. So, the cells whip up cytoplasmic storms and keep the factory running, finally developing into an embryo. The physics of the flows tell us how.
Microtubules, molecular machines, and coupled flows
Take the fruit fly egg cells, which are ellipsoidal, about 0.1 to 0.3 millimetres in length. “The cells’ boundaries are coated by thin hair-like filaments called microtubules,” said Brato. The microtubules are about ten times smaller in length (about 15 micrometres) and another thousand times smaller in breadth (about 10 nanometres) — and look like tinier versions of human hair.
The microtubules, anchored on the cell’s boundary, behave like highway tracks for molecular machines called ‘motor proteins’, which transport proteins and other functional material across the cell.
As multiple motor proteins move, the microtubules bend and buckle. The collective movement of many microtubules acts like many people swimming in a pool. They change the flow around them, which affects the motor proteins, which affect the flow. “These interactions collectively give rise to the emergent flows,” said Brato.
As a result, the fluid mechanics problem needs to consider all the interactions, transport, and geometry. Physicists working on fluid mechanics call such mathematical problems the ‘fluid structure interaction (FSI)’ problems. Another example of an FSI problem attempts to answer why a flag flaps in the wind.
“Wind flow deforms a flag, but the flag, in turn, affects the wind flow,” Brato said.
In egg cells, the cellular storms are connected to the microtubules’ deformations. “In isolation, they’re just stupid oscillators,” said Brato. Their powers combine to create spontaneous waves, which help the cell transport materials and information efficiently.
Olenka Jain, a graduate student at Princeton University and Brato’s collaborator, explained that motor proteins carrying cellular matter through the cytoplasm create a complex interaction cycle consisting of the proteins, the microtubules, and the flow. That means the independent bits of information the physicists need to model the entire flow run into a million. Even the most powerful supercomputers take anywhere between a week and a month to recreate the flows.
Too many calculations
To reduce the complexities, the researchers created a mathematical toy model for microtubule deformation. Using this model and numerical techniques which reduce the numerical challenges significantly, they cut down the calculations to about an hour on a laptop. They observed the flows settle down into patterns which sustain throughout the cell.
Earlier this year, Brato and his collaborators demonstrated the model can create flows which transport material all across the egg cells. Their study revealed that irrespective of what situation the flow starts with, a relatively simple flow pattern emerges.
However, the paper considered the cells to be spherical. In reality, they resemble ellipsoids or are oval-shaped, and imperfections in shape make them more complex, said Olenka, one of the authors of their more recent arXiv-ed paper.
In this work, the physicists investigated the role of the simplest imperfection: geometry. They have shown the ellipsoid nature of the egg cells still gives rise to flows similar to the spherical case. Even when the team used their simulations to mimic placing a nucleus within the cell, the factory kept running.
Cellular flows are symmetric, with no preferred direction. Still, they figured the cell’s ellipsoidal geometry helped it pick a direction, setting the stage for its development into the embryo’s head, body, and tail. “This [is an] interesting phenomenon where geometry can pick a solution of some problem in biology,” said Olenka.
‘An ill-posed inverse problem’
The researchers have gone beyond the simulations and tested their simulations against data. Olenka cultured fruit flies’s eggs in the Princeton laboratory and imaged the eggs under the microscope. Each video she captured shows about an hour’s long flow within Drosophila egg cells.
But, these observations capture only projections of the flow in two dimensions, whereas the simulations are in three dimensions.
Olenka said it is an “ill-posed inverse problem.” Still, when she used the earlier simulations and tweaked the input parameters to study the data, the observations matched the theory exactly.
The results indicate the extremely complex biological problem can now be solved with the unique blend of calculations on supercomputers and precise imaging. The physicists are now on a quest to understand embryo development in all its details.
To know more, read the following papers by the authors.
- Olenka Jain, Brato Chakrabarti, Reza Farhadifar, Elizabeth R. Gavis, Michael J. Shelley, Stanislav Y. Shvartsman: Geometric Effects in Large Scale Intracellular Flows
- Brato Chakrabarti, Manas Rachh, Stanislav Y. Shvartsman, Michael J. Shelley: Cytoplasmic stirring by active carpets
- Sayantan Dutta, Reza Farhadifar, Wen Lu, Gokberk Kabacaoğlu, Robert Blackwell, David B. Stein, Margot Lakonishok, Vladimir I. Gelfand, Stanislav Y. Shvartsman, Michael J. Shelley: Self-organized intracellular twisters
The author thanks Brato Chakrabarti and Olenka Jain for discussions.