The complicated 3D swimming motion of some types of algae has been reconstructed from 2D images. The work was done by a team of biophysicists in Italy and Germany, who say that their results suggest a “universal law” of motion for flagella propulsion. This, they claim, could be useful for the development of bio-inspired robots, particularly with medical applications.

Many swimming microorganisms propel themselves with whip-like structures called flagella. Most propulsion strategies involve planar and helical beating patterns, which are well studied. However, euglenids – a group of algae mainly found in freshwater – have a single anterior flagellum that moves in a fast spinning motion that deviates from these commonly-seen patterns. The movement is often described as a “spinning lasso” or “figure eight”, but as its complex 3D trajectory makes it difficult to study.

Now, Antonio DeSimone DeSimone at the International School for Advanced Studies in Trieste, Italy, and colleagues have used 2D images of specimens of the 50 μm long euglenid, Euglena gracilis to create 3D reconstructions of the beating flagellum’s path and the motion of the organism.

Filling a gap

“The direct observation techniques available today do not allow us to see the moving body in the third dimension with sufficient spatial and temporal detail,” explains DeSimone. “Our technique, which can be generalized to all flagellated organisms, and therefore useful for studying other species, fills this gap.”

Using a high-speed video camera, the researchers took standard 2D microscopy images at a high frame rate and combined these with a mathematical model based around some simple assumptions on the physics governing the propulsion system. In particular, the low Reynolds number hydrodynamics of the system puts limits on the possible trajectories and rotations of the algae.

The team says that its approach is like that used centuries ago by Johannes Kepler and Isaac Newton to identify the orbits of solar system planets around the Sun. The planets can appear to follow complicated and mysterious paths. But once it is understood that the planets are all orbiting the Sun it is possible to calculate and explain their movements.

“It’s a bit like knowing that the Earth revolves around an axis as it makes its orbit, and having a sequence of two-dimensional images – many disks – of the planet, just as it appears if seen from the Sun. By mounting the images in the correct orientations, you can reconstruct the 3D map of the Earth,” explains DeSimone.

Reference axes

Likewise, once reference axes for the movement of the euglenid are identified, it is possible to create a 3D reconstruction of the movement of the body and the shapes of the beating flagellum, from a set of 2D images.

Although the flagellum of the alga is attached to the front of the organism the researchers say that its movement cannot be adequately summarized as a backward beating to push the cell forward. They explain that the flagellum beats laterally, spanning a complex sequence of non-planar shapes and that no obvious symmetries can be exploited to guess the way the body moves. They add that the motion involves spiralling trajectories coupled to body rotations (see video).

The researchers say that their results fit with experimental observation and suggest that all flagellated microorganisms move with helical trajectories when they beat their flagellum periodically in time. This, they say, suggests a “universal law” of motion for flagella propulsion.

Tiny robots

The researchers say that understanding how flagellated organisms move could help with the development of tiny bio-inspired robots. “For years, many laboratories in the world have been studying how to exploit the way biological organisms move and apply it to technology. Small organisms such as eugenids are particularly interesting for medical applications, for example,” DeSimone says.

The research is described in the Proceedings of the National Academies of Sciences.