The motions involved in writing, waving goodbye or turning a jumprope all obey the same law of movement. As far back as the 19^th century, observers noted that sharper curves are tackled at lower speeds. Anyone thinking of violating this law should think again: Experiments have shown it is nearly impossible to force healthy subjects to generate arm movements that do not conform to this law, today known as the 2/3 power law of motion.

 

Why do the body’s movements comply with the power law? Some have argued that these forms of body movement are simply a byproduct of muscular action. Recent experiments, however, have shown that not only does the 2/3 power law constrain movement generation, it also comes into play when we visually perceive motion. In one such experiment, volunteers were asked to observe a dot on a computer screen that rotated around an ellipse according to one of three scenarios: 1: the dot travels around the ellipse at constant speed; 2: the dot speeds up at the straighter segments of the ellipse, and slows down as it rounds the bend; 3: the dot slows down in the straighter segment of the ellipse and speeds up at the bend. Contrary to intuition, the dot that appeared to the subjects to move more uniformly was not the first dot, which actually moves at a constant speed, but rather the second dot – the one that obeys the 2/3 power law. 

 

Until now, there was little evidence to suggest neural underpinnings to the 2/3 power law, and no one had been able to identify the brain areas that may be involved. Ph.D. student Eran Dayan and Prof. Tamar Flash of the Weizmann Institute’s Computer Science and Applied Mathematics Department, Nava Levit-Binnun of the Institute’s Physics of Complex Systems Department, and Dr. Talma Hendler of the Tel Aviv Sourasky Medical Center, Israel, in collaboration with Antonino Casile and Martin Giese of the Hertie Institute for Clinical Brain Research, Tubingen, Germany, have identified, for the first time, specific brain regions that are selectively activated in response to motion that obeys the 2/3 power law. These findings suggest that the body’s 2/3 power law of motion is controlled by neural mechanisms arising in the brain, as opposed to being a by-product of muscular action. The implication is that such trajectories are planned in detail in the brain prior to their execution. Their findings have recently been published in the journal Proceedings of the National Academy of Sciences (PNAS), USA.

 

In a variation on the original behavioral experiment, the team asked volunteers to observe a cloud of dots rotating around an ellipse according to the same three scenarios while fixing their eyes on a point in the middle of the ellipse. During some experiments, their eye movements were also monitored using special equipment, to eliminate the possibility that the eye movements themselves accounted for the observed results. With the help of functional magnetic resonance imaging, the scientists mapped the areas of the brain that were activated during the task. The results show that different areas of the brain are activated according to the type of motion the volunteers observe. The regions that respond to the 2/3 power law of motion are those that subserve the generation of movement, visual motion processing and action observation. The activation of these areas in response to the 2/3 power law of motion is much stronger than the response to any other form of motion.

 

Why does the brain seem to prefer the 2/3 power law of motion? And why do separate neuronal networks exist for different types of motion? Apart from the idea that the law keeps movement smooth, Flash and her colleagues have come up with a new theory: It all boils down to underlying geometrical features.

 

“After conducting various mathematical and geometrical analyses, we suggest that different areas of the brain seem to be using distinct geometries that take into account such features as curvature or straight lines, and this is why we see different brain areas responding to and generating different types of motion perception and action.”

 

A number of recent brain studies have found a strong coupling between perception and action: Seeing movement can activate the same brain areas as those activated by the physical act itself. Scientists have theorized that this dual activation helps us to learn by imitation as well as to understand the actions of others. The new findings show that this coupling extends to the most basic aspects of motion, and they identify the precise laws that govern the very flow of our movements. They suggest, says Flash, any number of future lines of research into how the brain is organized to control and perceive movement, as well as how possible impairments in these processes may be involved in neurological diseases. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The number of “species” in the “genus” Scientist is diverse – ranging from biologists to geneticists, chemists to physicists, and everything in between – each adapted to his or her own particular niche. What would happen if two such species were to “crossbreed”? Once inconceivable, a viable and growing population of physicists engaging in biology research has arisen in the past few years. Says Dr. Nir Gov of the Institute’s Chemical Physics Department in the Faculty of Chemistry: “With scientific equipment becoming ever more powerful, biologists are beginning to face gridlock in the vast amount of data they’ve accrued. Some physicists have seen this as an invitation to help biologists understand phenomena on a more fundamental level and, in the process, discover new physical principles that are unique to active, living matter.”

 

One area that Gov and his research team have been actively studying is how cells get their variety of shapes. Hair cells in the ear, for example, grow finger-like protrusions on their outer surface, and these are organized into rows of graded length. These fingers (stereocilia) convert sound vibrations to electrical signals that are then relayed to the brain. Biologists can now describe in detail the different stages of ear cell formation in a developing embryo, from the initial “deaf” stages, when the nascent fingers start growing in a disorderly fashion, to the final, highly ordered structure. Peeling away the outer membrane of these fingers reveals a scaffold-type protein structure – the cytoskeleton – within the stereocilia, and this scaffolding is the driving force behind their formation. Yet biologists still do not know exactly how stereocilia development takes place. For this, another layer needs to be peeled away to reveal the “invisible forces” that are at play. Gov: “By ‘forces,’ we mean such things as tension, compression, friction, and kinetic and chemical energies – physical mechanisms that act on the objects in a given system. Putting these basic ingredients together in equations gives us mathematical models. We can then use our models to make quantitative predictions about how cellular formations arise and how they behave under various conditions – predictions which can then be tested experimentally.”

 

The model that Gov and his team have been building starts with ATP – the energy currency of the cell. ATP causes elements in the protein scaffold structure – a tight bundle of protein filaments – to dissociate from and re-associate with each other. When balanced by forces in the membrane, the cell’s outer shape remains roughly constant; but the forces exerted by the scaffold proteins also deform the membrane, giving rise to the growth of the finger-like protrusions. The researchers have calculated how these forces exerted on the membranes initiate the process, and a group of experimentalists has recently validated some of their predictions.

 

The same mathematical model has helped the biophysicists gain insights into other, similar systems. For example, another member of Gov’s team is working on brain cells, which grow branched spines for communicating with their neighbors. The basic process underlying their growth appears to be the same as that which initiates the formation of the ear cell fingers, and it  may apply, as well, to the finger-like protrusions of both immune cells and cancer cells that are essential to motility.