Posts tagged mathematics

August 8, 2012

Researchers capture evolutionary dynamics in a new theoretical framework that could help explain some of the mysteries of how and why species change over time.

Although the qualitative description of evolution – its observed behavior and characteristics – is well-established, a comprehensive quantitative theory that captures general evolution dynamics is still lacking. There are also many lingering mysteries surrounding the story of life on Earth, including the question of why sex is such a prevalent reproductive strategy. A team of scientists from the Chinese Academy of Sciences; Jilin University in Jilin, China; and the State University of New York at Stony Brook, led by Prof. Jin Wang, has examined some of these puzzles from a physical science prospective. They propose a new theory of evolution with two ingredients: the underlying emergent “fitness” landscape and an associated evolutionary force called “curl flux,” which causes species to move through the emergent fitness landscape in a spiraling manner.

The researchers captured evolutionary relationships in a system of equations. They then created quantitative pictures that visualized evolutionary pathways as journeys through a mountainous terrain of peaks and valleys of biological fitness. The key breakthrough beyond the conventional quantitative theory of evolution is the emergent curl flux, which is generated by interactions between individuals within or across species. The underlying emergent landscape gradient and the curl flux act together as a “Yin and Yang” duality pair to determine the dynamics of general evolution, says Wang. An example of similar behavior is the particle and wave duality that determines the dynamics of the quantum world, he notes. The researchers also note that this combined effect is analogous to the way electric and magnetic forces both act on electrons.

The new theory provides a physical foundation for general evolution dynamics. The researchers found that interactions between individuals of different species can give rise to the curl flux. This can sustain an endless evolution that does not lead to areas of higher relative fitness, even if the physical environment is unchanged.

This finding offers a theoretical framework to explain the Red Queen Hypothesis, which states that species continually evolve in order to fend off parasites that are themselves continually evolving. The hypothesis, first proposed by evolutionary biologist Leigh Van Valen in 1973, gets its name from the character of the Red Queen in Lewis Carroll’s book Through the Looking-Glass, who observed that in her world it was necessary to keep running just to stay in one place. The idea of endless co-evolution through the maintenance of the genetic variation due to the curl flux could help explain the benefits of sexual reproduction, since the mixing and matching of genes preserves a greater diversity of traits. When a species’ arms race with a co-evolving parasite takes an unexpected twist, a previously unnecessary trait could suddenly turn into the key to surviving. In the co-evolving world, there is no guarantee for “survival of the fittest” and it is often necessary to keep running for survival.

Source: PHYS.ORG

August 8th, 2012

The brain has billions of neurons, arranged in complex circuits that allow us to perceive the world, control our movements and make decisions. Deciphering those circuits is critical to understanding how the brain works and what goes wrong in neurological disorders.

MIT neuroscientists have now taken a major step toward that goal. In a new paper appearing in the Aug. 9 issue of Nature, they report that two major classes of brain cells repress neural activity in specific mathematical ways: One type subtracts from overall activation, while the other divides it.

“These are very simple but profound computations,” says Mriganka Sur, the Paul E. Newton Professor of Neuroscience and senior author of the Nature paper. “The major challenge for neuroscience is to conceptualize massive amounts of data into a framework that can be put into the language of computation. It had been a mystery how these different cell types achieve that.”

Neuroscientists report that two major classes of brain cells repress neural activity in specific mathematical ways: One type subtracts from overall activation, while the other divides it.

The findings could help scientists learn more about diseases thought to be caused by imbalances in brain inhibition and excitation, including autism, schizophrenia and bipolar disorder.

Lead authors of the paper are grad student Caroline Runyan and postdoc Nathan Wilson. Forea Wang ’11, who contributed to the work as an MIT undergraduate, is also an author of the paper.

A fine balance

There are hundreds of different types of neuron in the brain; most are excitatory, while a smaller fraction are inhibitory. All sensory processing and cognitive function arises from the delicate balance between these two influences. Imbalances in excitation and inhibition have been associated with schizophrenia and autism.

“There is growing evidence that alterations in excitation and inhibition are at the core of many subsets of neuropsychiatric disorders,” says Sur, who is also the director of the Simons Center for the Social Brain at MIT. “It makes sense, because these are not disorders in the fundamental way in which the brain is built. They’re subtle disorders in brain circuitry and they affect very specific brain systems, such as the social brain.”

In the new Nature study, the researchers investigated the two major classes of inhibitory neurons. One, known as parvalbumin-expressing (PV) interneurons, targets neurons’ cell bodies. The other, known as somatostatin-expressing (SOM) interneurons, targets dendrites — small, branching projections of other neurons. Both PV and SOM cells inhibit a type of neuron known as pyramidal cells.

To study how these neurons exert their influence, the researchers had to develop a way to specifically activate PV or SOM neurons, then observe the reactions of the target pyramidal cells, all in the living brain.

First, the researchers genetically programmed either PV or SOM cells in mice to produce a light-sensitive protein called channelrhodopsin. When embedded in neurons’ cell membranes, channelrhodopsin controls the flow of ions in and out of the neurons, altering their electrical activity. This allows the researchers to stimulate the neurons by shining light on them.

The team combined this with calcium imaging inside the target pyramidal cells. Calcium levels reflect a cell’s electrical activity, allowing the researchers to determine how much activity was repressed by the inhibitory cells.

“Up until maybe three years ago, you could only just blindly record from whatever cell you ran into in the brain, but now we can actually target our recording and our manipulation to well-defined cell classes,” Runyan says.

Taking a circuit apart

In this study, the researchers wanted to see how activation of these inhibitory neurons would influence how the brain processes visual input — in this case, horizontal, vertical or tilted bars. When such a stimulus is presented, individual cells in the eye respond to points of light, then convey that information to the thalamus, which relays it to the visual cortex. The information stays spatially encoded as it travels through the brain, so a horizontal bar will activate corresponding rows of cells in the brain.

Those cells also receive inhibitory signals, which help to fine-tune their response and prevent overstimulation. The MIT team found that these inhibitory signals have two distinct effects: Inhibition by SOM neurons subtracts from the total amount of activity in the target cells, while inhibition by PV neurons divides the total amount of activity in the target cells.

“Now that we finally have the technology to take the circuit apart, we can see what each of the components do, and we found that there may be a profound logic to how these networks are naturally designed,” Wilson says.

These two types of inhibition also have different effects on the range of cell responses. Every sensory neuron responds only to a particular subset of stimuli, such as a range of brightness or a location. When activity is divided by PV inhibition, the target cell still responds to the same range of inputs. However, with subtraction by SOM inhibition, the range of inputs to which cells will respond becomes narrower, making the cell more selective.

Increased inhibition by PV neurons also changes a trait known as the response gain — a measurement of how much cells respond to changes in contrast. Inhibition by SOM neurons does not alter the response gain.

The researchers believe this type of circuit is likely repeated throughout the brain and is involved in other types of sensory perception, as well as higher cognitive functions.

Sur’s lab now plans to study the role of PV and SOM inhibitory neurons in a mouse model of autism. These mice lack a gene called MeCP2, giving rise to Rett Syndrome, a rare disease that produces autism-like symptoms as well as other neurological and physical impairments. Using their new technology, the researchers plan to test the hypothesis that a lack of neuronal inhibition underlies the disease.

Source: Neuroscience News