Simple Mathematcal Pattern Describes Shape of Neuron 'Jungle'

Neurons look remarkably like trees, and connect to other cells with many branches that effectively act like wires in an electrical circuit, carrying impulses that represent sensation, emotion, thought and action.

Over 100 years ago, Santiago Ramon y Cajal, the father of modern neuroscience, sought to systematically describe the shapes of neurons, and was convinced that there must be a unifying principle underlying their diversity.

Cajal proposed that neurons spread out their branches so as to use as little wiring as possible to reach other cells in the network. Reducing the amount of wiring between cells provides additional space to pack more neurons into the brain, and therefore increases its processing power.

New work by UCL neuroscientists, published recently in Proceedings of the National Academy of Sciences, has revisited this century-old hypothesis using modern computational methods. They show that a simple computer program which connects points with as little wiring as possible can produce tree-like shapes which are indistinguishable from real neurons -- and also happen to be very beautiful. They also show that the shape of neurons follows a simple mathematical relationship called a power law.

Power laws have been shown to be common across the natural world, and often point to simple rules underlying complex structures. Dr Herman Cuntz (UCL Wolfson Institute for Biomedical Research) and colleagues find that the power law holds true for many types of neurons gathered from across the animal kingdom, providing strong evidence for Ramon y Cajal's general principle.

The UCL team further tested the theory by examining neurons in the olfactory bulb, a part of the brain where new brain cells are constantly being formed. These neurons grow and form new connections even in the adult brain, and therefore provide a unique window into the rules behind the development of neural trees in a mature neural circuit.

The team analysed the change in shape of the newborn olfactory neurons over several days, and found that the growth of these neurons also follow the power law, providing further evidence to support the theory.

Dr Hermann Cuntz said: "The ultimate goal of neuroscience is to understand how the impenetrable neural jungle can give rise to the complexity of behaviour.

"Our findings confirm Cajal's original far-reaching insight that there is a simple pattern behind the circuitry, and provides hope that neuroscientists will someday be able to see the forest for the trees."

'Facebook for Animals' Tested On Wild Great Tits

How animals associate in groups can have important consequences in terms of the health and survival of both individuals and whole populations; influencing factors such as the spread of disease and the ability to find food or mates.

But revealing the networks underlying animal societies is a challenge when a large amount of fieldwork data consists of a long stream of automated observations of the times and locations of individuals, leaving scientists to try and reconstruct the 'big picture' of how individuals are connected.

The new approach can automatically identify periods of intense social activity within a large number of observations -- in this example around one million observations of wild great tits (Parus major). This makes it possible to examine these periods in greater detail and calculate which individuals are real 'friends', rather than random passers-by, and even which are looking to pair up and mate.

A report of the research is published in this week's Journal of the Royal Society Interface.

'If you think of the data about you in Facebook it records things like who you are friends with, where you've been, and what you share with others,' said Ioannis Psorakis of Oxford University's Department of Engineering Science, who led the research. 'What we have shown is that we can analyse data about individual animals, in this case great tits, to construct a 'Facebook for animals' revealing who affiliates with who, who are members of the same group, and which birds are regularly going to the same gatherings or 'events.''

They team tested the new technique on data from two breeding seasons of wild great tits (August 2007-March 2008 and August 2008-March 2009). The data came from transponders attached to thousands of birds and sensors that logged when individuals appeared at any one of 67 bird feeders spread throughout Wytham Woods, Oxford.

The researchers found that their predictions from this data about which birds were 'friends' that regularly foraged for food together, as well as which birds were starting the process of pairing up or were already in a pair, matched visual observations made by zoologists.

'What we've shown is that our technique can extract information about the networks that bind individuals together by sampling and analysing their mobility patterns,' said Ioannis Psorakis. 'Our approach makes it possible to look at huge amounts of data without having to decide what time resolution is best to extract meaning -- the model evaluates this automatically. This is just the first exalple of how zoologists are beginning to use our method to explore social networks of animals in a 'big data' context.'

Early results from the work with great tits suggest that individual birds do not participate in flocks at random, but have a bias towards other members of the population they interact with. The majority of networks extracted using the approach are strongly clustered, and in such tight bird communities, individuals forage together and interact with their current or future mating partner.

This approach is being used not only in great tits, but also in a mix of wild-bird social networks, exploring the animal sociality at an inter-species level. Some of the most important future steps in this work are to combine the 'social' information available through this method, with other types of information: for example combining it with genetic data is enabling researchers to explore the genetic basis of sociality: do genetically similar individuals attract each other, or is it the other way round? Can we find specific areas of the genome that account for gregariousness?

The work could also help researchers understand how information spreads through animal populations. Tits are a famous exemplar of social learning: for instance, the habit of pecking open milk bottles on doorsteps to get access to cream spread rapidly through England in the mid 20th Century. The new approach is helping scientists to test how specific social structures help or hinder the spread of novel information from individual to individual.

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