MATHEUS VIANA/USPThe structure of the connections between canals of a bone (red points are the knots): detours avoid obstructionsMATHEUS VIANA/USP
This time it is not neurologists, but physicists and engineers who are presenting new, and apparently useful, proposals concerning neurons and the working of the brain. A team from the Physics Institute of São Carlos has demonstrated that the capacity of the neurons to connect themselves does not depend only on the pathways already trodden or the linkages already established. It also depends on the very shape of the neurons themselves: the more branched off a neuron is, the more connections it can establish with other neurons.
The conclusion appears obvious, but not for that does it stop to be important. In Brazil it is probably the first time that the nervous system has been analyzed by way of Theory of Complex Networks, one of the mathematical artifacts by which one looks for an integrated vision of natural complexes. This pathway also leads to other conclusions, not so evident. For example, it can now be better understood why information circulates with different speeds in the nervous system. According to the physicists, the traffic is slowest in the cortex, the most superficial layer of the brain because the neurons distribute themselves in a relatively uniform manner in a planar space and all of them connect with their neighbors. The messages are faster when they leave the cortex point and follow on to the more distant regions by way of long reaching connections, with fewer intermediaries.
The Theory of Complex Networks offers other forms of explaining the origin of some types of mental retardation, which, seen from this point of view, results not from a lack of connections, as it had been thought, but from their excess, which upsets the flow of information. In any given person, the number and the efficiency of the connections govern both involuntary phenomena, such as heartbeats, and voluntary phenomena such as the choice of clothes in the morning.
As a consequence of genetic factors and of environmental stimuli, the shape of the neurons varies a lot, as they can be slightly or considerably ramified. Their ramification can be short or long. The short ones are the dendrites, which receive information from other neurons. The long ones, called axons, of close to half a meter, send the messages. The architecture of these cells, by allowing to establish more or less connections with others, can determine the connections and influence the working of the brain, in human behavior, and even in the development of some illnesses. This was what the São Carlos team demonstrated, by analyzing the biological data supplied by other research groups and computer simulations on the behavior of the neuron networks. According to this group, the format of the neuron marries with its function, in the same way that the short wings of chickens prevent them to flying, whilst the wings of the swallows, proportionally longer, allow them wide ranging flight. In the opinion of Luciano da Fontoura Costa, the coordinator of the team from the São Carlos Physics Institute of the University of São Paulo (USP), this interdependence between form and function of the neurons constitutes a paradigm only lightly explored by neurobiology.
“The global functioning of the nervous system totally depends on the shape, which, for its part, determines the interconnections between the neurons”, says David Schubert, the laboratory coordinator of cell neurobiology at the Salk Institute in the United States. Costa signed with professor Schubert a study published in the specialist magazine Journal of Neuroscience concerning the agglomeration of neurons, which can be determined by the adhesion between them and the extra-cellular environment: when they group together a lot, problems can come up such as Alzheimer’s disease. “The form of the nerve cells changes a lot in illnesses such as Alzheimer’s”, observes Schubert. “To understand the form of the neurons and how it’s regulated is essential for unmasking the working of the nervous system in normal or pathological conditions.”
Costa, this time with the participation of Marconi Barbosa, during his post-doctorate work, verified that groups of neurons with the same number of elements, each one of them with the same number of connections, but with distinct forms, can function differently. This conclusion emerged from a computer experiment in which a group of neurons was fixed together and this simulated a function – memory. Generally, memory more or less sharp depends on at least two variables: the ramifications and the spread of the neurons. “In the case of memory”, observes Costa, “the best situation is when the neurons present ramifications with a wide spatial distribution”.
In a study carried out by Fernando Rocha and Silene Lima, from the Federal University of Para (UFPA), Costa analyzed the distribution of the photo-receptors – neurons that specialize in capturing light – of the retina of a rodent, the agouti (Dasyprocta agouti). The result, published in Applied Physics Letters, indicates that a better or worse spreading of the neurons does not exist. “Depending on the situation”, says Costa, “the two types of distribution function well”.
Coordinator Costa and the veterinarian Marcelo Beletti, from the Federal University of Uberlandia (UFU), in Minas Gerais State, have demonstrated how the internal canals of the bones that house the arteries and veins through which the blood flows that irrigates and provides nutrients to the medulla bone, central to the production of blood cells, are organized. These spongy structures, known as Havers and Volkmann channels a hierarchy similar to that of streets and avenues in a city: there are main and secondary routes and alternatives that are much longer or shorter. As proposed in an article in Physical Review Letters, there is always a minimum pathway between two points, as well as neighboring ones: if one canal were to be blocked, the blood would meet diversions that would compensate the blockage.
The conclusions result from a study of a femur fragment of a cat, cut into extremely fine slices and converted into images. The 3-dimensional reconstruction of the bone revealed a network of canals with 852 knots and 1,016 connections. Within it the Costa and Beletti teams found less important axes, that could be closed without any problem, and those that were essential, whose lose would damage blood irrigation. This is knowledge that could help in the planning of surgeries, implants or safer medical treatments.
Small world
The theory of Complex Networks is feeding a more integrated vision of living organisms, the so-called systems biology. “The complex networks are adequate to model and to represent the problems in biology of the systems for incorporating the transformations of the network itself, with the loss or gain of elements or connections”, says Costa.
This coverage has already explained an unexpected characteristic of social interactions, by proposing that the distance between people was very small and that anyone could reach another person without many intermediaries: there are on average six stages of separation between any two inhabitants on the Earth. Theoretically, any reader of this magazine may well know someone, who knows someone who knows the super model Gisele Bündchen. This is the so-called “small world”, an expression to which scientists and sociologists help to give consistency.
One of the consequences of the application of this theory is that at times the elements of one grouping – people, cells, genes or proteins – are more important than others. Five years ago, the Hungarian physicist Albert-László Barabasi, today at Notre Dame University in the United States, mapped out the connections between the pages of the internet and discovered that they follow the so called Law of Scale: few of us – the hubs – make many connections, concentrating on the flux of information from the computer screen. The hubs are like airports, an example being that of Cumbica, in Greater São Paulo, which centralizes the national aircraft traffic.
The mathematical artifacts of this theory reduce different phenomena to groupings of connections between two or more points. Barabasi applied this concept to other systems biology problems, such as the protein interaction network: some are more important than others and, if they are damaged, they can put the working of the organism that helps to form them at risk.
A society of neurons
Costa began the application of the concepts of the Theory of Networks in 2002. This was when the physicist Dietrich Stauffer, from Cologne University in Germany, invited him to analyze the functioning of neural networks following the connection standards of Barabasi. According to the classical model, each neuron links itself with all of the others in close proximity, but the reality is not truly so democratic. Stauffer and Costa reached a more realistic model by way of scaled free networks, one of the most fertile offshoots of complex networks, that leads to the formation of hubs. According to this occurrence, some neurons will be more important and will have more connections than others. “The neurons are like individuals, who learn to live within a society, the brain”, compares Costa. “More stimuli tend to establish more connections between the neurons, but they can also reduce the connections.”
In his opinion, the functioning of the brain depends upon these connections, selected since birth. The brain is a newly born containing around 100 billion neurons. Afterwards when they have migrated to their definite locations, the nerve cells establish the greatest number possible of connections with other neurons – around 1 trillion more than they would be capable of using. There are those who believe that by about 10 years of age, only the most used connections survive, because of the environmental stimuli.
Costa believes that he has in his hands versatile tools, that cold help to study and to provide solutions to other problems, as in the case of the identification of literary text authors, interpretation of images or gene expression during animal development. But he also knows that mathematics on its own does not resolve everything. “Studies such as these are only developed with specialists from many areas, that don’t just offer biological data, but also are indispensable in the interpretation of research results.”
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