Theoretical neuromorphology
Encyclopedia
Theoretical neuromorphology is the science of using morphology
to mathematically describe the shape and the connectivity in the nervous system
.
(1974), founder of the "catastrophe theory" acknowledged what he owed to this work. A series of various branches of non-linear mathematics catastrophe theory
, the fractal theory, the theory of "dissipative structures", the chaos theory
have led to what Boutot (1993) called "the morphologic revolution", which has deeply modified the conception of forms in space. Theoretical neuromorphology discards morphogenesis (the way forms have been made) to limit its purpose to realised forms.
method allowing to see entire neurons. This gave raise to an abundant literature, with descriptions and figures. This allowed Ramon y Cajal (1911) to found definitely the "neuron theory" (the brain is constituted of separate cells that communicate together) and to formulate the law of "dynamic polarization" (axonalwards). With others, he pointed out the variety of patterns of neurons depending on particular cerebral places and already emitted hypotheses on the role that could be plaid by particular forms. Several attempts have been made later. One step has been the work of Mannen (1960) on closed and open nuclei reinsisting on dendritic morphology. This was followed by several papers of Ramon-Moliner defining types of neurons according to their dendritic arborisations.
, the system theory, the graph theory
.
,1983 ), because they are branched, have holes, or are too anfractuous, etc.. In their case the three dimensions are no more linked linearly. This is particularly true for surfaces and volumes. As already stressed by Stevens (1974) some morphological pattern may offer precise advantages. An example can be given from two extremes where the surface of objects is fundamental. The surface is the place where objects exchange between an inside and an outside. In the case where the more advantageous is to have the minimal exchange, the chosen shape is generally the ovoid (such are eggs, grains, fruits... cetaceans etc with the sphere as the perfect limit), which for a given volume limits the surface to its minimum. When the exchange is fundamental important surface is necessary an aminimal material cost. The binary branching increases considerably the surface without increasing much the volume of matter. This is the case for vegetal trees and vascular, pulmonary, urinary systems. The nervous system may be seen as a system of exchanges between emitting and receiving binary arborizations, offering a huge combinatorial range.
Tyner (1975) and Rowe and Stone (1977)have analysed the conceptual bases to be respected in the process of neuronal classification. They insisted on the necessity of separating classification and identification.
Classifications must be based on multifactorial techniques and to be hierarchical (following the bicentennial animal taxonomy).
When many namings or identifications were done on the characteristics of the soma, it appeared clear that only a quantitative study of complete dendritic arborisations was able to offer a means for a neutral neuronal taxonomy. A particular kind of a group of neuron in a localized part of the brain in one animal species is called a neuronal species. When neurons of about the same morphology is observed at the same place in another animal species, it is a neuronal genus. There are also neuronal families and so on. For example spiny neurons of the striatum of macaque are one species. Along with that of man and/or other species they form a genus. Statistical comparisons allow to analyse what remained the same or what has changed in evolution.
Starting from objectively defined neurons, it became possible to constitute neuronal sets.
These are complex and specialized cells. However, the improved understanding of cellular evolution achieved over the last several years has revealed that even the most sophisticated and unique properties of nerve cells represent an adaptation of basic functions observed in all eukaryotic cells, including unicellular organisms. Thus, cellular neurobiology has become an important chapter of cell biology. Studies of neurons greatly capitalize on progress in fundamental cell biology. Conversely, research on specialized features of neurons is producing major fall-outs in other areaas of biology. Projects of cellular neurobiology in the department focus on mechanisms in membrane traffic at the synapse, on the development and maintenance of cell polarity and on the mechanisms responsible for the heterogeneous distribution of organelles and macromolecules within the neuronal cytoplasm. Formation and plasticity of synapses are also investigated. In the tradition of the department, questions in these fields are approached in a multidisciplinary fashion using genetics, protein and lipid biochemistry, molecular biology and state of the art light and electron microscopy imaging techniques. Experimental systems include mouse models, cultured neurons, large model synapses, isolated synaptic preparations and cell free systems. Special emphasis is placed on interfaces between this basic research and disease.
Morphology (biology)
In biology, morphology is a branch of bioscience dealing with the study of the form and structure of organisms and their specific structural features....
to mathematically describe the shape and the connectivity in the nervous system
Nervous system
The nervous system is an organ system containing a network of specialized cells called neurons that coordinate the actions of an animal and transmit signals between different parts of its body. In most animals the nervous system consists of two parts, central and peripheral. The central nervous...
.
History
The rational study of shapes as been long to form. In the major progresses made during the last century, it is important to differentiate morphogenesis (the way forms are made) and morphology (realized forms).Morphogenesis
Important conceptual changes about forms came from d'Arcy Thompson’s essay (1917) dealing with forms in nature. These were not considered as static but as the result of morphogenetic factors. Not knowable in its intimate nature, form is defined as the simple result of forces. ThomRené Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
(1974), founder of the "catastrophe theory" acknowledged what he owed to this work. A series of various branches of non-linear mathematics catastrophe theory
Catastrophe theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry....
, the fractal theory, the theory of "dissipative structures", the chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
have led to what Boutot (1993) called "the morphologic revolution", which has deeply modified the conception of forms in space. Theoretical neuromorphology discards morphogenesis (the way forms have been made) to limit its purpose to realised forms.
Neuromorphology
In spite of some results, space and shapes were often not considered as susceptible of bringing information on the nervous system functioning. Neuromorphology yet had been intensively studied after the discovery of the GolgiGolgi
Golgi may refer to:*Camillo Golgi , Italian physician and scientist after which the following terms are named:**Golgi apparatus , an organelle in the eukaryotic cell...
method allowing to see entire neurons. This gave raise to an abundant literature, with descriptions and figures. This allowed Ramon y Cajal (1911) to found definitely the "neuron theory" (the brain is constituted of separate cells that communicate together) and to formulate the law of "dynamic polarization" (axonalwards). With others, he pointed out the variety of patterns of neurons depending on particular cerebral places and already emitted hypotheses on the role that could be plaid by particular forms. Several attempts have been made later. One step has been the work of Mannen (1960) on closed and open nuclei reinsisting on dendritic morphology. This was followed by several papers of Ramon-Moliner defining types of neurons according to their dendritic arborisations.
Formalisation
An approach of natural forms was proposed by Stevens (1974) who tried to rationally make classification of forms and to find their specific properties and advantages in terms of directness or economy of ways. Since almost one century, an important corpus of theoretical tools, still poorly exploited, has revealed to be very helpful for the understanding of the nervous system. These tools, generally , may be classified as «logical » or more narrowly as « logico-mathematical ». As will be seen, the most useful for the theoretical neuromorphology, along with geometry for metrical parameters, are the set theorySet theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, the system theory, the graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
.
General morphology
The classic traditional forms were emanating from and could be described by using Euclidian geometry for instance in relation to the cartesian triedre (one perpendicular axe for three "dimensions"). These forms can have material realisations (cubes, balls..). Many natural objects however cannot be satisfactorily described using the Euclidian geometry. Many of them are for instance fractals (MandelbrotMandelbrot
Mandelbrot, may refer to:* Benoît Mandelbrot , a mathematician associated with fractal geometry* Mandelbrot set, a fractal popularized by Benoît Mandelbrot* Mandelbrot Competition, a math competition- See also :...
,1983 ), because they are branched, have holes, or are too anfractuous, etc.. In their case the three dimensions are no more linked linearly. This is particularly true for surfaces and volumes. As already stressed by Stevens (1974) some morphological pattern may offer precise advantages. An example can be given from two extremes where the surface of objects is fundamental. The surface is the place where objects exchange between an inside and an outside. In the case where the more advantageous is to have the minimal exchange, the chosen shape is generally the ovoid (such are eggs, grains, fruits... cetaceans etc with the sphere as the perfect limit), which for a given volume limits the surface to its minimum. When the exchange is fundamental important surface is necessary an aminimal material cost. The binary branching increases considerably the surface without increasing much the volume of matter. This is the case for vegetal trees and vascular, pulmonary, urinary systems. The nervous system may be seen as a system of exchanges between emitting and receiving binary arborizations, offering a huge combinatorial range.
Identification and classification
One problem of neuromorphology is because it has not to describe one object, the brain, but an average brain. This justifies an extensive use of statistics.Tyner (1975) and Rowe and Stone (1977)have analysed the conceptual bases to be respected in the process of neuronal classification. They insisted on the necessity of separating classification and identification.
Classifications must be based on multifactorial techniques and to be hierarchical (following the bicentennial animal taxonomy).
When many namings or identifications were done on the characteristics of the soma, it appeared clear that only a quantitative study of complete dendritic arborisations was able to offer a means for a neutral neuronal taxonomy. A particular kind of a group of neuron in a localized part of the brain in one animal species is called a neuronal species. When neurons of about the same morphology is observed at the same place in another animal species, it is a neuronal genus. There are also neuronal families and so on. For example spiny neurons of the striatum of macaque are one species. Along with that of man and/or other species they form a genus. Statistical comparisons allow to analyse what remained the same or what has changed in evolution.
Starting from objectively defined neurons, it became possible to constitute neuronal sets.
Sets
«The theory of set underlies virtually every branch of mathematics» (Kahn, 1995). Great changes in the way of analysing and reasoning have been brought by set theory . This starts from simple concepts. For instance «a set is a collection of elements » (Kahn, 1995) which is intuitive and has not to be demonstrated. The elements have in common to be members of the set. A particular set is defined by the common properties of its elements. This raises problems of similarities and finally of typology and classification.Neuronal systems
Our ability to think, react and remember relies on the function of the nervous system. We cannot understand the human brain without first elucidating the properties and function of its main unit elements, the neurons.These are complex and specialized cells. However, the improved understanding of cellular evolution achieved over the last several years has revealed that even the most sophisticated and unique properties of nerve cells represent an adaptation of basic functions observed in all eukaryotic cells, including unicellular organisms. Thus, cellular neurobiology has become an important chapter of cell biology. Studies of neurons greatly capitalize on progress in fundamental cell biology. Conversely, research on specialized features of neurons is producing major fall-outs in other areaas of biology. Projects of cellular neurobiology in the department focus on mechanisms in membrane traffic at the synapse, on the development and maintenance of cell polarity and on the mechanisms responsible for the heterogeneous distribution of organelles and macromolecules within the neuronal cytoplasm. Formation and plasticity of synapses are also investigated. In the tradition of the department, questions in these fields are approached in a multidisciplinary fashion using genetics, protein and lipid biochemistry, molecular biology and state of the art light and electron microscopy imaging techniques. Experimental systems include mouse models, cultured neurons, large model synapses, isolated synaptic preparations and cell free systems. Special emphasis is placed on interfaces between this basic research and disease.