Topographic organization of nerve fields

The vertebrate nervous system has topographic interconnections in many parts, known for example as retinotopy, somatotopy, etc. It is plausible that modifiable synapses play an important role in forming and refining these connections together with the sensory experiences. To elucidate the mechanism of topographic organization, we propose a simple model consisting of two nerve fields connected by modifiable excitatory synapses. The model also includes modifiable inhibitory synapses. The behavior of the model is described by a set of simultaneous non-linear integro-differential equations. By analyzing the equations, we obtain the equilibrium solution of topographic connections. It is also proved that a part of the presynaptic field which is frequently stimulated comes to be mapped on a large area of the postsynaptic field so that it has a good resolution.     

The Caenorhabditis elegans Six/sine oculis class homeobox gene ceh-32 is required for head morphogenesis

Repulsion plays a fundamental role in the establishment of a topographic map of the chick retinotectal projections. This has been highlighted by studies demonstrating the role of opposing gradients of the EphA3 receptor tyrosine kinase on retinal axons and two of its ligands, ephrin-A2 and ephrin-A5, in the tectum. We have analyzed the distribution of these two ephrins in other retinorecipient structures in the chick diencephalon and mesencephalon during the period when visual connections are being established. We have found that both ephrin-A2 and ephrin-A5 and their receptors EphA4 and EphA7 are expressed in gradients whose orientation is consistent with the topography of the nasotemporal axis of the respective retinofugal projections. In addition, their distribution suggests that receptor-ligand interactions may be involved in the organization of connections between the different primary visual centers and, thus, in the topographic organization of secondary visual projections. Interestingly, where projections lack a clear topographic representation, a uniform expression of the Eph-ephrin molecules was observed. Finally, we also show that a similar patterning mechanism may be implicated in the transfer of visual information to the telencephalon. These results suggest a conserved function for EphA receptors and their ligands in the elaboration of topographic maps at multiple levels of the visual pathway.     

Non-uniformity of extrinsic connections and columnar organization

Afferent columns (>200 μm in diameter) have been intensively investigated in the context of thalamocortical and intrinsic connections. Many extrinsic cortical connections also form columnar terminations, but less is known about their fine organization. Results from intracellular injections of neighboring neurons (in rats: Johnson et al., 2000) suggest that even neurons within a common domain may have non-stereotyped projection patterns, with only partial overlap of terminal arbors. The issue of non-stereotyped projections at the columnar level is further considered by analysis of V1 axons terminating in primate area MT/V5 (an early visual area), and of an axon from temporal cortex terminating in area 7b (a higher cortical area). Both these axons have multiple non-uniform arbors. The implication is that each arbor recruits different numbers and possibly different combinations of postsynaptic elements. While more data are needed concerning convergence of connectional systems, and the actual identity and numbers of postsynaptic targets, the distributed spatial and laminar patterns do not evoke a repetitive uniformity, but rather a columnar substructure and the combinatoric possibilities of the 3-dimensional cortical organization.     

Mapping the organization of axis of motion selective features in human area MT using high-field fMRI

Functional magnetic resonance imaging (fMRI) at high magnetic fields has made it possible to investigate the columnar organization of the human brain in vivo with high degrees of accuracy and sensitivity. Until now, these results have been limited to the organization principles of early visual cortex (V1). While the middle temporal area (MT) has been the first identified extra-striate visual area shown to exhibit a columnar organization in monkeys, evidence of MT's columnar response properties and topographic layout in humans has remained elusive. Research using various approaches suggests similar response properties as in monkeys but failed to provide direct evidence for direction or axis of motion selectivity in human area MT. By combining state of the art pulse sequence design, high spatial resolution in all three dimensions (0.8 mm isotropic), optimized coil design, ultrahigh field magnets (7 Tesla) and novel high resolution cortical grid sampling analysis tools, we provide the first direct evidence for large-scale axis of motion selective feature organization in human area MT closely matching predictions from topographic columnar-level simulations.     

Metrics for cortical map organization and lateralization

Cerebral lateralization refers to the poorly understood fact that some functions are better controlled by one side of the brain than the other (e.g. handedness, language). Of particular concern here are the asymmetries apparent in cortical topographic maps that can be demonstrated electrophysiologically in mirror-image locations of the cerebral cortex. In spite of great interest in issues surrounding cerebral lateralization, methods for measuring the degree of organization and asymmetry in cortical maps are currently quite limited. In this paper, several measures are developed and used to assess the degree of organization, lateralization, and mirror symmetry in topographic map formation. These measures correct for large constant displacements as well as curving of maps. The behavior of the measures is tested on several topographic maps obtained by self-organization of an initially random artificial neural network model of a bihemispheric brain, and the results are compared with subjective assessments made by humans.     

Kinetics of the transient-phase and steady-state of the monocyclic enzyme cascades

We present a kinetic analysis of the whole course of the reaction, that is, of both the transient-phase and steady-state, of monocyclic enzyme cascade systems. The equations for the rapid equilibrium conditions are obtained as a particular case of the general transient-phase equations. An analysis of the kinetic data allows the determination of the equilibrium and the rate constants if adequate experimental results are available. Finally, our results for the steady-state are compared with those obtained by other authors.     

Development of mammalian nervous tissue transplanted into the brain and anterior chamber of the eye: problems and prospects

Some theoretical problems arising in connection with nervous tissue grafting in mammals are discussed. The survival of grafts in the brain and anterior eye chamber is provided by a complex of factors, including peculiarities of immunological reaction, blood-brain barrier and certain characteristics of embryonic nervous tissue. Organotypic development of ectopic grafts suggests a significant autonomy of inner genetic programmes in self-organization of brain structures. Development of the graft-host brain nervous connections is, to a great extent, determined by the factors of topographic closeness and the presence of free postsynaptic structures, without prominent specificity of the graft-brain relationships. Complex neurotrophic interactions, mainly provided by the glial cells, are also found between the graft and damaged host brain. A study of electric activity of the grafted neurons has shown a varying degree of dependence of the functional organization of the brain structures on the environmental afferent influences. The grafts can serve as a chronic endogenous source of neurotransmitters and neurohormones, and, possibly, restore interrupted structural connections, thus providing the compensation of some complex brain functions.     

Kinetics of reversible reactions on linear lattices with neighbor effects

As a model for a variety of reaction processes on long chain molecules, for example, helix formation, a kinetic theory on a linear lattice is presented. Each reaction site can undergo reversible transitions between two states (0 and 1) with rates depending on the slate of its nearest neighbors. The system of coupled rate equations for the frequencies of specified runs of 0's and 1's is infinite for an infinite chain. In contrast to the case of irreversible processes, the system cannot, be written down by inspection. A procedure for the systematic derivation of the rate equations is developed which can be programmed on a computer. Explicit expressions for runs up to length four, involving runs up to length five are obtained without recourse to the computer. For the solution of the rate equations a closure must necessarily be imposed, and a possible procedure is pointed out. Furthermore the equilibrium relations following from the model are considered. The well-known equilibrium results for nearest-neighbor interactions represent a special case of these equations.     

Sexual differences in the interhemispheric asymmetry of the transcallosal responses of the associative areas in the cat neocortex

Sex differences of hemisphere asymmetry of homo- and heterotopic transcallosal responses in association cortex of 48 cats (24 male and 24 female) immobilized by tubocurarine have been studied by means of topographic EPs recordings in both hemispheres. In males left hemisphere dominates by the amplitude of homotopic and positive wave of heterotopic EPs and right hemisphere dominates by the amplitude of negative wave of heterotopic sensorimotor cortex EPs. The individual asymmetry of EPs has been observed in sensomotor cortex of females and in parietal cortex of animals of both sex. The interhemispheric asymmetry is expressed distinctly in females than in males. It is concluded that sex dimorphism is present in functional organization of associative system of (callosal and intracortical) connections in cat's neocortex projection and association areas which means its more expressed hemisphere lateralization in males with more expressed interhemispheric asymmetry of functional transcallosal connections in females.     

Specificity and randomness: structure-function relationships in neural circuits

A fundamental but unsolved problem in neuroscience is how connections between neurons might underlie information processing in central circuits. Building wiring diagrams of neural networks may accelerate our understanding of how they compute. But even if we had wiring diagrams, it is critical to know what neurons in a circuit are doing: their physiology. In both the retina and cerebral cortex, a great deal is known about topographic specificity, such as lamination and cell-type specificity of connections. Little, however, is known about connections as they relate to function. Here, we review how advances in functional imaging and electron microscopy have recently allowed the examination of relationships between sensory physiology and synaptic connections in cortical and retinal circuits.     

Axospinal synapses in the forebrain cortex of aquatic and terrestrial turtles

An electron microscopical investigation of synaptic organization of the superficial plexiform layer of three forebrain cortical zones (hippocampal, dorsal and piriform) in two aquatic and two land Chelonia species has been performed. As demonstrate the data obtained and those from the literature, the main elements of the axo-spinal complexes (spines--synapses--neural terminals) possess both stability properties, contributing to structural firmness of the contacts and their reliability during activities, and plastisity ensuring the maintenance of dynamic equilibrium and a possibility for adequate rearrangements. Under normal conditions, the functional shifts in ultrastructure of the synaptic apparatuses are, possibly, so negligible that they cannot mask certain specific fractures of the synaptic organization of the neural centers. When comparing structures of the axo-spinal complexes in functionally dissimilar cortical zones, more constant, common for all species of Chelonia studied signs are definitely revealed. They characterize a certain level of the neural processes integration. There are signs more variable, evidently, ensuring adaptive rearrangements within limits of the given level of the interneuronal connections organization which can be considered as ecological and species-specific peculiarities.     

Relating Structure and Function in the Human Brain: Relative Contributions of Anatomy,Stationary Dynamics,and Non-stationarities

Investigating the relationship between brain structure and function is a central endeavor for neuroscience research. Yet, the mechanisms shaping this relationship largely remain to be elucidated and are highly debated. In particular, the existence and relative contributions of anatomical constraints and dynamical physiological mechanisms of different types remain to be established. We addressed this issue by systematically comparing functional connectivity (FC) from resting-state functional magnetic resonance imaging data with simulations from increasingly complex computational models, and by manipulating anatomical connectivity obtained from fiber tractography based on diffusion-weighted imaging. We hypothesized that FC reflects the interplay of at least three types of components: (i) a backbone of anatomical connectivity, (ii) a stationary dynamical regime directly driven by the underlying anatomy, and (iii) other stationary and non-stationary dynamics not directly related to the anatomy. We showed that anatomical connectivity alone accounts for up to 15% of FC variance; that there is a stationary regime accounting for up to an additional 20% of variance and that this regime can be associated to a stationary FC; that a simple stationary model of FC better explains FC than more complex models; and that there is a large remaining variance (around 65%), which must contain the non-stationarities of FC evidenced in the literature. We also show that homotopic connections across cerebral hemispheres, which are typically improperly estimated, play a strong role in shaping all aspects of FC, notably indirect connections and the topographic organization of brain networks.     

A specialized area in limbic cortex for fast analysis of peripheral vision

In primates, prostriata is a small area located between the primary visual cortex (V1) and the hippocampal formation. Prostriata sends connections to multisensory and high-order association areas in the temporal, parietal, cingulate, orbitofrontal, and frontopolar cortices. It is characterized by a relatively simple histological organization, alluding to an early origin in mammalian evolution. Here we show that prostriata neurons in marmoset monkeys exhibit a unique combination of response properties, suggesting a new pathway for rapid distribution of visual information in parallel with the traditionally recognized dorsal and ventral streams. Whereas the location and known connections of prostriata suggest a high-level association area, its response properties are unexpectedly simple, resembling those found in early stages of the visual processing: neurons have robust, nonadapting responses to simple stimuli, with latencies comparable to those found in V1, and are broadly tuned to stimulus orientation and spatiotemporal frequency. However, their receptive fields are enormous and form a unique topographic map that emphasizes the far periphery of the visual field. These results suggest a specialized circuit through which stimuli in peripheral vision can bypass the elaborate hierarchy of extrastriate visual areas and rapidly elicit coordinated motor and cognitive responses across multiple brain systems.     

Some game-theoretical aspects of parasitism and symbiosis

Given a two-person continuous non-constant sum game, a “solution” can be arrived at even in ignorance of the pay-off functions as each player tries to maximize his own pay-off by trial and error. The solution of the game considered here is either the intersection of two “optimal lines” (the case of the stable equilibrium) or parasitism of one player upon the other (the case of unstable equilibrium). The introduction of secondary satisfactions (linear combinations of the pay-offs) affects both the position and the stability of the equilibrium and thus the resulting primary satisfactions (the pay-offs). These effects of the matrix of transformation are investigated. In particular, it is shown that the social optimum, which is also the solution of the game where collusion is allowed, is attained if and only if the columns of the matrix are identical, and that this solution is generally stable. Some suggested connections with biological situations are discussed.     

Diffusion through a membrane: Approach to equilibrium

The transfer of solute through a membrane separating two aqueous solutions is studied with the time-dependent diffusion equation for composite media. By introducing new independent and dependent variables it is shown that the differential equations and boundary conditions can be transformed into a dimensionless form which does not explicitly depend on the diffusivities of the media. Laplace transforms are used to derive explicit solutions for the solute concentration as a function of position and time. It is shown that at large time the concentration approaches the equilibrium distribution exponentially. Explicit results are given for the decay time as a function of the parameters of the system. In addition, an accurate and simplified expression is derived for the decay time for the case of small membrane permeability. The accuracy of the analytic solutions for the concentration profiles is tested by comparing them with numerical results obtained by solving the diffusion equations by the method of finite differences. Excellent agreement is found. Research supported in part by a grant from the National Science Foundation.     

Central neural coding of sky polarization in insects

Many animals rely on a sun compass for spatial orientation and long-range navigation. In addition to the Sun, insects also exploit the polarization pattern and chromatic gradient of the sky for estimating navigational directions. Analysis of polarization-vision pathways in locusts and crickets has shed first light on brain areas involved in sky compass orientation. Detection of sky polarization relies on specialized photoreceptor cells in a small dorsal rim area of the compound eye. Brain areas involved in polarization processing include parts of the lamina, medulla and lobula of the optic lobe and, in the central brain, the anterior optic tubercle, the lateral accessory lobe and the central complex. In the optic lobe, polarization sensitivity and contrast are enhanced through convergence and opponency. In the anterior optic tubercle, polarized-light signals are integrated with information on the chromatic contrast of the sky. Tubercle neurons combine responses to the UV/green contrast and e-vector orientation of the sky and compensate for diurnal changes of the celestial polarization pattern associated with changes in solar elevation. In the central complex, a topographic representation of e-vector tunings underlies the columnar organization and suggests that this brain area serves as an internal compass coding for spatial directions.     

Investigations into the organization of information in sensory cortex

One might take the exploration of sensory cortex in the first decades of the last century as the opening chapter of modern neuroscience. The combined approaches of (i) measuring effects of restricted ablation on functional capacities, both in the clinic and the laboratory, together with (ii) anatomical investigations of cortical lamination, arealization, and connectivity, and (iii) the early physiological probing of sensory representations, led to a fundamental body of knowledge that remains relevant to this day. In our time, there can be little doubt that its organization as a mosaic of columnar modules is the pervasive functional property of mammalian sensory cortex [Brain 120 (1997) 701]. If one accepts the assertion that columns and maps must improve the functioning of the brain (why else would they be the very hallmark of neocortex?), then the inevitable question is: exactly what advantages do they permit? In this review of our recent presentation at the workshop on Homeostasis, plasticity and learning at the Institut Henri Poincaré, we will outline a systematic approach to investigating the role of modular, map-like cortical organization in the processing of sensory information. We survey current evidence concerning the functional significance of cortical maps and modules, arguing that sensory cortex is involved not solely in the online processing of afferent data, but also in the storage and retrieval of information. We also show that the topographic framework of primary sensory cortex renders the encoding of sensory information efficient, fast and reliable.     

An Analysis and Comparison of Convergence and Uniqueness of Time-Independent Bone Adaptation Models

Several stimuli are proposed in the bone remodeling theory. It is not clear, if a unique solution exists and if the result is convergent using a certain stimulus. In this study, the strain stimulus, strain energy stimulus and the von Mises stress stimulus for bone remodeling are compared and applied to a square plate model using the finite element method. In the plane stress state, the remodeling equilibrium equations are transformed into functions of only the principal strains and the graphs of these functions are drawn in a diagram using the principal strains as the variables of two coordinate axes. The equation of the sum of principal strain squared equal to a constant is a circle in the diagram. The remodeling equilibrium equation of the strain stimulus is a quadrangle fitting into the circle, the remodeling equilibrium equation of the strain energy stimulus is an ellipse and the remodeling equilibrium equation of the von Mises stress stimulus is also an ellipse close to the principal strains circle when we take the same constants in the above equations. Using the finite element method, two models are performed with the uniform initial elastic properties and with the semi-random initial distribution of the elastic properties. The principal strains as the final finite element results converge within 2% of the objective constant for all the different stimuli. The obtained Young's moduli of two models as the adaptation object are different but in equilibrium, i.e. the equilibrium solution of adaptation model is not unique. The principal strains can not be used to examine the uniqueness of solution, since two different solutions can have the same results of principal strains. Using a certain stimulus, certain initial properties and a certain iterative equation, the solution is unique in equilibrium. The results using the model in this study show also that the same results can be obtained using any of the three stimuli when a proper constant in each remodeling equilibrium equation is chosen.     

A thermodynamic and biomechanical theory of cell adhesion. Part I: General formulism

The equilibrium thermodynamics calculus of cell adhesion developed by Bell et al. (1984, Biophys. J. 45, 1051-1064) has been extended to the general non-equilibrium case. In contrast to previous models which could only compute the end results of equilibrium states, the present theory is able to calculate the kinetic process of evolution of adhesion, which may or may not approach towards equilibrium. Starting from a basic constitutive hypothesis for Helmholtz free energy, equations of balance of normal forces, energy balance at the edge of the contact area and rate of entropy production are derived using an irreversible thermodynamics approach, in which the restriction imposed by the Second Law of Thermodynamics takes the place of free energy minimization used by Bell et al. (1984). An explicit expression for adhesion energy density is derived for the general transient case as the difference of the usable work transduced from chemical energy liberation from bond formation of specific crosslinking molecules and the repulsive potential of non-specific interactions. This allows the energy balance to be used as an independent boundary equation rather than a practical way of computing the adhesion energy. Jump conditions are obtained from the conservation of crosslinking molecules across the edge of adhesion region which is treated as a singular curve. The bond formation and lateral motion of the crosslinking molecules are assumed to obey a set of reaction-diffusion equations. These equations and the force balance equation within the contact area, plus the jump conditions and the energy balance equation at the edge form a well-posed moving boundary problem which determines the propagation of the adhesion boundary, the separation distance between the two cell membranes over the contact area as well as the distributions of the crosslinking molecules on the cell surfaces. The behavior of the system depends on the relative importance of virtual convection, lateral diffusion and bond formation of the crosslinking molecules at the edge of the adhesion region, according to which two types of rate limiting cases are discussed, viz, reaction-limited and diffusion-limited processes.     

Control of phrenic nerve activity and blood pressure by the medullary raphe nuclei in cats

Electrical and chemical stimulation methods were used to determine the topographic organization of the medullary raphe nuclei (MRN) in controlling the systemic arterial blood pressure (BP) and phrenic nerve activities (PNA). Decerebrated, unanesthetized and bilateral vagotomized cats were used. Effective points in the MRN were systematically explored with constant current stimulation. We found stimulation of the rostral MRN produced a decrease in PNA amplitude and increase in BP and PNA frequency. Stimulation of the caudal MRN produced increases in BP and the amplitude and frequency of PNA. Microinjection of glutamate solution into the caudal or the rostral MRN points produced qualitatively similar results. Thus, we concluded that the caudal MRN neurons had excitatory connections whereas the rostral MRN neurons had excitatory and inhibitory connections to the cardiovascular preganglionic neurons and the phrenic nerve motoneurons.