Contributions to the mathematical biophysics of the central nervous system with special reference to learning

A learning theory based on the lowering of thresholds of neurons under certain conditions is applied to two “random net” models. The first, a so-called “ganglion-brain” is characterized by completely random connections of all afferent tracts except certain ones which form the pathways for unconditioned responses. Certain expressions are derived which measure the learning potentiality of the ganglion— in particular, with respect to the number of responses which can be learned (conditioning potential) and the amount of interference between the learned responses (redundance potential). The second model concerns the progressive refinement of a response. The efficiency of learning in this case is reflected in the eventual specificity of the response which, in turn, depends on the modification of the distribution of thresholds associated with the neurons governing the responses. Expressions are derived relating the initial distribution of thresholds, the relative effectiveness of the various responses, and certain other parameters to the final distribution of thresholds. For a particular choice of the effectiveness distribution of responses the progressive sharpening of the threshold curve (i.e., progressive specificity of response) is demonstrated. Some implications of the model with respect to the evolution of nervous systems are discussed.     

Suggestions for a mathematical biology of some cultural developments

In connection with the author's previous studies on the effects of imitation in social behavior it is shown how, owing to such effects, two societies which are both characterized by the same distribution functions for different abilities and tastes may differ very greatly in their respective outputs of scientific and inventive work. The course of development which occurs in a given society may be determined by purely accidental initial conditions. A theory of quantitative relations between some cultural and socioeconomic quantities is suggested.     

Contributions to the mathematical biophysics of the central nervous system

Various neural mechanisms are considered which deal with point to point correspondence between two sets of neural elements with a smaller number of conducting elements between them; the transmission of nerve impulses in a limited range of intensities; movement of the transmission of excitation along a contour; the reaction to the size of an object independent of its distance; and an interpretation of the effect of a warning stimulus and of stimulus intensity upon reaction time. For the latter cases a comparison of the theoretical equations is made with some of the available experimental data, and a general agrement is found.     

Immunohistochemical analysis of the rat central nervous system during experimental allergic encephalomyelitis, with special reference to Ia-positive cells with dendritic morphology

The rat central nervous system (CNS) during experimental allergic encephalomyelitis (EAE) was analyzed immunohistochemically from the preclinical to recovery stage by using monoclonal antibodies specific for rat T lymphocyte subsets and Ia antigen. Through combination of the avidin-biotin technique and carefully selected fixative, cells with dendritic morphology (DC) and infiltrating mononuclear cells were clearly and intensely demonstrated in the CNS parenchyma during EAE. In normal and complete Freund's adjuvant (CFA)-injected controls, there were no inflammatory foci. Ia (OX3)-positive parenchymal cells were not detected, whereas W3/25 stained DC that were located mainly in the white matter and W3/13 stained axons. At the preclinical stage, 11 days after CNS/CFA sensitization, a few clusters of Ia+ DC were detected in some sections of the spinal cord. The number of Ia+ DC increased as clinical signs developed (P less than 0.001). In rats with a clinical score of 1 or 2, Ia+ DC were mainly located in the perivascular region and closely associated with infiltrating T lymphocytes. However, at moribund state (score 3), Ia+ DC were evenly distributed in gray and white matter on almost all sections of the spinal cord. In recovered rats, the numbers of inflammatory foci and Ia+ DC were less than those in clinical EAE rats (P less than 0.001). Rats without clinical signs throughout the course also contained a few clusters of Ia+ DC. Double immunofluorescent staining with OX3 and anti-glial fibrillary acidic protein (GFAP) antiserum demonstrated that Ia+ DC were negative for GFAP. Their morphology and distribution were similar to those of nucleoside diphosphatase-positive cells, suggesting that Ia+ DC are microglia. In contrast to DC, no astrocytes or endothelial cells express detectable levels of Ia antigen in control and clinical EAE rats. These findings suggest that brain cells other than Ia+ DC may not be involved in the local immune interaction. Ia+ DC may play a significant role in antigen presentation in the CNS with EAE.     

Suggestions for a mathematical biophysics of auditory perception with special reference to the theory of aesthetic ratings of combinations of musical tones

Generalising the previously studied neurobiophysical schemes, consisting of excitatory and inhibitory elements, a neural mechanism is discussed, which may be involved in the perception of combinations of musical tones. Equations, giving the total value of central excitation for a combination of any two tones are derived, available observations are discussed in the light of the suggested theory.     

Suggestions for a mathematical biophysics of some psychoses

We may consider that most of the human behavior is a set of learned responses to certain patterns which recur frequently in the course of human life. Some “abnormal” events or experiences may result in the learning of abnormal responses, and thus in abnormal behavior. The “abnormal” responses may begin to be learned after some of the normal response patterns have been fairly well established. The development of both normal and abnormal behavior may thus be represented by learning curves of the type studied by H. D. Landahl. Applying some of the results of the theory of learning curves and considering that the normal and abnormal reactions may reciprocally inhibit each other, a quantitative theory of some psychoses may be developed. In particular, the effects of shock may be deduced from the assumption that they cause the more recently learned abnormal reactions to be “unlearned” more readily, than the earlier learned “normal” reactions. The effectiveness of shock treatments as a function of the duraction of psychosis is discussed from this point of view.     

Suggestions for a mathematical model of a pathological neuron with spontaneous repetitive discharges

A formal mathematical model is proposed for a spontaneously repetitively firing neuron. It is based on the assumption that an excitatory and inhibitory substance, possibly different from those involved in synaptic transmissions, is formed in the soma of everynormal neuron. Furthermore, the decay of the substances is ascribed to their combination with some other substances, present in healthy individuals. A generalized two factor system of differential equations is used. It is shown that when the normally present substances are absent, possibly due to genetic defects so that the decay constants become zero, the equations lead to undamped sinusoidal solutions of the difference between excitatory and inhibitory factors, thus producing a trulyspontaneous repetitive discharge, in the absence of external currents or other stimulation. It is suggested that convulsants may act by destroying the substances present in healthy individuals. It is further suggested that by administering to epileptics those substances, which are present in normal healthy persons, perhaps by using brain extracts fromhealthy higher animals which sometimes suffer from epilepsy, an actual cure rather than symptomatic treatment by anticonvulsants may be obtained.     

Further contributions to a probabilistic interpretation of the mathematical biophysics of the central nervous system

Following a previous paper, equations are derived for the most probable time of firing of an efferent neuron in terms of the intensityE of excitation of the afferent pathway, whenE is either constant or any given function of time. The equations are not differential equations, but in integral form. It is suggested that ε, correspondinglyj, represent the number of excitatory, correspondingly inhibitory, terminal bulbs excited within the period of latent addition at a given most probable time. The relation between the suggested theory and the old one, based on differential equations for ε andj is discussed.     

Functional morphology of the enteric nervous system with special reference to large mammals.

This short review reports the latest insights into the structural organization of the enteric nervous system, with special emphasis on the intrinsic innervation of the intestinal tract of large omnivorous mammals such as the pig. Using various techniques, including lesion experiments, morphological and neurochemical features of distinct neuronal populations as well as the direction of the axonal processes within the different nerve networks could be revealed. Special attention was paid to the considerable species differences in this respect between large omnivorous animals and humans on the one hand and small laboratory animals on the other hand.     

Head development in the onychophoran Euperipatoides kanangrensis with particular reference to the central nervous system

The neuroectoderm of the Euperipatoides kanangrensis embryo becomes distinguishable during germ band formation when the antennal segment is evident externally. During later stages of development, the neuroectoderm proliferates extensively and, at the anterior part of the head, newly-formed neuron precursor cells occupy most of the volume. The antenna forms from the dorsolateral side of the anterior somite. The antenna has no neuroectoderm of its own at the onset of its formation, but instead, neurons migrate out to the appendage from the nearby region of the developing brain. When the antennal tract is formed it is positioned horizontally in the brain, in line with the antennal commissure. Only later, and coincidentally with the anterior repositioning of the antenna, is the tract's distal part bent anteriorly and positioned laterally. The eye starts to develop posteriorly to the antenna and the antennal commissure. This suggests that the segment(s) associated with the onychophoran eye and antenna are not serially homologous with segments carrying equivalent structures within the Euarthropoda. Evidence is presented to further support the presence of a terminal mouth in the ground plan of the Onychophora and, hence, an acron may not exist in the arthropod clade.