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.     

Mathematical biology of social behavior

When an individual grows up in a society, he learns certain behavior patterns which are “accepted” by that society. He may in general have a tendency toward behavior patterns other than those which are “accepted” by the society. This tendency toward such unaccepted behavior may be due to a process of cerebration which results in doubt as to the “correctness” of the accepted behavior. Thus, on the one hand, the individual learns to follow the accepted rules almost automatically; on the other hand, he may tend to consciously break those rules. Using a neural circuit, suggested by H. D. Landahl in his theory of learning, a neurobiophysical interpretation of the above situation is outlined. Mathematical expressions are derived which describe the social behavior of an individual as a function of his age, social status, and some neurobiophysical parameters.     

Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver

Following previous studies, differential equations are established which determine the variation of the stimulus towards a corrective turn of the steering wheel and its effect on the excitation of the centers in the brain which results in the production of the corrective turn. The equations are derived under the highly oversimplified assumption that all excitation thresholds are so small that they can be neglected. Under these assumptions it is found that the tracking curve of a car is a sinusoid with negative damping, that is, with an ever increasing amplitude. Driving under these assumptions is imposible since the car will always eventually jump off the road. The possible effects of the threshold as well as stimuli towards corrective turns other than the distance from the edge of the lane are very briefly discussed. In spite of the negative results of the paper, its interest lies in the circumstance that with the complication of the model, we find that driving depends not only on the reaction times as the only “purely biological” parameter, but on three other neurobiophysical constants. In a subsequent paper (Rashevsky, 1967) it is shown how the introduction of one or more purely biological parameters of the driver makes a stable driving regime possible.     

Contribution to the probabilistic theory of neural nets: II. Facilitation and threshold phenomena

The output curve of a single neuron with a threshold of response with respect to the frequency of the stimuli is derived. If the stimuli are regularly spaced in time, the output curve has discontinuities. If the threshold and/or refractory period are sufficiently large, the output curve approaches the “all-or-none” curve. In the case of completely randomized stimuli, the output curve is sigmoid. The equation of this curve is derived and some properties are studied. Threshold and “all-or-none” effects can be achieved by “pyramiding” neurons of this type to converge on neurons of higher order.     

Lactate and malignant tumors: A therapeutic target at the end stage of glycolysis

Metabolic aberrations in the form of altered flux through key metabolic pathways are primary hallmarks of many malignant tumors. Primarily the result of altered isozyme expression, these adaptations enhance the survival and proliferation of the tumor at the expense of surrounding normal tissue. Consequently, they also expose a unique set of targets for tumor destruction while sparing healthy tissues. Despite this fact, development of drugs to directly target such altered metabolic pathways of malignant tumors has been under-investigated until recently. One such target is the ultimate step of glycolysis, which, as expected, presents itself as a metabolic aberration in most malignant tumors. Termed “aerobic glycolysis” due to abnormal conversion of pyruvic acid to lactic acid even under normoxia, the altered metabolism requires these tumors to rapidly efflux lactic acid to the microenvironment in order to prevent poisoning themselves. Thus, exposed is a prime “choke-point” to target these highly malignant, frequently chemo- and radio- resistant tumors. This review will focus on current outcomes in targeting lactate efflux in such tumors using glioma as a model, an ongoing project in our laboratory for the past half-decade, as well as supporting evidence from recent studies by others on targeting this “tail-end” of glycolysis in other tumor models.     

Further studies of some aspects of a neurobiophysical model of schizophrenia

The neurobiophysical model of schizophrenia discussed previously (Bull. Math. Biophysics,26, 167–185, 1964;27, 21–26, 1965) is generalized further, to include catatonic and stuporous states. It is concluded that the development of schizophrenia will proceed through different stages of catatonic and non-catatonic states, depending on parameters which characterize on one hand the general inhibition of the individual, on the other hand what may be called his “stability.” Suggestions for possible clinical verifications of the conclusions are made.     

Contribution to the mathematical theory of mass behavior: I. The propagation of single acts

The propagation of a single act in a large population is supposed to depend on some external circumstance and on an “imitation component”, where encounters with individuals who are performing or have already performed the act contribute to the tendency of an individual to perform it. The “tendency” to perform is supposed to be measured by the average frequency of stimuli, randomly distributed in time, impinging on the individual. The deduced equation is a relation between the fraction of the population who have performed the act and time, provided the time course of the “external circumstance” and the way in which the imitation component contributes are known. Several special cases are studied, in particular, cases without the imitation component, cases with imitation only, and various mixed cases. Examples are given of social situations in which such factors may operate and general suggestions are made for the systematization of observations and/or experiments to test the assumptions of the theory.     

The perfect learner

As a “base line” of memorization performance, the behavior of a “perfect learner” is considered. He is characterized by a perfect memory and by the ability to choose the best search procedure in problems where the correct response from a given repertoire is to be found to each of several stimuli under the condition of “right” and “wroing” promptings by the experimenter. Expected learning curves are derived for the case of disjoint response repertoires associated with the stimuli under cyclic and random presentation of the stimuli and for the case of a single response repertoire (a one-to-one matching problem) under cyclic presentation.     

Generalization and categorization of spectral colors in goldfish. II. Experiments with two and six training wavelengths

In part I of this study (Kitschmann and Neumeyer 2005), goldfish categorized spectral colors only in the sense that wavelengths in a range of about twice as large as the just noticeable difference were treated as similar to a given training wavelength. Now, we trained goldfish on more than one wavelength to prevent very accurate learning. In one experiment goldfish were trained on six adjacent wavelengths with equal numbers of rewards, and, thus, equal numbers of learning events. Generalization tests showed that some wavelengths were chosen more often than others. This indicated that certain spectral ranges are either more attractive or more easily remembered than others. As this is a characteristic of the “focal” colors or centers of color categories in human color vision, we interpret the findings in goldfish accordingly. We conclude (Figs. 5 and 6) that there are four categories in spectral ranges approximately coinciding with the maximal sensitivities of the four cone types, and three categories in-between. Experiments with two training colors indicate that there is no direct transition between categories analogous to human “green” and “red”, but that there is a color analogous to human “yellow” in-between (Figs. 2, 3; Table 1).     

About a possible role of parasomnias as a factor of stabilization of sleep cycles

Cyclical organization of sleep is one of necessary conditions of normal human and animal life activity and one of basic manifestations of the circadian cycle. Transition from the slowwave to the paradoxical sleep is often accompanied by brief, sometimes rhythmical motor and autonomic reactions that do not cause awakening, but seem to promote activation of the mechanisms providing the “switch” of the sleep phases. Immaturity (or a lesion) of the neurophysiologic mechanisms responsible for the “switch” of the sleep stages leads to hindering of alternation of the sleep phases, which disturbs their normal sequence and leads to deficit of reparative and homeostatic processes. This is manifested as deterioration of the neuropsychical state during wakefulness. The data are presented which allow suggesting that the stereotypical motor or autonomic reactionspathological parasomnias, for instance enuresis, can appear as a compensatory mechanism promoting the sleep phase switch. Episodes of the pathological parasomnias promote normalization of the sleep stage alternation and thereby affect positively recovery of its cyclical organization.     

Consciousness is Cheap, Even if Symbols are Expensive; Metabolism and the Brain’s Dark Energy

Use of symbols, the key to the biosemiotics field as to many others, required bigger brains which implied a promissory note for greater energy consumption; symbols are obviously expensive. A score years before the current estimate of 18–20% for the human brain’s metabolic demand on the organism, it was known that neural tissue is metabolically dear. This paper first discusses two evolutionary responses to this demand, on both of which there is some consensus. The first, assigning care of altricial infants with burgeoning brains (and in human infants the metabolic demand peaks at 65% of the total) to “allomothers” is not unique to humans. The second, using relatively small neurons as primates do, risks misfires past a certain minimal value. Moreover, in apparent paradox, there is an increasing consensus that large “Von Economo” neurons are critical for communication. This paper’s main contribution is the discussion of two further evolutionary tricks. The first is the use of self-similarity in the cortex, both in structure and process, to allow the cortex readily—and in energetic terms, parsimoniously—to shift between states in a high-dimensional space. This leads to discussion of the kind of formalism appropriate to model these shifts, a formalism which—it is tentatively suggested—may do double duty for the modeling of symbolic thought. The second trick is the superimposition on the background “white noise” of neural firing of EEG-detected waves like gamma. The paper describes a method, using the Hilbert transform, of calculating the dips in energy consumption as the brain is transitioned by gamma waves. It is hypothesized that consciousness may be a spandrel, the incidental result of a neurodynamic imperative that the brain enter a maximally sensitive (in sensory terms) “zero power” state a few times a second. If that is the case, then there are obvious benefits for health in meditation, which can be viewed as a state of consciousness extended over time by limiting afferent stimuli.     

Using sensory weighting to model the influence of canal,otolith and visual cues on spatial orientation and eye movements

 The sensory weighting model is a general model of sensory integration that consists of three processing layers. First, each sensor provides the central nervous system (CNS) with information regarding a specific physical variable. Due to sensor dynamics, this measure is only reliable for the frequency range over which the sensor is accurate. Therefore, we hypothesize that the CNS improves on the reliability of the individual sensor outside this frequency range by using information from other sensors, a process referred to as “frequency completion.” Frequency completion uses internal models of sensory dynamics. This “improved” sensory signal is designated as the “sensory estimate” of the physical variable. Second, before being combined, information with different physical meanings is first transformed into a common representation; sensory estimates are converted to intermediate estimates. This conversion uses internal models of body dynamics and physical relationships. Third, several sensory systems may provide information about the same physical variable (e.g., semicircular canals and vision both measure self-rotation). Therefore, we hypothesize that the “central estimate” of a physical variable is computed as a weighted sum of all available intermediate estimates of this physical variable, a process referred to as “multicue weighted averaging.” The resulting central estimate is fed back to the first two layers. The sensory weighting model is applied to three-dimensional (3D) visual–vestibular interactions and their associated eye movements and perceptual responses. The model inputs are 3D angular and translational stimuli. The sensory inputs are the 3D sensory signals coming from the semicircular canals, otolith organs, and the visual system. The angular and translational components of visual movement are assumed to be available as separate stimuli measured by the visual system using retinal slip and image deformation. In addition, both tonic (“regular”) and phasic (“irregular”) otolithic afferents are implemented. Whereas neither tonic nor phasic otolithic afferents distinguish gravity from linear acceleration, the model uses tonic afferents to estimate gravity and phasic afferents to estimate linear acceleration. The model outputs are the internal estimates of physical motion variables and 3D slow-phase eye movements. The model also includes a smooth pursuit module. The model matches eye responses and perceptual effects measured during various motion paradigms in darkness (e.g., centered and eccentric yaw rotation about an earth-vertical axis, yaw rotation about an earth-horizontal axis) and with visual cues (e.g., stabilized visual stimulation or optokinetic stimulation). Received: 20 September 2000 / Accepted in revised form: 28 September 2001     

Acquisition and transfer of visual Go/No-go discrimination by a chimpanzee

An adolescent female chimpanzee was trained to press a key in the presence of a computer-graphic geometric figure (“Go” stimulus) within 5 sec and not to press the key during 5-sec presentations of another figure (“No-go” stimulus) with food reinforcement. In the acquisition training, the accuracy of performance increased primarily as a result of learning to inhibit key presses in No-go trials. The chimpanzee acquired this “Go/No-go” visual discrimination task in 1,260 trials. She was then given 14 successive transfer problems. The results for these problems suggested that learning-set formation and repeated use of the same discriminative stimuli both influenced transfer to new problems.     

The roles of body size and phylogeny in fast and slow life histories

Species’ life histories are often classified on a continuum from “fast” to “slow”, yet there is no consistently used definition of this continuum. For example, some researchers include body mass as one of the traits defining the continuum, others factor it out by analysing body-mass residuals, a third group performs both of these analyses and uses the terms “fast” and “slow” in both ways, while still others do not mention body mass at all. Our analysis of European and North American freshwater fish, mammals, and birds (N = 2,288 species) shows the fundamental differences between life-history patterns of raw data and of body-mass residuals. Specifically, in fish and mammals, the number of traits defining the continuum decreases if body-mass residuals are analysed. In birds, the continuum is defined by a different set of traits if body mass is factored out. Our study also exposes important dissimilarities among the three taxonomic groups analysed. For example, while mammals and birds with a “slow” life history have a low fecundity, the opposite is true for fish. We conclude that our understanding of life histories will improve if differences between patterns of raw data and of body-mass residuals are acknowledged, as well as differences among taxonomic groups, instead of using the “fast–slow continuum” too indiscriminately for any covarying traits that appear to suit the idea.     

Carbohydrate tolerance,serum albumin and protein values of normal and “waster” marmosets (Callithrix jacchus)

The major objective of this study was to establish standard glucose and lactose tolerance curves for the common marmoset (Callithrix jacchus). These data were utilized to establish criteria for detection of abnormal glucose tolerance and characterization of some aspects of the “marmoset wasting syndrome” which has been observed in this species. Glucose and lactose tolerance tests were performed on healthy animals and typical “marmoset wasters.” Eighteen normal animals were 18 to 36 months old and weighed 194–280 g. Six “wasters” were in the age range of 24 to 84 months and weighed 163–253 g. Seven experiments were carried out for each glucose tolerance test. In each trial it was observed that the serum glucose concentration (SGC) of the healthy animal after 90 min was two times higher than the pre-administration concentrations. The SGC returned to the pre-administration concentration within 150–300 min in animals administered glucose at dosages of 2 g/kg and 1 g/kg of body weight. However, at the dosage level of 5 g/kg body weight, the SGC of the animals tripled after 30 min and required 300 min to return to the pre-administration level. The 2 g/kg dosage level was chosen as typical. When similar experiments were conducted with animals identified as “chronic wasters,” all of the animals except one were observed to be inefficient in the absorption of glucose. When lactose was administered at a level of 4 g/kg, similar results were obtained. Normal and “waster” marmosets were also subjected to serum total protein, albumin and electrophoresis determinations in an effort to establish additional criteria that may be utilized in the identification of the “marmoset wasting” syndrome. Serum albumin was significantly higher in the “waster” marmosets 30 min following an oral administration of glucose than was observed in normal animals. Total protein values were not significantly lower in the “wasters” when subjected to the same tolerance test. The albumin level in normal animals was not affected by similar glucose tolerance tests. The electrophoretic patterns of serum protein for normal animals exhibited more bands than was observed in patterns of serum protein for “waster” marmosets. From these data, it seems logical that these diagnostic tests may be useful in developing a profile for the early detection of the “wasting” syndrome in marmosets.     

Molecular-genetics analysis of natural and stimulated ovulation impairment

The influence of FMR1, INHα1, NAT2, GSTT1 and GSTM1 genes mutations on ovarian function and their association with POF and “poor response” to exogenous GT after ovulation stimulation were investigated. The carriers of Ala257Thr transition predominated in the studied “poor responders” group. In 1.6% POF patients and 2.5% persons from “poor responders” group, but nobody from control group this transition combined with intermediate alleles of FMR1 gene was observed. The frequency of deletion in GSTM1 gene in “poor responders” group was significantly higher (p = 0.01) than in normal ovulatory control group. The frequency of Ser680Ser-Ala307Ala polymorphic genotype (22.2%) in “poor responders” group was significantly higher (p = 0.028) than in normal-ovulatory control group (7.7%). The daily dosage of GT in intermediate alleles of FMR1 gene carriers as well in patients with “slow acetylation” NAT2 genotype was significantly higher in comparison to patients without intermediate alleles and patients with “quick acetylation” NAT2 genotype. Quantity of oocytes after stimulation ovulation in women with INHα1 gene Ala257Thr transition were significantly decreased in comparison to patients without such mutation. Further investigations of these genes can play a major role in POF studying and modulation of ovarian response to exogenous GT. Published in Ukrainian in Tsitologiya i Genetika, 2008, Vol. 42, No. 2, pp. 63–69. The text was translated by the authors.     

Ecological explanations for successful invasion of exotic plants

The intentional introduction of exotic species can increase the level of local biodiversity, enrich people’s material lives, and bring significant social and economic benefits that are also the symbols of human progress. However, along with the frequent intercourse among countries and regions, the frequency of uncontrolled crossregional migration of species is increased and there is a lack of scientific management strategy for the intentional introduction of exotic species. Exotic species invasion, which is behind habitat fragmentation, has become the second largest threatening factor to the maintenance of the global-scale level of biological diversity. Exotic species invasion can destroy the structure of an ecosystem, disturb the economic life of a society, and do harm to human health. In this paper, the authors review some of the ecological explanations for issues such as “what causes or mechanisms have led to the successful invasion of exotic species”, including the “ideal weeds characteristics”, “biodiversity resistance hypothesis”, “enemies release hypothesis”, “evolution of increased competitive ability hypothesis”, “niche opportunity hypothesis”, and “novel weapon hypothesis”. The authors also analyze and evaluate the background and theoretical basis of the hypotheses, providing explanations for some phenomena, as well as the deficiencies of these explanations.     

A quantum model for controlled enzymic reactions: II. Controlled biochemical networks

Two control units, the switching and the two factor discriminating net are described. They are derived as a consequence of the enzymic oscillatory behavior induced by substrate “perturbation”. A complex network encompassing long sequences of metabolic reactions is constructed and the organization of cellular metabolic activities in well defined “regimes” and “states” inferred.     

Edward Hitchcock’s Pre-Darwinian (1840) “Tree of Life”

The “tree of life” iconography, representing the history of life, dates from at least the latter half of the 18th century, but evolution as the mechanism providing this bifurcating history of life did not appear until the early 19th century. There was also a shift from the straight line, scala naturae view of change in nature to a more bifurcating or tree-like view. Throughout the 19th century authors presented tree-like diagrams, some regarding the Deity as the mechanism of change while others argued for evolution. Straight-line or anagenetic evolution and bifurcating or cladogenetic evolution are known in biology today, but are often misrepresented in popular culture, especially with anagenesis being confounded with scala naturae. Although well known in the mid 19th century, the geologist Edward Hitchcock has been forgotten as an early, if not the first author to publish a paleontologically based “tree of life” beginning in 1840 in the first edition of his popular general geology text Elementary Geology. At least 31 editions were published and those between 1840 and 1859 had this “paleontological chart” showing two trees, one for fossil and living plants and another for animals set within a context of geological time. Although the chart did not vary in later editions, the text explaining the chart did change to reflect newer ideas in paleontology and geology. Whereas Lamarck, Chambers, Bronn, Darwin, and Haeckel saw some form of transmutation as the mechanism that created their “trees of life,” Hitchcock, like his contemporaries Agassiz and Miller, who also produced “trees of life,” saw a deity as the agent of change. Through each edition of his book Hitchcock denounced the newer transmutationist hypotheses of Lamarck, then Chambers, and finally Darwin in an 1860 edition that no longer presented his tree-like “paleontological chart.”