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.     

Contributions to topological biology: Some considerations on the primordial graph and on some possible transformations

This paper is a continuation of some discussions published previously (Bull. Math. Biophysics,16, 317–347, 1954). A different example of a primordial graph is suggested and discussed. Then six different types of geometric transformations, similar in some respects to the one discussed in the previous paper are proposed. Another set of seven different transformations which emphasize the central role of the circulatory system is described. A theorem about the “lumping” of several points of a graph into one point is proved and possible biological aspects of it are discussed.     

Chain processes and their biophysical applications: Part I. General theory

A mathematical theory applicable to the biological effects of radiations as chain processes is developed. The theory may be interpreted substantially as a “hit theory” involving the concepts of “sensitive volume” or “target area”. The variability of the sensitivity of the organism to the radiation and its capacity of recovery between single hits is taken into account. It is shown that in a continuous irradiation of a biological aggregate in which the effect of each single hit cannot be observed, recovery and variation of sensitivity are formally equivalent to each other so that a discrimination between these two phenomena is possible only by discontinuous irradiation or by using different radiation intensities. Methods for the calculation of the “number of hits” and for the determination of the kinetics of the processes from “survival curves” or similar experimental data are given. The relation between the recovery and the Bunsen-Roscoe law is discussed. The case in which the injury of the organism is dependent on the destruction of more than one “sensitive volume” is also considered.     

Theoretical Assessment of Public Health Impact of Imperfect Prophylactic HIV-1 Vaccines with Therapeutic Benefits

This paper presents a number of deterministic models for theoretically assessing the potential impact of an imperfect prophylactic HIV-1 vaccine that has five biological modes of action, namely “take,” “degree,” “duration,” “infectiousness,” and “progression,” and can lead to increased risky behavior. The models, which are of the form of systems of nonlinear differential equations, are constructed via a progressive refinement of a basic model to incorporate more realistic features of HIV pathogenesis and epidemiology such as staged progression, differential infectivity, and HIV transmission by AIDS patients. The models are analyzed to gain insights into the qualitative features of the associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction numbers and a measure for vaccine impact or efficacy. The key findings of the study include the following (i) if the vaccinated reproduction number is greater than unity, each of the models considered has a locally unstable disease-free equilibrium and a unique endemic equilibrium; (ii) owing to the vaccine-induced backward bifurcation in these models, the classical epidemiological requirement of vaccinated reproduction number being less than unity does not guarantee disease elimination in these models; (iii) an imperfect vaccine will reduce HIV prevalence and mortality if the reproduction number for a wholly vaccinated population is less than the corresponding reproduction number in the absence of vaccination; (iv) the expressions for the vaccine characteristics of the refined models take the same general structure as those of the basic model.     

A control model of human tongue movements in speech

Tongue movements during speech production have been investigated by means of a simple yet realistic biomechanical model, based on a finite elements modeling of soft tissues, in the framework of the equilibrium point hypothesis (-model) of motor control. In particular, the model has been applied to the estimation of the “central” control commands issued to the muscles, for a data set of mid-sagittal digitized tracings of vocal tract shape, r ecorded by means of low-intensity X-ray cineradiographies during speech. In spite of the highly non-linear mapping between the shape of the oral cavity and its acoustic consequences, the organization of control commands preserves the peculiar spatial organization of vowel phonemes in acoustic space. A factor analysis of control commands, which have been decomposed into independent or “orthogonal” muscle groups, has shown that, in spite of the great mobility of the tongue and the highly complex arrangement of tongue muscles, its movements can be explained in terms of the activation of a small number of independent muscle groups, each corresponding to an elementary or “primitive” movement. These results are consistent with the hypothesis that the tongue is controlled by a small number of independent “articulators”, for which a precise biomechanical substrate is provided. The influence of the effect of jaw and hyoid movements on tongue equilibrium has also bee n evaluated, suggesting that the bony structures cannot be considered as a moving frame of reference, but, indeed, there may be a substantial interaction between them and the tongue, that may only be accounted for by a “global” model. The reported results also define a simple control model for the tongue and, in analogy with similar modelling studies, they suggest that, because of the peculiar geometrical arrangement of tongue muscles, the central nervous system (CNS) may not need a de tailed representation of tongue mechanics but rather may make use of a relatively small number of muscle synergies, that are invariant over the whole space of tongue configurations. Received: 27 August 1996 / Accepted in revised form: 25 February 1997     

“Ignition” phenomena in random nets

The spread of excitation in a “random net” is investigated. It is shown that if the thresholds of individual neurons in the net are equal to unity, a positive steady state of excitation will be reached equal to γ, which previously had been computed as the weak connectivity of the net. If, however, the individual thresholds are greater than unity, either no positive steady state exists, or two such states depending on the magnitude of the axone density. In the latter case the smaller of the two steady states is unstable and hence resembles an “ignition point” of the net. If the initial stimulation (assumed instantaneous) exceeds the “ignition point,” the excitation of the net eventually assumes the greater steady state. Possible connections between this model and the phenomenon of the “preset” response are discussed.     

Source-sink landscape theory and its ecological significance

Exploring the relationships between landscape pattern and ecological processes is the key topic of landscape ecology, for which, a large number of indices as well as landscape pattern analysis model were developed. However, one problem faced by landscape ecologists is that it is hard to link the landscape indices with a specific ecological process. Linking landscape pattern and ecological processes has become a challenge for landscape ecologists. “Source” and “sink” are common concepts used in air pollution research, by which the movement direction and pattern of different pollutants in air can be clearly identified. In fact, for any ecological process, the research can be considered as a balance between the source and the sink in space. Thus, the concepts of “source” and “sink” could be implemented to the research of landscape pattern and ecological processes. In this paper, a theory of sourcesink landscape was proposed, which include: (1) In the research of landscape pattern and ecological process, all landscape types can be divided into two groups, “source” landscape and “sink” landscape. “Source” landscape contributes positively to the ecological process, while “sink” landscape is unhelpful to the ecological process. (2) Both landscapes are recognized with regard to the specific ecological process. “Source” landscape in a target ecological process may change into a “sink” landscape as in another ecological process. Therefore, the ecological process should be determined before “source” or “sink” landscape were defined. (3) The key point to distinguish “source” landscape from “sink” landscape is to quantify the effect of landscape on ecological process. The positive effect is made by “source” landscape, and the negative effect by “sink” landscape. (4) For the same ecological process, the contribution of “source” landscapes may vary, and it is the same to the “sink” landscapes. It is required to determine the weight of each landscape type on ecological processes. (5) The sourcesink principle can be applied to non-point source pollution control, biologic diversity protection, urban heat island effect mitigation, etc. However, the landscape evaluation models need to be calibrated respectively, because different ecological processes correspond with different source-sink landscapes and evaluation models for the different study areas. This theory is helpful to further study landscape pattern and ecological process, and offers a basis for new landscape index design. __________ Translated from Acta Ecologica Sinica, 2006, 26(5): 1444–1449 [译自: 生态学报]     

From sepiamelanin to chemical ecology of opisthobranchs and diatoms: an exciting 40 years game in the field of marine natural products

This paper reports the lecture delivered on the occasion of the “Ceremony of Professional Recognition” to the author at the 6th European Conference on Marine Natural Products (Porto, Portugal, 19–23 July 2009). The most recent results obtained studying opisthobranchs and diatoms at ICB are presented after a synthetic overview of the most significant moves played during this exciting 40 years game in the field of Marine Natural Products. In a symbolic manner this career is compared to a chess game. After the “romantic” opening dedicated to the study of natural black (melanin) and red-brown (phaeomelanins) pigments in the prestigious group of Rodolfo A. Nicolaus, the research on marine organisms started in 1969 and rapidly led to the characterization of an impressive number of new compounds exhibiting very unusual structures. Substantially, the “structure hunt” ended with the publication of a series of alkaloids with absolutely unprecedented structural features: the saraines. Slowly, the scientific interest shifted “from structure to function”. Opisthobranchs were selected as models to investigate. The majority of the protective allomones possessed by opisthobranch molluscs are sequestered through the food chain from algae and invertebrates. However, opisthobranchs were also able to biosynthesize many compounds structurally related to typical molecules possessed by their prey. These aspects “from function to ecology, to biosynthesis, to evolution” are discussed in detail.     

Abstract mathematical molecular biology: II some relational consequences of the “one gene-one enzyme” hypothesis

Following the program outlined in a previous paper (Bull. Math. Biophysics,23, 237–260, 1961), a further abstract study is made of some simple relational systems which possess some properties of living organisms. It is shown that the “one gene-one enzyme” hypothesis leads to the conclusion that either all genes are built of the same chemical building blocks, or that at least all genes have a number of building blocks in common. A consistent relational application of the “one gene-one enzyme” hypothesis leads moreover to the conclusion that replication is not an inherent property of a gene. Rather there must be a set of enzymes which “copy” the genes. The number of enzymes in this set must be less than the number of genes and therefore the activity of those “copying” enzymes cannot be absolutely specific.     

Suggestion for a possible approach to molecular biology

A hypothetical “self-reproducing living molecule” has been recently frequently discussed in the literature. A physical theory of such a molecule is tentatively outlined. The relational, rather than the quantitative, aspects of the process are emphasized. The process of synthesis of such a molecule from its components is considered as a transition of a complex system between two quantum-mechanical states. The requirement that a “living molecule” should be able to multiply only by self-reproduction but not by a formationde novo leads to the conclusion that the above mentioned transition is a forbidden one. A constellation of conditions under which the forbiddenness is lifted by the presence of an already existing “living molecule” is suggested. The outlined mechanism leads to the conclusion that the property of self-reproduction does not so much reside in the self-reproducing molecule itself as in its relations to other molecules of a system.     

The basis for haplotype complexity in VCBPs, an immune-type receptor in amphioxus

Innate immune gene repertoires are restricted primarily to germline variation. Adaptive immunity, by comparison, relies on somatic variation of germline-encoded genes to generate extraordinarily large numbers of non-heritable antigen recognition motifs. Invertebrates lack the key features of vertebrate adaptive immunity, but have evolved a variety of alternative mechanisms to successfully protect the integrity of “self”; in many cases, these appear to be taxon-specific innovations. In the protochordate Branchiostoma floridae (amphioxus), the variable region-containing chitin-binding proteins (VCBPs) constitute a multigene family (comprised of VCBPs 1–5), which possesses features that are consistent with innate immune-type function. A large number of VCBP alleles and haplotypes are shown to exhibit levels of polymorphism exceeding the elevated overall levels determined for the whole amphioxus genome (JGI). VCBP genes of the 2 and 5 types are distinguished further by a highly polymorphic segment (exon 2) in the N-terminal immunoglobulin domain, defined previously as a “hypervariable region” or a “hotspot.” Genomic deoxyribonucleic acid (DNA) and complementary DNA (cDNA) sequences from large numbers of animals representing different populations reveal further significant differences in sequence complexity within and across VCBP2/5 haplotypes that arise through overlapping mechanisms of genetic exchange, gene copy number variation as well as mutation and give rise to distinct allelic lineages. The collective observations suggest that mechanisms were in place at the time of divergence of the cephalochordates that could selectively hyperdiversify immune-type receptors within a multigene family.     

Hidden treatments in ecological experiments: re-evaluating the ecosystem function of biodiversity

Interactions between biotic and abiotic processes complicate the design and interpretation of ecological experiments. Separating causality from simple correlation requires distinguishing among experimental treatments, experimental responses, and the many processes and properties that are correlated with either the treatments or the responses, or both. When an experimental manipulation has multiple components, but only one of them is identified as the experimental treatment, erroneous conclusions about cause and effect relationships are likely because the actual cause of any observed response may be ignored in the interpretation of the experimental results. This unrecognized cause of an observed response can be considered a “hidden treatment.” Three types of hidden treatments are potential problems in biodiversity experiments: (1) abiotic conditions, such as resource levels, or biotic conditions, such as predation, which are intentionally or unintentionally altered in order to create differences in species numbers for “diversity” treatments; (2) non-random selection of species with particular attributes that produce treatment differences that exceed those due to “diversity” alone; and (3) the increased statistical probability of including a species with a dominant negative or positive effect (e.g., dense shade, or nitrogen fixation) in randomly selected groups of species of increasing number or “diversity.” In each of these cases, treatment responses that are actually the result of the “hidden treatment” may be inadvertently attributed to variation in species diversity. Case studies re-evaluating three different types of biodiversity experiments demonstrate that the increases found in such ecosystem properties as productivity, nutrient use efficiency, and stability (all of which were attributed to higher levels of species diversity) were actually caused by “hidden treatments” that altered plant biomass and productivity. Received: 16 December 1996 / Accepted: 2 March 1997     

Retrospective and predictive systems of information on airborne pollen concentrations in relation to hay fever

Summary In this survey, the most important aspects concerning information on airborne pollen concentrations in relation to hay fever are reported. Six of these aspects are briefly discussed. They are: target group, “spectivity”, subject exactness, routes, frequency. These aspects of information system can concern airborne pollen and/or pollinosis. The “Leiden” system has two flows of information: daily hay-fever forecast and weekly pollen bulletin.     

On the Structural Regularity in Nucleobases and Amino Acids and Relationship to the Origin and Evolution of the Genetic Code

To explore how chemical structures of both nucleobases and amino acids may have played a role in shaping the genetic code, numbers of sp² hybrid nitrogen atoms in nucleobases were taken as a determinative measure for empirical stereo-electronic property to analyze the genetic code. Results revealed that amino acid hydropathy correlates strongly with the sp² nitrogen atom numbers in nucleobases rather than with the overall electronic property such as redox potentials of the bases, reflecting that stereo-electronic property of bases may play a role. In the rearranged code, five simple but stereo-structurally distinctive amino acids (Gly, Pro, Val, Thr and Ala) and their codon quartets form a crossed intersection “core”. Secondly, a re-categorization of the amino acids according to their β-carbon stereochemistry, verified by charge density (at β-carbon) calculation, results in five groups of stereo-structurally distinctive amino acids, the group leaders of which are Gly, Pro, Val, Thr and Ala, remarkably overlapping the above “core”. These two lines of independent observations provide empirical arguments for a contention that a seemingly “frozen” “core” could have formed at a certain evolutionary stage. The possible existence of this codon “core” is in conformity with a previous evolutionary model whereby stereochemical interactions may have shaped the code. Moreover, the genetic code listed in UCGA succession together with this codon “core” has recently facilitated an identification of the unprecedented icosikaioctagon symmetry and bi-pyramidal nature of the genetic code.     

Pioneer neurons: A basis or limiting factor of lophotrochozoa nervous system diversity?

It has been demonstrated by us and other authors that first nervous cells in developing larvae from various trochozoan groups differentiate at the periphery. These pioneer neurons are distinguished by the set of characters. They are located outside the forming central ganglia; outgrowing fibers of central neurons use their processes as a “scaffolding” transmitter expression in these neurons is transient. On the one hand, pioneer neurons mark the “frame” of the adult nervous system and thus play a limiting role. On the other hand, pioneering navigation provides possible mechanisms for evolutional plasticity of the nervous system in adults. In addition, pioneer neurons can underlie functional adaptation of trochophore animals, which minimizes fitness decrease during the transition from the larval to the adult form during metamorphosis.     

A reconsideration of “Races” and their impact on the origins of the Chalcolithic in the Levant using available anthropological and archaeological data

Populations of the Chalcolithic Levant as defined by archaeological excavations has in many cases reinforced the traditional scheme that a number of “races” are present. This scheme is usually based not only on differential cultural traditions as identified by archeologists, but also on the available skeletal evidence as discussed by physical anthropologists. Recently this view has been challenged and it has been suggested that the metrical and anatomical range of variability as identified within Chalcolithic populations can be subsumed into a single population or “racial” range. This paper examines both the available biological and archaeological evidence from the Chalcolithic Levant and concludes that there is no strong archaeological or biological evidence to support a multiple “racial” origin for the Chalcolithic of the Levant.     

Dynamic role of “illite-like” clay minerals in temperate soils: facts and hypotheses

Analysis of new data and reinterpretation of published information for clay minerals found in temperate climate soil profiles indicates that there is often a gradient of “illite-like” clay minerals with depth. We used the term “illite-like” because these observations are based on X-Ray Diffractogram patterns and not on layer charge measurements which allow to define properly illite. It appears that “illite-like” layers are concentrated in the upper, organic - rich portion of the soil profile both under grassland and forest vegetation. “Illite-like” layer quantity seems directly related to soil potassium status. Indeed, intensive agriculture practises without potassium fertilization reduce “illite-like” content in surface soils, whereas several years of potassic fertilization without plant growth can increase “illite-like” content. The potassic soil clay mineral, illite, is particularly important in that it can be the major source of readily available potassium for plants. Spatial and temporal dynamics of clay minerals should be related to the potassium cycle. We propose that the frequently observed general trend of increasing exchangeable potassium in the top soil can be correlated with an increase in “illite-like” in the clays and that the decrease of potassium caused by intensive agricultural practices leads to “illite-like” layer destabilization. This vision of “illite-like” layer as a potassium reservoir refueled by plants and emptied by intensive cropping renews the concept of potassium availability and indicates a need to be discussed as well in natural ecosystems as in cultivated ecosystems.     

HLA-C “blank” alleles express class I gene products. Biochemical analysis of four different HLA-C “blank” polypeptides

Monoclonal antibodies (mAbs) W6/32, HC10, and 4E were used to precipitate class I antigens from 21 selected individuals with at least oneHLA-C “blank” allele. In 19 of these individuals, characteristicHLA-C banding patterns which could be precipitated by all three HLA class I mAbs were observed on one-dimensional isoelectric focusing gels-obviously the gene products ofHLA-C “blank”. At least four allelic HLA-C “blank” gene products with different isoelectric points could be discerned. All of them segregated withHLA-C “blank” haplotypes in informative families; two of them were associated withHLA-B51, one withHLA-B38, and one withHLA-B18. Reactivity of the HLA-C “blank” heavy chains with mAb W6/32 indicates that they are able to associated with beta-2 microglobulin, and hence are most probably expressed at the cell surface.     

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).     

Processus and recessus adhaerentes: giant adherens cell junction systems connect and attract human mesenchymal stem cells

Substrate-adherent cultured cells derived from human bone marrow or umbilical cord blood (“mesenchymal stem cells”) are of special interest for regenerative medicine. We report that such cells, which can display considerable heterogeneity with respect to their cytoskeletal protein complement, are often interconnected by special tentacle-like cell processes contacting one or several other cells. These processus adhaerentes, studded with many (usually small) puncta adhaerentia and varying greatly in length (up to more than 400 μm long), either contact each other in the intercellular space (“ET touches”) or insert in a tight-fitting manner into deep plasma membrane invaginations (recessus adhaerentes), thus forming a novel kind of long (up to 50 μm) continuous cuff-like junction (manubria adhaerentia). The cell processes contain an actin microfilament core that is stabilized with ezrin, α-actinin, and myosin and accompanied by microtubules, and their adhering junctions are characterized by a molecular complement comprising the transmembrane glycoproteins N-cadherin and cadherin-11, in combination with the cytoplasmic plaque proteins α- and β-catenin, together with p120^ctn, plakoglobin, and afadin. The processes are also highly dynamic and rapidly foreshorten as cell colonies approach a denser state of cell packing. These structures are obviously able to establish cell-cell connections, even over long distances, and can form deep-rooted and tight cell-cell adhesions. The possible relationship to similar cell processes in the embryonic primary mesenchyme and their potential in cell sorting and tissue formation processes in the body are discussed. Patrick Wuchter and Judit Boda-Heggemann contributed equally to this work. This work was supported in part by the Joachim Siebeneicher Foundation, by the Deutsche Forschungsgemeinschaft (grant HO 914/4-1 to A.D.H.), by the Deutsche Krebshilfe (grant 10-2049-Fr 1 to W.W.F), and by a grant from the German Ministry for Research and Technology in the special funding program “Regenerative Medicine” (“START-MSC”, grants to A.D.H. and W.W.F).