ALBERT

Notes: Abstract More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.

Notes: Abstract The formal structure of evolutionary theory is based upon the dynamics of alleles, individuals and populations. As such, the theory must assume the prior existence of these entities. This existence problem was recognized nearly a century ago, when DeVries (1904,Species and Varieties: Their Origin by Mutation) stated. “Natural selection may explain the survival of the fittest, but it cannot explain the arrival of the fittest.” At the heart of the existence problem is determining how biological organizations arise in ontogeny and in phylogeny. We develop a minimal theory of biological organization based on two abstractions from chemistry. The theory is formulated using λ-calculus, which provides a natural framework capturing (i) the constructive feature of chemistry, that the collision of molecules generates specific new molecules, and (ii) chemistry's diversity of equivalence classes, that many different reactants can yield the same stable product. We employ a well-stirred and constrained stochastic flow reactor to explore the generic behavior of large numbers of applicatively interacting λ-expressions. This constructive dynamical system generates fixed systems of transformation characterized by syntactical and functional invariances. Organizations are recognized and defined by these syntactical and functional regularities. Objects retained within an organization realize and algebraic structure and possess a grammar which is invariant under the interaction between objects. An organization is self-maintaining, and is characterized by (i) boundaries established by the invariances, (ii) strong self-repair capabilities responsible for a robustness to perturbation, and (iii) a center, defined as the smallest kinetically persistent and self-maintaining generator set of the algebra. Imposition of different boundary conditions on the stochastic flow reactor generates different levels of organization, and a diversity of organizations within each level. Level 0 is defined by selfcopying objects or simple ensembles of copying objects. Level 1 denotes a new object class, whose objects are self-maintaining organizations made of Level 0 objects, and Level 2 is defined by self-maintaining metaorganizations composed of Level 1 organizations. These results invite analogy to the history of life, that is, to the progression from self-replication to self-maintaining procaryotic organizations to ultimately yield self-maintaining eucaryotic organizations. In our system self-maintaining organizations arise as a generic consequence of two features of chemistry, without appeal to natural selection. We hold these findings as calling for increased attention to the structural basis of biological order.

Notes: Abstract A model is developed to describe neuronal elongation as a result of the polymerization of microtubules and elastic stretching of the neurites by force produced by the growth cone. The model for a single segment with a single growth cone revealed a constant elongation rate, while the concentration of tubulin in the soma rises, and the concentration of tubulin becomes constant in the growth cone. Extending the model to a neurite with a single branch point and two growth cones revealed the same results. When the assembly or the disassembly rate of microtubules is unequal in both growth cones, transient retraction of one of the terminal segments occurs, which results in complete retraction of the segment when the difference in (dis)assembly rate between the two growth cones is large enough. When the model is applied to large trees, a maximal sustainable number of terminal segments as a function of the production rate of tubulin appears. Mechanisms to stop outgrowth are discussed in relation to the establishment of synaptical contacts between cells.

Notes: Abstract We have developed a new model describing the relationship between plasma and red cell tracers flowing through the lung. The model is the result of an analysis of the transport of radiolabeled plasma albumin between two flowing phases and shows that differences between red cell and plasma tracer curves are related to microvascular hematocrit. The model was tested in an isolated, blood-perfused dog lung preparation in which we injected51Cr-labeled red cells and125I-labeled plasma albumin into the pulmonary artery. From the tracer concentration-time curves at the venous outflow, we calculatedh r, the ratio of microvascular hematocrit to large-vessel hematocrit. In 18 baseline experiments,h r=0.92±0.01 (mn±sem) at a blood flow rate of 10.7±0.3 ml s−1. We determined the effects of (a) glass bead embolization, (b) alloxan, and (c) lobe ligation onh r. Embolization attenuated the separation between plasma and red cells (increasedh r), probably as a consequence of passive vasodilation. Alloxan enhanced separation of plasma and red cells (decreasedh r), possibly as a result of arteriolar vasoconstriction. Ligation of a fraction of the perfused tissue at constant flow did not cause significant change inh r in the remaining perfused tissue. The model assumes that large-vessel transit times are uniform and that all dispersion occurs in the microvasculature. A theoretical analysis apportioning dispersion between large and small vessels disclosed that the error associated with these assumptions is likely to be less than 15% of the measuredh r. We conclude from this study that the microvascular hematocrit model describes experimental plasma and red cell curves. The results imply thath r can be readily deduced from tagged red cells and plasma and can be accounted for in calculating permeability-surface area in diffusing tracer experiments.

Notes: Abstract We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.

Notes: Abstract We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the restriction sites with high probability. The motivation for the new approach comes from combinatorial results on the number of mutually homeometric sets in one dimension, where two sets ofn points are homeometric if the multiset ofn(n−1)/2 distances they determine are the same. Since experimental data contain errors, we propose algorithms for reconstructing sets from noisy interpoint distances, including the possibility of missing fragments. We analyse the performance of these algorithms under a reasonable probability distribution, establishing a relative error limit ofr=Θ(1/n 2) beyond which our technique becomes infeasible. Through simulations, we establish that our technique is robust enough to reconstruct data with relative errors of up to 7.0% in the measured fragment lengths for typical problems, which appears sufficient for certain biological applications.

Notes: Abstract A simple chemical model of the idiotypic network of immune systems, namely the AB model, has been developed by De Boeret al. The complexity of the system, such as the steady states, periodic oscillations and chaotic motions, has been examined by the authors mentioned above. In the present paper, the periodic motions and chaotic behaviours exhibited by the system are intuitively described. To clarify in which parameter domains concerned the system exhibits periodic oscillations and in which parameter domains the system demonstrates chaotic behaviours the Lyapounov exponent is explored. To characterize the strangeness of the attractors, the fractal dimension problem is worked out.

Notes: Abstract We consider a stochastic mechanism of the loss of resistance of cancer cells to cytotoxic agents, in terms of unstable gene amplification. Two models being different versions of a time-continuous branching random walk are presented. Both models assume strong dependence in replication and segregation of the extrachromosomal elements. The mathematical part of the paper includes the expression for the expected number of cells with a given number of gene copies in terms of modified Bessel functions. This adds to the collection of rare explicit solutions to branching process models. Original asymptotic expansions are also demonstrated. Fitting the model to experimental data yields estimates of the probabilities of gene amplification and deamplification. The thesis of the paper is that purely stochastic mechanisms may explain the dynamics of reversible drug resistance of cancer cells. Various stochastic approaches and their limitations are discussed.

Notes: Abstract Dextran has been the most commonly employed test molecule for probing the selectivity of glomerular filtration to macromolecules of varying size. The usual theories for hindered transport of solid spheres through pores have limited utility in interpreting clearance data for dextran or other linear polymers because such polymers in solution more closely resemble random, solvent-filled coils than solid spheres. To provide a model for glomerular filtration of random-coil macromolecules, the equilibrium partitioning of random coils between cylindrical pores and bulk solution was simulated using Monte Carlo calculations, and those results were combined with a hydrodynamic theory for restricted motion of solvent-filled polymer coils in pores. The rates of transport predicted for either neutral random coils or for solid spheres of the same Stokes-Einstein radius were significantly lower than observed transport rates of dextran through the glomerular capillary wall or across synthetic porous membranes. This facilitation of dextran transport was modeled by postulating weak, attractive interactions between dextran monomers and the pore wall. The random-coil model with attractive interactions, modeled using a short-range, square-well potential, was found to adequately represent dextran sieving data in normal rats. Various limitations of this approach are discussed.

Notes: Abstract Method-dependent mechanisms that may affect dynamic numerical solutions of a hyperbolic partial differential equation that models concentration profiles in renal tubules are described. Some numerical methods that have been applied to the equation are summarized, and ways by which the methods may misrepresent true solutions are analysed. Comparison of these methods demonstrates the need for thoughtful application of computational mathematics when simulating complicated time-dependent phenomena.

Notes: Abstract The regulation of the interactions between the actin binding proteins and the actin filaments are known to affect the cytoskeletal structure of F-actin. We develop a model depicting the formation of actin cytoskeleton, bundles and orthogonal networks, via activation or inactivation of different types of actin binding proteins. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs depending on the active actin binding protein concentration. Also, a minute change in the relative binding affinity of the actin binding proteins in the cell may lead to a major change in the actin cytoskeleton. Both the linear stability analysis and the numerical results indicate that the structures formed are highly sensitive to changes in the parameters, in particular to changes in the parameter ϕ, denoting the relative binding affinity and concentration of the actin binding proteins.

Notes: Abstract To investigate morphogenesis and in particular circularization mechanisms in young mycelia, we observe cultures of the zygomyceteMucor spinosus and develop discrete models of two-dimensional filamental branching growth. The models are based on the hypothesis that the fungus secretes a regulatory substance that diffuses into the surrounding medium and is detected by the growing hyphae. We also present a simple Markovian growth model without such a feedback, but yielding to analytical computations.

Notes: Abstract In vivo volume growth of two murine tumor cell lines was compared by mathematical modeling to their volume growth as multicellular spheroids. Fourteen deterministic mathematical models were studied. For one cell line, spheroid growth could be described by a model simpler than needed for description of growthin vivo. A model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to a model that did not include such a role. The von Bertalanffy model and the logistic model could not fit the data; this result contradicted some previous literature and was found to depend on the applied least squares fitting method. By the use of a particularly designed mathematical method, qualitative differences were discriminated from quantitative differences in growth dynamics of the same cells cultivated in two different three-dimensional systems.

Notes: Abstract This paper develops and applies a dynamic mathematical model for optimal scheduling of nitrogen fertilization and irrigation that minimizes nitrogen leaching subject to a target level of yield. The analysis assumes a single crop grown during a single growing season of a given length. It is shown that substitution of water for nitrogen along a given plant growth path decreases nitrogen leaching and, therefore, groundwater contamination. It is proved that a minimum leaching solution to the optimization problem is obtained with a single nitrogen application at the beginning of the season and irrigation scheduling that maintains a wet soil throughout the growing period. A numerical example utilizing experimental data for an irrigated summer corn in Israel confirms and quantifies the analytical findings.

Notes: Abstract We analyse the stochastic properties of dynamical systems with finite populations of a few differentreplicator species. Our main interest is to evaluate the typicallifetime, i.e. the time for the extinction of the first species in the network, for different catalytic structures, as a function of the population size.

Notes: Abstract The capacity of a model immune network in terms of the number of different antigens that can be vaccinated against without any memory lost is computed and tested by numerical simulations. We also investigate memory loss and failure to vaccinate due to overcrowding the network with too many antigens. The computations are done for two different strategies for proliferation, one implying all the antigen specific clones and the second one being more thrifty.

Notes: Abstract The technique of model-building a protein of known sequence but unknown tertiary structure from the structures of homologous proteins is probably so far the most reliable means of mapping from primary to tertiary structure. A key step towards the realization of the aim is to develop ways of aligning three-dimensional structures of homologus proteins, thereby deriving the rules useful for protein modelling. We have developed a generalized differential-geometric representation of protein local conformation for use in a protein comparison program which aligns protein sequences on the basis of their sequence and conformational knowledge. Because the differetial-geometric distance measure between local conformations is independent of the coordinate frame and remains chirality information, the comparison program is easily implemented, relatively rational and reasonably fast. The utility of this program for aligning closely and distantly related homologous proteins is demonstrated by multiple alignment of globins, serine proteinases and aspartic proteinase domains. Particularly, the method has reached the rational alignment between the mammalian and microbial serine proteinases as compared with many published alignment programs.

Notes: Abstract New formulas for deriving the sensitivities of stable stage structures and reproductive values to changes in vital rates are presented. They enable comparison of the sensities to changes of different elements in the projection matrix; in other words, comparison of partial derivatives of the eigenvectors. These kinds of sensitivities can be used in applied problems such as an analysis of the effect of harvesting on the population structure. However, in this paper, we examine the application of the sensitivities in a more general ecological context. We investigate why the stable stage structure of the mustard aphid,Lipaphis erysimi, changes very little in the temperature interval 10–30°C. The sensitivities of the stable stage structure at 15°C and 25°C were derived. The character of the sensitivites were the same in both temperatures although the stage structure was more sensitive to changes at 15°C than at 25°C. The sensitivity analysis also revealed that the temperature variation results in changes in fecundity and developmental rate that have a counteractive effect on the population structure.

Notes: Abstract Plankton populations undergo dramatic surges. Rapid increases and decreases by a factor of 10 or more are observed, often separated by relatively stable interludes. We propose a description of plankton communities as excitable systems. In particular, we present a model for the evolution of phytoplankton and zooplankton populations which resembles models for the behaviour of excitable media. The parameter dependency of the various “excitable” phenomena, trigger mechanism, threshold, and slow recovery, is clear, and permits ready investigation of the influence of properties of the physical environment, including variations in nutrient fluxes, temperature or pollution levels.

Notes: Abstract Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent action is close to the literal meaning of the term “non-interaction”. Since this concept does not depend on the mechanisms of actions nor on the type of effect scale used, it is suitable as one of the basic criterion for the definition of synergism and antagonism. A general mathematical framework of independent action is presented in this paper based on the concept of “relative effect” as used in the literature. The, different equations for independent action currently used in various areas are shown to be manifestations, of a general formula under different sets of boundary conditions, which are the natural limiting values of the effects of the corresponding system observed at low and at high doses of the agents. The framework can, be generalized to the combined action ofn-agents as well as to the interaction of an agent with itself. In addition, the differential form of the formula for independent action is derived. This framework of systematic definitions and derived equations enable a more in-depth study of the implications of the concept of independent action and its relation to other concepts of non-interaction.

Notes: Abstract We model how auto-reactiveB cells are kept under control by an idiotypic network. Autoimmunity occurs when the control is broken by an infection or not achieved through an abnormal ontogenetic evolution. We describe the idiotypic network, viz., the central immune system, by idiotype-anti-idiotype pairs which are coupled to a set of highly connected clones, which interact with each clone of the network. Some clones of the central immune system recognize self-antigen. We find a huge variety of fixed points which can be classified as tolerant, autoimmune, and neutral states according to the concentration of the auto-reactive antibody. Most significant are auto-reactive clones which are a member of an idiotype-anti-idiotype pair. In a healthy individual, an autoimmune disease is induced by an antigen infection which triggers a transition from a tolerant to an autoimmune state. Autoimmunity is induced more readily by an antigen coupling to theanti-idiotype than by one interacting with the auto-reactive clone itself. We indicate a possible therapy which simply reverses the processes that have lead to the autoimmune disease. In the early development of the central immune system its highly connected, core part serves to draw the more specific clones of idiotype-anti-idiotype pairs into the network. In order to avoid autoimmunity in ontogenetic evolution the anti-idiotype of an auto-reactive clone must be formed in advance by a sufficiently long period of time. Thus, a well ordered succession of the appearance of the more specific clones is required.

Notes: Abstract A method of dimensionless time-scaling based on extrinsic expectation of life at birth but intrinsic to a system generating a survival distribution is introduced. Such scaling allows the survival fraction function and its associated mortality function to serve as Green's functions for their generalized equivalents. i.e. a “population” function and a “death” function. The analytical mechanics of utilizing these concepts are formulated, applied to the classical Gompertz and Weibull survival models, and discussed with respect to biological relevance.

Notes: Abstract It is now widely accepted that localized high concentrations of Ca2+ (Ca2+ domains) play a major role in controlling the time course of neurotransmitter release. In the present work we calculate the magnitude and the time course of Ca2+ domains that evolve in the vicinity of a Ca2+ channel and an adjacent release site. In the calculations we consider a accurately dimensioned Ca2+ channel. Moreover, the Ca2+ current is continuously adjusted with regard to the accumulated intracellular Ca2+ and, in addition, endogenous buffers are considered. The calculations, carried out by the software FIDAP, based on finite element method, show that the Ca2+ concentrations achieved near the release sites are significantly lower than claimed by other investigators. Furthermore, we present arguments indicating that the Ca2+ domains, regardless of their magnitude, do not play a role in controlling the time course of release of neurotransmitter.

Notes: Abstract Mammalian white blood cells are known to bias the direction of their movement along concentration gradients of specific chemical stimuli, a phenomenon called chemotaxis. Chemotaxis of leukocyte cells is central to the acute inflammatory response in living organisms and other critical physiological functions. On a molecular level, these cells sense the stimuli termed chemotactic factor (CF) through specific cell surface receptors that bind CF molecules. This triggers a complex signal transduction process involving intracellular biochemical pathways and biophysical events, eventually leading to the observable chemotactic response. Several investigators have shown theoretically that statistical fluctuations in receptor binding lead to “noisy” intracellular signals, which may explain the observed imperfect chemotactic response to a CF gradient. The most recent dynamic model (Tranquillo and Lauffenburger,J. Math. Biol. 25, 229–262. 1987) couples a scheme for intracellular signal transduction and cell motility response with fluctuations in receptor binding. However, this model employs several assumptions regarding receptor dynamics that are now known to be oversimplifications. We extend the earlier model by accounting for several known and speculated chemotactic receptor dynamics, namely, transient G-protein signaling, cytoskeletal association, and receptor internalization and recycling, including statistical fluctuations in the numbers of receptors among the various states. Published studies are used to estimate associated constants and ensure the predicted receptor distribution is accurate. Model analysis indicates that directional persistence in uniform CF concentrations is enhanced by increasing rate constants for receptor cytoskeletal inactivation, ternary complex dissociation, and binary complex dissociation, and by decreasing rate constants for receptor internalization and recycling. For most rate constants, we have detected an optimal range that maximizes orientation bias in CF gradients. We have also examined different desensitization and receptor recycling mechanisms that yield experimentally documented orientation behavior. These yield novel insights into the relationship between receptor dynamics and leukocyte chemosensory movement behavior.

Notes: Abstract Given two independent sequences of letters, we seek the probability distribution of the length of the longest matching word. This word can be in different positions in the two sequences and we consider both perfect and nearly perfect matching. We derive bounds and approximations for the probability and compare them with other bounds and approximations. The results can be applied to DNA sequences in molecular biology and generalized matching between two independent random sequences.

Notes: Abstract Are there enough mast cells in denervated skeletal muscle to account for autopharmacological mediation of the antigen potentials (APs) elicited by microtaps? Through rough qualitative estimations, some authors have suggested a positive answer to this question. However, in view of measurements performed in this investigation of both the density of mast cells and the diffusion coefficient of antigens, the probability of such mediated effects was found to be relatively low:P=0.016 for egg albumin andP=0.004 for ferritin. Therefore, most APs induced by microtaps should be attributed to the direct effect of antigen over the sensitized muscle fibers. Yet, both the density of mast cells found in this work and the known amount of histamine they are capable of releasing when challenged with antigen, support the hypothesis regarding the involvement of these cells when antigen is massively superfused so as to induce Schultz-Dale reactions in muscle strips. Under this circumstance, the direct and mediated mechanisms may coexist.

Notes: Abstract We consider the phenomenon of self-focusing pattern formation of motile micro-organisms (“streamer”). The focusing mechanism is based on gyrotaxis, a physical phenomenon, and it results from the balance between viscous and gravitational moments on the organisms. Under particular circumstances such streamers are stabilized and sink, resulting in vertical transport of micro-organisms as well as horizontal heterogeneity in cell concentration. We develop a plume model for the streamer, which consists of the equations of continuity, momentum, and cell concentration. These equations are further simplified to three basic equations representing volume, momentum and concentration fluxes of the steady-state plume. Asymptotic analytical solutions for the plume are obtained. From numerical solutions we find the shape of the plume which takes the form of a vertical string with lengths ranging from 1 to 10 cm. The streamer formation can be related to algal blooms occurring in the sea and to algal cultures grown in the laboratory.

Notes: Abstract A mathematical model of the renal vascular and tubular systems was used to examine the possibility that synergistic interactions might occur between the tubuloglomerular feedback (TGF) and myogenic autoregulatory mechanisms in the kidney. To simulate the myogenic mechanism, the renal vasculature was modelled with a resistance network where the total preglomerular resistance varies with intravascular pressure. In addition, a steady-state model of glomerular filtration, proximal and Henle's loop reabsorption, and TGF-modulation of afferent arteriolar resistance was derived. The results show that, if TGF acts on the distal portion of the preglomerular vasculature, then any TGF-induced vasoconstriction should raise upstream intravascular pressure and, thereby, trigger a myogenic response in the more proximal vascular segments, a phenomenon referred to as an ascending myogenic (AMYO) response. The model further predicts that the magnitude of the AMYO response can be similar in magnitude to the TGF-induced increment in afferent resistance. Hence, the effects of TGF excitation on whole kidney hemodynamics may be much greater than pedicted from measurements in single nephrons. Moreover, a significant fraction of the intrinsic myogenic autoregulatory response to increased renal perfusion pressure may result from a synergistic interaction between the TGF and myogenic mechanisms.

Notes: Abstract To test whether a mathematical model combining dynamic models of the tubuloglomerular feedback (TGF) mechanism and the myogenic mechanism was sufficient to explain dynamic autoregulation of renal blood flow, we compared model simulations with experimental data. To assess the dynamic characteristics of renal autoregulation, a broad band perturbation of the arterial pressure was employed in both the simulations and the experiments. Renal blood flow and tubular pressure were used as response variables in the comparison. To better approximate the situationin vivo where as large number of individual nephrons act in parallel, each simulation was performed with 125 parallel versions of the model. The key parameters of the 125 versions of the model were chosen randomly within the physiological range. None of the constituent models, i.e., the TGF and the myogenic, could alone reproduce the experimental observations. However, in combination they reproduced most of the features of the various transfer functions calculated from the experimental data. The major discrepancy was the presence of a bimodal distribution of the admittance phase in the simulations. This is not consistent with most of the experimental data, which shows a unimodal curve for the admittance phase. The ability of the model to reproduce the experimental data supports the hypothesis that dynamic autoregulation of renal blood flow is due to the combined action of TGF and the myogenic response.

Notes: Abstract A model is presented of solute and water reabsorption along the proximal tubule of the rat kidney based on kinetic descriptions of the main membrane transport systems, in order to assess the extent to which these kinetics suffice to explain certain aspects of the global transport behaviour in this segment, especially with respect to bicarbonate reabsorption. The model includes in the apical membrane, an active proton pump, Na+/H+ antiport, Na-coupled transport of organic solutes, Cl−/formate exchange with formic acid recycling, and membrane conductances to protons and K+. In the baso-lateral membrane, besides the Na+/K+ pump, the model includes Na+-3HCO 3 − and electroneutral K+-Cl− cotransporters, and membrane conductances for K+, H+, and, optionally, for Cl−. Appropriate passive diffusional pathways were included in both cell membranes and in the paracellular pathway. Using mass balance and electoneutrality constraints, these transport systems were built into an epithelial model which was then integrated (by finite difference approximation) into a model of a longitudinal tubule. Simulated cellular solute concentrations and luminal concentration profiles were in good agreement with reported experimental observations. We show that, given the reported transport kinetics for the Na+/H+ antiporter, a hitherto unexplained observation concerning load-dependent bicarbonate reabsorption can be shown mainly to result from the nonlinear longitudinal concentration profile for bicarbonate and pH. We also discuss problems of transcellular Cl− transport in the light of recent reports of basolateral Cl− conductance and observations relevant to apical Cl−/formate (or other base) exchange.

Notes: Abstract Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, ɛ, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting ɛ to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L−1 can be generated by forces of the order of 20 mosm L−1. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.

Notes: Abstract Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where there idealized approximations begin to break down. In this paper we derive equations that govern membrane transport for non-dilute solutions and use these equations in a three-dimensional model of the concentrating mechanism. New numerical methods were employed that are more stable than those employed previously. Compared to ideal solution models, the urea non-ideality tends to increase predicted osmolarities, whereas NaCl non-ideality decreases predictions.

Notes: Abstract Chloride/formate exchange, in parallel with Na+/H+ exchange and nonionic diffusion of H2CO2, has been proposed as a mechanism of electroneutral transcellular Cl− reabsorption by the proximal tubule. However, the measured brush border H2CO2 permeability of the rat proximal tubule is at least an order of magnitude too low to support sufficient H2CO2 recycling. To investigate the possibility that an unstirred layer within the brush border might depress the measured H2CO2 permeability, we constructed a mathematical model of a villous membrane. Axial fluxes along villous and intervillous spaces were specified by Nernst-Planck diffusion equations. Model parameters were set to achieve agreement with ion and water fluxes measured in the rat proximal tubule. The equations were solved numerically to generate steady-state concentration profiles in the villous and intervillous spaces. An apparent brush border H2CO2 permeability was determined by perturbing luminal [H2CO2] and calculating the change in H2CO2 flux. Overall, the ratio of apparent brush border H2CO2 permeability to cell membrane H2CO2 permeability was greater than 90%. Contributing to the small decrease in apparent permeability are finite diffusion coefficients, folding of the membrane, and acidification of the luminal solution. An approximate analysis of this system shows the critical parameters of brush border formate transport to be the actual membrane H2CO2 permeability, and the diffusion coefficients of HCO 3 − and HCO 3 − . Nevertheless, decreasing the diffusion coefficients by one order of magnitude failed to depress apparent brush border H2CO2 permeability by more than an additional 25%. We conclude that although permeability is systematically underestimated across a villous membrane, unstirred layer effects in the brush border are still too small to resolve the discrepancy between the measured value of H2CO2 permeability and the value needed to allow recycling.

Notes: Abstract We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow direction. To obtain second-order convergence in space and time, we employ the recently developed ENO (Essentially Non-Oscillatory) methodology. We present examples of computed flows and concentration profiles in representative model contexts. Finally, we indicate briefly how model tubules may be coupled to construct large-scale simulations of the renal counterflow system.

Notes: Abstract Recently algorithms for parametric alignment (Watermanet al., 1992,Natl Acad. Sci. USA 89, 6090–6093; Gusfieldet al., 1992,Proceedings of the Third Annual ACM-SIAM Discrete Algorithms) find optimal scores for all penalty parameters, both for global and local sequence alignment. This paper reviews those techniques. Then in the main part of this paper dynamic programming methods are used to compute ensemble alignment, finding all alignment scores for all parameters. Both global and local ensemble alignments are studied, and parametric alignment is used to compute near optimal ensemble alignments.

Notes: Abstract A class of minimal models is constructed that can exhibit several salient phenomena associated with T-cell inoculations that prevent and cure autoimmune disease. The models consist of differential equations for the magnitude of two populations, the effectorsE (which cause the disease), and an interacting regulator populationR. In these models, normality, vaccination and disease are identified with stable steady-states of the differential equations. Thereby accommodated by the models are a variety of findings such as the induction of vaccination or disease, depending on the size of the effector inoculant. Features such as spontaneous acquisition of disease and spontaneous cure require that the models be expanded to permit slow variation of their coefficients and hence slow shifts in the number of steady-states. Other extensions of the basic models permit them to be relevant to vaccination by killed cells or by antigen, or to the interaction of a larger number of cell types. The discussion includes an indication of how the highly simplified approach taken here can serve as a first step in a modeling program that takes increasing cognizance of relevant aspects of known immunological physiology. Even at its present stage, the theory leads to several suggestions for experiments.

Notes: Abstract A mathematical model for steady flow through a discontinuity in the tight junction of an endothelial intercellular cleft is presented. Subject to plausible assumptions the problem of calculating the flow in the cleft, in either the presence or the absence of a fibre matrix, reduces to the solution of Laplace's equation in a two-dimensional domain. For an idealized geometry representing a discontinuity between two semi-infinite tight junction regions, a general analytic solution is found by means of conformal mappings. The model geometry, unlike those assumed in previous studies, allows the tight junction regions to be out of alignment with each other, and even to overlap, modelling flow through a tortuous, rather than a direct, pathway. Useful asymptotic approximations for the flow rate are derived when the discontinuity is either very small or very large. For small discontinuities, the predicted flow rate is much greater than a naïve estimate based on uniform parallel flow through the discontinuity. For the special case where the tight junction regions are aligned with each other, comparison of our results with those of an approximate treatment due to Tsayet al. [Chem. Engng Commun. 82, 67–102 (1989)] shows generally very close agreement.

Notes: Abstract A general description is given for the meristem of elongating organs such as for stem internode, monocotyledonous leaf and roots. The meristem is viewed as a cellular organization rather than traditionally as a region with certain growth dynamics; cell lineages are inspected and analyzed by cell packet features. Three features of the meristem are described by the displacement of the distal (bottom) transverse wall of a cell: (a) the duration of time the cell and its derivatives spend in the meristem, (b) the duration of cell cycle and (c) the number of cells in a clone derived from a meristematic cell. Cell packet analyses of data from the internode of the Purple Heart (Setcreasea) and the top epidermis of the leaf of the Wandering Jew (Zebrina) indicate meristem lengths of 33 and 50 cells, respectively, while growth and cell division rates in the meristem for both species follow Gaussian distributions.

Notes: Abstract I seek to explain phenomena observed in simulations of populations of gap junction-coupled bursting cells by studying the dynamics of identical pairs. I use a simplified model for pancreatic β-cells and decompose the system into fast (spike-generating) and slow subsystems to show how bifurcations of the fast subsystem affect bursting behavior. When coupling is weak, the spikes are not in phase but rather are anti-phase, asymmetric or quasi-periodic. These solutions all support bursting with smaller amplitude spikes than the in-phase case, leading to increased burst period. A key geometrical feature underlying this is that the in-phase periodic solution branch terminates in a homoclinic orbit. The same mechanism also provides a model for bursting as an emergent property of populations; cells which are not intrinsic bursters can burst when coupled. This phenomenon is enhanced when symmetry is broken by making the cells differ in a parameter.

Notes: Abstract Twining plants exhibit a striking oscillation of their stems in their quest for a support. The oscillations, called circumnutation, have periods generally of 1–5 hr, and virtually all species have a preferred direction of twining. I seek to explain these chiral asymmetries in plant behavior by hypothesizing a chiral asymmetry in plant anatomy. Such asymmetries already exist, for example, in phyllotaxis. I explore wave phenomena on asymmetric but isotropic rings, and seek systems which will only support (stable) waves in one direction around the ring, and not in the other. Simulations indicate that (1) oscillatory reaction-diffusion systems do not support unidirectional waves on rings; (2) excitable reaction-diffusion systems do support unidirectional waves on rings; and (3) unidirectional phase-locking (discrete unidirectional waves) occurs in rings of coupled oscillators. Thus, chiral asymmetries of circumnutating plants cannot be explained by continuum oscillator phenomena, but can be explained by general discrete oscillators, or excitable phenomena on the continuum.

Notes: Abstract A mathematical model has been considered in which the known equation of McKendrick and Von Foerster for cell age distribution is combined with that for substrate concentration. The dependence of cell division rate on cell age has been taken as a step function. The interrelation between culture parameters describing the substrate consumption and cell division has been found. The shape of cell age distribution as well as the values of substrate and cell concentrations in steady and transient states have been investigated. Stationary regimes at the initial culture state synchronized by ages have been found to be established as damped oscillations and age waves. Under definite conditions the transition from one steady growth regime to another includes sharp single-time age synchronization of the culture.

Notes: Abstract The simplex methods of nonlinear forecasting are used to study the data sets of hepatitis A and AIDS in various regions of the United States. The results are compared with those obtained from the traditional ARIMA methods. In many regions, the simplex methods developed from nonlinear dynamical system theory give smaller errors for the data of hepatitis A. A combination of the simplex methods and the traditional ARIMA methods can produce better results for the AIDS data sets.

Notes: Abstract We consider optimal strategies for harvesting a population that is composed of two local populations. The local populations are connected by the dispersal of juveniles, e.g. larvae, and together form a metapopulation. We model the metapopulation dynamics using coupled difference equations. Dynamic programming is used to determine policies for exploitation that are economically optimal. The metapopulation harvesting theory is applied to a hypothetical fishery and optimal strategies are compared to harvesting strategies that assume the metapopulation is composed either of single unconnected populations or of one well-mixed population. Local populations that have high per capita larval production should be more conservatively harvested than would be predicted using conventional theory. Recognizing the metapopulation structure of a stock and using the appropriate theory can significantly improve economic gains.

Notes: Abstract A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.

Notes: Abstract Most theoretical analyses of tracer kinetics in capillaries contain an implicit assumption that the tissues to which they are connected have homogeneous material properties. The microscopic description of the exchange of tracer molecules and tissues is then modeled in terms of first-order kinetics. We consider a class of more general models allowing us to assess the robustness of simplifying assumptions made above. It is shown that when amorphous properties are important the kinetics of the system may differ considerably from those predicted by standard theories.

Notes: Abstract An extension of an earlier model of the p170 glycoprotein pump is presented. In an earlier work (Michelson and Slate,Bull. math. Biol. 54, 1023–1038, 1992), the pump was modeled using an energy-dependent model of facilitated diffusion. In this paper we add an inhibitor to the model. New equations are derived which represent either competitive or non-competitive inhibition in the pumping action of the glycoprotein. Numerical simulations were run which provide a response surface (initial loading concentration of inhibitor and its ability to compete with an ideal anti-cancer drug vs a summary measure of cytoplasmic exposure) for each scenario. The importance of the exposure profile, how it is related to ultimate tumor cell survival, and the binding requirements for developing multidrug resistance inhibitors are discussed.

Notes: Abstract Both syntactic and phonetic features of the trill call accompanying the whistle-shake in adult male Shelducks are subject to cyclic annual changes. In the course of spring, the duration of the whole call increases gradually. This is caused by a prolongation of the first call element and insertion of additive elements in the final phrase. In contrast the second element is shortened by about 10 ms. At the same time, the pitch of all measured elements is raised. These findings are discussed in the framework of hormonal regulation and communicative function.

Notes: Abstract Mitochondrial DNA control region sequences of 25 Knots sampled from 10 populations and possibly four subspecies (canutus, islandica, rogersi, rufa) were obtained by PCR and direct sequencing. Only 7 haplotypes were found worldwide, all closely related to one another and differing by 1–3 substitutions. Knots have most probably expanded to their current population size from a refugial population that was severely bottlenecked late in the Pleistocene. Preliminary results from RAPDs are consistent with this prediction, in that Knots from North America appear to be genetically distinct from Knots elsewhere.

Notes: Abstract The investigation highlights the untypical nature of the intertidal sediments of the sheltered Königshafen embayment in the north of the island of Sylt. The area is characterized by medium sand, which might be explained by aeolian input from the adjacent dunes. Mudflats and sandy mudflats build up the western part of the bay. Other sandy mudflats, all with a small spatial distribution, are associated with mussel beds. A peculiarity of the sediments in the Königshafen embayment are the gravel and cobbles along the northern shore and parts of the southern shore. These can be interpreted as residual sediments from former stages of the “Ellenbogen” spit. A comparison of the present results with earlier studies by Wohlenberg (1937) and Felix (1981) shows a decline in mudflats and an increasing consolidation of the mud in the period up to 1981. Since 1981 the sediment distribution has not changed, hence this tidal embayment can today be qualified as representing a relatively stable depositional area.

Notes: Abstract Former stages of the morphological development of northern Sylt are reconstructed to extend knowledge of the type and approximate time of the formation of a sandy bay (Königshafen) in the Wadden Sea. Apart from an analysis of historical maps and nautical charts, this paper includes the representation of the results of recent borings and sedimentological findings. The two ways of tracing back the development led to different conclusions, which are discussed. The cartographical conclusions cannot confirm the assumption that Königshafen was a deep bay. The input of dune sand from westerly directions and the formation of a sand spit system from the south have caused great morphological changes up to present times. Since the middle of the 17th century there has been an extension of the Königshafen area. On the other hand, geological investigations show that the Ellenbogen could have been formed between the middle of the 17th century and the end of the 18th century. Before that, Königshafen was sheltered by a large sandy spitly at the Lister Tief. It might have been the location of the famous sea battle of 1644 between the Danish fleet and a Swedish/Dutch fleet. The Königshafen area is possibly a young formation and is, at least since its separation from the Lister Tief by the Ellenbogen, an area of prevailing sedimentation.

Notes: Abstract Four helminth parasites out of 19 species found in the Lübeck Bight, Baltic Sea, were chosen for investigations on the transfer from invertebrate to small-sized fish hosts: larvae of the tapewormsSchistocephalus sp. andBothriocephalus sp. (Cestoda) living in planktonic copepods as primary hosts;Podocotyle atomon (Digenea) andHysterothylacium sp. (Nematoda) were found in benthic crustaceans, especiallyGammarus spp. These hosts were the prey of 3 gobiid fishes,Gobiusculus flavescens (feeding mainly on plankton),Pomatoschistus minutus (preferring benthos), andP. pictus (feeding more on plankton than benthos). Because the fishes selected smaller sizes of crustaceans, they ingested all stages of the copepods but only the smaller-sized groups of gammarids which were often less infested by parasites. In order to evaluate the probability for a fish to be parasitized by a helminth, an infestation potential index (IP) was calculated.Podocotyle atomon andHysterothylacium sp. revealed an IP which was far lower in gobies than expected when the prevalences of the previous hosts were taken into consideration. The IP of tapeworm larvae was mainly influenced by the feeding pressure of the gobiid predators, which might change with developmental stage and season. It is concluded that parasite transfer to the next host decreases when sizes of prey and predator differ only moderately. This mechanism can reduce the numbers of parasites transferred to less suitable or wrong hosts.

Notes: Abstract Six specimens ofLeucon parasiphonatus n. sp. were collected at depths ranging from 15 to 424 m in the vicinity of King George Island (South Shetland Islands, Antarctica) and the south eastern Weddell Sea.Leucon parasiphonatus belongs to the subgenusLeucon and differs from the other already known antarctic and Subantarctic species of the genus, in the absence of a serrated dorsomedian line and in the presence of a long pseudorostrum with several fine setae at its tip, surrounding the very long branchial siphon. The surface of the carapace is granulated; the carapace displays no teeth except for a few at its antero-lateral margin and at its ventral margin. The species most similar toLeucon parasiphonatus isLeucon siphonatus, reported from Mediterranean and North Atlantic waters.

Notes: Abstract TBT (tributyltin)-induced imposex is observed in femaleBuccinum undatum from the arctic region. The fine structure of the male penis epithelium was investigated and the results were compared between specimens from non-polluted (Spitsbergen, Norway) and highly-polluted (Brittany, France) areas. Differences in the arrangement and structure of the apical microvilli-border, the intercellular spaces, RER and SER content, as well as a high rate of parasitism in the tissue of individuals from Brittany can be detected between the species of both areas. The results indicate a higher degree of pathological changes in the penis epithelial cells of individuals from TBT-polluted areas than in those from Spitsbergen.

Notes: Abstract A basic control mechanism for the input and output of materials in the Königshafen, a sandy backbarrier embayment, is the action of the tides. Thus, the description of the hydrodynamic conditions provides basic information for further investigations in the Königshafen. On the tidal fltas and in the western part of the tidal creek, the near-bottom residual currents are weakly fooddominated. In the other parts of the tidal creek, the flood and ebb currents are well balanced. During high tide, the suspended matter shows an increase towards the inner part of the bay. The concentration of suspended matter, its distribution and the currents are influenced by wind action. During westerly winds up to 4–5 Beaufort, the concentration of suspended matter in the embayment varies between 1 and 15 mg l−1. During storms with westerly winds, the near-bottom residual currents are orientated into the bay, and the concentration increase by a factor of about 2. Strong easterly winds in combination with a water level of 0.5 m below mean high water level and an increasing wave energy cause considerable resuspension on the tidal flats of the Königshafen embayment. For this reason, the concentration of suspended matter increases by factor of about 20.

Notes: Abstract On sedimentary tidal flats in the Wadden Sea near the Island of Sylt, the periwinkleLittorina littorea occurred preferentially on clusters and beds of mussels and on shell beds (100 to 350 m−2), achieved moderate densities on green algal patches or mats (20 to 50 m−2), and remained rare on bare sediments (〈5 m−2). Green algae covering〉10% of sediment surface appeared in summer on approximately one third of the tidal zone, mainly in the upper and sheltered parts and almost never on mussel and shell beds. In feeding experiments,L. littorea ingested more of the dominant alge,Enteromorpha, than ofUlva, irrespective of whether or not algae were fresh or decaying. The tough thalli ofChaetomorpha were hardly consumed. Snails feeding onEnteromorpha produced fecal pellets from which new growth ofEnteromorpha started. In the absence of periwinkles,Enteromorpha developed on mussels and the attached fucoids. Experimentally increased snail densities on sediments prevented green algal development, but the snails were unable to graze down established algal mats. It is concluded that natural densities ofL. littorea hardly affect the ephemeral mass development of green algae on sediments. However, where the snails occur at high densities, i.e. on mussel beds, green algal development may be prevented.

Notes: Abstract Many benthic species have been recorded to occur in the water column above the tidal flats in Königshafen. They were either passively suspended from the sediment or performed active migrations. Concerning both number of species and organisms, active migrations were more important. The causes for these migrations range from (1) individual escape from a sudden threat such as predator attack, over (2) group evasion of local subpopulations to avoid environmental deterioration, to (3) habitat changing of entire populations. The temporal scales involved range from seconds to seasons, and the spatial scales from cm to km. Such changes of distribution patterns have been demonstrated in juvenile molluscs and in meiofaunal copepods and plathelminths. Since migrations may interfere with many kinds of population studies in the field, new methods and concepts need to be developed to avoid and overcome pittalls. As a precaution, the migration potential of benthic species should be taken into account in any field study including population parameters.

Notes: Abstract The dinoflagellateGymnodinium heterostriatum Kofoid et Swezy is described anew from live material of the upwelling region off the NW African coast. The characteristics that distinguish it fromGymnodinium striatissimum Hulburt, a species with which it has been mistaken since the original description, are discussed.

Notes: Abstract By means of monthly in situ incubations, variations in oxygen uptake, nutrient release and C/N-ratio were monitored during a period of 14 months of a mussel population (Mytilus edulis L.) located on an exposed beach. A condition index calculated as weight/length3 showed that the condition of the mussels was highest in the spring. Specific oxygen uptake and nutrient release had separate maxima, with high oxygen uptake in the spring coinciding with a period of growth, and high nutrient release during summer when the temperature was highest. Oxygen uptake was significantly correlated with both the condition of the mussels and the temperature, while ammonium release was significantly correlated only with the temperature. Except in spring, the oxygen uptake, condition index and O/N-ratio were low, indicating a poor condition of the mussels. The mussels suffered from suboptimal conditions caused by inadequate food supply and failed to accumulate glycogen reserves essential for the development of mature gametes.

Notes: Abstract The phytoplankton development in the waters around Helgoland can be described as a function of the physical environment (derivates of the temperature). This is a consequence of the fundamental annual cycle regulated by the sun and, respectively, by dependent components. This simple statement can only give good results if the turbulent transport processes in the transition zone are considered. Investigations are impeded by the fact that the multiplication rate of the organisms is almost counterbalanced by losses that take place during the long lasting bloom. This situation is a product of the regional hydrography, whereby small changes in the environment on varied time scales influence the development of the population fundamentally. This becomes particularly clear when the numerical results of the exponential growth are examined. The dynamics of this complicated process can be seen best in the great annual differences of the phytoplankton maxima.

Notes: Abstract Growth and reproduction of the colonial hydroidCordylophora caspia were monitored during the breeding season in natural conditions. In 1987, a life history study was carried out on the upright stems of the main stolon. Mean size of uprights varied cyclically. The first peak coincided with the peak number of sexual hydranths, after which the mean upright length decreased, possibly indicating somatic costs of sexual reproduction. Extrinsic factors like flooding may also have contributed to cyclical changes in upright size. In 1988 and 1989, colonies were reared on experimental plates in the estuary. In 1988, colonies grew until mid July, after which they regressed to a dormant condition and then started growing again in mid August. Predation and space competition are discussed as possible causes for this dormancy in the middle of the growing season. In 1989, colonies grew continually, with the exception of a decline in colony biomass and number of feeding hydranths at the end of July, just following the peak of sexual reproduction. Sexual reproduction started in the early stages of colonial development for all years. During early summer,C. caspia allocated resources simultaneously in colonial growth and sexual reproduction. However, sexual reproduction had a clear peak in mid summer, and thereafter sexual reproduction ceased while colonial growth continued.

Notes: Abstract Two Knots, among 88 dissected, contained the trematodeCyclocoelum mutabile. One represents the first record of this trematode from the Afrotropics. Both birds showed retardation of moult, and it is possible that such parasites have an indirect lethal effect, and that they affect breeding performance of this migrant wader with a tight annual schedule.

Notes: Abstract Differences in the understanding of natural arts, especially between Germany and the Anglo-American as well as the Scandinavian countries, are discussed. A very brief synopsis of the history of bird-painting is given. The oldest illustrations for scientific books date back to the end of the Middle Ages. After three centuries of a separated development of ‘birds in art’ and ‘birds in science’ the art of bird-painting began to rise by the end of the 19th century. This change did not take place in Germany where a rather static view of art defines “art” from “kitsch”. The present generation of German bird artists seems to be on the right way to overcome this fatal prejudice and hopefully reaches the interested public.

Notes: Abstract As a result of pronation of the forelimb in the spread wing the peaks of the digital claws are orientated backwards. The 6th (Solnhofen) specimen ofArchaeopteryx demonstrates that its digital claws were orientated in the same way. Given is an interpretation of the position of the claws of Berlin and Eichstätt specimen. Shown are the consequences for theories of origin of birds' flight, functions of the digital claws and other problems.

Notes: Abstract The mitochondrial cytochrome b gene ofLarus argentatus, L. fuscus andL. cachinnans michahellis was amplified by PCR and partially sequenced. Sequence analysis by PAUP 3.1 indicated thatL. argentatus andL. cachinnans are genetically distinct and separated by 2% base exchanges.L. cachinnans seems to be closer related toL. fuscus than toL. argentatus. The three taxa represent a superspecies. Our data imply that gene flow between the 3 gull species must be negligible and furthermore, that they represent rather young species which may have split 100 000–500 000 years ago. The recognition ofL. cachinnans as a distinct species is supported by molecular evidence.

Notes: Abstract The diet of Mediterranean Gull chicks was investigated in a Macedonian wetland using three different sampling methods: stomachs from freshly dead chicks (1988), regurgitations (1987) and carcass stomachs (1986–88). In fresh stomachs, gastropods were the most important animal prey by mass and insects by numbers. In terms of overall volume and biomass, wheat grains were the most important food. In regurgitations and carcass stomachs insects were the most important prey. Comparison of the results from the different methods revealed considerable differences which are attributed to feeding behaviour of the gulls and prey dynamics rather than the methodology used. The importance of prey types is discussed; composition of diet probably differs considerably between geographical areas

Notes: Abstract The distribution and use of the element “kit” as terminal part of the song of Chaffinches was studied in 16 ♂. The frequency of occurrence of the “kit” was dependent on individual ♂ and on song types, and the “kit” was omitted significantly more often then any other part of the song pattern. The specific character of the “kit” as a terminal element, possible proximate factors for its occurrence, and the question whether it is a hetero-specific imitation are discussed.

Notes: Abstract The present population of Golden Eagles in Germany consists of 48–50 territorial pairs in the Alps (10 % of them with homeranges extending beyond the border to Austria) and a considerable amount of nonterritorial individuals (mostly immat.). As the production is very low (0.25 resp. 0.18 fledglings/pair x year) nonterritorial birds form an important breeding reserve. At least within last decades, the abundance seemed to be fairly constant. At present, the German population depends on immigration from other parts of the alpine population.

Notes: Abstract The orientation of displaced homing pigeons at the moment of their release was tested using an octagonal orientation cage. Under certain conditions, the cage bearings of old, experienced pigeons show rather good homeward orientation, while the directional choices of young birds are not related to the home direction.

Notes: Abstract In Schleswig-Holstein, most wet meadows have been transformed into cultivated grassland (1446 km2). The populations of 12 selected bird species have changed correspondingly: Corncrake and Ruff now are almost extinct in the lowlands; the Snipe drastically declined (from 13 000 pairs in 1970 to 1500 pairs in 1992). Due to a broader habitat choice and an increase in embanked areas a decline is less noticeable at least for the whole country in Lapwing (in 1992 63 % of 1970), Black-tailed Godwit (in 1970 1500–2000, in 1992 1250 pairs), Ruff (150 breeding females), Skylark (in 1992 20 % of 1975), Blue-headed Wagtail (in 1950 18 000, in 1992 2100 pairs), Whinchat (in 1950 13 000, in 1992 2200 pairs). Species for which the decline in lowlands does not seriously affect the total of Schleswig-Holstein are Oystercatcher 〉15 300, Redshank 〉6000, Meadowpipit 10 000–13 000 (all figures for 1992). In the Curlew the situation is not fully known (in 1985 260–310 pairs).