ALBERT

Notizen: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.

Notizen: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.

Notizen: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.

Notizen: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.

Notizen: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.

Notizen: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.

Notizen: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.

Notizen: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.

Notizen: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.

Notizen: Abstract The impressed field, “Window Field” (WF), due to a half-wave action potential on a muscle fiber, has been calculated on the basis of potential theory. It has been shown that in spite of the small intensity of the field, its integrated action can transfer the energy needed to induce, contraction from the membrane to the interior of the fiber. The energy of polarization has been found to be sufficient to exceed the energy of, thermal agitation on that length of fiber, which can be identified as the length of a sarcomere. The changes of ion concentration, caused by the WF, if calculated on the assumption of the semipermeability of theZ membranes, was found to be equal to the changes necessary to induce contraction of actomyosinin vitro.

Notizen: Abstract Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.

Notizen: Abstract The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply.

Notizen: Abstract Rate equations for the enzymatic oxidation of succinic acid are derived on the assumption that when a single molecule of substrate combines with an enzyme molecule, it can do so with either one or two sites on the enzyme, and that oxidation occurs only in the second case. In addition it is assumed that the product of the reaction, fumaric acid, combines reversibly with the enzyme. With certain enzyme preparations the data fitted such an equation satisfactorily. In others the rate was that of a first-order reaction, but addition of cytochrome changed it to the former type. It was concluded that the transfer of hydrogen to oxygen was a first-order reaction and dominated the whole rate when enzyme preparations were used which had been washed relatively free of cytochrome. When the limiting factor was succino-dehydrogenase the rates followed the new equation. Criteria for recognizing noncompetitive inhibition are given, and inhibition by di-tertiary butyl peroxide was shown to be of this type.

Notizen: Abstract This paper deals with the following question: Which distributions of radiosensitivity in a population can lead to an exponential survival curve? The problem is solved exactly, with statistical fluctuations in dose fully accounted for. It is shown that only an exponential distribution of sensitivities can give rise to an exponential survival curve.

Notizen: Abstract An approximation method is introduced which enables a number of diffusion-type problems to be solved in an approximate but simple manner. Many cases require only the solution of a simple first-order differential equation. The method is applied to a number of cases in which the exact solutions are available. A comparison shows that the method is quite satisfactory in these cases. The method is applied to diffusion problems with rate of consumption proportional to concentration or to the square of the concentration. In the latter case, the result obtained is essentially the same as that found by H. G. Landau (1950) after elaborate calculations.

Notizen: Abstract It is shown that a slight modification of a model of excitatory phenomena in irritable tissues, which has been treated before, exhibits spontaneous oscillations. The frequency of these oscillations and the time-course of the potential across the model membrane have been determined, together with the dependence of some of their characteristics on some important parameters, particularly (Ca++).

Notizen: Abstract It is demonstrated that, if the variations of viscosity throughout a cell are considered, swelling stresses may produce elongation and division. To do this it is necessary to generalize Betti's theorem to cover systems containing viscosity gradients and such a generalization is presented. On the basis of two special assumptions it is shown that most of the results of the diffusion drag theory of cell division may be duplicated by the present theory.

Notizen: Abstract The theory of imitative behavior, developed previously, is applied to the case of two social groups which are separated spatially. If the information of each group as to the behavior of the other is complete, the case reduces to that of a single group. When any information is lacking at all, the two groups are independent. If we have two mutually exclusive behaviorsA andB, all four combinationsAA, AB, BA, andBB are possible. If the mutual information gradually increases from zero, then for a certain value of it, the group which is more informed about the behavior of the other will change to that behavior if it did not already exhibit it. If for constant information the size of the group increases, then above a certain threshold value, the larger group imposes its behavior on the smaller.

Notizen: Abstract Local regulation of blood flow as determined by capillary diameter and the number of open capillaries in a region is considered. The local changes in capillary diameter and in the number of open capillaries are assumed to be due to concentration changes of a diffusible, nonspecified metabolite. This metabolite is produced in the tissue and carried away by the blood stream. Using these assumptions and applying pertinent data on capillaries, deductions are made concerning: (a) the law of blood flow as a function of temperature and capillary radius for the hyperemia of high temperature, (b) high flow as it depends on metabolism during strenuous exercise of muscle, and (c) a first approximation to the time duration of occlusion hyperemia.

Notizen: Abstract The necessary and sufficient condition is given forn integers to be the score structure of a society with a dominance relation. A proof is also given for a theorem showing that there are members who dominate every other member either directly or indirectly through a single intermediate member.

Notizen: Abstract On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed.

Notizen: Abstract It is shown on the basis of (1) conservation of mass, (2) positive concentrations, and (3) the principle of detail balancing that periodic reactions cannot occur in a closed system described bylinear differential equations. The matrix,A, of the rate equations must be such that |A|=0,a ij〉0 fori≠j,a ii〈0, andVAV −1=B, whereV is diagonal andB is symmetric. These properties ofA imply that the latent roots are real and non-positive and that neither catalysis nor inhibition can be described bylinear equations. It is further shown that periodic reactions cannot occur in anopen system for which the matrix associated with the chemical reactions has the above properties and in which thesimple law of diffusion is obeyed. The relation of these results to Onsager's reciprocal relations and to previous work on periodic and cyclic chemical reactions is discussed. The utility of certain of these results for the treatment of isotope kinetics is indicated.

Notizen: Abstract It is demonstrated that an explanation of the small radius effect or the so-called sigma phenomenon may be obtained by noting that one of the effects of the presence of suspended particles in a flowing fluid is to increase the velocity of flow near the wall over that existing in the absence of particles. This effect may be considered equivalent to relaxing the boundary conditions at the wall. An expression for the viscosity is compared with data and fit is found to be good.

Notizen: Abstract The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.

Notizen: Abstract A mechanism is described which accounts for the active transport of Na+ ions through a membrane. It is assumed that at one side of the membrane the ion combines with a carrier ion, the resulting carrier compound then diffuses through the membrane and decomposes at the other side of the membrane. The free diffusion of the ions is also taken into account. The time rate of accumulation of the ion in question at the latter side of the membrane is calculated in terms of the concentrations of the ion at both sides of the membrane.

Notizen: Abstract The recent extension of the approximation method is applied to enable us to arrive at the time course of the concentrations at both sides of a membrane. From the differential equations which govern these, the steady-state solution is obtained in terms of the parameters, which are determined by the thickness of the diffusion layers, the chemical composition and reactions, and the diffusion constant of the membrane.

Notizen: Abstract An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.

Notizen: Abstract The reflection of pressure waves in a fluid enclosed within a tube with an elastic wall is studied for the case of a localized change in diameter of the tube. The concept of impedance is introduced. The relation of the reflection characteristics of the parts of the tube at either side of the change is derived on the basis of the continuity of pressure and mass flow at the site of the change. This relations is used to derive the expression for the ratio of the pressure oscillations measured in front of, and behind, the constriction in terms of the constants of the system. As a result, a method is indicated to locate the coarctation from measurements of the pressures in front of, and behind it.

Notizen: Abstract The question is raised concerning the possible causes of abnormally small standard deviations found in counting samples in which particles are distributed at random (e.g., blood cells, fat globules in milk, etc.). The effect of discarding abnormal samples is discounted inasmuch as small standard deviations occur even when all samples are counted. An approximation method is used to calculate the effect of finite particle size, of known repulsive forces between particles and of convection currents. This calculation shows that neither finite size nor the known repulsive forces are sufficient to account for the observed abnormality of standard deviation, but that convection currents can possibly account for it. The possible presence of long-range repulsive forces cannot, however, be excluded.

Notizen: Abstract The effect of finite particle size on the standard deviation in sample counts is computed for the one-dimensional case. To a first order of approximation the correction is found to be identifical with that found by H. de Vries (1953) using a general approximation method.

Notizen: Abstract A critical examination of the “classical” theories of photoreception in view of more recent experimental findings yields the result that these theories do not possess the property to describe all the more significant phenomena of photoreception correctly, and to some extent suffer the lack of more general applicability. The basis for a new and presumably more general theory of photoreception based on dynamical aspects is laid out. Emphasis is put on the time course of afferent and efferent excitation in the photoreception model, consisting of a receptor element, an afferent and an efferent neuron of the one-factor Rashevsky-type, and an effector organ.

Notizen: Abstract A mathematical model for the development of human society, beginning with the earliest stages of urban cultures, is outlined. In the early stages of history, behavior was characterized largely by adherence to a number of beliefs and prejudices of diffeirent kinds, which were accepted on faith and not subject to critical rational analysis. Due to psychobiological variability a very small number of individuals spontaneously appear at all times who challenge the accepted beliefs and prejudices and do not follow the accepted patterns of social behavior. The effect of these individuals upon the rest of the society, especially upon the younger generation, depends on the facilities with which information spreads in society. In earliest societies, when modern methods of mass communication were unknown, the channels of communication were practically identical with the channels of economic transport. The latter in its turn depended on the nature of the roads, and especially on the presence of waterway, which facilitated transportation. The sizes of the earliest cities and the distances between them were largely determined by relative ease of transporation. Expressions are derived for the average size of the earliest cities and for the average distance between them. The calculated average populations of the earliest cities are of the order of 103; the distance of the order of 102 km. Both are in agreement with some archaeological findings. An expression for the time spaon required for the development from the earliest stages of urban cultures to the present time is derived and shown to depend on the specific shoreline of the country, that is, the length of the shorline divided by the area of the country. It is pointed out that western Europe's specific shoreline, including land bordering both seas and rivers, is ten times as large as the shoreline area of other parts of the world. It is shown that this greater specific shoreline may account quantitatively for the faster social and technological development of western Europe in the last few centuries. The calculated total span of time of development from earliest urban cultures to our days is found to be of the order of magnitude of ten thousand years. It is shown that the model accounts for the existence at the present time of primitive cultures. A number of suggestions is made in regard to other possible applications of mathematics to history.

Notizen: Abstract The assumptions latent in the derivation of the integral equation of Branson are rendered explicit and discussed. It is shown that the equation is valid only for systems in which the substance disappears according to a linear rate law.

Notizen: Abstract It is shown that the validity of Branson's integral description of metabolizing systems is subject to severe limitations. The validity is insured only in cases where the reaction is of first order, or quasi of first order. In all other cases Branson's equation has to be modified to insure general applicability. The consequences of a different definition of the metabolizing functionF have also been investigated. With the new definitionF describes the pure effect of metabolization. It is found that in this case the integral equation is only capable of describing first-order reactions. With a slight modification of the integral equation it is possible to describe metabolites “with age”, which do not have reactions of definite order, but which satisfy the superposition principle.

Notizen: Abstract A problem in probability is stated with included the problem of the distribution of bacterial mutants as a special case. This problem is solved exactly but since the resulting expressions are too complicated for practical use, various approximate expressions for the distribution are considered, especially for the bacterial mutation case.

Notizen: Abstract Simple reaction and discrimination reaction, under the influence of imitation, are considered for the situation in which the stimulus or the stimuli vary slowly with time. The result is analogous to hysteresis under certain conditions. The calculations are facilitated by the solution of $$x = \int_{ - \infty }^{a + \beta x} {g\left( \xi \right)d} \xi ,$$ g(ξ) being the normal error function. Values ofx(α, β) are given in a table.

Notizen: Abstract On the basis of simple physical considerations the blood flow in a branching circulatory system is studied. The case of two groups of parallel vessels is treated. The vessels of the same group are supposed to be identical. The resistance of each group is determined by the resistance of each vessel in the group and by the number of vessels in the group. From the dependence of the resistance of each vessel on its radius an expression is obtained for the blood flow through each group of vessels in terms of the numbers and sizes of the vessels in each group. The number of open vessels in an organ and the radius of each of those vessels are assumed to depend on the metabolic rate of that organ. The relations so obtained, together with the expression above, are applied to derive the blood flow through an organ as a function of the metabolic rate of that organ. It is indicated that the relations obtained might describe the shifting of blood from one organ to another if the activity of one of them changes. A way is pointed out to treat neural regulation of this phenomenon.

Notizen: Abstract A stochastic model of population growth is treated using the Bellman-Harris theory of agedependent stochastic branching processes. The probability distribution for the population size at any time and the expectation are obtained when it is assumed that there is probability (1−σ), 0≤σ〈1, of the organism dividing into two at the end of its lifetime, and probability σ that division will not take place.

Notizen: Abstract In a previous paper, in which a possible mathematical approach to history was outlined, it was shown that urbanization plays an important part in the propagation of new ideas. The rate of such propagation influences the rate of historical developments. The present paper deals in more detail with possible mechanisms of formation of earliest cities. Equations are derived which give the limiting size of such cities and their rate of growth. Of particular importance for the spread of new ideas is the spread of information. The latter largely depends on the fraction of individuals who travel between city and country. Expressions for this quantity are derived. An approach is outlined to the mathematical study of the earliest social classes, which may have been formed as a result of military, religious, or economic stratifications.

Notizen: Abstract The velocity of propagation of a disturbance wave in a liquid flowing in a distensible tube is computed. The mathematical model is more general than those used in previous analyses: the tube wall properties are realistic; the convective part of the axial inertia forces is taken into account; radial inertia forces of both the fluid and tube wall are present; viscous stresses are present. Four parameters influencing the velocity of propagation are obtained and discussed. Curves are plotted illustrating the effects of the parameters. Contrary to the results of previous analyses, viscous effects are shown to be appreciable in blood flow. It is also shown that radial inertia effects can be important in laboratory set-ups.

Notizen: Abstract A general theory of the drying of frozen tissue is developed and applied to the measurement of the drying rate of frozen guinea pig liver. It is shown that for a given temperature of the subliming ice crystals the mininum drying time of a piece of guinea pig liver is greater than the minimum sublimation time of a piece of ice of the same size and shape by a factor of the order of one thousand. This fact has many implications in the design of freeze-dry apparatus which will be developed in a following paper.

Notizen: Abstract The equations governing the time course of the exchange of substances between the blood in the capillaries and the extracellular space are solved for the case of substances which do not penetrate the cells. The equations given relate the time course of the exchange process to the various tissue and circulation parameters such as the specific capillary wall area, the pore area, the inter-capillary distance, the size of the extra-vascular, extra-cellular space, the diffusion coefficient in this space, and the velocity of blood in the capillaries. Some experimental work on capillary exchange is discussed in relation to the theory and estimates are made of the relative importance of the various tissue and circulation parameters in the exchange of substances in different tissues.

Notizen: Abstract Previous work (Macey, 1952) in the application of the one-factor theory to the heart is extended. The rate of production of the excitatory state is assumed to be linear. Two possible mechanisms are indicated whereby such a situation might arise. Assumptions are made regarding the mode of action of the chemical mediators on the heart, and an equation is derived relating the heart rate to the frequency of nerve impulses traveling along the cardiac nerves. This result compares favorably with the experimental findings of A. Rosenblueth and F. A. Simeone (1934). Other experimental results are interpreted in terms of the theory.

Notizen: Zusammenfassung Die ökologischen Faktoren wurden in kleinen Wattenpfützen während der Trockenzeit laufend untersucht. Dabei erwies sich Salzgehalt und Wassertemperatur als direkt von den Wetterbedingungen abhängig, während durch die Photosynthese der Sauerstoffgehalt, das Säurebindungsvermögen und pH weitgehend verändert werden können. Auch diese Faktoren sind indirekt von der Witterung abhängig, sie können großen Schwankungen unterliegen. Auf die biologische Bedeutung der Schwankungen im Chemismus von Wattenpfützen wird hingewiesen.

Notizen: Zusammenfassung Im Jahre 1953 wurde das Auftreten vonElminius modestus Darwin in der Elbmündung beobachtet. Der Siedlungsbereich vonElminius erstreckt sich von 0,5 unter bis 2,5 m über Tnw. Dabei tritt diese Seepocke im Bereich bis 1 m über Tnw mitBalanus balanoides und von 0,5 m über Tnw abwärts mitBalanus improvisus in Konkurrenz.Elminius ist vermutlich durch Schiffsbewuchs Mitte 1953 nach Cuxhaven gekommen. Zu besonderem Dank für ihre brieflichen Mitteilungen bin ich den Herren Dr.Crisp-Bangor, Dr.Knight-Jones-Bangor, Dr.Den Hartog-Den Helder, Dr.Engländer-Köln, Dr.Krause-Norderney und Dr.Schäfer-Wilhelmshaven verpflichtet. Herr Dr.Duncan-Waugh-Burnham on-Crouch über-ließ mir freundlicherweise Vergleichsmaterial vom River Roach-Essex.

Notizen: Zusammenfassung Der im Verlauf zweier Jahre untersuchte Algenbewuchs der Fahrwassertonnen um Helgoland bestand aus Algen der Gezeiten-, Supra- und oberen Sublitoralzone. Ihre Häufigkeit entsprach durchweg den Helgoländer Verhältnissen, es fehlten jedoch die drei bei Helgoland sehr reichlich vorkommendenFucus-Arten (F. platycarpus, F. vesiculosus undF. serratus). Einige Algen (fädige Grünalgen,Bangia, Enteromorpha, Punctaria, Ceramium, Polysiphonia undLaminaria) konnten in gürtelförmigen Zonen auftreten; diese sind schmäler als am natürlichen Standort. Der Algenanwuchs verringert sich mit zunehmender Entfernung von der Insel.

Notizen: Zusammenfassung Der Längen-Gewichts-Koeffizient der Schollen ist bei den kleinsten Tieren zunächst hoch, nimmt dann stark ab, um im späteren Leben erneut zu steigen. Bei gleichaltrigen Schollen sind die best- und schlechtestgewachsenen Tiere relativ schwerer als die große Masse. Langsames Wachstum und große Bestandesdichte setzen das auf eine bestimmte Länge bezogene Gewicht herab; mit der Entfernung vom Land steigt es. Die Größe der Schollen in den Marktfängen hängt außer von Alter und Wachstum entscheidend auch von der Marktauslese ab: Ist diese scharf, so ergeben sich selbst für langsam gewachsene Jahrgänge erhöhte Mittelwerte von Gewicht und Länge, die bis zum Fünffachen des Gewichts und dem Zweifachen der Länge der betreffenden Altersgruppen im natürlichen Bestande erreichen. Langsames Wachstum wirkt sich in der Fischerei mehr durch verspätet eintretende Marktgröße aus. Infolge des somit länger anhaltenden natürlichen Abgranges erleidet die wirtschaftliche Ertragfähigkeit langsamwüchsiger Altersgruppen Einbußen, die trotz erhöhten Alters nicht durch größere Stückgewichte ausgeglichen werden.

Notizen: Zusammenfassung 1. Der Entwicklungszyklus vonGiffordia fuscata umfaßt zwei heteromorphe Generationen, die durch die Heteroblastie ihrer Schwärmer in einem lockeren Zusammenhang stehen: a) Die langfädigeGiffordia fuscata, die sich durch die Schwärmer ihrer plurilokulären Sporangien selbständig vegetativ vermehren kann. Die Schwärmer ihrer unilokulären Sporangien zeigen Heteroblastie; die Mehrzahl ergibt Zwergpflanzen, ein kleiner Teil entwickelt sich unmittelbar zu der büscheligen Form. b) Die Zwerggeneration, die reichlich plurilokuläre und ganz selten unilokuläre Sporangien trägt. Die Schwärmer der plurilokulären Sporangien sind heteroblastisch, die meisten ergeben wieder Zwergpflanzen, so daß sich die Zwerggeneration selbständig vegetativ erhalten kann. Ein kleiner Bruchteil der Schwärmer entwickelt sich zu der büscheligenGiffordia-Pflanze. 2. Irgendwelche Anzeichen für eine Sexualität der Zwerggeneration sind nicht vorhanden;Giffordia-Pflanzen können aus den Schwärmern eines einzelnen Zwergpflänzchens und sogar eines einzelnen Sporangiums entstehen. 3. Das Vorkommen unilokulärer Sporangien an den Zwergpflanzen, die fehlende Sexualität der Zwerggeneration und die Heteroblastie in beiden Generationen berechtigen zu der Annahme, die beiden heteromorphen Generationen als Diplonten anzusehen. 4. Es wird auf ähnliche Beziehungen in der Entwicklung vonEudesme zosterae zuAscocyclus hingewiesen sowie auf die Möglichkeit, daß viele mikroskopische Braunalgen selbständig gewordene Partner eines früheren oder noch bestehenden Lebenszyklus sein könnten.

Notizen: Zusammenfassung Am 7. 1. 1954 wurden am Südstrand des Ellenbogens bei List a. Sylt in einem hochgelegenen Strandgürtel zahlreiche lebendeArenicola angetroffen, die hier durch das Morgenhochwasser angespült waren. Der Fund ist allem Anschein nach damit zu erklären, daß dieArenicola-Besiedlung der hochgelegenen Wattflächen, die meist aus kleineren und mittelgroßen Tieren besteht, auf der Wanderung nach tieferen Wohnplätzen begriffen war. Die unmittelbare Ursache waren der plötzliche Temperaturabfall und der durch Ostwindwetterlage abgesunkene Wasserstand des Januaranfangs. Es wird vermutet, daß die beschriebene Erscheinung Ausdruck eines regelmäßigen Verhaltens ist, das sich normalerweise über einen längeren Zeitraum bei Eintritt der kalten Jahreszeit erstreckt, das sich aber 1953/54 wegen des ungewöhnlich milden Wetters verzögert hat und erst Anfang Januar durch die schnell sinkenden Temperaturen ausgelöst wurde.

Notizen: Zusammenfassung Dieser Aufsatz ist eine Besinnung auf den Begriff Individuum, wie dieser in der Biologie gebraucht wird, und er beabsichtigt, den Inhalt dieses Begriffes theoretisch zu begründen. Es ist aber unmöglich für die nähere Bestimmung des Begriffes Individuum von der etymologischen Bedeutung „unteilbar” auszugehen, weil die biologischen Individuen nicht immer unteilbar sind. Beim Suchen nach einem richtigen Untersuchungsverfahren wird zunächst dargelegt, wie diese Untersuchung wesentlich ein Teil der theoretischen Biologie, also der Wissenschaft, ist, wenn man auch von deutlichen Zusammenhängen mit der Philosophie und dem spontanen Denken sprechen kann. Deshalb wird die Methode, nach der wir vorangehen müssen, die induktive Methode sein, weil diese in der Wissenschaft mit Recht hoch eingeschätzt wird. Bei den grossen Vertretern der verschiedenen Richtungen in der Biologie, beiHaeckel, von Bertalanffy, Driesch undBergson, werden in ihre Auffassungen über Individuum und Individualität derartige Übereinstimmungen festgestellt, dass darin nach den Gesetzen der Induktion die wesentlichen Momente des biologischen Individuumbegriffes erkannt werden können. Ausserdem stimmen diese Momente mit dem Inhalt des Begriffs zusammen, wie der sich aus dem spontanen Denken ergibt. Diese Momente sind: Subsistenz, Einheit und Totalität, Tendenz nach einem geschlossenen System und schliesslich die Unmöglichkeit einer erschöpfenden Definition. In dieser Reihenfolge werden sie kritisch erörtert, und daraufhin werden folgende biologische Begriffsbestimmungen vorgeschlagen (die nicht statischer, sondern dynamischer Art sind): Individualität ist die Tendenz des einzelnen Organismus nach ungeteilter subsistenter Totalität. Etwas ist Individuum in dem Masse, wo diese Tendenz verwirklicht ist. Durch einige Beispiele aus dem System und der Ontogenie wird die Anwendung dieses dynamischen Begriffes erläutert.

Notizen: Zusammenfassung Die vorliegende Arbeit ist eine Fortsetzung derThompson'schen Analysen des Parasitenzyklus bei Insekten, die mit der irrealen Folgerung endeten, dass unter gewissen Voraussetzungen — die wir in der gegenwärtigen Analyse akzeptiert haben —jeder Parasit in relativ kurzer Generationenfolge seinen Wirt, und damit sich selbst, zur Ausrottung bringen muss. Der Einfluss von wiederkehrenden Umwelt-katastrophen wie sie z.B. durch ungünstiges Wetter sehr häufig bedingt sind, wurde untersucht mit dem Ergebnis, dass solche Katastrophen, wenn sie in nicht allzugrossen Intervallen auftreten, völlig genügen, um die Unterbrechung der akkumulativen Parasitierung im Zyklus zu erklären. Die grössere Empfindlichkeit der Parasiten, welche aus allen Beobachtungen und Analysen sich ergibt, ist nicht physiologisch, sondern ökologisch bedingt. Methodisch hat sich gezeigt, dass die Analyse tierischer Populationen weitgehend ohne Anwendung von Integralen möglich ist. Die Ergebnisse, welche die hohe Bedeutung der Feinde bei grosser Wirtsdichte, und ihre minimale Wirksamkeit, wenn letztere niedrig ist, zeigen, sind unabhängig von einem besonderen Dichtefaktor der Feindvermehrung — wie er im allgemeinen besteht und die aufgezeigten Tendenzen noch verstärkt — gewonnen. Der Einfluss des Superparasiten wird unter dem Einfluss wiederkehrender Umwelt-katastrophen minimal. Am Modell einiger beobachteter Gradationen wird die Übereinstimmung mit unserer Analvse demonstriert.

Notizen: Summary After a short review of the historical development of the problem of cytoplasmic inheritance, the principles for the proof of cytoplasmic inheritance were discussed. At present the proof can be based on the maternal transmission of plasmagenes, on the missing of mendelian segregation and on the possibility of a segregation during ontogenetic development. In the following the most important possibilities for errors and their refutation onEpilobium were discussed: elimination of genotypes (examination of the elimination of gametes, zygotes, test of accidental distribution of chromosomes, crossing with tetrads), abnormal cytology (cytological investigation, crosses with hetero- and polyploids), maternal aftereffects (clone-multiplication), predetermination (exchange of nucleus by backcrossing), nuclear produced plasmagenes (contrarily acting cytoplasm and nucleus) and transmission of parasites or symbionts as virus (grafting). At the end the principles for the distinction between different cytoplasmic constituents were discussed.

Notizen: Summary Following A. V.Hill, those formulae are developed in a mathematical research which are of interest in the field of physiological diffusion processes in cylindrical objects. At first, an introduction into the problem is given. Then a development follows of the mathematical methods (Bernoulli's method [Produktansatz],Laplace-transformation) which are suitable for the integration of the partial differential equation of the diffusion. The special part contains the investigation of problems which are importance for the physiology of respiration. Thus the query is answered for the concentration of a substance in dependance of time and place for the diffusion in tissue cylinders taking into consideration a constant rate of consumption, as well as the query of the temporal alteration of the average concentration. The cylinder fed from the outside and the one fed from a central capillary (Krogh's) must hereby be specially treated according to the boundary conditions. The developed equations are explained by special examples and numerical lists. Further, the steady state of supply of tissue cylinders is investigated in case that apart from the radial also an axial diffusion component (Längsdiffusion) has to be counted with. The numerical results from the developed formulae are in good agreement with the values found by experiments.

Notizen: Zusammenfassung Die Autökologie will die Voraussetzungen für die Existenz der einzelnen Organismenart innerhalb ihres Verbreitungsgebietes erkennen. Diese Voraussetzungen sollen durch Vergleich der Standorte, an denen die Art — im Gegensatz zu anderen, mit ihr ökologisch vikariierenden Arten — zu existieren vermag, auf möglichst einfache Milieugegebenheiten zurückgeführt werden. Im Vordergrund stehen hierbei die auf zahlreiche Organismen gleichsinnig wirkenden abiotischen ökologischen Faktoren, die in Form von Milieuspektren dargestellt werden können. Die von einer Art geforderte Sonderbegrenzung jedes Faktors, seine Amplitude, ist ihre PlastizitÄt diesem Faktor gegenüber. Das ökologische Gesamtverhalten einer Art, ihre ökologische Valenz, kann durch ihre PlastizitÄt gegenüber den Einzelfaktoren einer bestimmten Faktorenkombination umschrieben werden. Arten, die sich den meisten Faktoren gegenüber euryplastisch verhalten, sind euryök (Gegensatz: stenök). HÄufig wird aber das Vorkommen einer Art durch — meist biotische — Milieueinzelheiten bestimmt, die zunÄchst nicht in QuantitÄten allgemein wirkender einfacher Faktoren aufgelöst werden können, sondern die als Komplexe qualitativ durch ihr Vorhandensein oder Fehlen ökologisch wirken. Die Beanspruchung eines solchen Komplexes durch eine Art muss durch die vielfach bestehenden Sonderbezeichnungen ausgedrückt werden. Wenn solche Komplexe gleichzeitig bestimmte physiognomisch abgrenzbare LebensstÄtten charakterisieren, so kann ein derartiges ökologisches Verhalten terminologisch durch die Bindung der Art an den Biotop charakterisiert werden (Eurytopie — Stenotopie bzw. Zönobiontie, Zönophilie, Zönoxenie).

Notizen: Riassunto Applicando il metodo comparativo gli autori hanno studiato l'influenza del nucleo sul tenore in dipeptidasi (substratod–l alanilglicina) degli eritrociti di Vertebrati eterotermi ed omeotermi dai Pesci all'uomo. La mancanza di materiale non ha permesso di comprendere per il momento, nelle osservazioni gli eritrociti dei Ciclostomi. Con il micrometodo diLinderström-Lang eHolter si è potuto localizzare l'enzima prevalentemente nel citoplasma degli eritrociti, inoltre si è potuto accertare: I. La quantità di dipeptidasi di un eritrocita è proporizionale al volume dell'eritrocita stesso. II. La quantità di dipeptidasi per unità di volume protoplasmatico è una costante negli eterotermi. III. Negli omeotermi la quantità di enzima, per unità di volume protoplasmatico, è minore che negli eterotermi. Il tenore enzimatico degli eritrociti dei Mammiferi è inferiore (a parità di volume protoplasmatico) a quello di tutti gli altri Vertebrati studiati. Dall'insieme delle ricerche è risultata l'influenza del nucleo e della termoregolazione (dedotta dalle condizione eteroterme e omeoterme degli organismi studiati) sul tenore in dipeptidasi degli eritrociti nucleati e anucleati dei Vertebrati.

Notizen: Summary (1)—In the rat, total extracts of cortex, cortisone and A.C.T.H. do not retard the fixation of a vital colorant at the level of a cutaneous zone irritated by chloroform. (2)—Phenergan prolongs the delay in the appearance of the blue. (3)—Sodium salicylate selectively inhibits the inflammatory cutaneous action of chloroform, even after adrenalectomy.

Notizen: Zusammenfassung Drei « wilde » Stämme vonEscherichia coli wurden auf vitaminfreien Nährböden gezüchtet. Zusatz von Vitamin B12 in Konzentrationen von 0,03 bis 0,06γ je ml ergab bei verschiedenen Stämmen eine ungleiche Hemmung der Pantothensäure-Synthese. Die eindeutigsten Resultate wurden mit frischen Stämmen erzielt, die nur kurz auf Agar gezüchtet wurden.

Notizen: Summary 3318 CT [bis(piperidinométhylcoumaranyl-5) cetone diméthiodide] a compound recently synthesized byA. Funke andK. von Däniken, is shown to be a potent and selective inhibitor, bothin vitro andin vivo, of the blood acetyl-cholinesterase (AcChE) of the dog. It produces acetylcholinomimetic symptoms in the animal and sensitizes different responses to acetylcholine and to stimulation of cholinergic nerves without inhibiting the blood non-specific cholinesterase (XChE). However, the action of 3318 CT appears to be limited, both in nature and in intensity, when compared to that of prostigmine, although the latter substance is a less potent inhibitor of AcChEin vitro than is 3318 CT. This difference is probably related to many factors, one of which may be the fact that prostigmine inhibits not only AcChE but also XChE; and it is not yet ascertained that XChE plays no role at all in the limitation of the effect of the stimulations of cholinergic nerves.

Notizen: Summary The volumetric determination of total iron in blood by titration with “Complexone III” is described. The method is simple, rapid, and accurate but not sensitive enough to permit the estimation of iron in blood-serum alone.

Notizen: Zusammenfassung Es werden verschiedene Reaktionen in der Oxindolreihe diskutiert. Man kann sie sich als ähnliche Mechanismen vorstellen, da alle über intramolekular gebildete Zwischenprodukte bzw. Endprodukte laufen.

Notizen: Summary When decalcified nacre is treated with ultrasonic waves, the organic matrix resolves itself into very thin lacelike protidic leaflets, which can be studied with the electron microscope. Controls have been made showing that the lacelike structure is not an artifact due to decalcification, fixation, treatment with ultrasonic waves, dessiccation or electronic bombardment. The ultramicroscopic structure of the lacelike mesh-work differs with the species. At this level, morphological features appear to characterize the three classes of Molluscs studied (Lamellibranchia, Gastropoda, Cephalopoda), and perhaps different genera within the same class. The extraction, by a borate buffer, of a water-soluble constituent of the protidic material does not appreciably modify the appearance of the structures studied. The extraction, by a sodium hydroxyde solution, of a second component, leaves a fibrous residue rich in alanine and glycine.

Notizen: Zusammenfassung Dem phenolischen Oxydationsprodukt, das beim Durchleiten von Sauerstoff durch geschmolzenestrans-Dekahydrochinolin entsteht, wird auf Grund der Analyse und spektrophotometrischen Daten die Konstitution III eines 3-Oxy-5, 6, 7, 8-tetrahydrochinolins beigelegt. Seine Entstehung erfolgt wahrscheinlich über das gleichfalls gebildete 5, 6, 7, 8-Tetrahydrochinolin.

Notizen: Zusammenfassung Aus den Arbeiten der letzten zwei Jahre auf dem Gebiet der Nebennierenrinden-Hormone stechen — was die Herstellung neuer, hochwirksamer Verbindungen anbetrifft — die Isolierung und Konstitutionsaufklärung des natürlichen Hormons Aldosteron und die synthetische Gewinnung der 9α-halogenierten Hydrocortisone hervor. Diese Ergebnisse haben den Weg zu weiteren wesentlichen Entwicklungen eines Gebietes geöffnet, das mit Cortison und Hydrocortison abgeschlossen schien. Auf dem Gebiete der Teilsynthese wurde die Herstellung von 11-oxygenierten aus 12-oxygenierten Derivaten und insbesondere aus Verbindungen ohne Sauerstoff im Ring C stark ausgebaut. Bei der letzteren liegen die wichtigsten Befunde wohl in den mikrobiologischen Hydroxylierungen in 11-Stellung und den anschliessenden chemischen Umwandlungen. Erst kürzlich ist es möglich geworden, auch die typischen Seitenketten durch mikrobiologische Methoden zu gewinnen. Die Totalsynthese der Hormone aus einfachsten chemischen Bausteinen wurde entwickelt und macht rasche Forschritte. Die Auffassungen über die Biosynthese haben konkretere Formen angenommen. Die unzähligen Arbeiten über Katabolismus und klinische Verwendung der Nebennierenrinden-Hormone konnten im Rahmen dieser Übersicht nicht einmal gestreift werden.

Notizen: Zusammenfassung Bei der Salzbildung offener oder zyklischer Schiffscher Basen, eingeschlossen aromatische Heterozyklen, wie Pyridin, Chinolin, Benzoxazin, Indolenin usw., können die im UV.- und UR.-Spektrum auftretenden bathooder hypsochromen Verschiebungen sowie das Auftreten oder Ausbleiben der für das Kation $$ 〉 C = \mathop N\limits^ \oplus H - $$ charackteristischen «Immonium-Banden» bei 4,5–5,5 µ zur Erkennung der Natur und der Position von Aminosubstituenten benutzt werden.

Notizen: Résumé Quelques questions concernant une généralisation de l'équation deLangevin sont discutées.

Notizen: Zusammenfassung Zusatz von Vitamin B12 in Kulturnährböden hemmt die Thiamin-Biosynthese von frisch isoliertenE.-coli-Stämmen. Diese Hemmung steht im Verhältnis zur zugesetzten Menge von Vitamin B12.

Notizen: Summary A previous experiment withEranthis showed thatRoentgen irradiation of “undivided” embryos led to a change in the number of cotyledons. In the present publication, the induction of anomalies of the cotyledon was shown after irradiation of early embryo stages on the mother plant in Arabidopsis thaliana, an example of a plant with “complete” embryos. Which aberration type (synkotyl, anisokotyl, trikotyl, tetrakotyl or multiple seedlings) will arise, seems to be determined neither by theRoentgen dose nor by the stage of development on irradiation. The appearance of predominately regular trikotyl types after application of 2000r, and their gradual disappearance with increasing doses in favour of the irregular trikotyl types, suggests that in the lower doses the main influences are upon the purely chemical reactions in the embryos, which are overlaid by cell damages occurring in a directly biophysical way with increase of the physical primary acts and lead to irregular growth.

Notizen: Zusammenfassung In Gewebskulturen von Hühnerfibroblasten sind Toluhydrochinon und Toluchinon unwirksam. Nach Zusatz von 10−3-M-Phosphat werden diese Substanzen antimitotisch wirksam. Der antimitotische Effekt von Toluhydrochinon + Phosphat ist erheblich grösser als derjenige von Toluchinon + Phosphat. Diese Beobachtungen können zur Deutung der antimitotischen Wirkung von Toluhydrochinondiphosphat herangezogen werden.

Notizen: Zusammenfassung Der genaue Angriffspunkt der Quecksilberpräparate an der Niere ist nicht geklärt. Widersprechende Befunde über den Effekt dieser Diuretica auf mikroskopische Veränderungen und histochemisch nachweisbare bernsteinsaure Dehydrogenase können in folgender Weise geklärt werden: Mercuhydrin in grossen Dosen führt schon innerhalb weniger Stunden zu einer schweren toxischen Nephrose in der Rattenniere, während Novurit anfangs oft langsamer wirkt. Nichtsdestoweniger ergeben beide Mittel nach 24 h ein ähnliches mikroskopisches Bild. Bernsteinsaure Dehydrogenase ist vermindert und verschwindet schliesslich vollkommen in den absterbenden Zellen. Daher ist schon in den ersten Stunden nach Injektion von Mercuhydrin eine sehr ausgedehnte Inaktivierung in den Zellen der geraden Anteile der Hauptstücke zu sehen. Dieser Effekt wird nur gelegentlich in den ersten Stunden nach Novurit beobachtet. Nach 24 h ist er aber regelmässig vorhanden. Mit beiden Präparaten konnte keine Verminderung der Enzymaktivität inHenlessche Schleifen beobachtet werden. Es wird auf die Notwendigkeit hingewiesen, dünne Schnitte zu studieren, weil die verschiedenen Anteile des Nephrons sonst kaum zu unterscheiden sind. Das Ergebnis dieser Versuche spricht eindeutig für eine Wirkung der Quecksilberdiuretica auf die Hauptstücke und nicht aufHenlessche Schleifen.

Notizen: Summary A series of demecolceinamids was examinedin vitro on chicken fibroblasts, leucocytes, and different bacteria. It was found that with increasing length of the side chain on ring C the antimitotic activity is decreasing while the antibacterial effect is increasing.

Notizen: Riassunto Gli autori hanno preparato ATP32 dai muscoli di coniglio trattato preventivamente con fosfato di sodio radioattivo. Iniettando per via endovenosa l'ATP32 e tiamina a ratti albini è stato possibile mettere in evidenza, impiegando la tecnica cromatografica su carta, la formazione nel fegato di questi animali di DP32T e TP32T. Questi risultati dimostrano che nell'animale vivente ha luogo una diretta trasposizione di gruppi fosforici dall'ATP alla tiamina.