“Ignition” phenomena in random nets

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

Life and death near a windy oasis

We propose a simple experiment to study delocalization and extinction in inhomogeneous biological systems. The nonlinear steady state for, say, a bacteria colony living on and near a patch of nutrient or favorable illumination (“oasis”) in the presence of a drift term (“wind”) is computed. The bacteria, described by a simple generalization of the Fisher equation, diffuse, divide A→A + A, die A→ 0, and annihilate A + A→ 0. At high wind velocities all bacteria are blown into an unfavorable region (“desert”), and the colony dies out. At low velocity a steady state concentration survives near the oasis. In between these two regimes there is a critical velocity at which bacteria first survive. If the “desert” supports a small nonzero population, this extinction transition is replaced by a delocalization transition with increasing velocity. Predictions for the behavior as a function of wind velocity are made for one and two dimensions. Received: 3 August 1998 / Revised version: 17 July 1999 / Published online: 4 July 2000     

Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population

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.     

The steady state kinetics of some biological systems: III. Thermodynamic aspects

Some thermodynamic aspects of steady systems are considered. The time rates of changes, “flux”, of various thermodynamic quantities are formulated. In particular the free energy flux in the steady state, the difference between the free energy flux in the steady and time dependent states and the change in free energy flux upon transition between steady states are discussed. Equations are derived which exhibit the formal similarities and differences between the free energy flux and the conventional free energy change. The temperature dependence of the steady state rate is examined and conditions for “mastery” by a single step discussed. A brief discussion of the role ofrate in the coupling of exergonic and endergonic reactions is given.     

A statistical approach to the theory of the central nervous system

A “probabilistic” rather than a “deterministic” approach to the theory of neural nets is developed. Neural nets are characterized by certain parameters which give the probability distributions of different kinds of synaptic connections throughout the net. Given a “state” of the net (i.e., the distribution of firing neurons) at a given moment, an equation for the state at the next moment of quantized time is deduced. Certain very special cases involving constant distributions are solved. A necessary condition for a steady state is deduced in terms of an integral equation, in general non-linear.     

pH-Induced Molten Globule State of <Emphasis Type="Italic">Rhizopus niveus</Emphasis> Lipase is More Resistant Against Thermal and Chemical Denaturation Than Its Native State

Here, we have characterized four pH-dependent states: alkaline state, “B” (pH 9.0), native state, “N” (pH 7.4), acid-induced state, “A” (pH 2.2) and molten globule state, “MG” (pH 1.8) of Rhizopus niveus lipase (RNL) by CD, tryptophanyl fluorescence, ANS binding, DLS, and enzyme activity assay. This “MG” state lacks catalytic activity and tertiary structure but it has native-like significant secondary structure. The “R _h” of all the four states of RNL obtained from DLS study suggests that the molecular compactness of the protein increases as the pH of solution decreases. Kinetic analysis of RNL shows that it has maximum catalytic efficiency at state “B” which is 15-fold higher than state “N.” The CD and tryptophanyl fluorescence studies of RNL on GuHCl and temperature-induced unfolding reveal that the “MG” state is more stable than the other states. The DSC endotherms of RNL obtained at pH 9.0, 7.4, and 2.2 were with two transitions, while at pH 1.8 it showed only a single transition.     

Density-dependent migration and stability in a system of linked populations

The effect of adding density-dependent migration between nearest neighbour populations of a single discrete-generation species in a chain of habitat fragments is investigated. The larger the population on a particular habitat fragment, the greater the fraction of inhabitants who migrate before reproducing. It has previously been shown for similar models with density-independent migration that coupling populations in this way has no effect on the stability of these populations. Here, it is demonstrated that this effect is also generally true if migration is density-dependent. However, if the migration rate is large enough and has density dependence of the correct form, then the steady state (with all the populations remaining at the same constant value through time) can be destabilised. The conditions for this to occur are obtained analytically. When this “destabilisation” occurs, the system settles down to an alternative steady state where half of the populations take one constant value which is below that of an equivalent isolated system, and the other populations all share a population value which is greater than the steady state of the isolated populations. Once this configuration is reached, the population size on each patch remains constant over time. hence the change might more properly be described as a decrease in homogeneity rather than in stability.     

Structure of the bank vole (<Emphasis Type="Italic">Myodes glareolus</Emphasis>) population cycles in the core and periphery of its species area

The results of long-term studies of two bank vole (Myodes glareolus) populations in stationary sites in the central part and periphery of its species area are described. Four phases of a multiannual population cycle and two of its structural parts have been detected for both populations. The first part of the cycle is “determined,” with the “peak” phase passing into a “depression” (population collapse). This transition is mainly determined by intrapopulation processes and is weakly dependent on the external conditions of each individual year. The second part is “stochastic,” starting from a stable point in the cycle in the depression phase. The duration of the second part is determined by the state of the population and its ability to increase its size, as well as by the weather and food factors, predation pressure, and location of the population within the species area. The transition from the peak phase to the depression phase (the determined part) for both populations takes place during one fall-winter-spring season and has no effect on the cycle duration. The duration of the stochastic part in the core of the species area (the period from depression phase to peak phase) is 1–3 years and in the periphery, 2–4 years.     

Mathematical models for cellular systems. The von foerster equation. Part II

This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly. This work was performed under the auspices of the U.S. Atomic Energy Commission.     

On the stochastic interpretation of a pathological cell renewal system,I: Theoretical basis

The population constituted by parenchymal liver cells is normally a static or slowly expanding one. This is in contrast with “renewal systems,” or cell populations which turn over more or less rapidly. In experimental situations tending to produce cirrhosis of the liver the rate of cell renewal is appreciable. The situation then corresponds to the definition of a “renewal system.” A repeating unit of the liver lattice structure is proposed in which liver cells are assumed to be sequestrated by anatomical constraints on cell migration, and the order of magnitude of its population determined. The characteristics of the simple birth-and-death process are reviewed to show how it leads to greater fluctuation than does a pure birth process with equivalent expected net growth. A hypothetical birth-and-death process is proposed for the renewal of the cell population of the liver unit. The rate of cell proliferation is placed at a level comparable to that found in reports of experimental cirrhosis taken from the literature. This example of a birth-and-death process leads to the prediction of appreciable fluctuation in the population of the liver unit. It is suggested that fluctuations of this kind may account for some of the morphological features of cirrhosis and lead to a new definition of “nodular regeneration.”     

The Jackprot Simulation Couples Mutation Rate with Natural Selection to Illustrate How Protein Evolution Is Not Random

Protein evolution is not a random process. Views which attribute randomness to molecular change, deleterious nature to single-gene mutations, insufficient geological time, or population size for molecular improvements to occur, or invoke “design creationism” to account for complexity in molecular structures and biological processes, are unfounded. Scientific evidence suggests that natural selection tinkers with molecular improvements by retaining adaptive peptide sequence. We used slot-machine probabilities and ion channels to show biological directionality on molecular change. Because ion channels reside in the lipid bilayer of cell membranes, their residue location must be in balance with the membrane’s hydrophobic/philic nature; a selective “pore” for ion passage is located within the hydrophobic region. We contrasted the random generation of DNA sequence for KcsA, a bacterial two-transmembrane-domain (2TM) potassium channel, from Streptomyces lividans, with an under-selection scenario, the “jackprot,” which predicted much faster evolution than by chance. We wrote a computer program in JAVA APPLET version 1.0 and designed an online interface, The Jackprot Simulation , to model a numerical interaction between mutation rate and natural selection during a scenario of polypeptide evolution. Winning the “jackprot,” or highest-fitness complete-peptide sequence, required cumulative smaller “wins” (rewarded by selection) at the first, second, and third positions in each of the 161 KcsA codons (“jackdons” that led to “jackacids” that led to the “jackprot”). The “jackprot” is a didactic tool to demonstrate how mutation rate coupled with natural selection suffices to explain the evolution of specialized proteins, such as the complex six-transmembrane (6TM) domain potassium, sodium, or calcium channels. Ancestral DNA sequences coding for 2TM-like proteins underwent nucleotide “edition” and gene duplications to generate the 6TMs. Ion channels are essential to the physiology of neurons, ganglia, and brains, and were crucial to the evolutionary advent of consciousness. The Jackprot Simulation illustrates in a computer model that evolution is not and cannot be a random process as conceived by design creationists.     

Longitudinal changes of dominance rank among the females of the Koshima group of Japanese monkeys

The changes of dominance rank among female Japanese monkeys of the Koshima group over a period of 29 years from 1957 were studied. The dominance rank order was relatively stable in the early population growing phase, while large scale-changes of dominance rank order occurred successively in the phase of population decrease brought about by the severe control of artificial feeding after 1972. Nevertheless, the rank order of several females of the highest status was stable. Furthermore, the reproductive success of these highest status females was high (Mori, 1979a;Watanabe et al., in prep.). Divergence of the dominance rank order fromKawamura's rules (Kawamura, 1958) was observed in the following respects: (1) Some females significantly elevated their rank depending on the leader males. (2) If mothers died when their daughters were still juveniles or nulliparous, the dominance rank of some of these offspring females was significantly lower than the mother's one. However 55% of daughters which lost their mothers at a young age inherited the mother's rank. (3) Dominance among sisters whose mother had died when at least one of the daughters was under 6 years old followed the rule of youngest ascendancy in 60% (Kawamura, 1958), and in 80% when both of the daughters were nulliparous at the mother's death. The mean rate of aggressive interactions for each female with subordinates to her was calculated by dividing the total aggressive interactions between the female in question and her subordinates by the number of subordinate females to the female in question. A female which showed a high rate of aggressive interactions with her subordinates was categorized as an “Attacker”, and a female showing a lower rate was categorized as a “Non-attacker”. Similarly, categories of “Attacked”, and “Non-attacked” were distinguished by using the rate of aggressive interactions with dominant females. Several females which were once categorized in one category in a year were repeatedly categorized in the same category over different years. The “Attacked” tended to be females of higher rank, and “Non-attackers” tended to be females of lower rank. “The second-higher-status females”, were “Attacked”, and their rank was unstable. In particular, females of lower rank within the lineage of the highest rank suffered this kind of severe status. Most of the daughters of these females showed a sharp drop of rank, and died when they were still at a young age, i.e. “the second-higher-status females” displayed low fitness. “Non-attackers” were significantly “Non-attacked”; i.e. they were females which showed a non-social attitude. Females which underwent a drop of rank tended to be “Non-attackers”. The most important factor which determined the females' rank was the memory of their dominance relations under the influence of their mother [dependent rank (Kawai, 1958)] in their early life during development. This finding corresponds well with the results in baboons obtained byWalter (1980); the target females of aggressive interactions by adolescent females were determined by the rank of the mothers when these adolescent females were born.     

The dynamic behavior of phycobilisome movement during light state transitions in cyanobacterium <Emphasis Type="Italic">Synechocystis</Emphasis> PCC6803

Light state transition is a physiological function of oxygenic organisms to balance the excitation of photosystem II (PSII) and photosystem I (PSI), hence a prerequisite of oxygen-evolving photosynthesis. For cyanobacteria, phycobilisome (PBS) movement during light state transition has long been expected, but never observed. Here the dynamic behavior of PBS movement during state transition in cyanobacterium Synechocystis PCC6803 is experimentally detected via time-dependent fluorescence fluctuation. Under continuous excitation of PBSs in the intact cells, time-dependent fluorescence fluctuations resemble “damped oscillation” mode, which indicates dynamic searching of a PBS in an “overcorrection” manner for the “balance” position where PSII and PSI are excited equally. Based on the parallel model, it is suggested that the “damped oscillation” fluorescence fluctuation is originated from a collective movement of all the PBSs to find the “balance” position. Based on the continuous fluorescence fluctuation during light state transition and also variety of solar spectra, it may be deduced that light state transition of oxygen-evolution organisms is a natural behavior that occurs daily rather than an artificial phenomenon at extreme light conditions in laboratory.     

On the theory of selection of coupled macromolecular systems

In this paper we examine a set of nonlinear rate equations (devised by M. Eigen (1971)) which describe the process of selection in a collection of self-reproducing, macromolecular information carriers. We construct exact solutions to the equations for the case of constant rate parameters and constant error distributions. The solutions allow the direct assessment of the effect of mutations on the “selective value” parameters discussed by Eigen as well as the distribution of the molecular species selected in steady state. In addition we show that the selection process may be characterized by an extremal principle.     

Estimation of relative contribution of “mobile phycobilisome” and “energy spillover” in the light–dark induced state transition in Spirulina platensis

Previously, it was clarified that phycobilisome (PBS) mobility and energy spillover were both involved in light-to-dark induced state transitions of intact Spirulina platensis cells. In this work, by taking advantage of the characteristic fluorescence spectra of photosystem I (PSI) trimers and monomers as indicators, the relative contributions for the “mobile PBS” and “energy spillover” are quantitatively estimated by separating the fluorescence contribution of PBS mobility from that of PSI oligomeric change. Above the phase transition temperature (T _PT) of the membrane lipids, the relative proportion of the contributions is invariable with 65% of “mobile PBS” and 35% of “energy spillover”. Below T _PT, the proportion for the “mobile PBS” becomes larger under lowering temperature even reaching 95% with 5% “energy spillover” at 0°C. It is known that lower temperature leads to a further light state due to a more reduced or oxidized PQ pool. Based on the current result, it can be deduced that disequilibrium of the redox state of the PQ pool will trigger PBS movement instead of change in the PSI oligomeric state.     

Decline in energy storage in the Antarctic minke whale (<Emphasis Type="Italic">Balaenoptera bonaerensis</Emphasis>) in the Southern Ocean

The annual trend in energy storage in the Antarctic minke whale was examined using catch data from all 18 survey years in the Japanese Whale Research Program (JARPA). Regression analyses clearly showed that blubber thickness, girth and fat weight have been decreasing for nearly 2 decades. The decrease per year is estimated at approximately 0.02 cm for mid-lateral blubber thickness and 17 kg for fat weight, corresponding to 9% for both measurements over the 18-year period. Furthermore, “date”, “extent of diatom adhesion”, “sex”, “body length”, “fetus length”, “latitude”, “age” and “longitude” were all identified as partially independent predictors of blubber thickness. The direct interpretation of this substantial decline in energy storage in terms of food availability is difficult, since no long-term krill abundance series is available. However, an increase in the abundance of krill feeders other than minke whales and a resulting decrease in the krill population must be considered as a likely explanation.     

Spatial stability analysis of Eigen's quasispecies model and the less than five membered hypercycle under global population regulation

A generalization of the “constant overall organization” constraint of Eigen's quasispecies and hypercycle models, called herein “global population regulation”, is shown to lead to mathematically tractable spatial generalizations of these two models. The spatially uniform steady state of Eigen's quasispecies model is shown to be stable and globally attracting for all possible values of the mutation and replication rates. In contrast, the spatially and temporally uniform solutions to the hypercycle with fewer than five members, the only ones insensitive to stochastic perturbations, are shown to be unstable, and a lower bound to the spatial inhomogeneities is obtained. The prospect that the spatially localized hypercycle might be immune to various instabilities cited in the literature is then briefly considered. Although spatial localization makes possible a much richer dynamical repertoire than previously considered, it is also more difficult to understand how Darwinian selection of hypercycles could result in a unique genetic code.     

Assessment of the Neva Estuary ecosystem state on the basis of structural characteristics of benthic animal communities in 1994–2005

In the years 1994–2005, the values of the integrated index IP’ at some stations of the Neva Bay changed from 38.1 to 81.9%, water quality changed from class 3 to class 5, and the states of some areas of the ecosystem that were evaluated as “tense” went to “catastrophic.” The integrated mean assessment of water quality according to the IP’ index over the entire Neva Bay throughout 12 years (1994–2005) remained relatively stable, waters were assessed as “polluted” (fourth class), and the state of the ecosystem was considered “critical.” The state of the eastern part of the Gulf of Finland in 1994–2005 was less favorable. The species diversity of zoobenthos in the resort zone of the eastern part of the Gulf of Finland is considerably lower than in the Neva Bay. Waters of the resort zone of the eastern part of the Gulf of Finland in 1994–2005 were assessed as one class lower than in the Neva Bay, i.e., as “polluted-dirty” (fourth-fifth class), and the state of the ecosystem was assessed as being in a “crisis.” In the resort zone, there was a decline in species diversity and abundance and biomass of benthic animals; i.e., all characteristics of the degradation of benthic animal communities were observed.     

On the spread of information with time and distance

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.     

The use of two radiotracers for transfer-rate determinations in closed two compartment systems

The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems. This paper is an outgrowth of work supported by grant AI 02457 from the National Institute of Allergy and Infectious Diseases, U.S. Public Health Service.