Some selection models in catalytically coupled selfreproducing macromolecular systems

Some models for selection in enzyme coupled, selfreproducing, macromolecular systems are considered. The enzyme coupling provides a mechanism for the buildup of systems with large information content. The concept of “selective value” and criteria for selection is discussed.     

The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb

A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722, 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as “reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., Development 130, 2027–2037, 2003), the limb model of Hentschel et al. is “morphodynamic,” since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with “morphostatic” mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction–diffusion system is unique in having been derived analytically from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its “Turing space.” Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.     

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

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

The effects of external potassium and magnesium concentrations on the magnesium and potassium inflow rates and growth of micropropagated cherry rootstocks, “F.12/1” (Prunus avium L.) and “Colt” (Prunus avium L.) × Prunus pseudocerasus L.)

The effects (and interaction) of two solution concentrations of Mg (50, 500, μM) and two of K (250, 4250 μM) on the growth of micropropagated plants of “F. 12/1” and “Colt” were investigated using a flowing solution culture system. Magnesium inflow and growth of “Colt” and “F. 12/1” were inhibited to a similar extent by an increased concentration of K in the nutrient solution. However, the consequences of this inhibition were different. Reduced inflow of Mg in “F. 12/1” caused Mg deficiency symptoms at high and low concentrations of K, whereas this only occurred with a combination of high K concentration and low Mg concentration in “Colt”. The distribution of dry matter within the plant was significant in determining susceptibility to Mg deficiency. Since “F. 12/1” has a smaller root:shoot ratio than Colt it is unable to sustain the same concentration of Mg in leaves as “Colt” irrespective of external K concentration. The molar ratio of K:Mg in soil solutions should remain <8.5:1 in order to ensure maximum growth of “F. 12/1” and “Colt”. This revised version was published online in June 2006 with corrections to the Cover Date.     

The perfect learner

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

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.     

Evolutionary ontogenetic aspects of pathogenetics of chronic human diseases

This article is a review of scientific publications, in which issues of pathogenetics of multifactorial diseases (MFDs) are considered from the viewpoint of evolution and ontogeny. Concepts explaining significance of evolutionary processes in the formation of genetic architecture of human chronic diseases (“thrifty” genomes and phenotypes, “drifty genes,” decanalization) are analyzed. The roles of natural selection and genetic drift in the formation of hereditary diversity of genes for susceptibility to MFDs are considered. The modern concept of “disease ontogeny” (somatic mosaicism, loss of heterozygosity, paradominant inheritance, epigenetic variability) is discussed. It is demonstrated that the evolutionary and ontogenetic approaches to analysis of genimuc and other “-omic” data are essential for understanding the biology of diseases.     

Physiological bases of oligotrophy of microorganisms and the concept of microbial community

Three groups of physiological processes in microorganisms are considered the physiological basis of oligotrophy: the greater substrate affinity of the oligotrophs' transport systems, efficient or “economical” metabolism, and existence of a “master reaction” or “rate-determining steps” controlling the rate of metabolism. Heterotrophic microorganisms are divided into three unequal groups according to “reaction norma.” Two groups representing the extremes are small groups with the “narrow” reaction norma, regarding the concentrations and structure of the assimilated organic compounds and variability limits of the physiological characteristics mentioned above. The third, intermediate group includes the majority of microorganisms with the “wide” reaction norma.     

A model for unequal ventilation of the lungs assuming a common dead space and two separate dead spaces

This is a model for the time-variation of helium concentrations in lung wash-out curves. The helium (or other inert gas) is in a spirometer, which is connected by a common dead space to two separate dead spaces, each of which leads into a chamber. The chambers expand and contract, thus taking in some helium at each “breath.” Equations for the changes in helium concentration in each part of the system are set up; in this way difference equations are derived for the amount of helium in the spirometer after each breath, in and out, and complete solutions when the initial concentration is zero in all parts of the system except the spirometer. A simple solution when the chambers do not essentially differ (“equal ventilation”) is compared with the general case. The concept of “unequal lung ventilation” is discussed critically in relation to the model; some physiological interpretations are also mentioned. Numerical examples are given to show the effect of changes in various constants, in particular tidal volumes, end volumes, and the common dead space.     

Correlations between the psychological peculiarities of an individual and the efficacy of a single neurofeedback session (by the EEG characteristics)

Modifications of different EEG rhythms induced by a single neurofeedback session (by the EEG characteristics) directed toward an increase in the ratio of the spectral powers (SPs) of the α vs θ oscillations were compared with the psychological characteristics of the tested subjects (the group included 30 persons). A generally accepted neurofeedback technique was used; the intensity of acoustic white noise served as the feedback signal. EEG potentials were recorded from the C3 and C4 leads. Psychological testing was carried out using Eysenck’s (EPQ), Rusalov’s (OST), and (16 PF) questionnaires. The directions of changes in the SPs of EEG frequency components were found to significantly correlate with some individuality-related peculiarities of the tested subjects. The SP of the δ rhythm correlated with the EPQ scale “neuroticism,” OST scale “social plasticity,” and 16 PF factors H (“parmia”), I (“premsia”), and Q₃ (“self-control of behavior”). The SP of the θ component demonstrated correlations with the OST scales “ergisity,” “plasticity,” and “social temp” and with 16 PF factors M (“autia”), Q₄ (“frustration”), and Q1 (“exvia”). The SP of the α rhythm correlated with 16 PF factors Q₃ (“self-control of behavior”), G (“strength of superEgo”), O (“hypothymia”), L (“protension”), and N (“shrewdness”). The SP of the β rhythm correlated with the OST scale “emotionality,” while that of the γ rhythm showed correlations with the 16 PF indices L (“protension”) and M (“autia”). Changes in the ratio of the α vs θ SPs correlated with the EPQ scale “neuroticism.” Thus, our data confirm the statement that a high individual variability of the results of a single (first in the series) neurofeedback session is to a great extent related to peculiarities of the individual psychological pattern of the subject. Neirofiziologiya/Neurophysiology, Vol. 38, No. 3, pp. 239–247, May–June, 2006.     

On the use of possibility theory in uncertainty analysis of life cycle inventory

Purpose  

The purpose of this paper is to enhance the mathematical and physical understanding of practitioners of uncertainty analysis of life cycle inventory (LCI), on the application of possibility theory. The main questions dealt with are (1) clear definition of the terms—“necessity–possibility,” “probability,” “belief–plausibility,” and of their mutual relationships; (2) what justifies the substitution of classical probability for possibility; (3) mutual comparison of, and transformations in both senses between probability and possibility uncertainty measures; (4) how to construct meaningful input possibility measures from available probabilistic/statistic information; and (5) comparative analysis of the solutions of the problem of data uncertainty propagation in LCI, afforded, respectively, by probabilistic Monte Carlo simulation and possibilistic fuzzy interval arithmetic.     

Physico-chemical model of a voltage-gated sodium channel

A permeant ion is known to create in the channel pore a local electrical field, the intensity of which exceeds the intensity of an electrical field produced by the membrane potential. In our study, we consider a sodium channel model, in which the effects of a permeant ion, an inactivating particle, and pharmacological agents on mobile charged groups of the channel are semi-phenomenologically taken into account by using motion equations for a generalized structural variable. Stationary solutions for the equation correspond to “open,” “closed,” and “inactivated” channel states. Because of this, the channel free energy profile, as a function of the structural variable, has three local minima. The three energy values of these states depend both on the electrical field applied externally and on the near-membrane concentrations of permeant ions and acting pharmacological agents. Sodium channel activation and inactivation kinetics are considered resulting from relative changes of the free energy typical of the above three states of the channel. The results we obtained in the course of channel activation and inactivation modeling and their voltage dependence are qualitatively consistent with the commonly known experimental data. The proposed model allows one to qualitatively predict the dependence of the sodium channel kinetic characteristics on the concentrations of permeant ions and pharmacological agents.     

The occurrence and significance of amino acids in floral nectar

Approximately 1 500 angiosperm species, in previous papers, have been sampled for the assessment of the amino acids (a. a.) in their nectar. We reaffirm that the findings provide statistically significant data linking differences in the concentration with pollinator type. Flowers that are pollinated by animals that have alternative sources of protein-building a. a.’s show lower a. a. concentration than those that are not. There is a tendency for woody plant nectar a. a.’s to be less concentrated than those of herbaceous plants, but there can be “phylogenetic constraints” which may reduce the correlations of a. a. concentration with pollinator type and with life form. The individual a. a.’s form complements which are qualitatively extremely constant within species. Proline is a normal constituent of many nectars and does not necessarily indicate contamination of the nectar by pollen. Criticism of our findings byGottsberger & al. (1984) is answered by reference to our previous publications and those of other workers, and to the presentation of data from California native species, not published previously. All previous postulates are borne out by these new data with the exception of positive correlations of a. a. concentration with “primitive” and “advanced” floral characteristics taken one at a time, which appear to be inconsistent and are affected strongly by the nature of the family in which they occur. Summary data are provided for families and genera which indicate that high or low a. a. concentration can typify certain families and genera of both relatively “primitive” and relatively “advanced” nature. Needs for future research on an ecosystem basis are quoted.     

Some remarks on the mathematical bio-sociology of the relativity of injustice

The author's theory of the adoption of certain types of behavior patterns (Rashevsky, N., 1957, “Contributions to the Theory Initiative Behavior”.Bull. Maths. Biophysics,19, 91–119; 1968,Looking at History through Mathematics, Cambridge, Massachusetts: M.I.T. Press) consisting of elementary behaviors for each of which there is an opposite one and the two are mutually exclusive, is applied to describe the changes in the general type of behavior of a society. The elementary acts of which the whole problem consists may be either overt activities or beliefs or opinions. The general behavior patternsadopted by the society are considered as the “proper” or “just” ones. Any deviation from it in either one or more of the component elementary behaviors is considered as “unjust” and is subject to some punitive action. The total number of possible mutually exclusive behavior patterns is very large but finite. Within this very large range of possible patterns, we find that this notion of justice is relative, because changes from any behavior pattern to any other may occur. It is further shown that the amount of punishment for the deviation from the accepted pattern in order to be effective as well as efficient must be applied in different ways to different individuals even for the same transgression.     

Analytical solution to isometric mechanogram of hill’s model of striated muscle

The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.     

Simulating a neural cross-talk model for between-hand interference during bimanual circle drawing

Studies on drawing circles with both hands in the horizontal plane have shown that this task is easy to perform across a wide range of movement frequencies under the symmetrical mode of coordination, whereas under the asymmetrical mode (both limbs moving clockwise or counterclockwise) increases in movement frequency have a disruptive effect on trajectory control and hand coordination. To account for these interference effects, we propose a simplified computer model for bimanual circle drawing based on the assumptions that (1) circular trajectories are generated from two orthogonal oscillations coupled with a phase delay, (2) the trajectories are organized on two levels, “intention” and “motor execution”, and (3) the motor systems controlling each hand are prone to neural cross-talk. The neural cross-talk consists in dispatching some fraction of any force command sent to one limb as a mirror image to the other limb. Assuming predominating coupling influences from the dominant to the nondominant limb, the simulations successfully reproduced the main characteristics of performance during asymmetrical bimanual circle drawing with increasing movement frequencies, including disruption of the circular form drawn with the nondominant hand, increasing dephasing of the hand movements, increasing variability of the phase difference, and occasional reversals of the movement direction in the nondominant limb. The implications of these results for current theories of bimanual coordination are discussed. Received: 23 June 1998 / Accepted in revised form: 20 April 1999     

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.     

Application of information networks to a theory of vision

Some principles of information theory are utilized in the design of neural nets of the McCulloch-Pitts type. In particular, problems are considered where signals from several neurons must pass through a single one, thus resulting in a “bottleneck” in the flow of information, an abstract model of the corresponding bottleneck from the retina to the optic nerve. The first part of the paper deals with a construction of a McCulloch-Pitts net in which the redundancy in the messages originating in two neurons is utilized so that the messages can be sent over a single neuron with little loss of information. In the second part, messages from a set of neurons are “pumped” into two channel neurons. The optimum connection scheme is computed for this case, i.e, one resulting in a minimum loss of information. Possible biological implications of this approach are indicated.     

In vitro separation of a rose chimera

“Fairmount 1 thorny” (“FM1 thorny”) (a Rosa multiflora Thunb ex. J. Murr.) and a thornless sport of “FM1 thorny” (“Fairmount 1” (“FM1”)) were established in vitro to investigate chimeral segregation under various levels of BA and to obtain a pure thornless rose. While the chimeral thornless sport was expected to segregate in vitro and yield both thorny and thornless plantlets, “FM1 thorny” was to yield only thorny plants. “FM1” segregated in vitro into its constituent genotypes and yielded thorny and thornless plantlets, suggesting that “FM1” is chimeral. “FM1 thorny” produced only thorny plants in vitro. These results indicate that the “FM1 thorny” clone was not chimeral (pure thorny) and that the thornless regenerates of “FM1” did not develop via somaclonal variation. There was a significant linear relationship between increasing BA concentration and the percentage of thorny plants. Among a population of 690 tissue culture derived plants from all the BA experiments, 6 plants were classified as pure thornless plants 1 year later.