An evolutionary analytical model of a complementary circular code simulating the protein coding genes, the 5′ and 3′ regions

The self-complementary subset ∪{AAA,TTT} with = {AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC} of 22 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. The subsets ∪{CCC} and ∪{GGG} of 21 trinucleotides have a preferential occurrence in the shifted frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5′-3′ direction). and are complementary to each other. The subset contains the subset which has the rarity property (6 × 10⁻⁸) to be a complementary maximal circular code with two permutated maximal circular codes and in the frames 1 and 2 respectively. is called a C³ code. A quantitative study of these three subsets in the three frames 0, 1, 2 of protein genes, and the 5′ and 3′ regions of eukaryotes, shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of in the frame 0 of protein genes are 49, 28.5 and 22.5% respectively. In contrast, the frequencies of in the 5′ and 3′ regions of eukaryotes, are independent of the frame. Indeed, the frequency of in the three frames of 5′ (respectively 3′) regions is equal to 35.5% (respectively 38%) and is greater than the frequencies and , both equal to 32.25% (respectively 31%) in the three frames. Several frequency asymmetries unexpectedly observed (e.g. the frequency difference between and in the frame 0), are related to a new property of the subset involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 22 codons (trinucleotides in frame 0) of with equiprobability (1/22) followed by t ≈ 4 substitutions per codon according to the proportions p ≈ 0.1; q ≈ 0.1 and r = 1 − p − q ≈ 0.8 in the three codon sites respectively, retrieves the frequencies of observed in the three frames of protein genes and explains these asymmetries. Furthermore, the same model (0.1, 0.1, t) after t ≈ 22 substitutions per codon, retrieves the statistical properties observed in the three frames of the 5′ and 3′ regions. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine.     

Some results in graph theory and their application to abstract relational biology

It has been shown in earlier work that one approach to what Rashevsky has called “abstract biology” is through the study of the class of ( )-systems that can be formed in an arbitrary subcategory of the category of sets. The concept of the ( )-system, however, depends on the availability of mappings that contain other mappings in their range. It is shown that, by introducing an appropriate measure for this property, the problem of characterizing those categories suitable for a rich theory of ( )-systems reduces to a problem familiar from the general theory of graphs. Some new results in these directions are obtained, and it is then shown that any category with mappings that possess properties we might expect to hold in the physical world will also admit a rich theory of ( )-systems. In particular, it is shown that a sufficiently large family of mappings drawn at random from such a category will with overwhelming probability contain an ( )-system. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Grant No. AF-AFOSR-9-63.     

The\dot V_A /\dot Q resolution of inert gas dataresolution of inert gas data

The non-uniqueness of distributions satisfying inert gas retention data without error is studied. The ability of such data to resolve blood flows at particular values is discussed through the application of linear programming and Backus-Gilbert theory. It is shown that the resolution deteriorates away from the extremes of low and high .     

On the derivation of a mean growth equation for cell cultures

IfN(t) is the expected number of cells in a culture at timet, the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.     

On the biotopology of protein biosynthesis

The present paper is an attempt to outline a possible approach to the study of concrete cellular systems in terms of relational biology as developed by Rashevsky and Rosen. The basic ideas and the formalism of Rosen’s (M,R)-systems, proposed as a model of abstract biological systems, are used in order to represent the cellular protein biosynthesis. A diagram corresponding to the activation of amino acids and synthesis of amino-acyl-transfer RNA, the attachment of _t RNA to a specific codon of messenger RNA and peptide bond synthesis with the release of a protein molecule, is constructed. The systemM thus obtained for the synthesis of a proteinp _k receives a set of environmental inputs, that is, the twently naturally occurring amino acids and emits a single output, thep _k protein. The problem of noncontractibility of inputs in the system is then analyzed. In our context, it is found that the noncontractibility is not associated with the whole amino acid setS _pk but with an “essential amino acid set” , so that and represent the set of amino acids which can be replaced or absent. According to our considerations, the biochemical concept of “essential amino acid” acquires a new significance, that is, what seems “essential” is linked with the ability to form a giventRNA _t ∼a _i complex in a suitable augmented dependent set essential for the biosynthesis of a functional protein. Eventually the discussion of re-establishability leads to some important biological implications concerning the existence of ambiguous codons and the degeneracy phenomenon in the genetic code, as anecessary biochemical tool involved in adaptive processes.     

Comment on biomass diversity in ecology

It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.     

Correlation between cell density,membrane fluidity,and the availability of transferrin receptors in friend erythroleukemic cells

Undifferentiated Friend erythroleukemic cells (FL cells) acquire membrane microviscosity ( ), in accord with the culture cell density. At low cell density poise, whereas at confluency it increases to poise. Concomitantly, the total number of available transferrin receptors per cell decreases by about 80% upon increase in cell density. Modulation of membrane microviscosity, by artificial alteration of the membrane cholesterol level, mediates similar modulations of the availability of the transferrin receptors. The correlation between the availability of the transferrin receptors and the membrane lipid fluidity may take part in the overt decrease in iron uptake by erythroid cells along the erythropoiesis pathway.     

Stochastic models for chemical reactions: I. Theory of the unimolecular reaction process

A stochastic model for the basic unimolecular chemical reaction is derived. This model provides a mathematical basis, altogether missing in the current kinetic theory, for the analysis of inherent random fluctuations about the strict concentration-time course prescribed by the existing deterministic theory. Limits on the extent of the predicted inherent variability are obtained and compared with those usually expected purely on the basis of random experimental errors of extraneous origin (not associated with the mechanism of reaction). The results support the extrapolation to chemical systems of a principle of statistical inaccuracy for physical systems which has been called by E. Schroedinger “the Law of Physics.”     

Modelling the dynamics of West Nile Virus

In this work we formulate and analyze a mathematical model for the transmission of West Nile Virus (WNV) infection between vector (mosquito) and avian population. We find the Basic Reproductive Number in terms of measurable epidemiological and demographic parameters. is the threshold condition that determines the dynamics of WNV infection: if the disease fades out, and for the disease remains endemic. Using experimental and field data we estimate for several species of birds. Numerical simulations of the temporal course of the infected bird proportion show damped oscillations approaching the endemic value.     

The complete heart-lead relationship in the einthoven triangle

The relationship between the source strength and the “manifest vector” in the Einthoven Triangle is derived for a line and a point dipole source and confirmed experimentally. The result permits the interpretation of the standard ECG leads in absolute terms and corrected for body size. The manifest vector is shown to be approximately times what it would be in an otherwise similar circular slab which circumscribes the triangle.     

Theoretical basis of single breath gas absorption tests

Absorption of gas from alveoli is examined in a simplified model of the respiratory system during a stylized single breath consisting of constant inspiratory flow, constant expiratory flow, and breathholding. The equations describing gas behavior are general since they are based upon conservation of mass. The equations simplify considerably when gases that are not soluble in pulmonary tissue and/or blood are utilized. In a three-compartment model, diffusing capacity of the lung for carbon monoxide (D _CO ) will be underestimated except when both uneven distribution of lung volume andD _CO are present; under most circumstances, the standard clinical 10-s method [9] is at least as accurate as any other. When pulmonary capillary blood flow is calculated by the one point method [2] in a one-compartment lung, it is underestimated; in the three-compartment model, it is underestimated except when both uneven distribution of . and lung volume are present. The multiple single breath method [2] accurately measuresD _CO and . Measurement of pulmonary tissue volume is improved by correcting the value of the intercept of acetylene absorption to the time when carbon monoxide apparently began rather than utilizing the beginning of inspiration.Nomenclature D _CO diffusing capacity of the lung for CO (ml CO, STPD/min/mm Hg) - pulmonary capillary blood flow rate (L/min) - V _t pulmonary tissue volume (L) - V _A alveolar compartment volume (L) - V _Ao alveolar compartment volume at conclusion of inspiratory flow (L) - inspiratory flow rate (L/sec) - expiratory flow rate (L/sec) - Bunsen coefficient of pulmonary tissue for test gas (ml test gas/ml tissue/atm) - Bunsen coefficient of pulmonary tissue for test gas (ml test gas/ml blood/atm) - F _A fractional pressure of test gas in the alveolar compartment (atm)     

Use of the force-velocity test to determine the optimal braking force for a sprint exercise on a friction-loaded cycle ergometer

A group of 15 untrained male subjects pedalled on a friction-loaded cycle ergometer as fast as possible for 5–7 s to reach the maximal velocity (V{immax}) against different braking forces (F _B). Power was averaged during a complete crank rotation by adding the power dissipated againstF _B to the power necessary to accelerate the flywheel. For each sprint, determinations were made of peak power output ( ) power output attained atV _max ( ) calculated as the product ofV _max andF _B and the work performed to reachV _max expressed in mean power output ( ). The relationships between these parameters andF _B were examined. A biopsy taken from the vastus lateralis muscle and tomodensitometric radiographs of both thighs were taken at rest to identify muscle metabolic and morphometric properties. The value was similar for allF _B. Therefore, the average of values was defined as corrected maximal power ( ). This value was 11 higher than the maximal power output uncorrected for the acceleration. Whereas the determination did not require high loads, the highest value ( ) was produced when loading was heavy, as evidenced by the -F _B parabolic relationship. For each subject, the braking force ( ) giving was defined as optimal. The , equal to 0.844 (SD 0.108) N · kg⁻¹ bodymass, was related to thigh muscle area (r = 0.78,P < 0.05). The maximal velocity ( ) reached against this force seemed to be related more to intrinsic fibre properties (% fast twitch b fibre area and adenylate kinase activity). Thus, from the determination, it is suggested that it should be possible to predict the conditions for optimal exercise on a cycle ergometer.     

A model of oxygen uptake kinetics in response to exercise: Including a means of calculating oxygen demand/deficit/debt

We present a new model of the underlying dynamics of the oxygen uptake kinetics for various exercise intensities. This model is in the form of a set of nonlinear coupled vector fields for the and , the derivative of the exercise intensity with respect to time. We also present a new and novel means for calculating the oxygen demand, D(v, t), and hence also the oxygen deficit and debt, given the time series of the . This enables us to give better predictions for these values especially for when exercising at or close to maximal exercise intensities. Our model also allows us to predict the oxygen uptake time series given the time series for the exercise intensity as well as to investigate the oxygen uptake response to nonlinear exercise intensities. Neither of these features is possible using the currently used three-phase model. We also present a review of both the underlying physiology and the three-phase model. This includes for the first time a complete set of the analytical solutions of the three-phase model for the oxygen deficit and debt.     

Analysis of spatial association between two species based on the interspecies mean crowding

Summary and Conclusion The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ andC _μ, are derived as geometric and weighted arithmetic means of the same component ratios related to inter- and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita’s (1959)C _δ index. Indices to measure the degree of spatial correlation between species, ω andR _μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra- and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested. This study was supported by Science Research Fund (No. 148041) from the Ministry of Education.     

Sulfur isotope values in a forested catchment over four years: Evidence for oxidation and reduction processes

A small catchment on the Swedish West Coast has been studied over four years to determine S dynamics by using S isotope ratios. A Norway spruce dominated forest covers the catchment, and small peat areas occur in the lower parts of the catchment. The runoff values varied both during the year, and from year to year. Over the period from February 1990 to December 1993, the values ranged from — 1%. to +11%. Over the same period, the throughfall values ranged from +1%. to +15%. There was no correlation (r ²= 0.01; Pr(F)=0.57) between values in throughfall and runoff. Since the only input of S to the catchment is atmospheric deposition, the long-term runoff S mass flux is controlled by the deposition. Therefore, processes in the catchment are responsible for the variation in the runoff values. During periods with enriched runoff, bacterial dissimilatory SO ₄ ^2– reduction occurs in the catchment. After very dry periods, oxidation of this reduced S, which is³²S-enriched, can be traced in runoff. Previous studies of the catchment have not been able to distinguish between: 1) oxidation of reduced S and dry deposition, and 2) reduction and adsorption. From the current study, it can be concluded that adsorption and dry deposition cannot cause the observed variation in runoff .     

The generation of the proton electrochemical potential and its role in energy transduction

Summary The evidence that all energy transducing membranes can generate a proton electrochemical potential difference, _H, across the membrane and that this potential can be used to transfer energy among energy transducing units and to generate ATP, has increased the interest for the view that _H plays an obligatory role in energy transduction and ATP synthesis. In the present article we shall concentrate on two experimental questions related with the generation and role of _H: (a) the charge/site ratio; (b) the relation between the proton electrochemical potential on one side and the cation electrochemical potential, the phosphate potential and the redox potential on the other. We shall then discuss the view that energy transduction corresponds to a molecular energy machine rather than to a fuel cell.     

Estimation of surface charges in some biological membranes

Summary The resting membrane potential data existing in the literature for the giant axon of the squid, frog muscle and barnacle muscle have been analyzed from the standpoint of the theory of membrane potential due to Kobatake and co-workers. The average values derived for the effective charge density (where is a constant, , and represents the fraction of counterions that are free, and is the stoichiometric charge density in the membrane) present on the different biomembranes existing in their normal ionic environment are 0.3, 0.325 and 0.17 M for the squid axon, frog and barnacle muscles, respectively. On the assumption that the values of are 0.4 and 0.2 for nerve and muscle membranes, respectively, values of 0.75, 1.62 and 0.85 M have been derived for the stoichiometric charge density present in the respective biological membranes. These correspond to 1 negative charge per 222, 103 and 195 Å of the membrane area of the squid axon, frog and barnacle muscles, respectively.     

Times to exhaustion at 100% of velocity at [(V)\dot]\textO\text2 \dot V{\text{O}}_{\text{2}} max and modelling of the time-limit / velocity relationship in elite long-distance runners

The aim of this study was to measure running times to exhaustion (Tlim) on a treadmill at 100% of the minimum velocity which elicits _{max max} in 38 elite male long - distance runners _max = 71.4 ± 5.5 ml.kg^–1.min^–1 and _max = 21.8 ± 1.2 km.h^–1). The lactate threshold (LT) was defined as a starting point of accelerated lactate accumulation around 4 mM and was expressed in _max. Tlim value was negatively correlated with _max (r = -0.362, p< 0.05) and _max (r = –0.347, p< 0.05) but positively with LT (%v _max) (r = 0.378, p < 0.05). These data demonstrate that running time to exhaustion at _max in a homogeneous group of elite male long-distance runners was inversely related to _max and experimentally illustrates the model of Monod and Scherrer regarding the time limit-velocity relationship adapted from local exercise for running by Hughson et al. (1984) .     

Skeletal muscle [(V)\dot]O2 \dot V_{O_2 } in rat and lemming: Effect of blood flow rate

Summary The rate of oxygen consumption ( ) by skeletal muscle was investigated in isolated perfused hindlimbs of laboratory rats and lemmings (Lemmus). In both species, increased in proportion to blood flow rate, even at flow rates 4–5 times above resting level. The slope of the line relating to skeletal muscle blood flow was significantly greater in the lemming than in the rat. This may be related to the inverse relationship between body weight and metabolic rate. These data support the hypothesis that in small animals a dependent relationship exists between blood flow and skeletal muscle .     

Chemiosmotic systems in bioenergetics: H+-cycles and Na+-cycles

The development of membrane bioenergetic studies during the last 25 years has clearly demonstrated the validity of the Mitchellian chemiosmotic H⁺ cycle concept. The circulation of H⁺ ions was shown to couple respiration-dependent or light-dependent energy-releasing reactions to ATP formation and performance of other types of membrane-linked work in mitochondria, chloroplasts, some bacteria, tonoplasts, secretory granules and plant and fungal outer cell membranes. A concrete version of the direct chemiosmotic mechanism, in which H⁺ potential formation is a simple consequence of the chemistry of the energy-releasing reaction, is already proved for the photosynthetic reaction centre complexes.Recent progress in the studies on chemiosmotic systems has made it possible to extend the coupling-ion principle to an ion other than H⁺. It was found that, in ceertain bacteria, as well as in the outer membrane of the animal cell, Na⁺ effectively substitutes for H⁺ as the coupling ion (the chemiosmotic Na⁺ cycle). A precedent is set when the Na⁺ cycle appears to be the only mechanism of energy production in the bacterial cell. In the more typical case, however, the H⁺ and Na⁺ cycles coexist in one and the same membrane (bacteria) or in two diffeerent membranes of one and the same cell (animals). The sets of and generators as well as and consumers found in different types of biomembranes, are listed and discussed.