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.     

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.     

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.     

A simple classification of the volvocine algae by formal languages

There are several explanations of why certain primitive multicellular organisms aggregate in particular forms and why their constituent cells cooperate with one another to a particular degree. Utilizing the framework of formal language theory, we have derived one possible simple classification of the volvocine algae—one of the primitive multicells—for some forms of aggregation and some degrees of cooperation among cells. The volvocine algae range from the unicellular Chlamydomonas to themulticellular Volvox globator, which has thousands of cells. The classification we use in this paper is based on the complexity of Parikh sets of families on Chomsky hierarchy in formal language theory. We show that an alga with almost no space closed to the environment, e.g., Gonium pectorale, can be characterized by , one with a closed space and no cooperation, e.g., Eudorina elegans, by , and one with a closed space and cooperation, e.g., Volvox globator, by . This classification should provide new insights into the necessity for specific forms and degrees of cooperation in the volvocine algae.     

?2\sqrt 2 Rule for Controlling the Tree Pattern in Forest Cut

A forest’s productivity can be optimized by the application of rules derived from monopolized circles. A monopolized circle is defined as a circle whose center is a tree and whose radius is half of the distance between the tree itself and its nearest neighbor. Three characteristics of monopolized circle are proved. (1) Monopolized circles do not overlay each other, the nearest relationship being tangent. (2) “Full uniform pattern” means that the grid of trees (a×b=N) covers the whole plot, so that the distance between each tree in a row is the same as the row spacing. The total monopolized circle area with a full uniform pattern is independent on the number of trees and times the plot area. (3) If a tree is removed, the area of some trees’ monopolized circle will increase without decreasing the monopolized circles of the other trees. According to the above three characteristics, “uniform index” is defined as the total area of monopolized circles in a plot divided by the total area of the monopolized circles, arranged in a uniform pattern in the same shaped plot. According to the definition of monopolized circle, the distribution of uniform index for a random pattern and the variance of L is . It is evident that E(L) is independent on N and the plot area; hence, L is a relative index. L can be used to compare the uniformity among plots with different areas and the numbers of trees. In a random pattern, where L is equivalent to the tree density of the plot in which the number of trees is 1 and the area is π, the influence of tree number and plot area to L is eliminated. When n→∞, D(L)→0 and it indicates that the greater the number of tree is in the plots, the smaller the difference between the uniform indices will be. There are three types of patterns for describing tree distribution (aggregated, random, and uniform patterns). Since the distribution of L in the random pattern is accurately derived, L can be used to test the pattern types. The research on Moarshan showed that the whole plot has an aggregated pattern; the first, third, and sixth parts have an aggregated pattern; and the second, fourth, and fifth parts have a random pattern. None of the uniform indices is more than 0.318 (1/∏), which indicates that uniform patterns are rare in natural forests. The rules of uniform index can be applied to forest thinning. If you want to increase the value of uniform index, you must increase the total area of monopolized circles, which can be done by removing select trees. “Increasing area trees” are the removed trees and can increase the value of the uniform index. A tree is an increasing area tree if the distance between the tree and its second nearest neighbor is times longer than that between the tree itself and its first nearest neighbor, which is called the rule. It was very interesting to find that when six plots were randomly separated from the original plot, the proportion of increasing area trees in each plot was always about 0.5 without exception. In random pattern, the expected proportion of increasing area trees is about 0.35–0.44, which is different from the sampling value of 0.5. The reason is very difficult to explain, and further study is needed. Two criteria can be used to identify which trees should be removed to increase the uniform index during forest thinning. Those trees should be (1) trees whose monopolized circle areas are on the small side and (2) increasing area trees, which are found via the rule. Translated from Acta Ecologica Sinica, 2005, 25(1) (in Chinese)     

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.     

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.     

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.     

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 .     

A mathematical model for assessing control strategies against West Nile virus

Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity , which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make . On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if , then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.     

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.     

Investigation of the Bernoulli model for RNA secondary structures

Within this paper we investigate the Bernoulli model for random secondary structures of ribonucleic acid (RNA) molecules. Assuming that two random bases can form a hydrogen bond with probability p we prove asymptotic equivalents for the averaged number of hairpins and bulges, the averaged loop length, the expected order, the expected number of secondary structures of size n and order k and further parameters all depending on p. In this way we get an insight into the change of shape of a random structure during the process . Afterwards we compare the computed parameters for random structures in the Bernoulli model to the corresponding quantities for real existing secondary structures of large subunit rRNA molecules found in the database of Wuyts et al. That is how it becomes possible to identify those parameters which behave (almost) randomly and those which do not and thus should be considered as interesting, e.g., with respect to the biological functions or the algorithmic prediction of RNA secondary structures.     

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.”     

A dynamical field theory for dissipative thermal systems. The first and second laws of irreversible thermodynamics

The thermodynamics of irreversible processes is derived from the principles of dynamical field theory independently of all elements of thermostatics, in particular the assumption of local equilibrium. Field thermodynamics proceeds from the premise that all driving forces experienced by the molecules in a continuum are conservative and arise from scalar potential functions. Dynamically the temperature potentialT is no different from the pressure potentialp. A field is converted to a force upon multiplication by a scale factor. A potential is converted to potential energy by the same scale factor. To scale the field −∇p to the force per mole of molecular speciesk, the partial molar, volume is the scale factor. Similarly the partial molar entropy, , scales the temperature field. The transition from the scale factors (which are physical parameters) to the systemic variables, for example , is not trivial. From the dynamics and the structure of the derived potential energy function are inducted the conjugate variables such as (p, V _I) and (T, s). The meta-mechanical properties of the thermal variables (T, s) are discovered via the local First Law of Thermodynamics, which relates internal energy, thermal flux, and work, and from the local Second Law, which prescribes, the possible partitions of internal energy between kinetic, potential, and thermal energies. From the form of the potential energy come Maxwell's relationships. From the energy partition comes the equation of continuity for entropy, with its important source term. In contrast to earlier theories of irreversible thermodynamics, the dissipation function does not include the stress tensor, a constitutive parameter.     

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.     

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)     

Age-Related Changes in Oxygen Consumption in the Edible Mussel <Emphasis Type="Italic">Mytilus edulis</Emphasis> from the White Sea

We determined the rate of oxygen consumption in the White Sea edible mussel Mytilus edulis of different ages. The mass-specific rate of oxygen consumption proved to decrease with mussel age according to the equation: = 40.1/(1 – e ^–0.194t ), where is mass-specific rate of oxygen consumption and t is age. Allometric coefficients of the oxygen consumption rate–soft tissue weight relationship were also determined.     

Energetics of the growth of Methanobacterium thermoautotrophicum and Methanococcus thermolithotrophicus on ammonium chloride and dinitrogen

Methanobacterium thermoautotrophicum was grown in continuous culture in a fermenter gassed with H₂ and CO₂ as sole carbon and energy sources, and in a medium which contained either NH₄Cl or gaseous N₂ as nitrogen source. Growth was possible with N₂. Steady states were obtained at various gas flow rates with NH₄Cl and with and the maintenance coefficient varied with the gas input and with the nitrogen source. Growth of Methanococcus thermolithotrophicus in continuous culture in a fermenter gassed with H₂, CO₂ as nitrogen, carbon and energy sources was also examined.Abbreviations molecular growth yield (g dry weight of cells per mol of CH₄ evolved) - growth rate (h^-1) - D dilution rate (h^-1) - rate (h_-1); relation of Neijssel and Tempest and of Stouthamer and Bettenhaussen - energy     

Blooms of tunicates Oikopleura spp. and Dolioletta gegenbauri in the Seto Inland Sea, Japan, during summer

The ecological importance of appendicularians Oikopleura dioica and O. longicauda, and a doliolid Dolioletta gegenbauri as metazoan secondary producers was assessed in summer 1997 in the Seto Inland Sea, Japan. Blooms by the appendicularians occurred twice within a month following peaks of pico-/nanoplankton biomass. The biomass of Oikopleura spp. averaged over the water column (<B> ranged 0.1 to 8.0 μgC l-¹ and temporal average of <B> over the survey period ( ) was 3.2 μgC l-¹, 70% of for calanoid copepods. Furthermore, the temporal average of the production for Oikopleura spp. was 2.4 times higher than that for calanoids, reflecting the extraordinary high growth rates of the appendicularians. D. gegenbauri developed its population following a diatom bloom and <B> reached to 37 μgC l-¹ at the peak time. Although individuals of D. gegenbauri were seldom observed during the first half of the survey, for the doliolid (8.4 μgC l-¹) nearly doubled that for calanoids. These results indicate that the gelatinous tunicates Oikopleura spp. and D. gegenbauri play important roles as metazoan secondary producers in the Seto Inland Sea during summer. This revised version was published online in September 2006 with corrections to the Cover Date.