Interactions among biological systems: An analysis of asymptotic stability

An analysis of the interactions among asymptotically stable dynamical systems is formulated by making use of the dynamical system theory. Some results coming from previous mathematical analyses have been slightly modified to take into account some typical biological constraints as the boundedness properties of the solutions. In particular it has been shown that when the “coupling” among the subsystems is “loose” enough (in a sense that has to be made mathematically precise) the asymptotic behaviour of a complex system is the same of that of its individual components. The mathematical theory has been used to analyze two systems of biological significance: the coupling among chemical reactions and the stability properties of a 4-dimensional system describing the kinetics of a chemical transmitter.     

On the Semio-Mathematical Nature of Codes

The relational structure of RNA, DNA, and protein bears an interesting similarity to the determination problem in category theory. In this paper, we present this deep-structure similarity and use it as a springboard for discussing some abstract properties of coding in various systems. These abstract properties, in turn, may shed light on the evolution of the DNA world from a semiotic perspective. According to the perspective adopted in this paper, living systems are not information processing systems but “meaning-making” systems. Therefore, what flows in the genetic system is not “information” but “value.” We define meaning, meaning-making, and value and then use these terms to explain the abstract dynamics of coding, which can illuminate many forms of sign-mediated activities in biosystems.     

A mathematical study of non-equimolar ternary gas diffusion

In view of the increasing evidence that multicomponent diffusion effects could be significant in biological gas exchange systems, a non-equimolar film model of multicomponent diffusion was derived. “Osmotic” ternary diffusion was studied for the gas systems He−N₂−O₂, He−SF₆−O₂, and N₂−SF₆−O₂. Diffusional fluxes and concentration profiles were calculated under both the “square-root” and the “product” flux conditions. Results were also compared with those obtained using the equimolar flux condition. It was found that the greater the difference of the diffusibilities between the two active components in a system, the greater the osmotic fluxes, and also the more alinear the concentration profiles. These results support the suggestion that the “product” condition applies to molecular diffusion in free space, the “square-root” condition to molecular diffusion in pores, and the equimolar flux condition to closed diffusion systems.     

Regulatory considerations when developing biological products

The Center for Biologics Evaluation and Research, whose regulatory authority includes monoclonal antibodies, cytokines, vaccines, toxins and somatic cellular therapies, communicates to sponsors issues for consideration in the development of biological products through the publication of “Points to Consider” and “Guideline” documents. This paper summarizes the available “Points to Consider” and “Guideline” documents and outlines recommendations from these documents for characterizing the cells used to produce biological products.     

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.     

Host range of Gonatocerus sp. near tuberculifemur ‘Clade 1’ in Argentina, an egg parasitoid newly associated to the glassy-winged sharpshooter, Homalodisca vitripennis (Hemiptera: Cicadellidae), and candidate for its biological control in California, USA

The South American egg parasitoid Gonatocerus sp. near tuberculifemur “Clade 1” (G. sp. “Clade 1”) (Hymenoptera: Mymaridae) is a new association of the glassy-winged sharpshooter (GWSS), Homalodisca vitripennis (Germar) (Cicadellidae) and a candidate for its biological control in California, USA. In Argentina, G. sp. “Clade 1” was screened in the laboratory (no-choice tests) and in the field (multiple choice tests) against eggs of 32 Auchenorrhyncha host species and other four potential hosts unrelated to sharpshooters. In no-choice assays, it parasitized only eggs within the leafhopper tribe Proconiini. In contrast, in the long term field tests, it emerged not only from eggs of the Proconiini but also from two species of Cicadellini at low numbers (five wasps out of 698 exposed eggs). Two interpretations arise from the results: (1) Host associations of G. sp. “Clade 1” are restricted to the Proconiini whereas field parasitization of the Cicadellini species were false positive, or (2) G. sp. “Clade 1” parasitizes also some Cicadellini species and its rejection in the laboratory was a false negative. Both interpretations are discussed. Insect motivation could be the explanation for the negative results in the no-choice tests. On the other hand, in the more natural field situations, the host selection process and oviposition behavior should not have been affected and host range would be more realistic. The parasitism of the Cicadellini species would be indicative of a potential non-target effect on the sharpshooters in the USA.     

Sexes,species, and genomes: why males and females are not like humans and chimpanzees

This paper describes, analyzes, and critiques the construction of separate “male” and “female” genomes in current human genome research. Comparative genomic work on human sex differences conceives of the sexes as like different species, with different genomes. I argue that this construct is empirically unsound, distortive to research, and ethically questionable. I propose a conceptual model of biological sex that clarifies the distinction between species and sexes as genetic classes. The dynamic interdependence of the sexes makes them “dyadic kinds” that are not like species, which are “individual kinds.” The concept of sex as a “dyadic kind” may be fruitful as a remedy to the tendency to conceive of the sexes as distinct, binary classes in biological research on sex more generally.     

Chaos in abstract kinetics: Two prototypes

“Spiral-type chaos” and “screw-type chaos” constitute two simple types of nonperiodic oscillatory flow in 3-variable continuous systems. The former type is exhibited, for example, by auniversal system in the switching mode, when the regimens of flow on the two stable branches of the slow manifold in state space are made to differ in an appropriate manner. Screw-type chaos occurs in ahysteresis oscillator between two stable limit cycles, if the rotation gain is positive. For either case, an analogous 2-dimensional “branched papersheet flow” exists. Both flows are determined by a single-variable discrete dynamical system of the Lorenz-Li-Yorke type (as a cross-section), as well as by an equivalent new map. Numerical simulations of two abstract reaction systems giving rise to non-idealized (that is, truly 3-dimensional) flows of either type are presented. The corresponding discrete dynamical systems (Poincaré maps) are 2-dimensional now, having the form of a flattened hairpin (“horseshoe”) in the simplest case. Thus, two actual examples for 3-dimensional flows suspended by a horseshoe diffeomorphism seem to have been found. One contains just a single functionally effective nonlinearity. Real systems of either type may be found in physics, chemistry, biochemistry, biophysics and economy.     

The PhyloCode is fatally flawed, and the “Linnaean” System can easily be fixed

Promoters of the PhyloCode have mounted an intensive and deceptive publicity campaign. At the centerpiece of this campaign have been slogans such as that the Linnaean System will “goof you up,” that the PhyloCode is the “greatest thing since sliced bread,” and that systematists are “afraid” to propose new names because of “downstream consequences.” Aside from such subscientific spin and sloganeering, proponents of the PhyloCode have offered nothing real to back up claims of greater stability for their new system. They have also misled many into believing that the PhyloCode is the only truly phylogenetic system. The confusion that has been fostered involves several discrete arguments, concerning: a new “method” of “designating” names, rank-free taxonomy, uninomial nomenclature, and issues of priority. Claims that the PhyloCode produces a more stable nomenclature are false, as shown with the example of “paleoherbs.” A rank-free system of naming requires an annotated reference tree for even the simplest exchanges of information. This would be confusing at best and would cripple our ability to teach, learn, and use taxonomic names in the field or in publications. We would be confronted by a mass of polynomial names, tied together only by a tree graphic, with no agreed name (except a uninomial, conveying no hierarchy) to use for any particular species. The separate issue of stability in reference to rules of priority and rank can be easily addressed within the current codes, by implementation of some simple changes, as we will propose in this article. Thus there is no need to “scrap” the current Linnaean codes for a poorly reasoned, logically inconsistent, and fatally flawed new code that will only bring chaos.     

Depicting the Tree of Life: the Philosophical and Historical Roots of Evolutionary Tree Diagrams

It is a popularly held view that Darwin was the first author to draw a phylogenetic tree diagram. However, as is the case with most popular beliefs, this one also does not hold true. Firstly, Darwin never called his diagram of common descent a tree. Secondly, even before Darwin, tree diagrams were used by a variety of philosophical, religious, and secular scholars to depict phenomena such as “logical relationships,” “affiliations,” “genealogical descent,” “affinity,” and “historical relatedness” between the elements portrayed on the tree. Moreover, historically, tree diagrams themselves can be grouped into a larger class of diagrams that were drawn to depict natural and/or divine order in the world. In this paper, we trace the historical roots and cultural meanings of these tree diagrams. It will be demonstrated that tree diagrams as we know them are the outgrowth of ancient philosophical attempts to find the “true order” of the world, and to map the world “as it is” (ontologically), according to its true essence. This philosophical idea would begin a fascinating journey throughout Western European history. It lies at the foundation of the famous “scala naturae,” as well as religious and secular genealogical thinking, especially in regard to divine, familial (kinship), and linguistic pedigrees that were often depicted by tree images. These scala naturae would fuse with genealogical, pedigree thinking, and the trees that were the result of this blend would, from the nineteenth century onward, also include the element of time. The recognition of time would eventually lead to the recognition of evolution as a fact of nature, and subsequently, tree iconographies would come to represent exclusively the evolutionary descent of species.     

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.     

Microheological properties of different erythrocyte populations in persons with elevated arterial pressure and in physically active persons

Microrheological properties (aggregation and deformability) of erythrocytes separated by centrifugation at 30000×g density gradient into “young” and “old” (the upper and lower fractions, respectively) were studied. The erythrocytes were taken from physically active persons (PAP) and from those with elevated arterial pressure (EAP). A significant difference in microrheological properties of the “young” and “old” erythrocytes was found. The aggregation degree of “old” cells was nearly twice that of “young” cells. The deformability of the erythrocyte subpopulations was significantly different, though the difference was not so pronounced as in the case of aggregation. The aggregation of “young” and “old” erythrocytes in the PAP group was the least (28% lower than in the control). Note, that “old” erythrocytes in the PAP group had better microrheological properties than in the other groups. All erythrocyte populations in the EAP group were characterized by higher aggregation, decreased deformability, and decreased capacity for oxygen transport.     

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     

Abstract mathematical molecular biology: II some relational consequences of the “one gene-one enzyme” hypothesis

Following the program outlined in a previous paper (Bull. Math. Biophysics,23, 237–260, 1961), a further abstract study is made of some simple relational systems which possess some properties of living organisms. It is shown that the “one gene-one enzyme” hypothesis leads to the conclusion that either all genes are built of the same chemical building blocks, or that at least all genes have a number of building blocks in common. A consistent relational application of the “one gene-one enzyme” hypothesis leads moreover to the conclusion that replication is not an inherent property of a gene. Rather there must be a set of enzymes which “copy” the genes. The number of enzymes in this set must be less than the number of genes and therefore the activity of those “copying” enzymes cannot be absolutely specific.     

Theoretical Assessment of Public Health Impact of Imperfect Prophylactic HIV-1 Vaccines with Therapeutic Benefits

This paper presents a number of deterministic models for theoretically assessing the potential impact of an imperfect prophylactic HIV-1 vaccine that has five biological modes of action, namely “take,” “degree,” “duration,” “infectiousness,” and “progression,” and can lead to increased risky behavior. The models, which are of the form of systems of nonlinear differential equations, are constructed via a progressive refinement of a basic model to incorporate more realistic features of HIV pathogenesis and epidemiology such as staged progression, differential infectivity, and HIV transmission by AIDS patients. The models are analyzed to gain insights into the qualitative features of the associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction numbers and a measure for vaccine impact or efficacy. The key findings of the study include the following (i) if the vaccinated reproduction number is greater than unity, each of the models considered has a locally unstable disease-free equilibrium and a unique endemic equilibrium; (ii) owing to the vaccine-induced backward bifurcation in these models, the classical epidemiological requirement of vaccinated reproduction number being less than unity does not guarantee disease elimination in these models; (iii) an imperfect vaccine will reduce HIV prevalence and mortality if the reproduction number for a wholly vaccinated population is less than the corresponding reproduction number in the absence of vaccination; (iv) the expressions for the vaccine characteristics of the refined models take the same general structure as those of the basic model.     

Terahertz vibrational properties of water nanoclusters relevant to biology

Water nanoclusters are shown from first-principles calculations to possess unique terahertz-frequency vibrational modes in the 1–6 THz range, corresponding to O–O–O “bending,” “squashing,” and “twisting” “surface” distortions of the clusters. The cluster molecular-orbital LUMOs are huge Rydberg-like “S,” “P,” “D,” and “F” orbitals that accept an extra electron via optical excitation, ionization, or electron donation from interacting biomolecules. Dynamic Jahn–Teller coupling of these “hydrated-electron” orbitals to the THz vibrations promotes such water clusters as vibronically active “structured water” essential to biomolecular function such as protein folding. In biological microtubules, confined water-cluster THz vibrations may induce their “quantum coherence” communicated by Jahn–Teller phonons via coupling of the THz electromagnetic field to the water clusters’ large electric dipole moments.     

The probabilistic approach to the effects of radiations and variability of sensitivity

The calculation of the size of the “sensitive volume” or “control center” in biological effects of radiations is discussed from the viewpoint of the probabilistic theory of these phenomena based on the concept of random “effective events”. On the bases of that theory, the resistivity of a microorganism to radiation is defined as its “mean life” under a radiation of one roentgen per minute. This mean is calculated for processes with and without recovery. The case of variable sensitivity, as it occurs for instance during mitosis, is discussed in detail. Methods are given to calculate this variability from survival curves or similar experimental data. The theory is applied to experiments of A. Zuppinger on irradiation ofAscaris eggs with X-rays.     

Concept of energy in biological systems and the effects of irradiations of low energies on enzyme-substrate systems

The recent mathematical formalization of the concepts of matter and extrinsical energy, which are used for the relational representation of biological systems, is employed in the analysis of the important experimental discoveries of Comorosanet al. related to low energy electromagnetic irradiations on enzyme substrates. By means of the present analysis one of the properties inherent to the experimental phenomena is more precisely exposed, and theoretical developments corresponding to “energetical evolutions” in a biological system (Leguizamón, 1976) may now have an experimental basis. Important limitations are introduced for the validity of the commutativity and associativity of cartesian product of sets, when they represent matter and its linked extrinsical energy. In connection with this last aspect, new important knowledge is obtained for the relational mathematical representation of biological systems.     

Degeneracy-Driven Self-Structuring Dynamics in Selective Repertoires

Numerous biological interactions, such as interactions between T cell receptors or antibodies with antigens, interactions between enzymes and substrates, or interactions between predators and prey are often not strictly specific. In such less specific, or “sloppy,” systems, referred to here as degenerate systems, a given unit of a diverse resource (antigens, enzymatic substrates, prey) is at risk of being recognized and consumed by multiple consumers (lymphocytes, enzymes, predators). In this study, we model generalized degenerate consumer-resource systems of Lotka–Volterra and Verhulst types. In the degenerate systems of Lotka–Volterra, there is a continuum of types of consumer and resource based on variation of a single trait (characteristic, or preference). The consumers experience competition for a continuum of resource types. This non-local interaction system is modeled with partial differential-integral equations and shows spontaneous self-structuring of the consumer population that depends on the degree of interaction degeneracy between resource and consumer, but does not mirror the distribution of resource. We also show that the classical Verhulst (i.e. logistic) single population model can be generalized to a degenerate model, which shows qualitative behavior similar to that in the degenerate Lotka–Volterra model. These results provide better insight into the dynamics of selective systems in biology, suggesting that adaptation of degenerate repertoires is not a simple “mirroring” of the environment by the “fittest” elements of population.     

Malaria: Origin of the Term “Hypnozoite”

The term “hypnozoite” is derived from the Greek words hypnos (sleep) and zoon (animal). Hypnozoites are dormant forms in the life cycles of certain parasitic protozoa that belong to the Phylum Apicomplexa (Sporozoa) and are best known for their probable association with latency and relapse in human malarial infections caused by Plasmodium ovale and P. vivax. Consequently, the hypnozoite is of great biological and medical significance. This, in turn, makes the origin of the name “hypnozoite” a subject of interest. Some “missing” history that is now placed on record (including a letter written by P. C. C. Garnham, FRS) shows that Miles B. Markus coined the term “hypnozoite”. While a PhD student at Imperial College London, he carried out research that led to the identification of an apparently dormant form of Cystoisospora (synonym: Isospora). In 1976, he speculated: “If sporozoites of Isospora can behave in this fashion, then those of related Sporozoa, like malaria parasites, may have the ability to survive in the tissues in a similar way.” He adopted the term “hypnozoite” for malaria in 1978 when he wrote in a little-known journal that this name would “… describe any dormant sporozoites or dormant, sporozoite-like stages in the life cycles of Plasmodium or other Haemosporina.” At that time, the existence of a hypnozoite form in the life cycle of Plasmodium was still a hypothetical notion. In 1980, however, Wojciech A. Krotoski published (together with several co-workers) details concerning his actual discovery of malarial hypnozoites, an event of considerable importance.