Dynamics of protein evolution

Protein sequences of the SWISS-PROT data bank were analysed by fractal techniques and harmonic analysis. In both cases, the results show the presence of self-affinity, a kind of self-similarity, in the sequences. Self-similarity is a sign of fractality and fractality is a consequence of a chaotic dynamical process. The evolution of the protein sequences is modelled as a dynamical system. The abundance of the fractal form in biology and creation of fractal forms as a result of “chaos” is already established. It may be noted that the word “chaos” here implies that most predictable processes can also become unpredictable under certain conditions, and that the most unpredictable processes are not as unpredictable as they are expected to be. In evolutionary dynamics, this allows scope for mutations and variations in otherwise predictable situations, potentially leading to increased diversity. Part of this work was presented at the National Symposium on Evolution of Life.     

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.     

The pcsA gene from Streptomyces diastaticus var. 108 encodes a polyene carboxamide synthase with broad substrate specificity for polyene amides biosynthesis

Two structurally related polyene macrolides are produced by Streptomyces diastaticus var. 108: rimocidin (3a) and CE-108 (2a). Both bioactive metabolites are biosynthesized from the same pathway through type I polyketide synthases by choosing a starter unit either acetate or butyrate, resulting in 2a or 3a formation, respectively. Two additional polyene amides, CE-108B (2b) and rimocidin B (3b), are also produced “in vivo” when this strain was genetically modified by transformation with engineered SCP2*-derived vectors carrying the ermE gene. The two polyene amides, 2b and 3b, showed improved pharmacological properties, and are generated by a tailoring activity involved in the conversion of the exocyclic carboxylic group of 2a and 3a into their amide derivatives. The improvement on some biological properties of the resulting polyenes, compared with that of the parental compounds, encourages our interest for isolating the tailoring gene responsible for the polyene carboxamide biosynthesis, aimed to use it as tool for generating new bioactive compounds. In this work, we describe the isolation from S. diastaticus var. 108 the corresponding gene, pcsA, encoding a polyene carboxamide synthase, belonging to the Class II glutamine amidotransferases and responsible for “in vivo” and “in vitro” formation of CE-108B (2b) and rimocidin B (3b). The fermentation broth from S. diastaticus var. 108 engineered with the appropriate pcsA gene construction, showed the polyene amides to be the major bioactive compounds.     

Some views on the role of noise in “self”-organizing systems

This paper deals with information transfer from the environment and “self”-organization in open, nonlinear systems far from thermodynamic equilibrium — in the presence of either non-stationary phase jitter noise, or amplitude stationary noise. By “self”-organization we mean here the progressive formation within the system of sequential, ordered (coherent) relationships between appropriate dynamical variables-like for example, the phase differences between the oscillating components of the system. We take up (in Section II) the classical Laser as a specific example and examine in detail the influence of phase jitter noise in the mode (phase) locking process. We find—as expected—that phase fluctuations in the cavity cause degradation of the coherent behaviour (i.e. increase the entropy) of the system — which, however, levels off, or saturates with time. Further (in Section III) we examine systems where the number of self-sustained oscillating components may vary with time in such a way that the maximum entropy of the system increases faster than the overall instantaneous entropy. We put forth the hypothesis that in such cases — because of the increase of the redundancy — the system gets organized not just in spite of, but merely because of the presence of Noise. Possible applications in biological systems (especially concerning a model of cerebral organization) are briefly discussed. It is understood here, that the system has to display some preliminary dynamical structure before the organizing procedure takes over. What happens afterwards is the subject of this paper.     

A comparative investigation of certain difference equations and related differential equations: Implications for model-building

Many mathematical models for physical and biological problems have been and will be built in the form of differential equations or systems of such equations. With the advent of digital computers one has been able to find (approximate) solutions for equations that used to be intractable. Many of the mathematical techniques used in this area amount to replacing the given differential equations by appropriate difference equations, so that extensive research has been done into how to choose appropriate difference equations whose solutions are “good” approximations to the solutions of the given differential equations. The present paper investigates a different, although related problem. For many physical and biological phenomena the “continuum” type of thinking, that is at the basis of any differential equation, is not natural to the phenomenon, but rather constitutes an approximation to a basically discrete situation: in much work of this type the “infinitesimal step lengths” handled in the reasoning which leads up to the differential equation, are not really thought of as infinitesimally small, but as finite; yet, in the last stage of such reasoning, where the differential equation rises from the differentials, these “infinitesimal” step lengths are allowed to go to zero: that is where the above-mentioned approximation comes in. Under this kind of circumstances, it seems more natural tobuild themodel as adiscrete difference equation (recurrence relation) from the start, without going through the painful, doubly approximative process of first, during the modeling stage, finding a differential equation to approximate a basically discrete situation, and then, for numerical computing purposes, approximating that differential equation by a difference scheme. The paper pursues this idea for some simple examples, where the old differential equation, though approximative in principle, had been at least qualitatively successful in describing certain phenomena, and shows that this idea, though plausible and sound in itself, does encounter some difficulties. The reason is that each differential equation, as it is set up in the way familiar to theoretical physicists and biologists, does correspond to a plethora of discrete difference equations, all of which in the limit (as step length→0) yield the same differential equation, but whose solutions, for not too small step length, are often widely different, some of them being quite irregular. The disturbing thing is that all these difference equations seem to adequately represent the same (physical or biological) reasoning as the differential equation in question. So, in order to choose the “right” difference equation, one may need to draw upon more detailed (physical or) biological considerations. All this does not say that one should not prefer discrete models for phenomena that seem to call for them; but only that their pursuit may require additional (physical or) biological refinement and insight. The paper also investigates some mathematical problems related to the fact of many difference equations being associated with one differential equation.     

<Emphasis Type="Italic">Rubribacterium polymorphum</Emphasis> gen. nov., sp. nov., a novel alkaliphilic nonsulfur purple bacterium from an Eastern Siberian soda lake

An alkaliphilic nonsulfur purple bacterial (NPB) strain “Green” was isolated from sediments of the littoral zone of the soda lake (mineralization 22 g/l, pH 9.5) in the Barguzin River valley (Eastern Siberia). The cells of the new isolate are ovoid or polymorphic at latter stages. The photosynthetic membrane structures are of vesicular type. Bacteriochlorophyll a and carotenoids of both spheroidene and spirilloxanthin type are the photosynthetic pigments. Two light-harvesting systems (LH1 and LH2) are present. The new isolate is a photoheterotroph and a facultative aerobe. It grows well in the dark on organic substrates; anaerobic phototrophic growth is poor. The isolate is alkaliphilic with pH optimum of 8.5–9.5. The most abundant cell growth occurred at 5–40 g/l NaCl (optimum at 10 g/l) and 30 °C. The DNA G+C base content was 69.9 mol %. Analysis of 16S rRNA gene sequences revealed a 10% difference with the most closely related NPB (Rhodobacter species). Rubrimonas cliftoensis, a bacteriochlorophyll a-containing bacterium, is the closest relative (93.3% similarity). It is proposed that strain “Green” should be placed in the new genus and new species Rubribacterium polymorphum gen. nov., sp. nov. GenBank accession number: 16S rRNA-EU857676.     

Age changes of the carpal bones in macaques: Application of the fourier analysis on the radiographs

A method based on the Fourier analysis is proposed, which describes and analyzes the contour morphology of carpal bones by separating morphology into factors of shape and size. Here, “size” refers to the average diameter of the contour. The “shape” is expressed byshape factors which are derived from the Fourier series and the “shape” of a monkey is expressed by ashape index which is calculated fromshape factors. The age change in the morphology of the lunate and capitate ofMacaca fuscata fuscata was analyzed by this method. The development of “shape” approximately completes by 3 years of age, whereas increase in “size” begins its spurt at that age as do body weight and anterior trunk length. By applying this method to other macaque species, it was found thatM. mulatta, M. f. yakui andM. cyclopis exhibit similar patterns of growth and development of carpal bones to those ofM. f. fuscata. Patterns found inM. fascicularis differ in that its bones develop faster than in the other macaques with respect to the “shape,” but remain small with respect to the “size.”     

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.     

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     

The cancer cell’s “power plants” as promising therapeutic targets: An overview

This introductory article to the review series entitled “The Cancer Cell’s Power Plants as Promising Therapeutic Targets” is written while more than 20 million people suffer from cancer. It summarizes strategies to destroy or prevent cancers by targeting their energy production factories, i.e., “power plants.” All nucleated animal/human cells have two types of power plants, i.e., systems that make the “high energy” compound ATP from ADP and P _i . One type is “glycolysis,” the other the “mitochondria.” In contrast to most normal cells where the mitochondria are the major ATP producers (>90%) in fueling growth, human cancers detected via Positron Emission Tomography (PET) rely on both types of power plants. In such cancers, glycolysis may contribute nearly half the ATP even in the presence of oxygen (“Warburg effect”). Based solely on cell energetics, this presents a challenge to identify curative agents that destroy only cancer cells as they must destroy both of their power plants causing “necrotic cell death” and leave normal cells alone. One such agent, 3-bromopyruvate (3-BrPA), a lactic acid analog, has been shown to inhibit both glycolytic and mitochondrial ATP production in rapidly growing cancers (Ko et al., Cancer Letts., 173, 83–91, 2001), leave normal cells alone, and eradicate advanced cancers (19 of 19) in a rodent model (Ko et al., Biochem. Biophys. Res. Commun., 324, 269–275, 2004). A second approach is to induce only cancer cells to undergo “apoptotic cell death.” Here, mitochondria release cell death inducing factors (e.g., cytochrome c). In a third approach, cancer cells are induced to die by both apoptotic and necrotic events. In summary, much effort is being focused on identifying agents that induce “necrotic,” “apoptotic” or apoptotic plus necrotic cell death only in cancer cells. Regardless how death is inflicted, every cancer cell must die, be it fast or slow.     

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

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

Coenzyme Q,peroxidation and cytochrome oxidase features after Parkinson's-like disease by MPTP toxicity in intra-synaptic and non-synaptic mitochondria fromMacaca Fascicularis cerebral cortex and hippocampus: action of dihydroergocriptine

The effects of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) administration on respiratory chain features were studied in synaptic and non-synaptic mitochondrial populations from cerebral cortex andhippocampus ofMacaca Fascicularis (Cynomolgus monkey). Enzymatic activity, cytochromea+a ₃ content and turnover numbers of Complex IV, contents of Coenzyme Q₁₀, of hydroperoxides and membrane fluidity were assessed in non-synaptic “perikaryal” and intra-synaptic “light” and “heavy” mitochondria isolated: (a) from the dopaminergic ascending terminal areas of cerebral cortex of monkeys treatedp.o. with dihydroergocriptine at the dose of 2, 6 or 20 mg/kg/day for 52 weeks; (b) from the dopaminergic terminal areas ofhippocampus of monkeys treatedp.o. with dihydroergocriptine at the dose of 12 mg/kg/day before and during the induction of a Parkinson's-like syndrome by MPTP administration (i.v., 0.3 mg/kg/day for 5 days). Dihydroergocriptine administration moderately increased both cytochrome oxidase activity and cytochromea+a ₃ content in “light” intra-synaptic mitochondria and hydroperoxides/CoQ₁₀ ratio in all the types of mitochondria, as a consequence of the enhanced energy metabolism. The Parkinson's-like syndrome by MPTP changed the biochemical investigated parameters, affecting both directly the respiratory chain structures,i.e. by respiratory chain complexes inhibition and indirectly,i.e. by free radical mediated damages. MPTP administration negatively influenced Complex IV activity and Turnover Number of intra-synaptic mitochondria, without affecting the total cytochromea+a ₃ amount. In all types of mitochondria and particularly on the “light” intra-synaptic ones, MPTP-induced lesion enhanced hydroperoxides/Coenzyme Q₁₀ molar ratio due to the fall in Coenzyme Q₁₀ levels and the concomitant increase in hydroperoxides. Dihydroergocriptine treatment appeared to be effective in MPTP-treated animals in improving those mitochondrial features that probably suffered free radical insults.     

Phalaenopsis bellina (Rchb.f.) Christenson,a segregate from P. violacea Witte (Orchidaceae: Aeridinae)

A reevaluation of floral and vegetative morphology together with data from analysis of floral fragrance and flavonoid co-pigment chemistry suggest that specific status is warranted for the two kinds ofPhalaenopsis violacea Witte known informally as the “Bornean type” and the “Malayan type.”Phalaenopsis violacea var.bellina Rchb.f. is elevated to specific rank, providing a name for the “Bornean type” plants.     

Polymorphism of canonical and noncanonical <Emphasis Type="Italic">gypsy</Emphasis> sequences in different species of <Emphasis Type="Italic">Drosophila </Emphasis><Emphasis Type="Italic">melanogaster</Emphasis> subgroup: possible evolutionary relations

Mobile genetic elements constitute a substantial part of eukaryotic genome and play an important role in its organization and functioning. Co-evolution of retrotransposons and their hosts resulted in the establishment of control systems employing mechanisms of RNA interference that seem to be impossible to evade. However, “active” copies of endogenous retrovirus gypsy escape cellular control in some cases, while its evolutionary elder “inactive” variants do not. To clarify the evolutionary relationship between “active” and “inactive” gypsy we combined two approaches: the analysis of gypsy sequences, isolated from G32 Drosophila melanogaster strain and from different Drosophila species of the melanogaster subgroup, as well as the study of databases, available on the Internet. No signs of “intermediate” (between “active” and “inactive”) gypsy form were found in GenBank, and four full-size G32 gypsy copies demonstrated a convergence that presumably involves gene conversion. No “active” gypsy were revealed among PCR generated gypsy ORF3 sequences from the various Drosophila species indicating that “active” gypsy appeared in some population of D. melanogaster and then started to spread out. Analysis of sequences flanking gypsy variants in G32 revealed their predominantly heterochromatic location. Discrepancy between the structure of actual gypsy sites in G32 and corresponding sequences in database might indicate significant inter-strain heterochromatin diversity. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.     

Theory of transport in linear biological systems: I. Fundamental integral equation

The conditions under which the output,γ _b (t), of a biological system is related to the input,γ _a (t), by an integral equation of the typeγ _b (t) = ∫ ₀ ^t γ _a (ω)w(t−ω)dω, where ω(t) is a transport functioncharacteristic of the system, are analyzed in detail. Methods of solving this type of integral equation are briefly discussed. The theory is then applied to problems in tracer kinetics in which input and output are sums of exponentials, and explicit formulae, which are applicable whether or not the pool is uniformly mixed, are derived for “turnover time” and “pool” size.     

Cell-pool tryptophan phases in ergot alkaloid fermentation

Three cell-pool tryptophan phases are recorded as characteristics of the alkaloid fermentation byClaviceps paspali grown on a simple defined medium without tryptophan. Within the early phase designated “tryptophan down” the alkaloid-biosynthetic activity of the mycelium attains the maximum, protein synthesis is reduced and extracellular proteases are formed. Cell-pool tryptophan level (b) drops, tryptophan synthetase activity (c) intensifies and sums of logb+logc after different time intervals remain constant. In the subsequent “tryptophan up” phase tryptophan level (b) increases, alkaloid yield (a) becomes a function of time and reaches the top level still tolerable by tryptophan synthetase. The difference of the logb—logc is constant. The tryptophan synthetase diminishes its activity simultaneously with the alkaloid-biosynthetic activity of the mycelium. The district between the “tryptophan down” and “tryptophan up” phase is an especially promising target for the investigation of the regulation of alkaloid formation and continuous fermentation of these compounds. During the third, i.e. “tryptophan over” phase, cell-pool tryptophan accumulates and attains a concentration exerting a negative effect on the alkaloid biosynthesis.     

Energy and biological evolution—I. The equilibrium states of biochemical processes

The Thom gradient model of morphogenesis poses the followinga posteriori problem: “From the observed morphology of a given natural process (effect) determine the dynamics of the process (cause)”. In this paper we consider the classicala priori problem: “Given the cause (dynamics) determine the effect (resultant morphology)”. We find that in biochemical processes the mechanisms for energy activation, energy-matter interaction and energy dissipation determine the dynamics. Furthermore there exists basic energy mechanisms which drive the equilibrium states through the elementary catastrophes of Thom. A comparison with current theories shows that our models describe open ecological food chains and their dynamical systems generalize the equations of organisation posed by M. Eigen. Work supported by a Research Associateship of the International Centre for Theoretical Physics, P.O.B. 586, Miramare, 34100 Trieste, Italy.