Complete chaos in a simple epidemiological model

A first-order difference equation which constitutes a simple model for a lethal parasite-host interaction is studied. Completing a study initiated by May and Anderson, the dynamics are shown to be completely chaotic.     

On the appearance of chaos in a model of the Belousov reaction

Summary A modified version of the Oregonator is analysed as a model of oscillations, bistability and chaos in the bromate-malonic acid-cerium reaction.This study was supported by the National Cancer Institute, USA, Grant No. 5 F32 CAO5152-02.     

On the Origins of a Crowded Cytoplasm

Contemporary cells show a highly crowded macromolecular content, the processes which originated this state being largely unknown. We propose that a driving force leading to the crowded cellular state could be the increase in growth rate produced by an enhanced cytoplasmic protein concentration. Briefly, in a diluted scenario, an increase in protein concentration has two opposing effects on growth rate. The favorable effect is the increase in the activity per unit volume of the component proteins and the disadvantageous effect is the concomitant increase in the protein mass per unit volume which has to be produced. In this work we show that the first effect is quantitatively more important, resulting in an overall increase in growth rate. This result was obtained with a model of E. coli and using nonmechanistic physiological arguments. The proposed driving force operates even at low protein concentrations, where the nonspecific interactions of macromolecular crowding are not significant, and could be as ancient as the first protocells. Experimental measurement of this cytoplasmic protein concentration effect in present organisms is hindered by the prevailing nonspecific interactions, product of long-term evolution. However, chemical/biochemical systems, built up to mimic properties of living cells, could be an adequate tool to test this effect. [Reviewing Editor: Dr. Antony Dean]     

Melnikov analysis of chaos in a simple epidemiological model

 Melnikov’s method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model. Received 8 August 1995; received in revised form 21 November 1995     

Question 1: Peptide Nucleic Acids and the Origin and Homochirality of Life

The possibilities of pseudo peptide DNA mimics like PNA (peptide nucleic acid) having a role for the prebiotic origin of life prior to an RNA world is discussed. In particular a scenario is proposed in which protocells with an achiral genetic material through several generations stepwise is converted into a chiral genetic material, e.g., by incorporation of RNA units. Provided that a sufficiently large sequence space is occupied, a selection process based on catalytic function in which a single cell (first common ancestor) has a definite evolutionary advantage, selection of this cell would by contingency also lock it into homochirality. Presented at: International School of Complexity – 4th Course: Basic Questions on the Origins of Life; “Ettore Majorana” Foundation and Centre for Scientific Culture, Erice, Italy, 1–6 October 2006.     

Systems and synthetic biology approaches to cell division

Cells proliferate by division into similar daughter cells, a process that lies at the heart of cell biology. Extensive research on cell division has led to the identification of the many components and control elements of the molecular machinery underlying cellular division. Here we provide a brief review of prokaryotic and eukaryotic cell division and emphasize how new approaches such as systems and synthetic biology can provide valuable new insight.     

Study of Plasma Induced Chemistry by DC Discharges in CO<Subscript>2</Subscript>/N<Subscript>2</Subscript>/H<Subscript>2</Subscript>O Mixtures Above a Water Surface

The chemistry induced by atmospheric pressure DC discharges above a water surface in CO(2)/N(2)/H(2)O mixtures was investigated. The gaseous mixtures studied represent a model prebiotic atmosphere of the Earth. The most remarkable changes in the chemical composition of the treated gas were the decomposition of CO(2) and the production of CO. The concentration of CO increased logarithmically with the increasing input energy density and an increasing initial concentration of CO(2) in the gas. The highest achieved concentration of CO was 4.0 +/- 0.6 vol. %. The production of CO was crucial for the synthesis of organic species, since reactions of CO with some reactive species generated in the plasma, e. g. H* or N* radicals, were probably the starting point in this synthesis. The presence of organic species (including the tentative identification of some amino acids) was demonstrated by the analysis of solid and liquid samples by high-performance liquid chromatography, infrared absorption spectroscopy and proton-transfer-reaction mass spectrometry. Formation of organic species in a completely inorganic CO(2)/N(2)/H(2)O atmosphere is a significant finding for the theory of the origins of life.     

Self-organization in dissipative structures: A thermodynamic theory for the emergence of prebiotic cells and their epigenetic evolution

This paper presents a discussion on self-organization processes in dissipative structures, in order to highlight the general conditions for raising complexity and generate order. In particular, some concepts were introduced from non-equilibrium thermodynamics and from the Molecular Anamorphic Evolution Theory, especially concerning processes of matter randomization.     

Internal lipid synthesis and vesicle growth as a step toward self-reproduction of the minimal cell

One of the major properties of the semi-synthetic minimal cell, as a model for early living cells, is the ability to self-reproduce itself, and the reproduction of the boundary layer or vesicle compartment is part of this process. A minimal bio-molecular mechanism based on the activity of one single enzyme, the FAS-B (Fatty Acid Synthase) Type I enzyme from Brevibacterium ammoniagenes, is encapsulated in 1-palmitoyl-2oleoyl-sn-glycero-3-phosphatidylcholine (POPC) liposomes to control lipid synthesis. Consequently molecules of palmitic acid released from the FAS catalysis, within the internal lumen, move toward the membrane compartment and become incorporated into the phospholipid bilayer. As a result the vesicle membranes change in lipid composition and liposome growth can be monitored. Here we report the first experiments showing vesicles growth by catalysis of one enzyme only that produces cell boundary from within. This is the prototype of the simplest autopoietic minimal cell.     

An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model

Chaos is a central feature of human locomotion and has been suggested to be a window to the control mechanisms of locomotion. In this investigation, we explored how the principles of chaos can be used to control locomotion with a passive dynamic bipedal walking model that has a chaotic gait pattern. Our control scheme was based on the scientific evidence that slight perturbations to the unstable manifolds of points in a chaotic system will promote the transition to new stable behaviors embedded in the rich chaotic attractor. Here we demonstrate that hip joint actuations during the swing phase can provide such perturbations for the control of bifurcations and chaos in a locomotive pattern. Our simulations indicated that systematic alterations of the hip joint actuations resulted in rapid transitions to any stable locomotive pattern available in the chaotic locomotive attractor. Based on these insights, we further explored the benefits of having a chaotic gait with a biologically inspired artificial neural network (ANN) that employed this chaotic control scheme. Remarkably, the ANN was quite robust and capable of selecting a hip joint actuation that rapidly transitioned the passive dynamic bipedal model to a stable gait embedded in the chaotic attractor. Additionally, the ANN was capable of using hip joint actuations to accommodate unstable environments and to overcome unforeseen perturbations. Our simulations provide insight on the advantage of having a chaotic locomotive system and provide evidence as to how chaos can be used as an advantageous control scheme for the nervous system.     

Phenotypic plasticity and diversity in insects

Phenotypic plasticity in general and polyphenic development in particular are thought to play important roles in organismal diversification and evolutionary innovation. Focusing on the evolutionary developmental biology of insects, and specifically that of horned beetles, I explore the avenues by which phenotypic plasticity and polyphenic development have mediated the origins of novelty and diversity. Specifically, I argue that phenotypic plasticity generates novel targets for evolutionary processes to act on, as well as brings about trade-offs during development and evolution, thereby diversifying evolutionary trajectories available to natural populations. Lastly, I examine the notion that in those cases in which phenotypic plasticity is underlain by modularity in gene expression, it results in a fundamental trade-off between degree of plasticity and mutation accumulation. On one hand, this trade-off limits the extent of plasticity that can be accommodated by modularity of gene expression. On the other hand, it causes genes whose expression is specific to rare environments to accumulate greater variation within species, providing the opportunity for faster divergence and diversification between species, compared with genes expressed across environments. Phenotypic plasticity therefore contributes to organismal diversification on a variety of levels of biological organization, thereby facilitating the evolution of novel traits, new species and complex life cycles.     

Phase locking,period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias

A mathematical model for the perturbation of a biological oscillator by single and periodic impulses is analyzed. In response to a single stimulus the phase of the oscillator is changed. If the new phase following a stimulus is plotted against the old phase the resulting curve is called the phase transition curve or PTC (Pavlidis, 1973). There are two qualitatively different types of phase resetting. Using the terminology of Winfree (1977, 1980), large perturbations give a type 0 PTC (average slope of the PTC equals zero), whereas small perturbations give a type 1 PTC. The effects of periodic inputs can be analyzed by using the PTC to construct the Poincaré or phase advance map. Over a limited range of stimulation frequency and amplitude, the Poincaré map can be reduced to an interval map possessing a single maximum. Over this range there are period doubling bifurcations as well as chaotic dynamics. Numerical and analytical studies of the Poincaré map show that both phase locked and non-phase locked dynamics occur. We propose that cardiac dysrhythmias may arise from desynchronization of two or more spontaneously oscillating regions of the heart. This hypothesis serves to account for the various forms of atrioventricular (AV) block clinically observed. In particular 22 and 42 AV block can arise by period doubling bifurcations, and intermittent or variable AV block may be due to the complex irregular behavior associated with chaotic dynamics.     

Interactions between neural networks: a mechanism for tuning chaos and oscillations

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability. URL: http:// www.ntu.edu.sg/home/elpwang     

Evolution in biological and nonbiological systems under different mechanisms of generation and inheritance

The majority of definitions of life and evolution include the notion that part of an organism has to be copied to its offspring and that this includes some form of coded information. This article presents the thesis that this conception is too restrictive and that evolution can occur in systems in which there is no copy of information between generations. For that purpose, this article introduces a new set of concepts and a theoretical framework that is designed to be equally applicable to the study of the evolution of biological and nonbiological systems. In contrast to some theoretical approaches in evolution, like neo-Darwinism, the approach presented here is not focused on the transmission and change of hereditary information that can be copied (like in the case of DNA). Instead, multiple mechanisms by which a system can generate offspring (with and without copying) and by which information in it affects the structure and evolution of its offspring are considered. The first part of this article describes in detail these new concepts. The second part of this article discusses how these concepts are directly applicable to the diversity of systems that can evolve. The third part introduces hypotheses concerning (1) how different mechanisms of generation and inheritance can arise from each other during evolution, and (2) how the existence of several inheritance mechanisms in an organism can affect its evolution.     

Top-predator abundance and chaos in tritrophic food chains

Nonlinear models and laboratory experiments suggest that populations can be chaotic, whereas field data show that a fair proportion of observed populations are not too far from being chaotic. Thus, a natural question arises: do ecosystems enjoy special properties at the edge of chaos? By limiting the analysis to three classes of tritrophic food chains and to the role played by the nutrient available to the bottom of the ecosystem, we show that top-predator mean abundance is maximum at the edge of chaos. The geographical variability of species abundance along nutrient gradients and the dynamic complexity of observed natural populations are consistent with our findings. Effective guidelines for the sustainability of exploited ecosystems are also derived.     

Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems

Real food chains are very rarely investigated since long data sequences are required. Typically, if we consider that an ecosystem evolves with a period corresponding to the time for maturation, possessing few dozen of cycles would require to count species over few centuries. One well known example of a long data set is the number of Canadian lynx furs caught by the Hudson Bay company between 1821 and 1935 as reported by Elton and Nicholson in 1942. In spite of the relative quality of the data set (10 undersampled cycles), two low-dimensional global models that settle to chaotic attractors were obtained. They are compared with an ad hoc 3D model which was proposed as a possible model for this data set. The two global models, which were estimated with no prior knowledge about the dynamics, can be considered as direct evidences of chaos in real ecosystems.     

Genetic requirements for cell division in a genomically minimal cell

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Insights to the minimal model of insulin secretion through a mean-field beta cell model

The present work introduces an extension of the original minimal model of second phase insulin secretion during the intravenous glucose tolerance test (IVGTT), which can provide both physiological and mathematical insights to the minimal model. The extension is named the mean-field beta cell model since it returns the average response of a large number of nonlinear secretory entities. Several secretion models have been proposed for the IVGTT, and we shall identify two fundamentally different theoretical features of these models. Both features can play a central role during the IVGTT, including the one presented in the mean-field beta cell model.