Chaos, fractals and nonlinear dynamics in evolution and phylogeny

Biological evolution is a dynamic system that can be modelled using physical-time-evolution equations, Even simple iterative models can have complex dynamics, and replication, the fundamental evolutionary property of living things, is an iterative process. All living things can be conceived in abstract geometric terms as elements comprising an infinite fractal set in n-dimensional euclidian space. Phylogeny, the ancestral-descendant time series connecting individuals through successive generations, is also fractal. This article shows how dynamic models and fractal geometry can be applied to phylogeny and evolutionary theory, providing a basis for refuting linnaean categorical ranks in taxonomy, for recognizing limits to the naturalness of any classification and for understanding the physics of the evolutionary process.     

Minimal self-replicating systems

Minimal self-replicating systems typically consist of three components: a product molecule, and two substrate molecules that become joined to form another product molecule. An important characteristic of self-replicating systems is the ability of the product to catalyze the formation of additional product, resulting in autocatalytic behavior. Recent advances in the area of self-replication have led to improved efficiency of autocatalysis, both by increasing the fraction of product molecules that can participate in further rounds of replication, and by improving the efficiency of the catalysts themselves. This review analyzes chemical self-replicating systems that have been developed to date and discusses ongoing challenges in this area of research.     

An example of design optimization for high evolvability: string rewriting grammar

As an example of the optimization of an evolutionary system design, a string rewriting system is studied. A set of rewriting rules that defines the growth of a string is experimentarily optimized in terms of maximizing the 'replicative capacity', that is the occurrence ratio of self-replicating strings. It is shown that the most optimized rule set allows many strings to self-replicate by using a special character able to copy an original string sequentially. Then, using various different rewriting rule sets, the connectivity between self-replicating strings is studied. A set of 'hyperblobs' covering the self-replicating strings is extracted and their connectivity is studied. The experimental results show that a large replicative capacity assures strong connectivity between self-replicating genotypes, making the system highly evolvable.     

Models of Replicator Proliferation Involving Differential Replicator Subunit Stability

Several models for the origin of life involve molecules that are capable of self-replication, such as self-replicating polymers composed of RNA or DNA or amino acids. Here we consider a hypothetical replicator (AB) composed of two subunits, A and B. Programs written in Python and C programming languages were used to model AB replicator abundance as a function of cycles of replication (iterations), under specified hypothetical conditions. Two non-exclusive models describe how a reduced stability for B relative to A can have an advantage for replicator activity and/or evolution by generating free A subunits. In model 1, free A subunits associate with AB replicators to create AAB replicators with greater activity. In simulations, reduced stability of B was beneficial when the replication activity of AAB was greater than two times the replication activity of AB. In model 2, the free A subunit is inactive for some number of iterations before it re-creates the B subunit. A re-creates the B subunit with an equal chance of creating B or B′, where B′ is a mutant that increases AB’ replicator activity relative to AB. In simulations, at moderate number of iterations (< 15), a shorter survival time for B is beneficial when the stability of B is greater than the inactive time of A. The results are consistent with the hypothesis that reduced stability for a replicator subunit can be advantageous under appropriate conditions.     

Evolution and the nature of time.

The concept of time is critical in evolutionary thought, but rarely has it been considered as an object of theoretical research by evolutionary biologists. Evolution is an organism's possibility of access to the future; in other words, evolutionary reward is paid out as increased time. Replicating entities are granted time, but for them, time only serves to allow replication and evolution, and to further expand the frontier of time. The present review discusses the possible influence of considering time not as a pure dimension (or an a priori intuitive condition of human experience) but as an object in itself. At least as a metaphor, time can be considered as a self-replicating entity rooted in physical (including biological) beings, with the result of producing dimensional time. Time self-replication forces beings to replicate, which, in turn, further sustains the replication of time. In that sense, time-replication may constitute the driving force, i.e., the basic engine, providing directional energy to the evolutionary process. The philosophical roots, caveats, and perspectives of this hypothesis are presented here. The metaphor of replicating-time plays with the possibility of viewing time not as a merely regulatory component of scientific inquiry but instead, as a real and creative constituent of nature and, for this reason, an object worthy of research in the natural sciences.     

Peptide Amyloids in the Origin of Life

How life can emerge from non-living matter is one of the fundamental mysteries of the universe. A bottom-up approach to this problem focuses on the potential chemical precursors of life, in particular the nature of the first replicative molecules. Such thinking has led to the currently most popular idea: that an RNA-like molecule played a central role as the first replicative and catalytic molecule. Here, we review an alternative hypothesis that has recently gained experimental support, focusing on the role of amyloidogenic peptides rather than nucleic acids, in what has been by some termed “the amyloid-world” hypothesis. Amyloids are well-ordered peptide aggregates that have a fibrillar morphology due to their underlying structure of a one-dimensional crystal-like array of peptides in a β-strand conformation. While they are notorious for their implication in several neurodegenerative diseases including Alzheimer's disease, amyloids also have many biological functions. In this review, we will elaborate on the following properties of amyloids in relation to their fitness as a prebiotic entity: they can be formed by very short peptides with simple amino acids sequences; as aggregates they are more chemically stable than their isolated component peptides; they can possess diverse catalytic activities; they can form spontaneously during the prebiotic condensation of amino acids; they can act as templates in their own chemical replication; they have a structurally repetitive nature that enables them to interact with other structurally repetitive biopolymers like RNA/DNA and polysaccharides, as well as with structurally repetitive surfaces like amphiphilic membranes and minerals.     

Performing abstraction: two ways of modelling<Emphasis Type="Italic"> Arabidopsis thaliana</Emphasis>

What is the best way to analyse abstraction in scientific modelling? I propose to focus on abstracting as an epistemic activity, which is achieved in different ways and for different purposes depending on the actual circumstances of modelling and the features of the models in question. This is in contrast to a more conventional use of the term ‘abstract’ as an attribute of models, which I characterise as black-boxing the ways in which abstraction is performed and to which epistemological advantage. I exemplify my claims through a detailed reconstruction of the practices involved in creating two types of models of the flowering plant Arabidopsis thaliana, currently the best-known model organism in plant biology. This leads me to distinguish between two types of abstraction processes: the ‘material abstracting’ required in the production of Arabidopsis specimens and the ‘intellectual abstracting’ characterising the elaboration of visual models of Arabidopsis genomics. Reflecting on the differences between these types of abstracting helps to pin down the epistemic skills and research commitments used by researchers to produce each model, thus clarifying how models are handled by researchers and with which epistemological implications.     

Noisy clues to the origin of life

The origin of stable self-replicating molecules represents a fundamental obstacle to the origin of life. The low fidelity of primordial replicators places restrictions on the quantity of information encoded in a primitive nucleic acid alphabet. Further difficulties for the origin of life are the role of drift in small primordial populations, reducing the rate of fixation of superior replicators, and the hostile conditions increasing developmental noise. Thus, mutation, noise and drift are three different stochastic effects that are assumed to make the evolution of life improbable. Here we show, to the contrary, how noise present in hostile early environments can increase the probability of faithful replication, by amplifying selection in finite populations. Noise has negative consequences in infinite populations, whereas in finite populations, we observe a synergistic interaction among noise sources. Hence, two factors formerly considered inimical to the origin of life-developmental noise and drift in small populations-can in combination give rise to conditions favourable to robust replication.     

Autonomous replication sequences in an extrachromosomal element of a pathogenic Entamoeba histolytica.

Entamoeba histolytica possesses a 24.5 kilobase plasmid-like molecule which encodes for the organism's ribosomal RNAs. Sequence analysis of this extrachromosomal element revealed the presence of AT rich sequences which show homology to the origin of replication of other lower eucaryotes. An 802 bp fragment containing these sequences was cloned into a yeast shuttle vector lacking the origin of replication and the construct tested for its ability to replicate autonomously in yeast. Mitotic stability tests as well as evidence for plasmid maintenance indicate that the transformed cells contained self-replicating episomes and not stably integrated molecules. The nucleotide sequence of this ARS-containing fragment is presented.     

Survival of the fittest before the beginning of life: selection of the first oligonucleotide-like polymers by UV light

Background  

A key event in the origin of life on this planet has been formation of self-replicating RNA-type molecules, which were complex enough to undergo a Darwinian-type evolution (origin of the "RNA world"). However, so far there has been no explanation of how the first RNA-like biopolymers could originate and survive on the primordial Earth.     

The cosmological model of eternal inflation and the transition from chance to biological evolution in the history of life

Background  

Recent developments in cosmology radically change the conception of the universe as well as the very notions of "probable" and "possible". The model of eternal inflation implies that all macroscopic histories permitted by laws of physics are repeated an infinite number of times in the infinite multiverse. In contrast to the traditional cosmological models of a single, finite universe, this worldview provides for the origin of an infinite number of complex systems by chance, even as the probability of complexity emerging in any given region of the multiverse is extremely low. This change in perspective has profound implications for the history of any phenomenon, and life on earth cannot be an exception.     

On the Origin of Macromolecular Sequences

The origin of the degree and type of order found in biological macromolecules is not adequately explained solely as an accumulation of genetic restrictions acquired through natural selection from otherwise unrestricted primeval sequences capable of self-replication, since the biological process of replication is itself dependent on the pre-existence of such order, and since the number of sequences that could have ever been tested by selection on the earth is an insignificant fraction of the number of unrestricted sequences which would be possible. Therefore the hypothesis is considered that replication and selection began from well ordered sequences, rather than random sequences. It is shown how the Turing concept of computation in fed-back, discrete-state automata can lead to the generation of order withour pre-existing instructions, and how this computation can result in self-repeating, random-like, but well ordered sequences of great length. Macromolecular models of such computers are suggested on the basis of mechanisms proposed for the growth of eutactic polymers. Such self-replicating, mutable sequences may then evolve genetic control which is sufficient to accommodate the information accumulated by natural selection. The structure and function of enzymes and structural proteins is related to this model, and statistical evidence from known amino acid sequences is shown to be consistent with some degree of non-genetic ordering.     

Test of models for replication of simian virus 40 DNA following ultraviolet irradiation.

When mammalian cells are irradiated with ultraviolet light, semiconservative DNA replication is inhibited and the length of newly synthesized daughter strands is reduced. We have used the simian virus 40 (SV40) viral system to examine the molecular mechanism by which this inhibition of DNA replication occurs immediately following ultraviolet irradiation. We tested two models for DNA replication-inhibition by using a procedure first developed by Danna, K. J., and D. Nathans (1972, Proc. Natl. Acad. Sci. USA, 69:3097-3100) in which the distribution of 3H-label in segments of newly completed SV40 form-I molecules is measured after short pulse labeling with 3H-thymidine. Our experimental results were compared with those predicted by mathematical models that describe two possible molecular mechanisms of replication inhibition. Our data are best fit by a "blockage" model in which any pyrimidine dimer encountered by the replication fork prevents complete replication of the SV40 genome. An alternative model called "slowdown" in which DNA damage causes a generalized slowdown of replication fork movement on all genomes has more adjustable parameters but does not fit the data as well as the blockage model.     

Effect of lethality on the extinction and on the error threshold of quasispecies

In this paper the effect of lethality on error threshold and extinction has been studied in a population of error-prone self-replicating molecules. For given lethality and a simple fitness landscape, three dynamic regimes can be obtained: quasispecies, error catastrophe, and extinction. Using a simple model in which molecules are classified as master, lethal and non-lethal mutants, it is possible to obtain the mutation rates of the transitions between the three regimes analytically. The numerical resolution of the extended model, in which molecules are classified depending on their Hamming distance to the master sequence, confirms the results obtained in the simple model and shows how an error catastrophe regime changes when lethality is taken in account.     

Statistical mechanics of protein folding by exhaustive enumeration

It is hard to construct theories for the folding of globular proteins because they are large and complicated molecules having enormous numbers of nonnative conformations and having native states that are complicated to describe. Statistical mechanical theories of protein folding are constructed around major simplifying assumptions about the energy as a function of conformation and/or simplifications of the representation of the polypeptide chain, such as one point per residue on a cubic lattice. It is not clear how the results of these theories are affected by their various simplifications. Here we take a very different simplification approach where the chain is accurately represented and the energy of each conformation is calculated by a not unreasonable empirical function. However, the set of amino acid sequences and allowed conformations is so restricted that it becomes computationally feasible to examine them all. Hence we are able to calculate melting curves for thermal denaturation as well as the detailed kinetic pathway of refolding. Such calculations are based on a novel representation of the conformations as points in an abstract 12-dimensional Euclidean conformation space. Fast folding sequences have relatively high melting temperatures, native structures with relatively low energies, small kinetic barriers between local minima, and relatively many conformations in the global energy minimum's watershed. In contrast to other folding theories, these models show no necessary relationship between fast folding and an overall funnel shape to the energy surface, or a large energy gap between the native and the lowest nonnative structure, or the depth of the native energy minimum compared to the roughness of the energy landscape. Proteins 32:425–437, 1998. © 1998 Wiley-Liss, Inc.     

A method for parameter optimization in computational biology

Models in computational biology, such as those used in binding, docking, and folding, are often empirical and have adjustable parameters. Because few of these models are yet fully predictive, the problem may be nonoptimal choices of parameters. We describe an algorithm called ENPOP (energy function parameter optimization) that improves-and sometimes optimizes-the parameters for any given model and for any given search strategy that identifies the stable state of that model. ENPOP iteratively adjusts the parameters simultaneously to move the model global minimum energy conformation for each of m different molecules as close as possible to the true native conformations, based on some appropriate measure of structural error. A proof of principle is given for two very different test problems. The first involves three different two-dimensional model protein molecules having 12 to 37 monomers and four parameters in common. The parameters converge to the values used to design the model native structures. The second problem involves nine bumpy landscapes, each having between 4 and 12 degrees of freedom. For the three adjustable parameters, the globally optimal values are known in advance. ENPOP converges quickly to the correct parameter set.     

Is There an Optimal Level of Open-Endedness in Prebiotic Evolution?

In this paper we explore the question of whether there is an optimal set up for a putative prebiotic system leading to open-ended evolution (OEE) of the events unfolding within this system. We do so by proposing two key innovations. First, we introduce a new index that measures OEE as a function of the likelihood of events unfolding within a universe given its initial conditions. Next, we apply this index to a variant of the graded autocatalysis replication domain (GARD) model, Segre et al. (P Natl Acad Sci USA 97(8):4112-4117, 2000; Markovitch and Lancet Artif Life 18(3), 2012), and use it to study - under a unified and concise prebiotic evolutionary framework - both a variety of initial conditions of the universe and the OEE of species that evolve from them.     

Viroids: petite RNA pathogens with distinguished talents

Viroids are small, circular, single-stranded RNA molecules that cause several infectious plant diseases. Viroids do not encode any pathogen-specific peptides but nonetheless, the subviral pathogens replicate autonomously and spread in the plant by recruiting host proteins via functional motifs encoded in their RNA genome. During the past couple of years, considerable progress has been made towards comprehending how viroids interact with their hosts. Here, we summarize recent findings on the structure-function relationships of viroids, their strategies and mechanisms of replication and trafficking, and the identification and characterization of interacting host proteins. We also describe the impact of the RNA silencing machinery of plants on viroid RNAs and how this has started to influence our models of viroid replication and pathogenicity.