A Darwinian evolutionary system. II. Experiments on protein evolution and evolutionary aspects of the genetic code

On the basis of the principles of Darwinian evolutionary systems laid out earlier, a system is constructed which simulates protein evolution. Two types of situations are studied: adaptation to highest possible alkalinity (“alkalinity model”), and adaptation to an arbitrary sequence (“sequence model”). No restrictions in adaptability were found for the (comparably special) alkalinity model, but severe restrictions were found for the sequence model. Approximately 15% of all possible evolutionary paths from one amino acid to another turned out to be impossible, in the sense that no chain of intermediate steps exists which leads to a higher fitness level, in this case an increased chemical similarity of the two amino acids.The evolutionary efficiency of the natural genetic code was also investigated by comparing it with two classes of artificially constructed codes: semi-random and random codes. It was found that the natural code possesses the highest evolutionary efficiency, given by the mean number of generations required to reach identity in 5 of 10 sites, if originally all 10 were different. Closest to the natural code in evolutionary efficiency were the random codes, next, the semi-random codes.This pattern could be explained by a theoretical measure, called the code efficiency. The most important component of the code efficiency is the percentage of impossible paths. The natural code is far superior to the other code types in this respect. However, the random codes are superior to the natural code with respect to the mean shortest path length of the possible paths, the other important component of the code efficiency.It is suggested that the natural genetic code might have arisen from a semi-random code during a process of optimizing several of its features, of which the evolutionary efficiency is a very important one; or that the natural code is the most efficient edition of a large variety of semi-random codes which originated by chance.     

A Darwinian evolutionary system. 3. Experiments on the evolution of feeding patterns

Another application of the Darwinian evolutionary system introduced earlier is presented. The evolution of spiraling and meandering feeding patterns, as exemplified by the marine polychaete Paraonis fulgens, was simulated by constructing an artificial “worm”, called Rectangulus, because it was capable of turning around 90 ° only. The behavioural program of Rectangulus contained six parameters, which controlled the following properties: (i) turning spontaneously after a given number of steps, (ii) turning before a former track, (iii) avoiding entering a “channel”, i.e. a path flanked by former tracks, (iv) keeping contact with former tracks, (v) performing a turn at the beginning (which in combination with contact-keeping leads to a spiral), and (vi) switching from spiraling to meandering behaviour after a given number of steps. These parameters were binary-coded in the “genomes” of Rectangulus, and were capable of mutating and recombining.Evolutionary experiments were performed with populations consisting of 50 individuals, inhabiting an area of 100 × 100 “unit steps”. Each individual had to “forage” for 140 steps, and the number of successful (uncovered area) and unsuccessful (area covered previously) steps were recorded. Individuals with greater “yield” (successful minus unsuccessful steps, divided by the total number of steps) had a greater probability of being reproduced (selection). It was found that Rectangulus soon “learned” to turn in front of a former track and a channel, and to keep contact, both if one starts with individuals who at the beginning could only go straight ahead, or with ones turning after every step. Evolution from this stage onward proceeded more variably. Different types of meandering, spiraling, and a combination of both emerged; however, in two out of six cases, evolution did not proceed beyond the turning and contact-keeping stage. It is suggested that the different outcomes represent separate adaptive peaks. The highest yield was obtained by the combination of spiraling and meandering, as used by Paraonis fulgens, followed by pure spiraling and meandering. This was confirmed by calculations made for populations with fixed parameters. The results further show that selection for non-crossing could only have been effective in producing these patterns for population densities much higher than the ones found for P. fulgens at the present time.     

Models of Darwinian processes and evolutionary principles

Evolutionary processes are described as stochastic motions in a genotype space (set of sequences with a Hamming distance) and a phenotype space (vector space of phenotypic properties). Real value functions are introduced which form a landscape over these spaces; smoothness postulates are formulated. Evolution is considered as a kind of hill climbing on these adaptive landscapes. A rather simple diffusion approximation for the phenotypic processes is proposed which leads to similar mathematical problems as the Schrödinger equation for disordered potential distributions.     

Darwinian fitness, evolutionary entropy and directionality theory

Two recent articles provide computational and empirical validation of the following analytical fact: the outcome of competition between an invading genotype and that of a resident population is determined by the rate at which the population returns to its original size after a random perturbation. This phenomenon can be quantitatively described in terms of the demographic parameter termed "evolutionary entropy", a measure of the variability in the age at which individuals produce offspring and die. The two articles also validate certain predictions of directionality theory, an evolutionary model that integrates demography and ecology with population genetics. In particular, directionality theory predicts that in populations that spend the greater part of their life cycle in the stationary growth phase, evolution will result in an increase in entropy. These species will be described by a late age of sexual maturity, small progeny sets and a broad reproductive time-span. In populations that undergo large fluctuations in size, however, the evolutionary outcome will be different. When the average size is large, evolution will result in a decrease in entropy-these populations will be described by early age of sexual maturity, large numbers of offspring and narrow reproductive span but when the average size is small, the evolutionary outcome will be random and non-directional.     

A Definition of Optimum Nutrient Requirements in Birch Seedlings. I.

The aim of the investigation was to find a method of growing birch seedlings with a constant optimum nutrient status. The studies in this paper have indicated important factors in such a growth method which must be comprised in a definition of nutrient requirements. The optimum nutrient proportions in the seedlings and the optimum total concentration in the solution must be known. Special attention must be paid to the ratio between NH₄⁺ and NO₃^?in the solution and in the uptake. The amounts of nutrients taken up at optimum nutrition can be followed by measurement of pH and conductivity. Thus, the nutrients consumed may be replaced by titrations which may be automated by standard equipment. The nutrient proportions to be added are determined by the optimum internal proportions. It is not necessary to change the nutrient solution even if the volume is relatively small in relation to plant mass. There was no evidence of effects of accumulation of root exudates or infections. By using the system described, it is possible to attain considerably greater fresh and dry matter production in birch seedlings than when an optimum conventional solution is used.     

A distant evolutionary relationship between bacterial sphingomyelinase and mammalian DNase I.

The three-dimensional structure of bacterial sphingomyelinase (SMase) was predicted using a protein fold recognition method; the search of a library of known structures showed that the SMase sequence is highly compatible with the mammalian DNase I structure, which suggested that SMase adopts a structure similar to that of DNase I. The amino acid sequence alignment based on the prediction revealed that, despite the lack of overall sequence similarity (less than 10% identity), those residues of DNase I that are involved in the hydrolysis of the phosphodiester bond, including two histidine residues (His 134 and His 252) of the active center, are conserved in SMase. In addition, a conserved pentapeptide sequence motif was found, which includes two catalytically critical residues, Asp 251 and His 252. A sequence database search showed that the motif is highly specific to mammalian DNase I and bacterial SMase. The functional roles of SMase residues identified by the sequence comparison were consistent with the results from mutant studies. Two Bacillus cereus SMase mutants (H134A and H252A) were constructed by site-directed mutagenesis. They completely abolished their catalytic activity. A model for the SMase-sphingomyelin complex structure was built to investigate how the SMase specifically recognizes its substrate. The model suggested that a set of residues conserved among bacterial SMases, including Trp 28 and Phe 55, might be important in the substrate recognition. The predicted structural similarity and the conservation of the functionally important residues strongly suggest a distant evolutionary relationship between bacterial SMase and mammalian DNase I. These two phosphodiesterases must have acquired the specificity for different substrates in the course of evolution.     

Feedback theory and Darwinian evolution.

Feedback loops can have a significant impact on biological systems that are evolving under Darwinian natural selection. Many of the striking and sometimes bizarre patterns that characterize the evolution of such systems have simple, natural explanations that involve the effects of feedback loops. The two fundamental types of feedback loops, positive and negative, have effects that are radically different: negative feedback tends to produce stability and resistance to change; positive feedback produces instability and even catastrophe. Both types of feedback loops are important in biological systems, and both can produce chaos, whose mathematical complexity often produces strange, beautiful and totally unexpected patterns that have only begun to be explored using the computational capabilities of modern electronic computers. An understanding of the patterns that can result from the effects of feedback loops can produce important new insights into the patterns that mark the evolutionary development of biological systems.     

Genetical ESS-models. I. Concepts and basic model

Evolutionarily Stable Strategies (ESS) in phenotypic models are used to explain the evolution of animal interactive behaviour. As the behavioural features under consideration are assumed to be genetically determined, the question arises how underlying a genetical system might affect the results of phenotypic ESS-models. This question can be fully treated in terms of ESS-theory. A method of designing Genetical ESS-Models is proposed, which transfers the question of evolutionary stability to a "lower" level, the genetical basis. Genetical ESS-models - although nonlinear even in the simplest cases - can be analysed in a way that is familiar to ESS-theorists and yield immediate results on gene pool ESSs, which then may or may not maintain ESSs on the phenotypic level. Moreover, general results can be obtained to characterize evolutionarily stable gene pool states and their interrelation with commonsense, phenotypic ESSs. This part of the article presents the basic concepts and an outline of the method of genetical ESS-models. It gives, as a demonstration, a complete analysis for phenotypic two-strategy models (linear or nonlinear) based on a diploid, diallelic single-locus system under random mating. The results in this case suggest that a phenotypic ESS should indeed be expected to evolve but, maybe, only after passing through a succession of temporarily stable states.     

Predicting evolutionary potential. I. Predicting the evolution of a lactose-PTS system in Escherichia coli.

Genomes contain not only information for current biological functions, but also information for potential novel functions that may allow the host to adapt to new environments. The field of experimental evolution studies that potential by selecting for novel functions and deducing the means by which the function evolved, but until now it has not attempted to predict the outcomes of such experiments. Here I present a model system that is being developed specifically to examine the issue of what kind of information is most useful in predicting how novel functions will evolve. The system is the evolution of a Lac-PTS transport system and a phospho-beta-galactosidase hydrolase system as a novel pathway for metabolism of lactose in Escherichia coli. Two kinds of information, sequence-based phylogenetic inference and biochemical activity, are considered as predictors of which E. coli genes will evolve the required new functions. Both biochemical data and phylogenetic inference predict that the cryptic celABC genes, which currently specify a PTS-beta-glucoside transport system, are most likely to evolve into a PTS-lactose transport system. Phylogenetic inference predicts that the bglA gene, which currently specifies a phospho-beta-glucosidase, is most likely to evolve into a phospho-beta-galactosidase. In contrast, biochemical data predict that the cryptic bglB gene, which also currently specifies a phospho-beta-glucosidase, is most likely to evolve into a phospho-beta-galactosidase.     

Network study of integrated biochemical switching system. I: Connection of basic elements

As a first step to network study, a series of integrated biochemical switching systems (prototype of artificial neuronic device) was assumed based on Rosen's work and on the results of our previous studies. The effects of an excitatory stimulus on the switching properties of the proposed system were examined using computer simulations. The results can be summarized as follows: (i) the number of excited elements in sequentially connected systems is proportionally related to the value of the excitatory stimulus; (ii) when the introduction of the excitatory stimulus is too late, it can no longer be transmitted to any elements; (iii) the excitatory stimulus (signal) is amplified to a certain limit and is attenuated during propagation; (iv) by assuming several excitatory stimuli and varying their frequencies, the so-called long-term potentiation phenomenon can be observed; (v) supposing reversible interactions between two elements, a continuous switching pattern of the output is observed.     

Methodological problems in evolutionary biology I. Testability and tautologies

The impact of philosophy of science on biology is slight. Evolutionary biology, however, is nowadays an exception. The status of the neo-Darwinian (synthetic) theory of evolution is seriously challenged from a methodological perspective. However, the methodology used in the relevant discussions is plainly defective. A correct application of methodology to evolutionary theory leads to the following conclusions. (a) The theory of natural selection (the core of neo-Darwinism) is unfalsifiable in a strict sense of the term. This, however, does not militate against the theory, because no scientific theory whatever is testable in this way. Under a more liberal testability criterion, the theory is surely testable. None the less, certain (not all) research programs may tend to make the theory untestable in practice. (b) It has often been argued that the tautologous character of the principle of natural selection, allegedly the focus of evolutionary theory, makes the theory untestable through circular reasoning. Actually, the principle is only a tautology if ‘fitness’ is wrongly defined in terms of actual survival. But even then circular reasoning need not ensue. (c) Evolutionary principles do not permit, without additional information, the derivation of statements about evolutionary events concerning particular species or populations. If this were a reason to criticize the theory (as has been argued in the literature), any other scientific theory would be inadequate by the same token.     

Differences between alcohol dehydrogenases. Structural properties and evolutionary aspects.

Comparisons of the primary structures of yeast and horse liver alcohol dehydrogenases reveal that the enzymes are homologous but distantly related. The overall positional identity is 25% between common regions, and several deletions/insertions occur in either enzyme, the longest apparently corresponding to 21 residues, showing that the different subunit sizes are largely explained by internal differences. Variabilities in the structural similarities can be coupled with functional requirements but not directly with whole domains in the previously known tertiary structure of the horse protein. The two most similar regions of the enzymes affect active-site segments and the two most dissimilar regions seem to affect a loop structure without known function, and a segment participating in subunit interactions. The dissimilarities may probably be correlated with changes in zinc-binding properties and quaternary structures. The extra region corresponding to the large internal chain-length difference shows an apparent coincidence in sequence to a following segment of the horse enzyme, and additional elements of internal coincidences, or superficial similarities with other dehydrogenases, are noticed. These characteristics are not fully distinguishable from chance distributions but in view of the extensive species variations in alcohol dehydrogenases some evolutionary considerations may not be excluded, in which case a model relating all regions of these and associated enzymes to a common ancestor is shown to be compatible with all known observations.