Stability and selection in self-reproducing macromolecular systems

In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.     

Some selection models in catalytically coupled selfreproducing macromolecular systems

Some models for selection in enzyme coupled, selfreproducing, macromolecular systems are considered. The enzyme coupling provides a mechanism for the buildup of systems with large information content. The concept of “selective value” and criteria for selection is discussed.     

Role of selection in fixation of gene duplications

New genes commonly appear through complete or partial duplications of pre-existing genes. Duplications of long DNA segments are constantly produced by rare mutations, may become fixed in a population by selection or random drift, and are subject to divergent evolution of the paralogous sequences after fixation, although gene conversion can impede this process. New data shed some light on each of these processes. Mutations which involve duplications can occur through at least two different mechanisms, backward strand slippage during DNA replication and unequal crossing-over. The background rate of duplication of a complete gene in humans is 10(-9)-10(-10) per generation, although many genes located within hot-spots of large-scale mutation are duplicated much more often. Many gene duplications affect fitness strongly, and are responsible, through gene dosage effects, for a number of genetic diseases. However, high levels of intrapopulation polymorphism caused by presence or absence of long, gene-containing DNA segments imply that some duplications are not under strong selection. The polymorphism to fixation ratios appear to be approximately the same for gene duplications and for presumably selectively neutral nucleotide substitutions, which, according to the McDonald-Kreitman test, is consistent with selective neutrality of duplications. However, this pattern can also be due to negative selection against most of segregating duplications and positive selection for at least some duplications which become fixed. Patterns in post-fixation evolution of duplicated genes do not easily reveal the causes of fixations. Many gene duplications which became fixed recently in a variety of organisms were positively selected because the increased expression of the corresponding genes was beneficial. The effects of gene dosage provide a unified framework for studying all phases of the life history of a gene duplication. Application of well-known methods of evolutionary genetics to accumulating data on new, polymorphic, and fixed duplication will enhance our understanding of the role of natural selection in the evolution by gene duplication.     

The non-existence of a principle of natural selection

The theory of natural selection is a rich systematization of biological knowledge without a first principle. When formulations of a proposed principle of natural selection are examined carefully, each is seen to be exhaustively analyzable into a proposition about sources of fitness and a proposition about consequences of fitness. But whenever the fitness of an organic variety is well defined in a given biological situation, its sources are local contingencies together with the background of laws from disciplines other than the theory of natural selection; and the consequences of fitness for the long range fate of organic varieties are essentially applications of probability theory. Hence there is no role and no need for a principle of the theory of natural selection, and any generalities that may hold in that theory are derivative rather than fundamental.     

A model for macromolecular selection in complementary instructing systems

Summary In this paper we consider a model for the selection and evolution of biological macromolecules when their reproduction is based on complementary instruction. The model is an extension of one of Eigen's models for selection and takes in account explicitly the formation of both single stranded and double stranded molecular complexes. We construct exact solutions to the rate equations for the case of constant rate parameters and error distributions. Criteria for selection are discussed.     

On the theory of selection of coupled macromolecular systems

In this paper we examine a set of nonlinear rate equations (devised by M. Eigen (1971)) which describe the process of selection in a collection of self-reproducing, macromolecular information carriers. We construct exact solutions to the equations for the case of constant rate parameters and constant error distributions. The solutions allow the direct assessment of the effect of mutations on the “selective value” parameters discussed by Eigen as well as the distribution of the molecular species selected in steady state. In addition we show that the selection process may be characterized by an extremal principle.     

Stochastic simulations of minimal self-reproducing cellular systems

This paper is a theoretical attempt to gain insight into the problem of how self-assembling vesicles (closed bilayer structures) could progressively turn into minimal self-producing and self-reproducing cells, i.e. into interesting candidates for (proto)biological systems. With this aim, we make use of a recently developed object-oriented platform to carry out stochastic simulations of chemical reaction networks that take place in dynamic cellular compartments. We apply this new tool to study the behaviour of different minimal cell models, making realistic assumptions about the physico-chemical processes and conditions involved (e.g. thermodynamic equilibrium/non-equilibrium, variable volume-to-surface relationship, osmotic pressure, solute diffusion across the membrane due to concentration gradients, buffering effect). The new programming platform has been designed to analyse not only how a single protometabolic cell could maintain itself, grow or divide, but also how a collection of these cells could 'evolve' as a result of their mutual interactions in a common environment.     

Adaptive Significance of Circadian Clocks

Circadian clocks are ubiquitous and are found in organisms ranging from bacteria to mammals. This ubiquity of occurrence implies adaptive significance, but to date there has been no rigorous empirical evidence to support this. It is believed that an organism possessing circadian clocks gains fitness advantage in two ways: (i) by synchronizing its behavioral and physiological processes to cyclic environmental factors (extrinsic adaptive value); (ii) by coordinating its internal metabolic processes (intrinsic adaptive value). There is preliminary circumstantial evidence to support both. Several studies using organisms living in constant environments have shown that these organisms possess functional circadian clocks, suggesting that circadian clocks may have some intrinsic adaptive value. Studies to assess the adaptive value of circadian clocks in periodic environments suggest that organisms may have a fitness advantage in those periodic environments, which closely match their own intrinsic periodicity. Furthermore, evidence from organisms living in the wild, selection studies, and studies on latitudinal clines suggest that circadian clocks may have an extrinsic adaptive value as well. In this paper, I have presented several hypotheses for the emergence of circadian clocks and have reviewed some major empirical studies suggesting adaptive significance of circadian clocks.     

Adaptive significance of circadian clocks

Circadian clocks are ubiquitous and are found in organisms ranging from bacteria to mammals. This ubiquity of occurrence implies adaptive significance, but to date there has been no rigorous empirical evidence to support this. It is believed that an organism possessing circadian clocks gains fitness advantage in two ways: (i) by synchronizing its behavioral and physiological processes to cyclic environmental factors (extrinsic adaptive value); (ii) by coordinating its internal metabolic processes (intrinsic adaptive value). There is preliminary circumstantial evidence to support both. Several studies using organisms living in constant environments have shown that these organisms possess functional circadian clocks, suggesting that circadian clocks may have some intrinsic adaptive value. Studies to assess the adaptive value of circadian clocks in periodic environments suggest that organisms may have a fitness advantage in those periodic environments, which closely match their own intrinsic periodicity. Furthermore, evidence from organisms living in the wild, selection studies, and studies on latitudinal clines suggest that circadian clocks may have an extrinsic adaptive value as well. In this paper, I have presented several hypotheses for the emergence of circadian clocks and have reviewed some major empirical studies suggesting adaptive significance of circadian clocks.     

A comparison of restricted selection index and linear programming in sire selection

Summary The objective of restricted selection index is to enhance genetic change in one trait while restricting to zero change in a second trait. Linear programming is another, yet conceptually different, technique to maximize one function while enforcing limits on others. The objective of this research was to compare restricted selection index and linear programming in ability to maximize performance in one trait while limiting change in a second trait to zero. Results of a numerical study demonstrate that linear programming is a more effective method to limit correlated response than restricted selection index. On average, both methods limited response in a correlated trait to zero. However, the squared deviation of actual response in the restricted trait from zero was smaller with linear programming than with restricted selection index. Response to selection in the unrestricted trait is greater with restricted selection index than with linear programming.     

Some basic properties of immune selection

We analyze models for the evolutionary dynamics of viral or other infectious agents within a host. We study how the invasion of a new strain affects the composition and diversity of the viral population. We show that--under strain-specific immunity--the equilibrium abundance of uninfected cells declines during viral evolution. In addition, for cytotoxic immunity the absolute force of infection, and for non-cytotoxic immunity the absolute cellular virulence increases during viral evolution. We prove global stability by means of Lyapunov functions. These unidirectional trends of virus evolution under immune selection do not hold for general cross-reactive immune responses, which introduce frequency-dependent selection among viral strains. Therefore, appropriate cross-reactive immunity can lead to a viral evolution within a host which limits the extent of the disease.     

Evolution of virulence: interdependence, constraints, and selection using nested models

Natural selection acts on virus populations at two distinct but interrelated levels: within individual hosts and between them. Studies of the evolution of virulence typically focus on selection acting at the epidemiological or between-host level and demonstrate the importance of trade-offs between disease transmission and virulence rates. Within-host studies reach similar conclusions regarding trade-offs between transmission and virulence at the level of individual cells. Studies which examine selection at both scales assume that between- and within-host selection are necessarily in conflict. We explicitly examine these ideas and assumptions using a model of within-host viral dynamics nested within a model of between-host disease dynamics. Our approach allows us to evaluate the direction of selection at the within- and between-host levels and identify situations leading to conflict and accord between the two levels of selection.     

Polymorphism in sexual versus non-sexual disease transmission

Pathogens causing sexually transmitted diseases (STDs) often consist of related strains that cause non-sexually transmitted, or ''ordinary infectious'', diseases (OIDs). We use differential equation models of single populations to derive conditions under which a genetic variant with one (e.g. sexual) transmission mode can invade and successfully displace a genetic variant with a different (e.g. non-sexual) transmission mode. Invasion by an STD is easier if the equilibrium population size in the presence of an OID is smaller; conversely an OID can invade more easily if the equilibrium size of the population with the STD is larger. Invasion of an STD does not depend on the degree of sterility caused by the infection, but does depend on the added mortality caused by a resident OID. In contrast, the ability of an OID to invade a population at equilibrium with an STD decreases as the degree of sterility caused by the STD increases. When equilibrium population sizes for a population infected with an STD are above the point at which non-sexual contacts exceed sexual contacts (the sexual–social crossover point) and when equilibrium population sizes for an OID are below this point, there can be a stable genetic polymorphism for transmission mode. This is most likely when the STD is mildly sterilizing, and the OID causes low or intermediate levels of added mortality. Because we assume the strains are competitively equivalent and there are no heterogeneities associated with the transmission process, the polymorphism is maintained by density-dependent selection brought about by pathogen effects on population size.     

Structural principles governing domain motions in proteins.

With the use of a recently developed method, twenty-four proteins for which two or more X-ray conformers are known have been analyzed to reveal structural principles that govern domain motions in proteins. In all 24 cases, the domain motion is a rotation about a physical axis created through local interactions both covalent and noncovalent. In many cases, two or more mechanical hinges separated in space create a stable hinge axis for precise control of the domain closure. The terminal regions of alpha-helices and beta-sheets have been found to act as mechanical hinges in a significant number of cases. In some cases, the two terminal regions of neighboring strands of a single beta-sheet can create a hinge axis, as can the two termini of a single alpha-helix. These two structures have been termed the "double-hinged beta-sheet" and "double-hinged alpha-helix," respectively. A flexible loop that attaches one domain to another and through which the effective hinge axis passes is another construct that is used to create a hinge. Noncovalent interactions between segments remote along the polypeptide chain can also form hinges. In addition alpha-helices that preserve their hydrogen bonding structure when bent have been found to behave as mechanical hinges. It is suggested that these alpha-helices act as a store of elastic energy that drives the closing of domains for rapid capture of the substrate. If the repertoire of possible interdomain structures is as limited as this study suggests, the dynamic behavior of proteins could soon be predicted using bioinformatics techniques. Proteins 1999;36:425-435.     

Efficient selection intensity in early generation index selection in groundnut (Arachis hypogaea L.)

Summary The F₂ potential of single and three-way crosses was evaluated using a set of physiological and yield components. Results were based on an index of selection using (a) only yield components and (b) both physiological and yield components. The indices were constructed using the percentage improvement of F₂ over the better parent of the corresponding F₁ cross for every character. The performance of F₂ plants assessed by the expected value of the regression index was ranked in descending order to provide a ranked F₂ distribution (FRD). The FRD was divided into four equal parts, T₂₅ (top 25%), T₅₀ (26–50%), T₇₅ (51–75%) and T₁₀₀ (76–100%). F₃ families derived from F₂ plants in T₂₅ were found to provide a higher frequency of selections for pod number than T₅₀, T₇₅ and T₁₀₀. The frequency of selections was higher in three-way than single crosses. Selection index based on physiological and yield components was more efficient in trapping F₂ plants providing selections in F₃ than the index based on yield components only. The results brought out the importance of bunch x bunch crosses as a complement to the usually advocated bunch x runner ones.     

Tumor heterogeneity: Causes and consequences

With rare exceptions, spontaneous tumors originate from a single cell. Yet, at the time of clinical diagnosis, the majority of human tumors display startling heterogeneity in many morphological and physiological features, such as expression of cell surface receptors, proliferative and angiogenic potential. To a substantial extent, this heterogeneity might be attributed to morphological and epigenetic plasticity, but there is also strong evidence for the co-existence of genetically divergent tumor cell clones within tumors. In this perspective, we summarize the sources of intra-tumor phenotypic heterogeneity with emphasis on genetic heterogeneity. We review experimental evidence for the existence of both intra-tumor clonal heterogeneity as well as frequent evolutionary divergence between primary tumors and metastatic outgrowths. Furthermore, we discuss potential biological and clinical implications of intra-tumor clonal heterogeneity.     

Calculation of hydrodynamic properties of macromolecular bead models with overlapping spheres

For the calculation of hydrodynamic properties of rigid macromolecules using bead modelling, models with overlapping beads of different sizes are used in some applications. The hydrodynamic interaction tensor between unequal overlapping beads is unknown, and an oversimplified treatment with the Oseen tensor may introduce important errors. Here we discuss some aspects of the overlapping problem, and explore an ad hoc form of the interaction tensor, proposed by Zipper and Durchschlag. We carry out a systematic numerical study of the hydrodynamic properties of a two-spheres model, showing how the Zipper-Durchschlag correction removes efficiently the numerical instabilities, and predicts the correct limits. Received: 15 February 1999 / Revised version: 29 April 1999 / Accepted: 11 May 1999     

Methods for and results from the study of design principles in molecular systems

Most aspects of molecular biology can be understood in terms of biological design principles. These principles can be loosely defined as qualitative and quantitative features that emerge in evolution and recur more frequently than one would expect by chance alone in biological systems that perform a given type of process or function. Furthermore, such recurrence can be rationalized in terms of the functional advantage that the design provides to the system when compared with possible alternatives. This paper focuses on those design features that can be related to improved functional effectiveness of molecular and regulatory networks. We begin by reviewing assumptions and methods that underlie the study of such principles in molecular networks. We follow by discussing many of the design principles that have been found in genetic, metabolic, and signal transduction circuits. We concentrate mainly on results in the context of Biochemical Systems Theory, although we also briefly discuss other work. We conclude by discussing the importance of these principles for both, understanding the natural evolution of complex networks at the molecular level and for creating artificial biological systems with specific features.