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The domain model for eukaryotic DNA organization. 2: A molecular basis for constraints on development and evolution.

A model for eukaryotic DNA organization has been proposed in which DNA regulatory processes depend on multiple site-specific DNA-nuclear matrix interactions throughout a DNA domain. In this model gene regulation depends on combinations of a few control factors in a cell to activate cell type-specific genes. This model suggests simple molecular mechanisms for organismal development which can account for sequential activation of appropriate groups of genes throughout development and for specific constraints on developmental pathways. Additionally, these suggested developmental pathways are consistent with mechanisms of evolution in which gradualism and punctuated equilibrium are not exclusive of one another and are interrelated mechanisms of evolution that are both induced by specific chromosomal mutations.

Animals↗

Models of molecular evolution and phylogeny.

Phylogenetic reconstruction is a fast-growing field that is enriched by different statistical approaches and by findings and applications in a broad range of biological areas. Fundamental to these are the mathematical models used to describe the patterns of DNA base substitution and amino acid replacement. These may become some of the basic models for comparative genome research. We discuss these models, including the analysis of observed DNA base and amino acid mutation patterns, the concept of site heterogeneity, and the incorporation of structural biology data, all of which have become particularly important in recent years. We also describe the use of such models in phylogenetic reconstruction and statistical methods for the comparison of different models.

Amino Acid Substitution↗

Animal models for the evolution of thrombotic disease.

Naturally occurring hemorrhagic and thrombotic diseases of animals closely parallel their human counterparts. While such models may be particularly useful in studying the pathogenesis of human disease, it is usually more realistic to depend upon experimentally induced disease models. The species selected for use is therefore of major importance in providing meaningful extrapolation to humans, as are the experimental design and type of procedure (in vitro, ex vivo, in vivo). Regardless of the test system used when in vitro procedures are employed, these must be translated eventually to the in vivo situation. Information about the normal aging process of different species is important here and should influence selection of the species and test system. The ideal situation may not be feasible or pertain because of cost, availability, size, and investigator familiarity, or lack thereof, with the most suitable species or model.

Animals↗

Modelling the isotopic evolution of the Earth.

We present a flexible multi-reservoir (primitive lower mantle, depleted upper mantle, upper continental crust, lower continental crust and atmosphere) forward-transport model of the Earth, incorporating the Sm-Nd, Rb-Sr, U-Th-Pb-He and K-Ar isotope-decay systematics. Mathematically, the model consists of a series of differential equations, describing the changing abundance of each nuclide in each reservoir, which are solved repeatedly over the history of the Earth. Fluxes between reservoirs are keyed to heat production and further constrained by estimates of present-day fluxes (e.g. subduction, plume flux) and current sizes of reservoirs. Elemental transport is tied to these fluxes through 'enrichment factors', which allow for fractionation between species. A principal goal of the model is to reproduce the Pb-isotope systematics of the depleted upper mantle, which has not been done in earlier models. At present, the depleted upper mantle has low (238)U/(204)Pb (mu) and (232)Th/(238)U (kappa) ratios, but Pb-isotope ratios reflect high time-integrated values of these ratios. These features are reproduced in the model and are a consequence of preferential subduction of U and of radiogenic Pb from the upper continental crust into the depleted upper mantle. At the same time, the model reproduces the observed Sr-, Nd-, Ar- and He-isotope ratios of the atmosphere, continental crust and mantle. We show that both steady-state and time-variant concentrations of incompatible-element concentrations and ratios in the continental crust and upper mantle are possible. Indeed, in some cases, incompatible-element concentrations and ratios increase with time in the depleted mantle. Hence, assumptions of a progressively depleting or steady-state upper mantle are not justified. A ubiquitous feature of this model, as well as other evolutionary models, is early rapid depletion of the upper mantle in highly incompatible elements; hence, a near-chondritic Th/U ratio in the upper mantle throughout the Archean is unlikely. The model also suggests that the optimal value of the bulk silicate Earth's K/U ratio is close to 10000; lower values suggested recently seem unlikely.

Atmosphere↗

Empirical and mechanistic mathematical models of temporal evolution of milk production in ruminants.

In the various sectors of animal science there has been little exploration of the theoretical mathematical aspects of data analysis and modelling. The dominant statistical methods used for the analysis of experimental data are rarely valuable for developing a deeper understanding of the problem. In addition they do not take account of the evolution over time of those variables of major interest to be studied. Only recently have more sophisticated methods of mathematical modelling begun to be used. Nonetheless attention tends to be focused exclusively on empirical models. Mathematical models with greater explanatory power, in particular those which use differential equations, are as yet little used. This work develops a mathematical approach to a problem that is of great interest in animal science: the development over time of milk production in economically important ruminant species.

Animals↗

Delineation of distinct subgroups of multiple myeloma and a model for clonal evolution based on interphase cytogenetics.

To delineate multiple myeloma (MM) subgroups and their clonal evolution, we analyzed 81 newly diagnosed patients by interphase fluorescence in situ hybridization using a comprehensive probe set for 10 chromosomes and two IGH rearrangements. A median of 5 probes per patient displayed aberrant signal numbers (range, 1-10). Additional copies most frequently found were for 15q22, 19q13, 9q34, 11q23, and 1q21. Losses commonly observed were of 13q14.3, 17p13, and 22q11. Predominance of gain or loss was quantified by a copy number score (CS) for each patient. Two peaks (CS = +3 and CS = 0) were found by plotting patient copy number scores over CS values corresponding to hyperdiploid and nonhyperdiploid MM. Cluster analysis revealed four major branches: (i) gain of 9q, 15q, 19q, and/or 11q; (ii) deletion of 13q and t(4;14); (iii) t(11;14); and (iv) gain of 1q. Statistical modeling of an oncogenetic tree indicated that early independent events were gain of 15q/9q and/or 11q, t(11;14); deletion of 13q followed by t(4;14); and gain of 1q. Aberrations of 17p13, 22q11, 8p12, and 6q21 were found as subsequent events. MM with gain of 1q was delineated as a subentity with significantly higher beta-2-microglobulin and lower hemoglobin levels, indicating a poor prognosis. From our results, we propose a model of MM for clonal evolution.

Evolution, Molecular↗

Human and rodent DNA sequence comparisons: a mosaic model of genomic evolution.

Three patterns of DNA sequence conservation have been identified from five human and rodent genomic sequence comparisons. First, a divergent pattern was observed in the noncoding sequences of the beta-globin and gamma-crystallin gene clusters, and second, a highly conserved pattern was observed in the noncoding regions of the T cell receptor C alpha-C delta, and the alpha- and beta-myosin-heavy-chain genes. A third, mixed pattern has also been found in the immunoglobulin IgH C mu-C delta gene region. These three patterns of genomic evolution pose the fascinating possibility that large portions of the genome evolve at different rates.

Animals↗

Computational evolution of a model polymer that folds to a specified target conformation.

A method is described for folding polymers to specific target conformations. The approach uses a fast but approximate dynamics algorithm, coupled with a genetic algorithm that is used to evolve the large number of free parameters needed. The dynamics algorithm uses a state transition matrix approach. At each time step, the distances between pairs of atoms are adjusted by shifting them from Dij to Dij + Sij where Sij is an element of the state transition matrix S. Atom pairs that are attractive have Sij < 0 and pairs that are repulsive have S ij > 0. The atomic movement is carried out by gradient minimizing the molecular mechanics energy of the molecule subject to harmonic distance constraints. The method is applied to a simple test case, a 19 atom 2-D polymer. The paper also show that the S matrices can correctly fold a limited variety of initial conformations that differ from the one used during the evolution phase.

Algorithms↗

Spatial models of prebiotic evolution: soup before pizza?

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance of any feasible replicator system. Based on a detailed critical survey of spatial models on prebiotic information integration, we suggest a possible scenario for replicator system evolution leading to the emergence of the first protocells capable of independent life. We show that even the spatial versions of the hypercycle model are vulnerable to selfish parasites in heterogeneous habitats. Contrary, the metabolic system remains persistent and coexistent with its parasites both on heterogeneous surfaces and in chaotically mixing flowing media. Persistent metabolic parasites can be converted to metabolic cooperators, or they can gradually obtain replicase activity. Our simulations show that, once replicase activity emerged, a gradual and simultaneous evolutionary improvement of replicase functionality (speed and fidelity) and template efficiency is possible only on a surface that constrains the mobility of macromolecule replicators. Based on the results of the models reviewed, we suggest that open chaotic flows ('soup') and surface dynamics ('pizza') both played key roles in the sequence of evolutionary events ultimately concluding in the appearance of the first living cell on Earth.

Animals↗

Minimal model for genome evolution and growth.

Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random mutation but primarily grows by random segmental duplication. That genomes grew mostly by duplication is consistent with the observation that repeat sequences in all genomes are widespread and intragenomic and intergenomic homologous genes are preponderant across all life forms.

DNA, Bacterial↗

A Prisoner's Dilemma model of the evolution of paternal care.

The heavy energetic demands of gestation, lactation and rearing of offspring mean that studies of paternal care in primates usually focus on female reproductive effort. Here it is shown that both male and female reproductive effort must be considered in order to understand how paternal care evolved. This is done using the Prisoner's Dilemma, best known as a model of reciprocal altruism. It is found that the relative cost of reproduction for males and females is crucially important in determining co-operative and competitive strategies. In particular, when male reproductive costs are less than female reproductive costs, males co-operate with females even when females do not reciprocate. This surprising behaviour, termed non-reciprocal altruism, is comparable with male investment in a female and her offspring.

Altruism↗

The gene structure of Xenopus nuclear lamin A: a model for the evolution of A-type from B-type lamins by exon shuffling.

Nuclear lamins are intermediate filament (IF) type proteins that form a fibrillar network underlying the inner nuclear membrane. The existence of multiple subtypes of lamins in vertebrates has been interpreted in terms of functional specialization during cell division and differentiation. The structure of a gene encoding an A-type lamin of Xenopus laevis was analysed. Comparison with that of a B-type lamin of the same species shows remarkable conservation of the exon/intron pattern. In both genes the last exon, only 9-12 amino acids in length, encodes the complete information necessary for membrane targeting of lamins, i.e. a ras-related CaaX motif. The lamin A specific extension of the tail domain is encoded by a single additional exon. The 5' boundary of this exon coincides with the sequence divergence between human lamins A and C, for which an alternative splice mechanism had previously been suggested. Arguments are presented suggesting that B-type lamins represent the ancestral type of lamins and that A-type lamins derived there from by exon shuffling. The acquisition of the new exon might explain the different fates of A- and B-types lamins during cell division.

Amino Acid Sequence↗

Application of a mathematical model and Differential Evolution algorithm approach to optimization of bacteriocin production by Lactococcus lactis C7.

The effect of pH and temperature on cell growth and bacteriocin production in Lactococcus lactis C7 was investigated in order to optimize the production of bacteriocin. The study showed that the bacteriocin production was growth-associated, but declined after reaching the maximum titer. The decrease of bacteriocin was caused by a cell-bound protease. Maximum bacteriocin titer was obtained at pH 5.5 and at 22 degrees C. In order to obtain a global optimized solution for production of bacteriocin, the optimal temperature for bacteriocin production was further studied. Mathematical models were developed for cell growth, substrate consumption, lactic acid production and bacteriocin production. A Differential Evolution algorithm was used both to estimate the model parameters from the experimental data and to compute a temperature profile for maximizing the final bacteriocin titer and bacteriocin productivity. This simulation showed that maximum bacteriocin production was obtained at the optimal temperature profile, starting at 30 degrees C and terminating at 22 degrees C, which was validated by experiment. This temperature profile yielded 20% higher maximum bacteriocin productivity than that obtained at a constant temperature of 22 degrees C, although the total amount of bacteriocin obtained was slightly decreased.

Algorithms↗

Modelling neutral and selective evolution of protein folding.

We examine a model evolutionary space consisting of genotypes mapped to their corresponding phenotypes. This mapping is derived from a lattice model for proteins which, despite its highly idealized nature, has been shown to share general properties with real proteins. Large evolutionary networks are observed, with genotypes corresponding to non-lethal phenotypes linked by unit mutational steps. Neutral mutations are necessary for traversing the evolutionary networks, and even one neutral mutation in a genotype can change the phenotypes attainable by a unit mutational step.

Biological Evolution↗

Novel continuum modeling of crystal surface evolution.

We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual approach where the continuum limit is achieved when typical surface features consist of many steps, our continuum limit is approached when the number of step configurations of the ensemble is very large. The model can handle singular surface structures such as corners and facets. It has a clear computational advantage over discrete models.

Journal Article↗