Evolution probabilities and phylogenetic distance of dinucleotides

We develop here an analytical evolution model based on a dinucleotide mutation matrix 16 x 16 with six substitution parameters associated with the three types of substitutions in the two dinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices 4 x 4. It determines at some time t the exact occurrence probabilities of dinucleotides mutating randomly according to these six substitution parameters. Furthermore, several properties and two applications of this model allow to derive 16 evolutionary analytical solutions of dinucleotides and also a dinucleotide phylogenetic distance. Finally, based on this mathematical model, the SED (Stochastic Evolution of Dinucleotides) web server has been developed for deriving evolutionary analytical solutions of dinucleotides.     

The fixed-size Luria-Delbruck model with a nonzero death rate

What is the expected number of mutants in a stochastically growing colony once it reaches a given size, N? This is a variant of the famous Luria-Delbruck model which studies the distribution of mutants after a given time-lapse. Instead of fixing the time-lapse, we assume that the colony size is a measurable quantity, which is the case in many in-vivo oncological and other applications. We study the mean number of mutants for an arbitrary cell death rate, and give partial results for the variance. For a restricted set of parameters we provide analytical results; we also design a very efficient computational method to calculate the mean, which works for most of the parameter values, and any colony size, no matter how large. We find that a cellular population with a higher death rate will contain a larger number of mutants than a population of equal size with a smaller death rate. Also, a very large population will contain a larger percentage of mutants; that is, irreversible mutations act like a force of selection, even though here the mutants are assumed to have no selective advantage. Finally, we investigate the applicability of the traditional, 'fixed-time' approach and find that it approximates the 'fixed-size' problem whenever stochastic effects are negligible.     

Blowing-up of deterministic fixed points in stochastic population dynamics

We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system.     

Repair competence assay in studies of the influence of environmental exposure to c-PAHs on individual susceptibility to induction of DNA damage

Previous results from studies performed in three European cities suggested a decrease in DNA repair efficiency observed in lymphocytes of subjects occupationally exposed to environmental carcinogenic polycyclic aromatic hydrocarbons (c-PAHs). The aim of this study was to investigate whether a relationship between exposure to environmental c-PAHs and cellular vulnerability to the induction of DNA damage and its repair is confirmed in a pooled group of subjects from Prague, Košice and Sofia. The investigated pool consisted of 144 subjects occupationally exposed to environmental c-PAHs, who were municipal policemen or bus drivers. A control group of 115 matched individuals consisted of males unexposed at work to c-PAHs. The repair efficacy was evaluated by a comparison of the DNA damage detected by the single cell gel electrophoresis (SCGE) immediately after challenging the cells with X-ray irradiation, with residual damage (RD) being measured after an incubation period of 60 min. A stochastic concept for a mechanism of the interaction between DNA and various genotoxic exposures, was applied to analyze a relationship between exposure and biological effect in the studied sample. The outcome of the study confirms that the exposure to environmental c-PAHs or smoking cigarettes, significantly decreases DNA repair efficiency (repair efficiency in the pooled group of exposed individuals was 61.8 ± 11.8% versus 67.9 ± 9.9 in control, p < 0.001, and repair efficiency in group of smoking individuals was 63.0 ± 11.5% versus 65.9 ± 11.1 in nonsmokers, p < 0.005). The repair efficiency can be affected by a genetic polymorphism, such as subjects with a homozygous mutation in polymorphic CYP1A1_(Val/Val) enzyme, or slow NAT2 acetylators, who showed a considerably lower DNA repair efficiency (i.e. average repair efficiency in subgroups of fast acetylators was for the control subgroup 68.1% versus 66.5% in exposed subjects, while in the case of subgroups of slow acetylators, for the control group was 68.0% versus significantly less in the exposed subjects, 60.6%, p < 0.05). Smoking habits, or the diet's vitamin content, significantly affected the process. The results obtained confirm a potential value of the method as a biomarker of susceptibility in molecular epidemiology or preclinical studies, aimed at predicting susceptibility to various genotoxic exposures (environmental, occupational, therapeutic). To conclude, the research proved the influence of environmental c-PAHs, genotypes, and life styles on DNA damage and on its repair efficiency. Even low exposure to environmental c-PAHs altered DNA repair abilities of the subjects, which may result in an increased cancer risk. The findings confirm that c-PAHs should become pollutants that are subject to regulation.     

Regional variation in the postcranial robusticity of late Upper Paleolithic humans

Early modern humans from the European Upper Paleolithic (UP) demonstrate trends in postcranial biomechanical features that coincide with the last glacial maximum (LGM). These features have been interpreted as evidence that ecological changes of the LGM played a critical role in cultural and biological adaptation in European UP populations. In areas outside of Europe, similar environmental changes occurred with the LGM. This analysis introduces postcranial material from the Late Upper Paleolithic (LUP) of North Africa and Southeast Asia and tests two related hypotheses: 1) LUP samples across the Old World had similar patterns of postcranial robusticity and 2) relative to an available Early Upper Paleolithic (EUP) sample, regional LUP samples demonstrate similar trends in robusticity that may be attributable to climatic effects of the LGM. Cross-sectional geometric data of the humeri and femora were obtained for 26 EUP and 100 LUP humans from Europe, Africa, and Asia. Despite regional differences, LUP samples are similar relative to the EUP sample. In the humerus, bilateral asymmetry decreases in all LUP samples relative to the EUP sample. In the femur, LUP samples demonstrate increasingly circular femoral midshaft sections, reflecting reduced anteroposterior bending strength relative to the EUP sample. These patterns suggest changes in subsistence behavior and mobility after the LGM across the Old World that are most consistent with reduced mobility and broad-spectrum resource exploitation.     

In vivo bone strain and bone functional adaptation

Mechanistic interpretations of bone cross-sectional shapes are based on the paradigm of shape optimization such that bone offers maximum mechanical resistance with a minimum of material. Recent in vivo strain studies (Demes et al., Am J Phys Anthropol 106 (1998) 87-100, Am J Phys Anthropol 116 (2001) 257-265; Lieberman et al., Am J Phys Anthropol 123 (2004) 156-171) have questioned these interpretations by demonstrating that long bones diaphyses are not necessarily bent in planes in which they offer maximum resistance to bending. Potential limitations of these in vivo studies have been pointed out by Ruff et al. (Am J Phys Anthropol 129 (2006) 484-498). It is demonstrated here that two loading scenarios, asymmetric bending and buckling, would indeed not lead to correct predictions of loads from strain. It is also shown that buckling is of limited relevance for many primate long bones. This challenges a widely held view that circular bone cross sections make loading directions unpredictable for bones which is based on a buckling load model. Asymmetric bending is a potentially confounding factor for bones with directional differences in principal area moments (I(max) > I(min)). Mathematical corrections are available and should be applied to determine the bending axis in such cases. It is concluded that loads can be reliably extrapolated from strains. More strain studies are needed to improve our understanding of the relationships between activities, bone loading regimes associated with them, and the cross-sectional geometry of bones.     

The stochastic model of non-equilibrium mutagen-induced alterations of DNA: implication to genetic instability in cancer

Genetic alterations such as point mutations, chromosomal rearrangements, modification of DNA methylation and chromosome aberrations accumulate during the lifetime of an organism. They can be caused by intrinsic errors in the DNA replication and repair as well as by external factors such as exposure to mutagenic substances or radiation. The main purpose of the present work is to begin an exploration of the stochastic nature of non-equilibrium DNA alteration caused by events such as tautomeric shifts. This is done by modeling the genetic DNA code chain as a sequence of DNA-bit values ('1' for normal bases and '-1' for abnormal bases). We observe the number of DNA-bit changes resulting from the random point mutation process which, in the model, is being induced by a stochastic Brownian mutagen (BM) as it diffuses through the DNA-bit systems. Using both an analytical and Monte Carlo (MC) simulation techniques, we observe the local and global number of DNA-bit changes. It is found that in 1D, the local DNA-bit density behaves like 1/t, the global total number of the switched (abnormal) DNA-bit increases as t. The probability distribution P(b, 0, t) of b(0, t) is log-normal. It is also found that when the number of mutagens is increased, the number of the total abnormal DNA-bits does not grow linearly with the number of mutagens. All analytic results are in good agreement with the simulation results.     

A Riemannian manifold analysis of endothelial cell monolayer impedance parameter precision

Endothelial cell adhesion and barrier function play a critical role in many biological and pathophysiological processes. The decomposition of endothelial cell adhesion and barrier function into cell–cell and cell–matrix components using frequency dependent cellular micro-impedance measurements has, therefore, received widespread application. Few if any studies, however, have examined the precision of these model parameters. This study presents a parameter sensitivity analysis of a representative cellular barrier function model using a concise geometric formulation that includes instrumental data acquisition settings. Both model state dependence and instrumental noise distributions are accounted for within the framework of Riemannian manifold theory. Experimentally acquired microimpedance measurements of attached endothelial cells define the model state domain, while experimentally measured noise statistics define the data space Riemannian metric based on the Fisher information matrix. The results of this analysis show that the sensitivity of cell–cell and cell–matrix impedance components are highly model state dependent and several well defined regions of low precision exist. The results of this study further indicate that membrane resistive components can significantly reduce the precision of the remaining parameters in these models. This work was supported by a National Science Foundation CAREER Award (AE), BES-0238905, and in part by the American Heart Association under Grant 0265029B (AE).     

An Extended RNA Code and its Relationship to the Standard Genetic Code: An Algebraic and Geometrical Approach

An algebraic and geometrical approach is used to describe the primaeval RNA code and a proposed Extended RNA code. The former consists of all codons of the type RNY, where R means purines, Y pyrimidines, and N any of them. The latter comprises the 16 codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type), and the third, (YRN type) reading frames. In each of these reading frames, there are 16 triplets that altogether complete a set of 48 triplets, which specify 17 out of the 20 amino acids, including AUG, the start codon, and the three known stop codons. The other 16 codons, do not pertain to the Extended RNA code and, constitute the union of the triplets YYY and RRR that we define as the RNA-less code. The codons in each of the three subsets of the Extended RNA code are represented by a four-dimensional hypercube and the set of codons of the RNA-less code is portrayed as a four-dimensional hyperprism. Remarkably, the union of these four symmetrical pairwise disjoint sets comprises precisely the already known six-dimensional hypercube of the Standard Genetic Code (SGC) of 64 triplets. These results suggest a plausible evolutionary path from which the primaeval RNA code could have originated the SGC, via the Extended RNA code plus the RNA-less code. We argue that the life forms that probably obeyed the Extended RNA code were intermediate between the ribo-organisms of the RNA World and the last common ancestor (LCA) of the Prokaryotes, Archaea, and Eucarya, that is, the cenancestor. A general encoding function, E, which maps each codon to its corresponding amino acid or the stop signal is also derived. In 45 out of the 64 cases, this function takes the form of a linear transformation F, which projects the whole six-dimensional hypercube onto a four-dimensional hyperface conformed by all triplets that end in cytosine. In the remaining 19 cases the function E adopts the form of an affine transformation, i.e., the composition of F with a particular translation. Graphical representations of the four local encoding functions and E, are illustrated and discussed. For every amino acid and for the stop signal, a single triplet, among those that specify it, is selected as a canonical representative. From this mapping a graphical representation of the 20 amino acids and the stop signal is also derived. We conclude that the general encoding function E represents the SGC itself.