Gene family evolution: an in-depth theoretical and simulation analysis of non-linear birth-death-innovation models

Background  

The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs). Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome evolution.     

Three palmar dermatoglyphic traits and their asymmetry in Bulgarian right-, mixed- and left-handers

Summary: In a sample, comprising 264 right-, 246 mixed- and 360 left-handers (RH, MH and LH, correspondingly), the atd-angle, the a-b ridge count and the hypothenar radial arch were investigated, the asymmetry of both quantitative traits differentiated into directional (DA) and fluctuating (FA) one. Except for the FA of the a-b ridge count in females, which decreased significantly from RH to LH, the trends observed in the relations between the investigated dermatoglyphic values and handedness were not significant. In both quantitative traits the most important finding was the categorical left-palm excess over the right palm, since it was significantly related to sex and handedness, being much more expressed in females than in males and in the non-right-handers than in the right-handers. The hypothenar radial arch, along with its considerably higher frequency in females than in males and on the right palm than on the left, as well as its rarity combined with a very high symmetry, displayed another interesting peculiarity. The pattern was 3.9-fold more frequent in the MH and 3.4-fold more frequent in the LH as compared to RH. As witnessed by the odds ratio, if a given palm belongs to a non-right-hander, the probability that it bears a hypothenar radial arch is nearly 4-fold higher than if it were a palm of a right-hander. Arguments are adduced that left-handedness, although not a pathological character is, to say the least, a modified condition and that, similarly, the hypothenar radial arch is a subnormal dermatoglyphic finding. If such is the case, their relationship found by the present study is not surprising, although its causal background still remains unclear.     

Population models with singular equilibrium

A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from the biological standpoint. This regime corresponds to the presence of a family of homoclinics to the origin, so-called elliptic sector. The complete analysis of possible topological structures in a neighborhood of the origin, as well as asymptotics to orbits tending to this point, is given. An algorithmic approach to analyze system behavior with parameter changes is presented. The developed methods and algorithm are applied to existing mathematical models of biological systems. In particular, we analyze a model of anticancer treatment with oncolytic viruses, a parasite-host interaction model, and a model of Chagas' disease.     

Finger dermatoglyphics and their asymmetry in Bulgarian right-, mixed- and left-handers

Since Bulgarians have never been investigated concerning the relationship between handedness and dermatoglyphics, the present study was aimed to investigate the aforementioned relationship in a Bulgarian sample. Digital dermatoglyphics and their asymmetries have been studied in 870 apparently healthy students from randomly selected Bulgarian secondary schools: 264 right-handers (RH), 246 mixed-handers (MH) and 360 left-handers (LH). The whorls were significantly less frequent and the ulnar loops more frequent in RH than in the other two handedness categories. Right-handers exceeded significantly MH and LH in the ulnar fluctuating asymmetries of the first and the fourth finger pairs. As compared to the number of investigated variables and especially to the important psychological and behavioral differences between handedness categories reported earlier in the same sample, the presented significant findings are rather scarce. Nevertheless they could contribute to the accumulation of data concerning the investigated relationship and to its better understanding.     

Modeling genome evolution with a diffusion approximation of a birth-and-death process

MOTIVATION: In our previous studies, we developed discrete-space birth, death and innovation models (BDIMs) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and model parameters that provide for the evolution of these distributions within a realistic time frame have been identified. However, extracting the temporal dynamics of genome evolution from discrete-space BDIM was not technically feasible. We were interested in obtaining dynamic portraits of the genome evolution process by developing a diffusion approximation of BDIM. RESULTS: The diffusion version of BDIM belongs to a class of continuous-state models whose dynamics is described by the Fokker-Plank equation and the stationary solution could be any specified Pareto function. The diffusion models have time-dependent solutions of a special kind, namely, generalized self-similar solutions, which describe the transition from one stationary distribution of the system to another; this provides for the possibility of examining the temporal dynamics of genome evolution. Analysis of the generalized self-similar solutions of the diffusion BDIM reveals a biphasic curve of genome growth in which the initial, relatively short, self-accelerating phase is followed by a prolonged phase of slow deceleration. This evolutionary dynamics was observed both when genome growth started from zero and proceeded via innovation (a potential model of primordial evolution), and when evolution proceeded from one stationary state to another. In biological terms, this regime of evolution can be tentatively interpreted as a punctuated-equilibrium-like phenomenon whereby evolutionary transitions are accompanied by rapid gene amplification and innovation, followed by slow relaxation to a new stationary state.     

Digital dermatoglyphics of Bulgarians from northeast Bulgaria

Digital dermatoglyphics were collected from 1,065 male and 1,065 female Bulgarians from northeast Bulgaria. None of the subjects had a diagnosed or suspected genetic or chronic disease of any kind. The fingerprints were classified by the 18-type system of Monique de Lestrange, modified to provide rapid and easy comparison with simpler classification systems. All the standard finger pattern indices were calculated. Certain modifications were introduced into the delta indices, it being borne in mind that each tented arch possesses a triradius and each complex (three-centered, accidental) whorl contains three triradii. A deltadiagram was constructed and its configuration was compared with those of some other populations. In addition, a new radioulnar index was proposed, representing a ratio between all the radial and all the ulnar patterns. The total, absolute, ulnar and radial finger ridge counts were calculated and their sample distributions were investigated. The dermatoglyphic features were evaluated and presented for each sex and each hand separately in order to investigate both the sex and bilateral differences. The set of data presented in this paper is a component of the physical anthropology of the general Bulgarian population. At the same time these data can be used as controls when analyzing the dermatoglyphic findings in Bulgarian patients with genetic diseases or congenital malformations.     

Biological applications of the theory of birth-and-death processes

In this review, we discuss applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural and formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer and somatic evolution of cancers. We further describe how empirical data, e.g. distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. We conclude that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological processes, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.     

Replicator Equations and the Principle of Minimal Production of Information

Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize the KL-divergence of the initial and current distributions under time-dependent constraints, which in their turn, can be computed explicitly at every instant due to the system dynamics. Therefore, the Kullback principle of minimum discrimination information, as well as the maximum entropy principle, for systems governed by the replicator equations can be derived from the system dynamics rather than postulated. Applications to the Malthusian inhomogeneous models, global demography, and the Eigen quasispecies equation are given.