p-Adic hierarchical properties of the genetic code

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

On the psychological origins of tool use

The ubiquity of tool use in human life has generated multiple lines of scientific and philosophical investigation to understand the development and expression of humans' engagement with tools and its relation to other dimensions of human experience. However, existing literature on tool use faces several epistemological challenges in which the same set of questions generate many different answers. At least four critical questions can be identified, which are intimately intertwined-(1) What constitutes tool use? (2) What psychological processes underlie tool use in humans and nonhuman animals? (3) Which of these psychological processes are exclusive to tool use? (4) Which psychological processes involved in tool use are exclusive to Homo sapiens? To help advance a multidisciplinary scientific understanding of tool use, six author groups representing different academic disciplines (e.g., anthropology, psychology, neuroscience) and different theoretical perspectives respond to each of these questions, and then point to the direction of future work on tool use. We find that while there are marked differences among the responses of the respective author groups to each question, there is a surprising degree of agreement about many essential concepts and questions. We believe that this interdisciplinary and intertheoretical discussion will foster a more comprehensive understanding of tool use than any one of these perspectives (or any one of these author groups) would (or could) on their own.

DNA numerical encoding schemes for exon prediction: a recent history

Bioinformatics in the present day has been firmly established as a regulator in genomics. In recent times, applications of Signal processing in exon prediction have gained a lot of attention. The exons carry protein information. Proteins are composed of connected constituents known as amino acids that characterize the specific function. Conversion of the nucleotide character string into a numerical sequence is the gateway before analyzing it through signal processing methods. This numeric encoding is the mathematical descriptor of nucleotides and is based on some statistical properties of the structure of nucleic acids. Since the type of encoding extremely affects the exon detection accuracy, this paper is devised for the review of existing encoding (mapping) schemes. The comparative analysis is formulated to emphasize the importance of the genetic code setting of amino acids considered for application related to computational elucidation for exon detection. This work covers much helpful information for future applications.

p-adic numbers encode complex networks

The Erdős-Rényi (ER) random graph G(n, p) analytically characterizes the behaviors in complex networks. However, attempts to fit real-world observations need more sophisticated structures (e.g., multilayer networks), rules (e.g., Achlioptas processes), and projections onto geometric, social, or geographic spaces. The p-adic number system offers a natural representation of hierarchical organization of complex networks. The p-adic random graph interprets n as the cardinality of a set of p-adic numbers. Constructing a vast space of hierarchical structures is equivalent for combining number sequences. Although the giant component is vital in dynamic evolution of networks, the structure of multiple big components is also essential. Fitting the sizes of the few largest components to empirical data was rarely demonstrated. The p-adic ultrametric enables the ER model to simulate multiple big components from the observations of genetic interaction networks, social networks, and epidemics. Community structures lead to multimodal distributions of the big component sizes in networks, which have important implications in intervention of spreading processes.

p-Adic mathematics and theoretical biology

The principal objective of this article is a brief overview of the main parts of p-adic mathematics, which have already had valuable applications and may have a significant impact in the near future on the further development of some fields of theoretical and mathematical biology. In particular, we present the basics of ultrametrics, p-adic numbers and p-adic analysis, as well as insight into their applications for modeling some cognitive processes, genetic code and protein dynamics. We also argue that ultrametric concepts and p-adic mathematics are natural tools for the viable description of biological systems and phenomena with a hierarchical structure.

Mapping sequence to feature vector using numerical representation of codons targeted to amino acids for alignment-free sequence analysis

The phylogenetic analysis based on sequence similarity targeted to real biological taxa is one of the major challenging tasks. In this paper, we propose a novel alignment-free method, CoFASA (Codon Feature based Amino acid Sequence Analyser), for similarity analysis of nucleotide sequences. At first, we assign numerical weights to the four nucleotides. We then calculate a score of each codon based on the numerical value of the constituent nucleotides, termed as degree of codons. Accordingly, we obtain the degree of each amino acid based on the degree of codons targeted towards a specific amino acid. Utilizing the degree of twenty amino acids and their relative abundance within a given sequence, we generate 20-dimensional features for every coding DNA sequence or protein sequence. We use the features for performing phylogenetic analysis of the set of candidate sequences. We use multiple protein sequences derived from Beta-globin (BG), NADH dehydrogenase subunit 5 (ND5), Transferrins (TFs), Xylanases, low identity (<40%) and high identity (⩾40%) protein sequences (encompassing 533 and 1064 protein families) for experimental assessments. We compare our results with sixteen (16) well-known methods, including both alignment-based and alignment-free methods. Various assessment indices are used, such as the Pearson correlation coefficient, RF (Robinson-Foulds) distance and ROC score for performance analysis. While comparing the performance of CoFASA with alignment-based methods (ClustalW, ClustalΩ, MAFFT, and MUSCLE), it shows very similar results. Further, CoFASA shows better performance in comparison to well-known alignment-free methods, including LZW-Kernal, jD2Stat, FFP, spaced, and AFKS-D2s in predicting taxonomic relationship among candidate taxa. Overall, we observe that the features derived by CoFASA are very much useful in isolating the sequences according to their taxonomic labels. While our method is cost-effective, at the same time, produces consistent and satisfactory outcomes.

Solvability of the p-adic Analogue of Navier–Stokes Equation via the Wavelet Theory

P-adic numbers serve as the simplest ultrametric model for the tree-like structures arising in various physical and biological phenomena. Recently p-adic dynamical equations started to be applied to geophysics, to model propagation of fluids (oil, water, and oil-in-water and water-in-oil emulsion) in capillary networks in porous random media. In particular, a p-adic analog of the Navier–Stokes equation was derived starting with a system of differential equations respecting the hierarchic structure of a capillary tree. In this paper, using the Schauder fixed point theorem together with the wavelet functions, we extend the study of the solvability of a p-adic field analog of the Navier–Stokes equation derived from a system of hierarchic equations for fluid flow in a capillary network in porous medium. This equation describes propagation of fluid’s flow through Geo-conduits, consisting of the mixture of fractures (as well as fracture’s corridors) and capillary networks, detected by seismic as joint wave/mass conducts. Furthermore, applying the Adomian decomposition method we formulate the solution of the p-adic analog of the Navier–Stokes equation in term of series in general form. This solution may help researchers to come closer and find more facts, taking into consideration the scaling, hierarchies, and formal derivations, imprinted from the analogous aspects of the real world phenomena.