The application of a linear algebra to the analysis of mutation rates

DNA sequence reconstruction based on innovated hybridization technique of probabilistic cellular automata and particle swarm optimization

DNA sequence reconstruction is a challenging research problem in the computational biology field. The evolution of the DNA is too complex to be characterized by a few parameters. Therefore, there is a need for a modeling approach for analyzing DNA patterns. In this paper, we proposed a novel framework for DNA pattern analysis. The proposed framework consists of two main stages. The first stage is for analyzing the DNA sequences evolution, whereas the other stage is for the reconstruction process. We utilized cellular automata (CA) rules for analyzing and predicting the DNA sequence. Then, a modified procedure for the reconstruction process is introduced, which is based on the Probabilistic Cellular Automata (PCA) integrated with Particle Swarm Optimization (PSO) algorithm. This integration makes the proposed framework more efficient and achieves optimum transition rules. Our innovated model leans on the hypothesis that mutations are probabilistic events. As a result, their evolution can be simulated as a PCA model. The main objective of this paper is to analyze various DNA sequences to predict the changes that occur in DNA during evolution (mutations). We used a similarity score as a fitness measure to detect symmetry relations, which is appropriate for numerous extremely long sequences. Results are given for the CpG-methylation-deamination processes, which are regions of DNA where a guanine nucleotide follows a cytosine nucleotide in the linear sequence of bases. The DNA evolution is handled as the evolved colored paradigms. Therefore, incorporating probabilistic components help to produce a tool capable of foretelling the likelihood of specific mutations. Besides, it shows their capabilities in dealing with complex relations.

A simple formula for obtaining markedly improved mutation rate estimates

In previous work by M. E. Jones and colleagues, it was shown that mutation rate estimates can be improved and corresponding confidence intervals tightened by following a very easy modification of the standard fluctuation assay: cultures are grown to a larger-than-usual final density, and mutants are screened for in only a fraction of the culture. Surprisingly, this very promising development has received limited attention, perhaps because there has been no efficient way to generate the predicted mutant distribution to obtain non-moment-based estimates of the mutation rate. Here, the improved fluctuation assay discovered by Jones and colleagues is made amenable to quantile-based, likelihood, and other Bayesian methods by a simple recursion formula that efficiently generates the entire mutant distribution after growth and dilution. This formula makes possible a further protocol improvement: grow cultures as large as is experimentally possible and severely dilute before plating to obtain easily countable numbers of mutants. A preliminary look at likelihood surfaces suggests that this easy protocol adjustment gives markedly improved mutation rate estimates and confidence intervals.

Reconstruction of DNA sequences using genetic algorithms and cellular automata: towards mutation prediction?

Change of DNA sequence that fuels evolution is, to a certain extent, a deterministic process because mutagenesis does not occur in an absolutely random manner. So far, it has not been possible to decipher the rules that govern DNA sequence evolution due to the extreme complexity of the entire process. In our attempt to approach this issue we focus solely on the mechanisms of mutagenesis and deliberately disregard the role of natural selection. Hence, in this analysis, evolution refers to the accumulation of genetic alterations that originate from mutations and are transmitted through generations without being subjected to natural selection. We have developed a software tool that allows modelling of a DNA sequence as a one-dimensional cellular automaton (CA) with four states per cell which correspond to the four DNA bases, i.e. A, C, T and G. The four states are represented by numbers of the quaternary number system. Moreover, we have developed genetic algorithms (GAs) in order to determine the rules of CA evolution that simulate the DNA evolution process. Linear evolution rules were considered and square matrices were used to represent them. If DNA sequences of different evolution steps are available, our approach allows the determination of the underlying evolution rule(s). Conversely, once the evolution rules are deciphered, our tool may reconstruct the DNA sequence in any previous evolution step for which the exact sequence information was unknown. The developed tool may be used to test various parameters that could influence evolution. We describe a paradigm relying on the assumption that mutagenesis is governed by a near-neighbour-dependent mechanism. Based on the satisfactory performance of our system in the deliberately simplified example, we propose that our approach could offer a starting point for future attempts to understand the mechanisms that govern evolution. The developed software is open-source and has a user-friendly graphical input interface.

Measuring bidirectional mutation

The estimation of mutation rates is usually based on a model in which mutations are rare independent Poisson events. Back-mutation of mutants, an even rarer event, is ignored. In the hypermutating B cells of the immune system, mutation between phenotypes exhibiting, vs. not exhibiting, surface immunoglobulin is common in both directions. We develop three strategies for the estimation of mutation rates under circumstances such as these, where mutation rates in both directions are estimated simultaneously. Our model for the growth of a cell culture departs from the classical assumption of cell division as a memoryless (Poisson) event; we model cell division as giving rise to sequential generations of cells. On this basis, a Monte-Carlo simulation is developed. We develop also a numerical approach to calculating the probability distribution for the proportion of mutants in each culture as a function of forward- and backward-mutation rates. Although both approaches are too computationally intensive for routine laboratory use, they provide the insight necessary to develop and evaluate a third, 'hand-calculator' approach to extracting mutation rate estimators from experiments of this type.

Methods for determining spontaneous mutation rates

Spontaneous mutations arise as a result of cellular processes that act upon or damage DNA. Accurate determination of spontaneous mutation rates can contribute to our understanding of these processes and the enzymatic pathways that deal with them. The methods that are used to calculate mutation rates are based on the model for the expansion of mutant clones originally described by Luria and Delbrück (1943) and extended by Lea and Coulson (1949). The accurate determination of mutation rates depends on understanding the strengths and limitations of these methods and how to optimize a fluctuation assay for a given method. This chapter describes the proper design of a fluctuation assay, several of the methods used to calculate mutation rates, and ways to evaluate the results statistically.

A cellular automaton model for the study of DNA sequence evolution

Cellular automata are introduced as a model for DNA structure, function and evolution. DNA is modeled as a one-dimensional cellular automaton with four states per cell. These states are the four DNA bases A, C, T and G. The four states are represented by numbers of the quaternary number system. Linear evolution rules, represented by square matrices, are considered. Based on this model a simulator of DNA evolution is developed and simulation results are presented. This simulator has a user-friendly input interface and can be used for the study of DNA evolution.

Population genetics from an information perspective

Some basic effects of population genetics are derived governing the occurrences of alleles A(i)and genotypes A(i)A(j)among its members. A principle of extreme physical information (EPI) is used. These effects are (1) the equation of genetic change, (2) Fisher's theorem of partial change, (3) a new uncertainty principle, and (4) the monotonic decrease of Fisher information with time, indicating increased disorder for the population. General conditions of population change are allowed: fitness coefficients w(ij)generally changing with time [except in effect (2)], population randomly or non-randomly mating, and a general number of loci present within each chromosome. EPI is a practical tool for deriving probability laws. It is an outgrowth of a physical process that occurs during any act of measurement. Here the measurement is the random observation of a genotype A(i)A(j). This observation is to be used to estimate the time of the observation, called "evolutionary time". The measurement activity incurs errors in the estimated observation time and fitness value of the observed genotype. By the Cramer-Rao inequality, the product of the two uncertainties must exceed unity [effect (3)]. The Fisher information I in data space is postulated to originate in the space of the genotype where it had some generally larger value J. The EPI principle extremizes the loss of information (I--J) with I=1/2 J. The solution gives rise to effects (1) and (2). Finally, it is shown that effect (4) holds when the population approaches an equilibrium state, e.g. for time values greater than a threshold if fitness coefficients w(ij)are constant. EPI provides a common framework for deriving physical laws and laws of population genetics. The new effects (3) and (4) are confirmed through computer simulation.