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Quasispecies
The quasispecies model is a description of the process of the Darwinian evolution of certain self-replicating entities within the framework of physical chemistry. A quasispecies is a large group or "cloud" of related genotypes that exist in an environment of high mutation rate (at stationary state), where a large fraction of offspring are expected to contain one or more mutations relative to the parent. This is in contrast to a species, which from an evolutionary perspective is a more-or-less stable single genotype, most of the offspring of which will be genetically accurate copies. It is useful mainly in providing a qualitative understanding of the evolutionary processes of self-replicating macromolecules such as RNA or DNA or simple asexual organisms such as bacteria or viruses (see also viral quasispecies), and is helpful in explaining something of the early stages of the origin of life. Quantitative predictions based on this model are difficult because the parameters that s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viral Quasispecies
A viral quasispecies is a population structure of viruses with a large number of variant genomes (related by mutations). Quasispecies result from high mutation rates as mutants arise continually and change in relative frequency as viral replication and selection proceeds. The theory predicts that a viral quasispecies at a low but evolutionarily neutral and highly connected (that is, flat) region in the fitness landscape will outcompete a quasispecies located at a higher but narrower fitness peak in which the surrounding mutants are unfit. This phenomenon has been called 'the quasispecies effect' or, more recently, the 'survival of the flattest'. The term quasispecies was adopted from a theory of the origin of life in which primitive replicons consisted of mutant distributions, as found experimentally with present-day RNA viruses within their host. The theory provided a new definition of wild type when describing viruses, and a conceptual framework for a deeper understanding of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gard Model
In evolutionary biology, the GARD (Graded Autocatalysis Replication Domain) model is a general kinetic model for homeostatic-growth and fission of compositional-assemblies, with specific application towards lipids. In the context of abiogenesis, the lipid-world suggests assemblies of simple molecules, such as lipids, can store and propagate information, thus undergo evolution. These 'compositional assemblies' have been suggested to play a role in the origin of life. The idea is the information being transferred throughout the generations is '' compositional information '' – the different types and quantities of molecules within an assembly. This is different from the information encoded in RNA or DNA, which is the specific sequence of bases in such molecule. Thus, the model is viewed as an alternative or an ancestor to the RNA world hypothesis. The model The composition vector of an assembly is written as: v=n_1\cdots n_. Where n_1\cdots n_ are the molecular counts of lipid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Species
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. Other ways of defining species include their karyotype, DNA sequence, morphology, behaviour or ecological niche. In addition, paleontologists use the concept of the chronospecies since fossil reproduction cannot be examined. The most recent rigorous estimate for the total number of species of eukaryotes is between 8 and 8.7 million. However, only about 14% of these had been described by 2011. All species (except viruses) are given a two-part name, a "binomial". The first part of a binomial is the genus to which the species belongs. The second part is called the specific name or the specific epithet (in botanical nomenclature, also sometimes i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manfred Eigen
Manfred Eigen (; 9 May 1927 – 6 February 2019) was a German Biophysical chemistry, biophysical chemist who won the 1967 Nobel Prize in Chemistry for work on measuring fast chemical reactions. Eigen's research helped solve major problems in physical chemistry and aided in the understanding of chemical processes that occur in living organisms. In later years, he explored the biochemical roots of life and evolution. He worked to install a multidisciplinary program at the Max Planck Institute to study the underpinnings of life at the molecular level. His work was hailed for creating a new scientific and technological discipline: evolutionary biotechnology. Education and early life Eigen was born on 9 May 1927 in Bochum, the son of Hedwig (Feld) and Ernst Eigen, a chamber musician. As a child he developed a deep passion for music, and studied piano. World War II interrupted his formal education. At age fifteen he was drafted into service in a German antiaircraft unit. He was ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Threshold (evolution)
In evolutionary biology and population genetics, the error threshold (or critical mutation rate) is a limit on the number of base pairs a self-replicating molecule may have before mutation will destroy the information in subsequent generations of the molecule. The error threshold is crucial to understanding "Eigen's paradox". The error threshold is a concept in the origins of life (abiogenesis), in particular of very early life, before the advent of DNA. It is postulated that the first self-replicating molecules might have been small ribozyme-like RNA molecules. These molecules consist of strings of base pairs or "digits", and their order is a code that directs how the molecule interacts with its environment. All replication is subject to mutation error. During the replication process, each digit has a certain probability of being replaced by some other digit, which changes the way the molecule interacts with its environment, and may increase or decrease its fitness, or ability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emmanuel David Tannenbaum
Emmanuel David Tannenbaum (June 28, 1978 – May 28, 2012) was an Israeli/American biophysicist and applied mathematician. He worked as a professor and researcher in the Department of Chemistry at the Ben-Gurion University of the Negev and the Department of Biology at the Georgia Institute of Technology, specializing in the fields of mathematical biology, systems biology, and quantum physics. Tannenbaum's initial work was in quantum chemistry as part of his Harvard University doctoral thesis where he developed a novel partial differential equation approach to the EBK quantization of nearly separable Hamiltonians in the quasi-integrable regime. Emmanuel Tannenbaum subsequently devoted his research to studying various problems in evolutionary dynamics using quasispecies models. His seminal work centered on the key question of the evolutionary advantages of sexual reproduction. Tannenbaum demonstrated a strong selective advantage for sexual reproduction with fewer and much less ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System Of Linear Equations
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variable (math), variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in the three variables . A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A Equation solving, solution to the system above is given by the Tuple, ordered triple :(x,y,z)=(1,-2,-2), since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually. In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolution
Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation tends to exist within any given population as a result of genetic mutation and recombination. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on this variation, resulting in certain characteristics becoming more common or more rare within a population. The evolutionary pressures that determine whether a characteristic is common or rare within a population constantly change, resulting in a change in heritable characteristics arising over successive generations. It is this process of evolution that has given rise to biodiversity at every level of biological organisation, including the levels of species, individual organisms, and molecules. The theory of evolution by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonalizable Matrix
In linear algebra, a square matrix A is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P and a diagonal matrix D such that or equivalently (Such D are not unique.) For a finite-dimensional vector space a linear map T:V\to V is called diagonalizable if there exists an ordered basis of V consisting of eigenvectors of T. These definitions are equivalent: if T has a matrix representation T = PDP^ as above, then the column vectors of P form a basis consisting of eigenvectors of and the diagonal entries of D are the corresponding eigenvalues of with respect to this eigenvector basis, A is represented by Diagonalization is the process of finding the above P and Diagonalizable matrices and maps are especially easy for computations, once their eigenvalues and eigenvectors are known. One can raise a diagonal matrix D to a power by simply raising the diagonal entries to that power, and the determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutation
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitosis, or meiosis or other types of damage to DNA (such as pyrimidine dimers caused by exposure to ultraviolet radiation), which then may undergo error-prone repair (especially microhomology-mediated end joining), cause an error during other forms of repair, or cause an error during replication (translesion synthesis). Mutations may also result from insertion or deletion of segments of DNA due to mobile genetic elements. Mutations may or may not produce detectable changes in the observable characteristics (phenotype) of an organism. Mutations play a part in both normal and abnormal biological processes including: evolution, cancer, and the development of the immune system, including junctional diversity. Mutation is the ultimate source o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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