We build a model of storage of well-defined positional information in probabilistic sequence patterns. Once a pattern is defined, it is possible to judge the effect of any mutation in it. We show that the frequency of...We build a model of storage of well-defined positional information in probabilistic sequence patterns. Once a pattern is defined, it is possible to judge the effect of any mutation in it. We show that the frequency of beneficial mutations can be high in general and the same mutation can be either advantageous or deleterious depending on the pattern’s context. The model allows to treat positional information as a physical quantity, formulate its conservation law and to model its continuous evolution in a whole genome, with meaningful applications of basic physical principles such as optimal efficiency and channel capacity. A plausible example of optimal solution analytically describes phase transitions-like behavior. The model shows that, in principle, it is possible to store error-free information on sequences with arbitrary low conservation. The described theoretical framework allows one to approach from novel general perspectives such long-standing paradoxes as excessive junk DNA in large genomes or the corresponding G- and C-values paradoxes. We also expect it to have an effect on a number of fundamental concepts in population genetics including the neutral theory, cost-of-selection dilemma, error catastrophe and others.展开更多
Let Ro be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal ra and residue class field K = Rim. For a graded ideal I in R we show that for k 〉〉 0: (1) the Artin-Rees number of the syzy...Let Ro be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal ra and residue class field K = Rim. For a graded ideal I in R we show that for k 〉〉 0: (1) the Artin-Rees number of the syzygy modules of Ik as submodules of the free modules from a free resolution is constant, and thereby the Artin-Rees number can be presented as a proper replacement of regularity in the local situation; and (2) R is a polynomial ring over the regular Ro, the ring R/Ik is Golod, its Poincar4-Betti series is rational and the Betti numbers of the free resolution of K over R/I^k are polynomials in k of a specific degree. The first result is an extension of the work by Swanson on the regularity of I^k for k 〉〉 0 from the graded situation to the local situation. The polynomiality consequence of the second result is an analog of the work by Kodiyalam on the behaviour of Betti numbers of the minimal free resolution of R/Ik over R.展开更多
文摘We build a model of storage of well-defined positional information in probabilistic sequence patterns. Once a pattern is defined, it is possible to judge the effect of any mutation in it. We show that the frequency of beneficial mutations can be high in general and the same mutation can be either advantageous or deleterious depending on the pattern’s context. The model allows to treat positional information as a physical quantity, formulate its conservation law and to model its continuous evolution in a whole genome, with meaningful applications of basic physical principles such as optimal efficiency and channel capacity. A plausible example of optimal solution analytically describes phase transitions-like behavior. The model shows that, in principle, it is possible to store error-free information on sequences with arbitrary low conservation. The described theoretical framework allows one to approach from novel general perspectives such long-standing paradoxes as excessive junk DNA in large genomes or the corresponding G- and C-values paradoxes. We also expect it to have an effect on a number of fundamental concepts in population genetics including the neutral theory, cost-of-selection dilemma, error catastrophe and others.
文摘Let Ro be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal ra and residue class field K = Rim. For a graded ideal I in R we show that for k 〉〉 0: (1) the Artin-Rees number of the syzygy modules of Ik as submodules of the free modules from a free resolution is constant, and thereby the Artin-Rees number can be presented as a proper replacement of regularity in the local situation; and (2) R is a polynomial ring over the regular Ro, the ring R/Ik is Golod, its Poincar4-Betti series is rational and the Betti numbers of the free resolution of K over R/I^k are polynomials in k of a specific degree. The first result is an extension of the work by Swanson on the regularity of I^k for k 〉〉 0 from the graded situation to the local situation. The polynomiality consequence of the second result is an analog of the work by Kodiyalam on the behaviour of Betti numbers of the minimal free resolution of R/Ik over R.