A Rational Model In Theoretical Genetics
Keywords: Self-organizing and self-replicating systems, Information processing in biosystems, Multidimensional partitions, Interaction between sequences and mixtures, Number theory of biology, Linearisation of structured sets
AbstractThis model connects information processing in biological organisms with methods and concepts used in classical, technical information processing. The central concept shows copying and regulatory interaction between a logical sequence consisting of triplets and the amount of constituents of a set. The basic mathematical model of information processing within a biological cell has been worked out. The cell in the model copies its present state into a sequence and reads it off the sequence. The sequence comes in triplets and is not one sequence but appears in two almost identical varieties. We treat consecutive and contemporary assemblies of information carrying media as equally suited to contain information. Methods used so far utilised the consecutive property of media, while in biology one observes the concurrent existence of specific realisations of possibilities. Genetics connects the two approaches by using an interplay between consecutively (sequentially) ordered logical markers (the DNA) and the state of the set engulfing the DNA. Several mathematical tools have been evolved to assemble an interface between sequentially ordered carriers and the same number of carriers if they arrive contemporaneously. Using linguistic theory and formal logic one concludes that measurement(s) on a cell are a (set of) logical sentence(s) relating to an assembly of n objects with group structures among each other. We linearise and count all possible group relations on a set of n objects and introduce the concept of multidimensional partitions hitherto left undefined. We introduce the concept of a maximally structured set by establishing an upper limit to the information carrying capacity of n objects used commutatively and sequentially at the same time (like genetics does). The copying and re-copying mechanism which is the core matter with genetics appears in the model as differing transmission efficiency coefficients of media if the media are used once sequentially and once commutatively. In dependence of the strength of the assembly, one can transmit up to several hundred % more information using n carriers if the carriers are used commutatively, as long as the number of the objects remains within some limits.
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