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In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
They have a regular geometry, being constrained to specific values of the dihedral angles ψ and φ on the Ramachandran plot. Both the α-helix and the β-sheet represent a way of saturating all the hydrogen bond donors and acceptors in the peptide backbone. Some parts of the protein are ordered but do not form any regular structures.
The postulate has also been used to predict the shape of reaction coordinate diagrams. For example, electrophilic aromatic substitution involves a distinct intermediate and two less well defined states. By measuring the effects of aromatic substituents and applying Hammond's postulate it was concluded that the rate-determining step involves ...
Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example: ψ: (R → S) & (T → S) is a substitution ...
Silica pseudomorph after gypsum crystals and silicified serpulid polychaete tubes Pseudomorph of goethite after pyrite. In mineralogy, a pseudomorph is a mineral or mineral compound that appears in an atypical form (crystal system), resulting from a substitution process in which the appearance and dimensions remain constant, but the original mineral is replaced by another due to alteration, or ...
One PAM unit is defined as 1% of the amino acid positions that have been changed. To create a PAM1 substitution matrix, a group of very closely related sequences with mutation frequencies corresponding to one PAM unit is chosen. Based on collected mutational data from this group of sequences, a substitution matrix can be derived.
A conservative replacement (also called a conservative mutation or a conservative substitution or a homologous replacement) is an amino acid replacement in a protein that changes a given amino acid to a different amino acid with similar biochemical properties (e.g. charge, hydrophobicity and size). [1] [2]
In biology, a substitution model, also called models of sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules, such as DNA sequences or protein sequences, that can be represented as sequence of symbols (e.g., A, C, G, and T in the case of DNA or the 20 "standard" proteinogenic amino acids in the case of ...