PTMs in Conversation: Activity and Function of Deubiquitinating Enzymes Regulated via Post-Translational Modifications

Deubiquitinating enzymes (DUBs) constitute a diverse protein family and their impact on numerous biological and pathological processes has now been widely appreciated. Many DUB functions have to be tightly controlled within the cell, and this can be achieved in several ways, such as substrate-induced conformational changes, binding to adaptor proteins, proteolytic cleavage, and post-translational modifications (PTMs). This review is focused on the role of PTMs including monoubiquitination, sumoylation, acetylation, and phosphorylation as characterized and putative regulative factors of DUB function. Although this aspect of DUB functionality has not been yet thoroughly studied, PTMs represent a versatile and reversible method of controlling the role of DUBs in biological processes. In several cases PTMs might constitute a feedback mechanism insuring proper functioning of the ubiquitin proteasome system and other DUB-related pathways

Completeness of Hoare logic with inputs over the standard model

Hoare logic for the set of while-programs with the first-order logical language L and the first-order theory T subset of L is denoted by HL(T). Bergstra and Tucker have pointed out that the complete number theory Th(N) is the only extension T of Peano arithmetic PA for which HL(T) is logically complete. The completeness result is not satisfying, since it allows inputs to range over nonstandard models. The aim of this paper is to investigate under what circumstances HL(T) is logically complete when inputs range over the standard model N. PA(+) is defined by adding to PA all the unprovable Pi(1)-sentences that describe the nonterminating computations. It is shown that each computable function in N is uniformly Sigma(1)-definable in all models of PA(+), and that PA(+) is arithmetical. Finally, it is established, based on the reduction from HL(T) to T, that PA(+) is the minimal extension T of PA for which HL(T) is logically complete when inputs range over N. This completeness result has an advantage over Bergstra's and Tucker's one, in that PA(+) is arithmetical while Th(N) is not. (C) 2015 Elsevier B.V. All rights reserved.Hoare logic for the set of while-programs with the first-order logical language L and the first-order theory T subset of L is denoted by HL(T). Bergstra and Tucker have pointed out that the complete number theory Th(N) is the only extension T of Peano arithmetic PA for which HL(T) is logically complete. The completeness result is not satisfying, since it allows inputs to range over nonstandard models. The aim of this paper is to investigate under what circumstances HL(T) is logically complete when inputs range over the standard model N. PA(+) is defined by adding to PA all the unprovable Pi(1)-sentences that describe the nonterminating computations. It is shown that each computable function in N is uniformly Sigma(1)-definable in all models of PA(+), and that PA(+) is arithmetical. Finally, it is established, based on the reduction from HL(T) to T, that PA(+) is the minimal extension T of PA for which HL(T) is logically complete when inputs range over N. This completeness result has an advantage over Bergstra's and Tucker's one, in that PA(+) is arithmetical while Th(N) is not. (C) 2015 Elsevier B.V. All rights reserved