A new class of critical sets in Latin squares

Previously the process of finding critical sets in Latin squares has been inside cumbersome by the complexity and number of Latin trades that, must be constructed. In this paper we develop a theory of Latin trades that yields more transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the Latin square of order 2 with a. back circulant Latin square of odd order.

Inhibition of cell-wall autolysis and pectin degradation by cations

Modification of cell wall components such as cellulose, hemicellulose and pectin plays an important role in cell expansion. Cell expansion is known to be diminished by cations but it is unknown if this results from cations reacting with pectin or other cell wall components. Autolysis of cell wall material purified from bean root (Phaseolus vulgaris L.) occurred optimally at pH 5.0 and released mainly neutral sugars but very little uronic acid. Autolytic release of neutral sugars and uronic acid was decreased when cell wall material was loaded with Ca, Cu, Sr, Zn, Al or La cations. Results were also extended to a metal-pectate model system, which behaved similarly to cell walls and these cations also inhibited the enzymatic degradation by added polygalacturonase (EC 3.2.1.15). The extent of sugar release from cation-loaded cell wall material and pectate gels was related to the degree of cation saturation of the substrate, but not to the type of cation. The binding strength of the cations was assessed by their influence on the buffer capacity of the cell wall and pectate. The strongly bound cations (Cu, Al or La) resulted in higher cation saturation of the substrate and decreased enzymatic degradability than the weakly held cations (Ca, Sr and Zn). The results indicate that the junction zones between pectin molecules can peel open with weakly held cations, allowing polygalacturonase to cleave the hairy region of pectin, while strongly bound cations or high concentrations of cations force the junction zone closed, minimising enzymatic attack on the pectin backbone. (C) 2004 Elsevier SAS. All rights reserved.