Fruit softening has been largely associated with cell wall degradation by a number of loosening proteins. Firmness is a major quality attribute of fresh cherries and also an important factor affecting the susceptibility to postharvest rots. By analyzing the solubilization, depolymerization and composition of pectins and hemicelluloses in cultivars with contrasting firmness we found that the pattern and extent of their wall disassembly was quite similar. No marked pectin or hemicellulose depolymerization was observed and a similar reduction in tightlybound pectins and hemicellulose was detected in both cultivars during ripening. However, firm cherries presented pectic polymers with lower proportion of neutral sugars compared to uronic acids, suggesting that the variation in total wall polysaccharide and the branching of pectins assembled early in development or the proportion of homogalacturonan (HG) to type rhamnogalacturonan-I (RG-I) may contribute to the differences in firmness between cultivars. Dismantling of the cell wall by the action of relatively "well known" loosening agents is involved in the progressive softening occurring during ripening. Two of these proteins include polygalacturonases (PG) which are known to hydrolyze homogalacturonans and expansins (Exp) believed to participate in the relaxation of the cell wall by reducing hydrogen bonding between cellulose microfibrils and xyloglucan. We investigated the in vivo roles of these wall-disassembling proteins, by overexpressing PG and Exp1 both alone and in combination in a non-ripening rin tomato background. The simultaneous overexpression of PG and Exp1 in rin fruit restored softening in these non-ripening fruit. Unexpectedly, PG overexpression resulted in higher hemicellulose depolymerization while increased levels of Exp1 accelerated pectin turnover. This shows that besides their "well known" in vitro functions these proteins act in muro by facilitating the degradation of non-directly targeted wall components, likely by increasing the accessibility of pre-existing wall-degrading proteins to their polysaccharide substrates.
Applications of percents are often taught by solving proportions that require variables and some familiarity with algebra. Such formal approaches to teaching percent have not been successful for many junior high and high school students (Wiebe 1986). This article present an alternative method that focuses on the basic concept of percent, that of “parts per hundred.” A 10 × 10 grid, which is a common model for visualizing percents, is extended in the following examples to solve various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution.
A survey of modern elementary textbooks reveals that the concept of integer subtraction is usually introduced by using integer addition.
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