Question

An amylose chain is 5000 glucose units long. At how many places must it be cleaved to reduce the average length to 2500 units? To 1000 units? To 200 units? What percentage of the glycosidic links are hydrolyzed in each case? (Even partial hydrolysis can drastically alter the physical properties of polysaccharides and thus affect their structural role in organisms.)

Short answer

1 cleavage for 2500 units, 4 cleavages for 1000 units, and 24 cleavages for 200 units. Hydrolysis percentages: 0.02% for 2500 units, 0.08% for 1000 units, and 0.48% for 200 units.

Step-by-step solution

Understand the problem

Identify the initial length of the amylose chain and its desired average lengths for each case. The initial length given is 5000 glucose units.

Calculate the number of cleavages needed for each average length

To reduce the average length to a given value, we divide the total number of units by the desired average length. Then subtract 1 to account for the segments created.

Step 2.1: For 2500 units

We need to calculate the number of cleavage points to achieve an average length of 2500 units: \[ \text{number of segments} = \frac{5000}{2500} = 2 \] Since we need segments, cleavages required: \[ 2 - 1 = 1 \]

Step 2.2: For 1000 units

We need to calculate the number of cleavage points to achieve an average length of 1000 units: \[ \text{number of segments} = \frac{5000}{1000} = 5 \] Since we need segments, cleavages required: \[ 5 - 1 = 4 \]

Step 2.3: For 200 units

We need to calculate the number of cleavage points to achieve an average length of 200 units: \[ \text{number of segments} = \frac{5000}{200} = 25 \] Since we need segments, cleavages required: \[ 25 - 1 = 24 \]

Calculate the percentages of hydrolyzed glycosidic links

To find the percentage of hydrolyzed glycosidic links for each case, calculate the ratio of cleavages to the total number of glucose units and multiply by 100.

Step 3.1: For 2500 units

The percentage of glycosidic links hydrolyzed is: \[ \frac{1}{5000} \times 100 = 0.02\text{\text{%}} \]

Step 3.2: For 1000 units

The percentage of glycosidic links hydrolyzed is: \[ \frac{4}{5000} \times 100 = 0.08\text{\text{%}} \]

Step 3.3: For 200 units

The percentage of glycosidic links hydrolyzed is: \[ \frac{24}{5000} \times 100 = 0.48\text{\text{%}} \]

Key concepts

Glycosidic Bonds

Glycosidic bonds are essential for forming polysaccharides, which are long chains of monosaccharide units. These bonds are covalent and occur when a carbohydrate molecule binds to another group, which could be another carbohydrate.

Glycosidic bonds are formed through a dehydration reaction, where a water molecule is released as a result. For example, in amylose, a type of polysaccharide, glucose molecules are linked via glycosidic bonds.

The stability of polysaccharides stems largely from these glycosidic bonds, determining the physical properties like solubility and structure of the molecule.

Enzyme Cleavage

Enzyme cleavage is crucial for breaking down polysaccharides into smaller units. Enzymes known as glycosidases specifically target glycosidic bonds to hydrolyze them, a process requiring water.

This enzymatic hydrolysis is vital in biological processes like digestion, where enzymes break down polysaccharides into simple sugars that can be absorbed by the body. For example, amylase, an enzyme found in saliva and the pancreas, cleaves amylose into smaller glucose units.

Understanding enzyme specificity and functionality is critical in biochemistry and medicine, as certain enzymes can target specific glycosidic bonds, affecting how substances like polysaccharides function and are metabolized.

Polysaccharide Structure

Polysaccharides are complex carbohydrates composed of long chains of monosaccharide units. These units are bonded together by glycosidic bonds, giving the polysaccharide its unique structure and properties.

The structure of a polysaccharide can range from a simple linear chain to highly branched forms. Amylose, for instance, is a linear polymer made entirely of glucose units. In contrast, amylopectin, another form of starch, is branched.

The structure affects the polysaccharide's function and physical properties. Linear chains like amylose tend to form helical structures and are less soluble in water. On the other hand, branched polysaccharides like glycogen are highly soluble and rapidly mobilized by enzymes. Understanding these structural differences is important for fields ranging from nutrition to materials science, as they influence how polysaccharides behave and are used in various applications.