Why might it be advantageous for a storage polysaccharide to have a branched-chain structure instead of a linear structure?

The branched chain is more advantageous due to the increased availability of carbon ends to be hydrolyzed. The "branched" or many ended (more than two) polysaccharide molecule can liberate more free glucose for utilization than the linear polysaccharide chain with only two defined ends. All glucose molecules broken down for energy will continue to be hydrolyzed until it gets to the final monomer. If two polysaccharides with the same glucose molecules are side by side, the branched-chain structure will always be utilized faster than the linear structure.

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