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Phosphate Backbone

The repeating sugar-phosphate linkage that forms the structural foundation of both DNA and RNA polymers.
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The statement of the theorem

Let SiS_i be the sugar unit and PiP_i be the phosphate group at position ii. The backbone is a polymer sequence defined by the repeating linkage Si−Pi−Si+1S_i - P_i - S_{i+1}. The phosphate group PiP_i links the 5′5'-hydroxyl group of SiS_i to the 3′3'-hydroxyl group of Si+1S_{i+1}. The chemical structure is formalized by the phosphodiester bond formation:\nSi−O−Pi−O−Si+1S_i - O - P_i - O - S_{i+1} \nwhere PiP_i is represented by the phosphate group PO2−\text{PO}_2^-. The backbone connectivity is defined by the sequence of linkages L={(S1,P1,S2),(S2,P2,S3),…,(SN−1,PN−1,SN)}\mathcal{L} = \{(S_1, P_1, S_2), (S_2, P_2, S_3), \dots, (S_{N-1}, P_{N-1}, S_N)\}. The overall charge density ρcharge\rho_{charge} is determined by the negative charges of the phosphate groups.