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The telomeric DNA, a distal region of eukaryotic chromosome containing guanine-rich repetitive sequence of (TTAGGG)n, has been shown to adopt higher-order structures, specifically G-quadruplexes (G4s). Previous studies have demonstrated the implication of G4 in tumor inhibition through chromosome maintenance and manipulation of oncogene expression featuring their G-rich promoter regions. Besides higher order structures, several regulatory roles are attributed to DNA epigenetic markers. In this work, we investigated how the structural dynamics of a G-quadruplex, formed by the telomeric sequence, is affected by inosine, a prevalent modified nucleotide. We used the standard (TTAGGG)_ntelomere repeats with guanosine mutated to inosine at each G position. Sequences (GGG)₄, (IGG)₄, (GIG)₄, (GGI)₄, (IGI)₄, (IIG)₄, (GII)_4,and (III)₄, bridged by TTA linker, are studied using biophysical experiments and molecular modeling. The effects of metal cations in quadruplex folding were explored in both Na⁺and K⁺containing buffers using CD and UV-melting studies. Our results show that antiparallel quadruplex topology forms with the native sequence (GGG)₄and the terminal modified DNAs (IGG)₄and (GGI)₄in both Na⁺and K⁺containing buffers. Specifically, quadruplex hybrid was observed for (GGG)₄in K⁺buffer. Among the other modified sequences, (GIG)₄, (IGI)₄and (GII)₄show parallel features, while (IIG)₄and (III)₄show no detectable conformation in the presence of either Na⁺or K⁺. Our studies indicate that terminal lesions (IGG)₄and (GGI)₄may induce certain unknown conformations. The folding dynamics become undetectable in the presence of more than one inosine substitution except (IGI)₄in both buffer ions. In addition, both UV melting and CD melting studies implied that in most cases the K⁺cation confers more thermodynamic stability compared to Na⁺. Collectively, our conformational studies revealed the diverse structural polymorphisms of G4 with position dependent G-to-I mutations in different ion conditions. 

As a class of approximate measurement approaches, sketching algorithms have significantly improved the estimation of network flow information using limited resources. While these algorithms enjoy sound error-bound analysis under worst-case scenarios, their actual errors can vary significantly with the incoming flow distribution, making their traditional error bounds too "loose" to be useful in practice. In this paper, we propose a simple yet rigorous error estimation method to more precisely analyze the errors for posterior sketch queries by leveraging the knowledge from the sketch counters. This approach will enable network operators to understand how accurate the current measurements are and make appropriate decisions accordingly (e.g., identify potential heavy users or answer "what-if" questions to better provision resources). Theoretical analysis and trace-driven experiments show that our estimated bounds on sketch errors are much tighter than previous ones and match the actual error bounds in most cases.