Topology-aware thermodynamics for DNA probe design under fixed stringency: Retained paired boxes link mismatch placement, nearest-neighbor stability and room-temperature diagnostic specificity

DNA probe specificity is usually screened by mismatch number, melting temperature and full-duplex nearest-neighbor free energy. These scalar quantities are necessary but obscure the spatial organization of pairing: an off-target can retain one long paired box or split the same matches into short fragments. We define thermodynamics without topology as scalar full-duplex nearest-neighbor DeltaG and thermodynamics with topology as redistribution of nearest-neighbor contributions over retained paired boxes. The practical score family begins with edge-corrected effective complementary islands, extends to the count Nbox(L,k) of contiguous boxes of length at least k, and culminates in Zbox,NN(k,T), a retained-box partition weighted by nearest-neighbor stability. Reanalysis of published mismatch-probe datasets shows why the distinction matters: distributed or staggered mismatches are far more disruptive than clustered mismatches at comparable burden; 50-mer mismatch probes show distribution- and temperature-dependent residual signal; maximum perfect-match length explains a substantial fraction of 60-mer mismatch signal ratios; and zipper/partition-function modeling explains position-dependent mismatch discrimination. An Affymetrix fixed-mismatch subset and an ambient-temperature HPV probe panel provide independent control and diagnostic context. The framework offers an auditable rule for fixed-stringency probe design: preserve intended retained continuity, fragment the strongest off-target retained box, then validate in the final buffer and readout.