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The pairing of homologous chromosomes (homologs) in meiosis is essential for distributing the correct numbers of chromosomes into haploid gametes. In budding yeast, pairing depends on the formation of 150 to 200 Spo11-mediated double-strand breaks (DSBs) that are distributed among 16 homolog pairs, but it is not known if all, or only a subset, of these DSBs contribute to the close juxtaposition of homologs. Having established a system to measure the position of fluorescently tagged chromosomal loci in three-dimensional space over time, we analyzed locus trajectories to determine how frequently and how long loci spend colocalized or apart. Continuous imaging revealed highly heterogeneous cell-to-cell behavior of foci, with the majority of cells exhibiting a “mixed” phenotype where foci move into and out of proximity, even at late stages of prophase, suggesting that the axial structures of the synaptonemal complex may be more dynamic than anticipated. The observed plateaus of the mean-square change in distance (MSCD) between foci informed the development of a biophysical model of two diffusing polymers that captures the loss of centromere linkages as cells enter meiosis, nuclear confinement, and the formation of Spo11-dependent linkages. The predicted number of linkages per chromosome in our theoretical model closely approximates the small number (approximately two to four) of estimated synapsis-initiation sites, suggesting that excess DSBs have negligible effects on the overall juxtaposition of homologs. These insights into the dynamic interchromosomal behavior displayed during homolog pairing demonstrate the power of combining time-resolved in vivo analysis with modeling at the granular level. 

Density functional theory (DFT) is widely used in transition-metal chemistry, yet essential properties such as spin-state energetics in transition-metal complexes (TMCs) are well known to be sensitive to the choice of the exchange-correlation functional. Increasing the amount of exchange in a functional typically shifts the preferred ground state in first-row TMCs from low-spin to high-spin by penalizing delocalization error, but the effect on properties of second-row complexes is less well known. We compare the exchange sensitivity of adiabatic spin-splitting energies in pairs of mononuclear 3d and 4d mid-row octahedral transition metal complexes. We analyze hundreds of complexes assembled from four metals in two oxidation states with ten small monodentate ligands that span a wide range of field strengths expected to favor a variety of ground states. We observe consistently lower but proportional sensitivity to exchange fraction among 4d TMCs with respect to their isovalent 3d TMC counterparts, leading to the largest difference in sensitivities for the strongest field ligands. The combined effect of reduced exchange sensitivities and the greater low-spin bias of most 4d TMCs means that while over one-third of 3d TMCs change ground states over a modest variation (ca. 0.0–0.3) in exchange fraction, almost no 4d TMCs do. Differences in delocalization, as judged through changes in the metal–ligand bond lengths of spin states, do not explain the distinct behavior of 4d TMCs. Instead, evaluation of potential energy curves in 3d and 4d TMCs reveals that higher exchange sensitivities in 3d TMCs are likely due to the opposing effect of exchange on the low-spin and high-spin states, whereas the effect on both spin states is more comparable in 4d TMCs.