Two types of meiotic crossovers coexist in maize

Abstract

We apply modeling approaches to investigate the distribution of late recombination nodules in maize (Zea mays). Such nodules indicate crossover positions along the synaptonemal complex. High-quality nodule data were analyzed using two different interference models: the "statistical" gamma model and the "mechanical" beam film model. For each chromosome, we exclude at a 98% significance level the hypothesis that a single pathway underlies the formation of all crossovers, pointing to the coexistence of two types of crossing-over in maize, as was previously demonstrated in other organisms. We estimate the proportion of crossovers coming from the noninterfering pathway to range from 6 to 23% depending on the chromosome, with a cell average of approximately 15%. The mean number of noninterfering crossovers per chromosome is significantly correlated with the length of the synaptonemal complex. We also quantify the intensity of interference. Finally, we develop inference tools that allow one to tackle, without much loss of power, complex crossover interference models such as the beam film. The lack of a likelihood function in such models had prevented their use for parameter estimation. This advance will allow more realistic mechanisms of crossover formation to be modeled in the future.

Figure 1.

Interference Intensity and Proportion of Noninterfering COs Using the GS Model. Estimated values of the interference intensity (ν) in the pathway P1 and proportion of pathway P2 COs (p), obtained by maximum likelihood fitting the GS model to maize LN data for each chromosome. Horizontal and vertical bars indicate 95% confidence intervals based on 1000 simulated data sets. For chromosome 8, the upper bound of the CI on ν is 14.1.

Figure 2.

Quality of the Fits Obtained with Single-Pathway or Two-Pathway Models. Density distribution of distances between adjacent LNs in all SCs with at least two LNs for maize chromosomes 1 and 10. The x axis shows the relative genetic distance. Bars indicate experimental observations. Lines indicate simulations with no interference (NI), single-pathway gamma model (G), two-pathway gamma-sprinkling model (GS), single-pathway BF model (BF), or two-pathway BFS model (BFS). The sum of squares of differences between experimental and simulated densities are in parentheses.

Figure 3.

Electron Micrograph Showing Late Nodules on SCs. Electron micrograph of a portion of a spread of SCs from maize primary microsporocytes in pachytene showing bivalents 4, 8, and part of 5 (left) and higher magnification views (right) of SC segments with RNs (labeled with arrowheads and the same lowercase letters at the two magnifications). Each SC has been identified based on its relative length and arm ratio, and in this set, the kinetochores (K) of bivalents 4 and 8 are fused together. A halo of dispersed chromatin is visible around each SC. Bar = 5 μm (left). Magnification for the right column is 2.5 times higher.

Figure 4.

Landscape of the PLS Score to Be Maximized for Two-Dimensional Parameter Inference. Projected likelihood score (PLS; based on inter-CO distances; see text) as a function of the two parameters of the BFS model. λ, interference intensity in the interfering pathway; p, proportion of COs formed through the noninterfering pathway (P2).