Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

The Mechanism of Rhythmic Ethylene Production in Sorghum. The Role of Phytochrome B and Simulated Shading1

Mutant sorghum (Sorghum bicolor [L.] Moench) deficient in functional phytochrome B exhibits reduced photoperiodic sensitivity and constitutively expresses a shade-avoidance phenotype. Under relatively bright, high red:far-red light, ethylene production by seedlings of wild-type and phytochrome B-mutant cultivars progresses through cycles in a circadian rhythm; however, the phytochrome B mutant produces ethylene peaks with approximately 10 times the amplitude of the wild type. Time-course northern blots show that the mutant's abundance of the 1-aminocyclopropane-1-carboxylic acid (ACC) oxidase mRNA SbACO2 is cyclic and is commensurate with ethylene production, and that ACC oxidase activity follows the same pattern. Both SbACO2 abundance and ACC oxidase activity in the wild-type plant are very low under this regimen. ACC levels in the two cultivars did not demonstrate fluctuations coincident with the ethylene produced. Simulated shading caused the wild-type plant to mimic the phenotype of the mutant and to produce high amplitude rhythms of ethylene evolution. The circadian feature of the ethylene cycle is conditionally present in the mutant and absent in the wild-type plant under simulated shading. SbACO2 abundance in both cultivars demonstrates a high-amplitude diurnal cycle under these conditions; however, ACC oxidase activity, although elevated, does not exhibit a clear rhythm correlated with ethylene production. ACC levels in both cultivars show fluctuations corresponding to the ethylene rhythm previously observed. It appears that at least two separate mechanisms may be involved in generating high-amplitude ethylene rhythms in sorghum, one in response to the loss of phytochrome B function and another in response to shading.

Water Deficit and Spatial Pattern of Leaf Development. Variability in Responses Can Be Simulated Using a Simple Model of Leaf Development1

We analyzed the effect of short-term water deficits at different periods of sunflower (Helianthus annuus L.) leaf development on the spatial and temporal patterns of tissue expansion and epidermal cell division. Six water-deficit periods were imposed with similar and constant values of soil water content, predawn leaf water potential and [ABA] in the xylem sap, and with negligible reduction of the rate of photosynthesis. Water deficit did not affect the duration of expansion and division. Regardless of their timing, deficits reduced relative expansion rate by 36% and relative cell division rate by 39% (cells blocked at the G0-G1 phase) in all positions within the leaf. However, reductions in final leaf area and cell number in a given zone of the leaf largely differed with the timing of deficit, with a maximum effect for earliest deficits. Individual cell area was only affected during the periods when division slowed down. These behaviors could be simulated in all leaf zones and for all timings by assuming that water deficit affects relative cell division rate and relative expansion rate independently, and that leaf development in each zone follows a stable three-phase pattern in which duration of each phase is stable if expressed in thermal time (C. Granier and F. Tardieu [1998b] Plant Cell Environ 21: 695–703).