Tracing the minimum-energy path on the free-energy surface

The free energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum energy path directly on the free energy surface (FES) at a given temperature. First, we follow the blue-moon ensemble method to derive the expression of the free energy gradient for a given RC. These derivatives are then used to find the actual minimum energy reaction path at finite temperature, in a way similar to the Intrinsic Reaction Path of Fukui on the potential energy surface [K Fukui J. Phys. Chem. 74, 4161 (1970)]. Once the path is know, one can calculate the free energy profile using thermodynamic integration. We also show that the mass-metric correction cancels for many types of constraints, making the procedure easy to use. Finally, the minimum free energy path at 300 K for the addition of the 1,1'-dichlorocarbene to ethylene is compared with a path based on a simple one-dimensional reaction coordinate. A comparison is also given with the reaction path at 0 K.Comment: Minor revisions: Citation and Equation numbers corrected. 26 pages, 6 figures, to appear in J. Chem. Phy

Vacuolar organization in the nodule parenchyma is important for the functioning of pea root nodules

Different models have been proposed to explain the operation of oxygen diffusion barrier in root nodules of leguminous plants. This barrier participates in protection of oxygen-sensitive nitrogenase, the key enzyme in nitrogen fixation, from inactivation. Details concerning structural and biochemical properties of the barrier are still lacking. Here, the properties of pea root nodule cortical cells were examined under normal conditions and after shoot removal. Microscopic observations, including neutral red staining and epifluorescence investigations, showed that the inner and outer nodule parenchyma cells exhibit different patterns of the central vacuole development. In opposition to the inner part, the outer parenchyma cells exhibited vacuolar shrinkage and formed cell wall infoldings. Shoot removal induced vacuolar shrinkage and formation of infoldings in the inner parenchyma and uninfected cells of the symbiotic tissue, as well. It is postulated that cells which possess shrinking vacuoles are sensitive to the external osmotic pressure. The cells can give an additional resistance to oxygen diffusion by release of water to the intercellular spaces