The reaction force and the transition region of a reaction

The reaction force F(R) and the position-dependent reaction force constant κF(R) are defined by F(R)=-∂V(R)/∂R and κ(R)=∂²V(R)/∂R², where V(R) is the potential energy of a reacting system along a coordinate R. The minima and maxima of F(R) provide a natural division of the process into several regions. Those in which F(R) is increasing are where the most dramatic changes in electronic properties take place, and where the system goes from activated reactants (at the force minimum) to activated products (at the force maximum). κ(R) is negative throughout such a region. We summarize evidence supporting the idea that a reaction should be viewed as going through a transition region rather than through a single point transition state. A similar conclusion has come out of transition state spectroscopy. We describe this region as a chemically-active, or electronically-intensive, stage of the reaction, while the ones that precede and follow it are structurally-intensive. Finally, we briefly address the time dependence of the reaction force and the reaction force constant.     

A finite viscoelastic–plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress–strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress–strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.     

Effects of Internal K+ and ABA on the Voltage- and Time-dependence of the Outward K+-rectifier in Vicia Guard Cells

One of the main effects of abscisic acid (ABA) is to induce net loss of potassium salts from guard cells enabling the stomata to close. K⁺ is released from the vacuole into the cytosol and then to the extracellular space. The effects of increasing cytosolic K⁺ on the voltage- and time-dependence of the outwardly rectifying K⁺-current (I _K,out) in guard cell protoplasts (GCP) was examined in the whole-cell configuration of the patch-clamp technique. The same quantitative analysis was performed in the presence of ABA at different internal K⁺ concentrations ([K⁺] _i ). Varying [K⁺] _i in the patch pipette from 100 to 270 mm increased the magnitude of I _K,out in a nonlinear manner and caused a negative shift in the midpoint (V _0.5) of its steady-state activation curve. External addition of ABA (10–20 μm) also increased the magnitude of I _K,out at all [K⁺] _i , but caused a shift in V _0.5 of the steady-state activation curve only in those GCP loaded with 150 mm internal K⁺ or less. Indeed, V _0.5 did not shift upon addition of ABA when the [K⁺] _i was above 150 mm and up to 270 mm, i.e., the shift in V _0.5 caused by ABA depended on the [K⁺] _i . Both increase in [K⁺] _i and external addition of ABA, decreased (by ≈ 20%) the activation time constant (τ _n ) of I _K,out. The small decrease in τ _n , in both cases, was found to be independent of the membrane voltage. The results indicate that ABA mimics the effect of increasing cytoplasmic K⁺, and suggest that ABA may increase I _K,out and alter V _0.5 of its steady-state activation curve via an enhancement in cytosolic K⁺. This report describes for the first time the effects of [K⁺] _i on the voltage- and time-dependence of I _K,out in guard cells. It also provides an explanation for the quantitative (total membrane current) and qualitative (current kinetics) differences found between intact guard cells and their protoplasts. Received: 1 December 1995/Revised: 8 May 1996