Directional flow of information and energies is characteristic of many types of biochemical reactions, for instance, ion transport, energy coupling during ATP synthesis, and muscle contraction. Can a fluctuating force field, or a noise, induce such a directional flux? Previous work has shown that Na,K-ATPase of human erythrocyte can absorb free energy from an externally applied random-telegraph-noise (RTN) electric field to pump Rb+ up its concentration gradient. However, the RTN field used in these experiments was constant in amplitude and would not mimic fluctuating electric fields of a cell membrane. Here we show that electric fields which fluctuate both in life time and in amplitude, and thus, better mimicking the transmembrane electric fields of a cell, can also induce Rb+ pumping by Na,K-ATPase. A Gaussian-RTN-electric field, or a field with amplitude fluctuating according to the Gaussian distribution, with varied standard deviation (sigma), induced active pumping of Rb+ in human erythrocyte, which was completely inhibited by ouabain. Increased values for sigma led to a nonmonotonic reduction in pumping efficiency. A general formula for calculating the ion transport in a biochemical cycle induced by fluctuating electric field has been derived and applied to a simple four-state electroconformational coupling (ECC) model. It was found that the calculated efficiency in the energy coupling decreased with increasing sigma value, and this effect was relatively small and monotonic, whereas experimental data were more complex: monotonic under certain sets of conditions but nonmonotonic under different sets. The agreement in general features but disagreement in some fine features suggest that there are other properties of the electric activation process for Na,K-ATPase that cannot be adequately described by the simple ECC model, and further refinement of the ECC model is required.
We were very interested in the paper by Chen et al. (2001) on the modeling of the kinetic and equilibrium binding of myosin S1 to regulated actin filaments, containing actin, tropomyosin, and troponin (ATmTn). This is a formidable task, and the authors of the paper are to be commended on their considerable achievement. They have made a detailed comparison of the Hill et al. two-state model (1980) (referred to as the Hill model) and the McKillop and Geeves three-state model (1993) (referred to as the M and G model) and concluded that both can adequately describe the data. This could be interpreted, using Occam's razor, that a three-state model is not necessary. Although we would not wish to disagree with their calculations, we wish to point out that the authors: 1) have considered only some of the available data to test the two models; 2) have not compared the ability of the models to address fundamental issues in thin filament regulation; and 3) have not related the mathematical parameters of the models to the properties of the components. We believe that the M and G model is a more useful model compared with the Hill model because: 1) the three states of ATmTn (Blocked-Closed-Open (M)) can be more readily related to three positions of Tm observed on actin, although the model was developed independently of structural information. 2) The two-step binding of myosin to actin can easily be integrated into the three states, including the coupling between the isomerization step and the CO equilibrium. 3) It is more readily testable because the parameters that are used can be directly related to the properties of Tm, the regulatory component (such as strength of end-to-end interactions and flexibility which depend on amino acid sequence), and the modification of Tm function by Tn and Ca 2ϩ , the allosteric components of the thin filament. 4) The M and G model is a complete biochemical model that involves equilibria between states that are affected by Ca 2ϩ and myosin, rather than states that are defined by the absence or presence of Ca 2ϩ or myosin. A given state, therefore, may not be fully occupied under a given set of experimental conditions (Table 1). 5) The M and G model can explain a much larger set of data, which were not considered in the Chen et al. (2001) paper. These issues are expanded upon as follows: The properties of the two-and three-states must be defined. Chen et al. described the Hill model as having two states, each with three substates (0, 1, and 2 Ca 2ϩ bound for a total of six states). The M and G model on the other hand is described as a three-state model. Unless the meaning of
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