Independence principle

Note that the interference of chemical reactions may alter the effective rate constant of the secondary reaction and break the independence principle of elementary chemical reactions. Moreover, under these conditions non-spontaneous reactions may proceed, which are eliminated in parallel and consecutive reactions. 

When there is doubt about an analytical result, it may be necessary to carry out a further test. This is termed a confirmatory analysis if it involves a different technique based on an independent principle. 

The block was intensified by hyperpolarization. The voltage dependence of block indicates that calcium ions bind to sodium channels at a site located 37 + 2% of the electrical distance from the outside. Sodium ions also blocked sodium channels in a voltage-dependent manner, with dissociation constants of 185 and 204 mM at -50 and 0 mV, respectively. A model consisting of a one-ion pore with four barriers and three wells can account for the observations that deviate from the independence principle,... 

Three assumptions are usually made in calculating ion current density through a membrane (a) an ion does not interact with any other ion while traversing the membrane (independence principle) (b) the membrane is homogeneous and (c) the electric field in the membrane is constant in space. The linear transport equation then leads to the Goldman-Hodgkin-Katz equation - for the I -V relation ... 

Such an assumption is not easy to evaluate quantitatively since the independence assumption is violated and special assumptions must be made about the nature of the K+ ion interactions in the channels. The possibility that there are interactions between two or more K+ within an anomalous rectification K.+ channel is supported by the experimental evidence that K+ ions do interact in the K+ channels of the squid nerve fiber membrane. i The interaction is the type expected if three or more K+ were in single file in the channel. Thus, it seems possible that the anomalous rectification properties of the K+ channels in muscle membranes have a potential energy profile similar to that in Fig. 3b but that there are usually two or three K+ in any one channel. This implies that ion transit time is two to three times larger than the time between successful collisions of ions with the channel entrances. By contrast, Na+ channels obey the independence principle implying that a Na+ ion traverses a channel before there is another successful collision of an ion with the channel entrance. The longer transit time of K+ ions could be due to deeper minima (tighter binding) in K+ channels as compared with Na+ channels. 

The confidence level in the identificadon capabiUty for gc/ir/ms is enhanced by the ability to perform computer library searching of large spectral databases. Unknown spectra are searched against reference databases and a hit quality number, indicating how well the unknown spectrum matches the library spectra, is generated. For the very small peak at 19 min in Figure 4, peak 6 in the TIC, the library search identified the component as a-phellandrene [99-83-2]y for both the ic and ms data. Because these data are complementary and generated from two completely independent principles of... 

Here, // is called efflux and /, influx. The ionic current apparently is Ii = 2uF ji id- The efflux ji linearly depends on the inside concentration but is independent of the outside concentration, while the influx depends only on the outside concentration. Thus, for instance, by varying the inside concentration we may affect the efflux while leaving the influx unchanged, provided of course the potential difference is kept constant. This means that in the Goldman approximation the effluxes and influxes are independent of each other. In the case of biological membranes it is essential to verify whether the independence principle is valid or not, for that would answer unambiguously whether the precepts of the theory are valid. Experiments have shown that there are cases where the independence principle does hold true. More than a few exceptions have also been found, however, to which the electrodiffusion theory has been found to be inapplicable. In Section 5 we will discuss this important issue in considerable detail. 

This formula, called the Ussing equation, is, furthermore, extremely important for the assessment of the fundamental principles of the electrodiffusion theory, although those unidirectional fluxes which satisfy the Ussing equation may, at the same time, not obey the independent principle. 

We will now illustrate the above rationale in application to the sodium channels of biomembranes. Since a sodium channel under physiological conditions obeys the independence principle, one has to conclude that yNa(Na) 1. Now, consider the case where all the sodium ions in the solution have been replaced with another type of cations. Without going into details of the treatment undertaken on the basis of the experimental data reported in Reference (96) and Eqs. (123)-(125), we will only cite the distribution coefficients and relative rate constants thus obtained (Table 2). 

Ion entry contains both a competitive, saturable component (in contradiction to the independence principle ) and a nonsaturable component. The nonobedience to the independence principle has been repeatedly reported and needs no further reiteration. 

When discussing the factor related to the concentration evolution of a reaction system (Figure 4.6) one should make an essential stipulation. Separating the block of species concentration dynamics from that of information about the reactivity of species in elementary chemical reactions is some kind of abstraction. It is based on the independence principle between the specific rates of elementary reactions. Sometimes this prineiple may be violated because of the following reasons ... 

---