Simple sequential model

Figure 10.16. Simple Sequential Model for a Tetrameric Allosteric Enzyme. The binding of a ligand (L) to a subunit changes the conformation of that particular subunit from the T (square) to the R (circle) form. This transition affects the affinity of the other subunits for the ligand.

The mechanism depicted in Fig. 13.9d is only a schematic of the basic mechanochemical cycle. Fundamental chemical transitions such as ATP hydrolysis and ADP release are not depicted because our data do not uniquely locate these transitions. In a simple sequential model, in which each subunit binds ATP, hydrolyzes it, releases products, and steps, before activating the next subunit, these processes are uniquely determined by the simple requirement that ATP is hydrolyzed before products are released. However, in a more complicated kinetic model in which the individual hydrolysis cycles of the identical subunits are interwoven, such as that depicted in Fig. 13.9, there is no longer a single unique position for these important kinetic events. ATP hydrolysis, for example, might occur immediately after the tight binding of each ATP and before the next subunits is active for ATP docking. 

The simple sequential model predicts that the fraction of catalytic chains in the R state, /r, is equal to the fraction containing bound substrate, Y. The concerted model, in contrast, predicts that/R increases more rapidly than Y as the substrate concentration is increased. The change in/R leads to the change in Y on addition of substrate, as predicted by the concerted model. 

A simple sequential model for open channel block of the general type first proposed by Adams (52) provides a good first fit to the (+)-TC data ... 

FIGURE 10.16 Simple sequential model for a tetrameric allosteric enzyme. The... 

The concerted symmetry model is much more versatile than simple sequential models described by Adair or Hill. This model is endowed by the variable values of Kr, L, and c, and therefore may provide explanations for many properties of allosteric enzymes and proteins, including... 

What are the relative merits of the simple sequential model, the KNF model, and the MWC model Let us compare the rate equations for the tetrameric allosteric enzyme, derived with the aid of each model, and establish the differences (Table 4). 

Figure 17 Global analysis of the reduced (rank = 3) matrix A to a simple sequential model generates the spectra of the chemical species A, B and C, see text.

In Fig. 4.8 we depict the probability for double ionization of helium calculated from (4.123) by neglecting the correlation part of g. It is clear that all functionals tested yield a significant improvement over the simple sequential model. Due to the incorrect asymptotic behavior of the ALDA potential, the ALDA overestimates ionization The outermost electron of helium is not sufficiently bound and ionizes too easily. 

The depth resolution Az in sputter profiling can be derived from a simple sequential layer sputtering (SLS) model, see [104], as... 

Another example is a network of parallel and sequential first-order reactions. This simple network model is often suitable for describing the technically important partial oxidation reactions. 

From the binding sequences in reaction (13.79), we can see that the general KNF model takes into account a variety of possible subunit interactions that are able to affect affinities of vacant sites. Therefore, the general KNF model is far more versatile than the simple sequential interaction model or, for that matter, than the MWC model. 

The simple sequential interaction model is more general than the concerted-symmetry model in that there are many combinations of values for a, b, and c, for which there are no equivalent values of L and c. Furthermore, the... 

Sequential models, assirming simple linear dependences in accidents, explaining accidents as... 

Three-state model, 1 1 1 Stoichiometry This simple sequential two-step unfolding reaction is described by the following equations... 

There are two basic types of unconstrained optimization algorithms (I) those reqmring function derivatives and (2) those that do not. The nonderivative methods are of interest in optimization applications because these methods can be readily adapted to the case in which experiments are carried out directly on the process. In such cases, an ac tual process measurement (such as yield) can be the objec tive function, and no mathematical model for the process is required. Methods that do not reqmre derivatives are called direc t methods and include sequential simplex (Nelder-Meade) and Powell s method. The sequential simplex method is quite satisfac tory for optimization with two or three independent variables, is simple to understand, and is fairly easy to execute. Powell s method is more efficient than the simplex method and is based on the concept of conjugate search directions. 

In Fig. 4 we compare the timings for three different models, the simple one K per processor, the wrapped algorithm, and a model where two states are assigned per processor sequentially. Note that until J = 50 the one K per processor model job uses the smallest amount of wall clock time. It is clear, however, that this method does not make efficient use of computer resources. The wrapped model, however, scales very well and outperforms the sequential two K per processor model at every / > 0, a clear illustration of the degradation of performance due to load imbalance. 

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