banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Kinetic models for mechanoenzymes: Structural aspects under large loads
Rent this article for
View: Figures


Image of FIG. 1.
FIG. 1.

Examples of well-known kinetic models for enzymes: (a) sequential -state model; (b) parallel-chain model with one sequential -state pathway and a second -state pathway. Extensions yielding tractable models: (c) a side chain attached to a state () of a kinetic scheme; (d) a looped side chain at a state ().

Image of FIG. 2.
FIG. 2.

Example of a general -state enzymatic cycle. The various dots and circles and the square labeled [0] represent the biochemical states () of the enzyme, while the bonds (or links) connect states that can be reversibly transformed into one another. Those states which have transitions to more than two other distinct states are nodes and are indicated by open circles, distinguishing them from the remaining states marked by solid dots. The waiting (or initial) state is [0].

Image of FIG. 3.
FIG. 3.

The same enzymatic cycle depicted in Fig. 2 but now unfolded into a (potentially infinite) periodic chain of which only two unit cells, and , are shown. The absorbing boundaries introduced on the left and on the right at states and serve to cut the chain and generate a two-cell representation that then specifies a first-passage problem. This enables the efficient calculation of the average characteristics of the enzymatic cycles.

Image of FIG. 4.
FIG. 4.

Illustration of a bridge () connecting nodes () and () with associated bridge sites/states, , where the first and last bridge states are identified with the nodes () and (). The probability flow properties of the bridges are used in the algorithm to reduce the complexity of models of interest.

Image of FIG. 5.
FIG. 5.

Reduction of the basic sequential model: (a) cyclic representation; (b) two-cell representation with absorbing boundaries and mean occupation times indicated; (c) reduced scheme with effective rates, and , see text. Note the individual occupation times, and , indicated.

Image of FIG. 6.
FIG. 6.

Reduction of the parallel-chain model: (a) cyclic representation; (b) two-cell representation with absorbing boundaries; (c) reduced scheme with the parallel effective rates: , , , and ; (d) final reduction to an -state model with effective rates and .

Image of FIG. 7.
FIG. 7.

A side chain extending from a state(). The integrated probability flow along a side chain vanishes.

Image of FIG. 8.
FIG. 8.

A looped side chain attached to a state (). This motif like the side chain in Fig. 7 is an example of an additional structure that does not contribute to the integrated probability flow distribution.

Image of FIG. 9.
FIG. 9.

The basic divided-pathway model: (a) cyclic representation; (b) two-cell representation with absorbing boundaries; (c) a series of steps to reduce the original kinetic scheme to an sequential model and, thence, to the simplest model with appropriate effective rates, see text.

Image of FIG. 10.
FIG. 10.

Examples of small enzymatic cycles belonging to the class of divided-pathway models; compare with Fig. 9. The mean properties of all these cycles can be extracted explicitly from the unified solution presented in Sec. V, see Eqs. (5.5)–(5.15).


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Kinetic models for mechanoenzymes: Structural aspects under large loads