The phosphorylation-dephosphorylation cycle

The simplest kinetic model for the phosphorylation-dephosphorylation cycle assumes that the concentration of substrate S is sufficiently lower than the Michaelis-Menten constants [S] C K and K2, where K1 and K2 are the effective Michaelis-Menten constants for S for the kinase and phosphatase, respectively. Similarly, [S ] C K and K, where K and are the effective Michaelis-Menten constants 

Equivalently, we model the system with mass action kinetics as  

Equation (5.6) is the fundamental equation for a phosphorylation-dephosphorylation switch. The parameter 6 is the control parameter that represents the ratio of the apparent kinase activity to that of phosphatase K catalyzes phosphorylation and P catalyzes dephosphorylation. The parameter // characterizes the level of S in the absence of the kinase K (when 0 = 0) /i determines the basal activity and is usually very small. 

Equation (5.6) indicates that if there is no available free energy for ATP hydrolysis (y = 1) then 

The inequality indicates that the optimal y for the maximal AOS is when /i = -j=. Substituting AGatp = RT In y, we have the optimal AOS 

---

For the purpose of discussion, crossbridge regulation can be split into three overlapping sets of reactions (a) the Ca-calmodulin cascade (MLCK activation), (b) the phosphorylation-dephosphorylation cycle (the Four State Model), and (c) actin-myosin cycle (chemomechanical transduction). 

The control of glycogen phosphorylase by the phosphorylation-dephosphorylation cycle was discovered in 1955 by Edmond Fischer and Edwin Krebs50 and was at first regarded as peculiar to glycogen breakdown. However, it is now abundantly clear that similar reactions control most aspects of metabolism.51 Phosphorylation of proteins is involved in control of carbohydrate, lipid, and amino acid metabolism in control of muscular contraction, regulation of photosynthesis in plants,52 transcription of genes,51 protein syntheses,53 and cell division and in mediating most effects of hormones. 

Figure 17-14 (A) The reductive carboxylation system used in reductive pentose phosphate pathway (Calvin-Benson cycle). The essential reactions of this system are enclosed within the dashed box. Typical subsequent reactions follow. The phosphatase action completes the phosphorylation-dephosphorylation cycle. (B) The reductive pentose phosphate cycle arranged to show the combining of three C02 molecules to form one molecule of triose phosphate. Abbreviations are RCS, reductive carboxylation system (from above) A, aldolase, Pase, specific phosphatase and TK, transketolase.

Figure 5.4 Switch-like behavior of the phosphorylation-dephosphorylation cycle. The left panel illustrates the off position (unphosphorylated) of the biochemical switch, in which the phosphatase activity is higher than the kinase activity. When the kinase activity exceeds the phosphatase activity, as in the right panel, the biochemical switch is in the opposite state.

In analyzing the temporal behavior of a biochemical switching molecule, we can study either of the equivalent models of the phosphorylation-dephosphorylation cycle or the GTPase signaling module. In particular, we are interested in the duration of each activation event at the single-molecule level. 

Consider a chemical system as shown in fig. 7.1. Mechanisms of this type are common in biochemical networks. For example, the subnetwork of fig. 7.1 containing S3 to S5 is based on a simple model of fructose interconversion in glycolysis [2] (see fig. 1.2) and the subnetwork composed of Se to S7 is similar to the phosphorylation/dephosphorylation cycles found in cyclic cascades [3,4]. As an aside, this mechanism performs the function... 

Although the fundamental chemomechanical transduction processes seem to be the same in all types of vertebrate muscle, contraction in smooth muscle is characterized by much greater involvement of enzymatically catalyzed control reactions. In smooth muscle the control reactions themselves involve the use of phosphorylation-dephosphorylation cycles. Moreover, they are futile in the sense they cause the expenditure of bond energy without a tangible work resultant, i.e., compounds synthesized or external work done. 

The two-step reduction of HMG-CoA to mevalonate (Fig. 22-1, step a)n 15 is highly controlled, a major factor in regulating cholesterol synthesis in the human liver.121617 The N-terminal portion of the 97-kDa 888-residue mammalian FlMG-CoA reductase is thought to be embedded in membranes of the ER, while the C-terminal portion is exposed in the cytoplasm.16 Tire enzyme is sensitive to feedback inhibition by cholesterol (see Section D, 2). The regulatory mechanisms include a phosphorylation-dephosphorylation cycle and control of both the rates of synthesis and of proteolytic degradation of this key en-... 

Yoda, A. Yoda, S. (1987). Two different phosphorylation-dephosphorylation cycles of Na,K-ATPase proteoliposomes accompanying Na+ transport in the absence of K+. J. Biol. Chem. 262,110-115. 

If we concentrate on one particular component of this map - the phosphorylation of PI(4,5)P2 to PI(3,4,5)P3 by PI3K and the dephosphorylation of PI(3,4,5)P3 to PI(4,5)P2 by F TEN, we can study the detailed enzyme kinetic scheme of this so-called phosphorylation-dephosphorylation cycle, which is illustrated in Figure 5.2. This illustrated cycle represents a ubiquitous module in biochemical signaling, ft could, for example, represent the phosphorylation of mitogen-activation protein kinase (MAPK) by MAPK kinase (MAPKK) and dephosphorylation of MAPK by MAPK phosphatase (MKP). 

Figure 5.2 A typical cellular biochemical switch consisting of a phosphorylation-dephosphorylation cycle. The substrate molecule S may be a protein or other signaling molecule. If S is a protein then the phosphorylation of S is catalyzed by a protein kinase (K) and the dephosphorylation is catalyzed by a protein phosphatase (P). The entire cycle is accompanied by the reaction ATP ADP+PI. In the context of mitogen-activation protein kinase pathway, S, K, and P correspond to MAPK, MAPKK, and MKP, respectively. In the context of the example from the PIP3 pathway, the kinase is PI3K and the phosphatase is PTEN.

Figure 5.3 Phosphorylation-dephosphorylation cycle activation as a function of the activating signal 6 and available free energy y. The solid lines and dashed lines are without and with enzyme saturation, i.e., Equations (5.6) and (5.18), respectively. In both cases, from top to bottom y = 1010,104, and 103. All computations are done with /x = 0.001, and for the dashed lines = - = 0.01. If y = 1, then both the solid and dashed lines will be strictly horizontal.

Ultrasensitivity and the zeroth-order phosphorylation-dephosphorylation cycle... 

Consider a phosphorylation-dephosphorylation cycle for a substrate protein (S) with saturated kinase (K) but unsaturated, first-order, phosphatase (P). For simplicity, we neglect the cofactors such as ATP, ADP, and PI ... 

Regulation of pyruvate dehydrogenase (PD) by inactivation and reactivation by a non-cAMP-dependent phosphorylation-dephosphorylation cycle. Although PD kinase phosphorylates three specific seryl residues in the a-subunit of PD, phosphorylation at any of these sites inactivates PD. The kinase and the phosphatase are under the influence of several regulators, and the dephospho-active PD is also regulated by end products. 0 = Activation 0 = inhibition E2 = dihydrolipoyl transacetylase E3 = dihydrolipoyl dehydrogenase. 

---