A Fundamental Trade-off in Covalent Switching and Its Circumvention by Enzyme Bifunctionality in Glucose Homeostasis

Abstract

Background: Covalent modification cycles are widely used as regulatory switches. Results: Mathematical analysis reveals, under very general assumptions, an unavoidable trade-off between switching efficiency and cell-to-cell coherence. Conclusion: Enzyme bifunctionality offers a way to circumvent this trade-off. Significance: This may explain the bifunctionality of PFK-2/FBPase-2 in controlling the switch between glycolysis and gluconeogenesis in the mammalian liver.Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/ FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.An enzyme-catalyzed modification cycle is illustrated in Fig. 1A. The forward enzyme, E, catalyzes the covalent addition of an M moiety (phosphoryl, methyl, acetyl, etc.), carried by the donor, D-M, to form the modified substrate, S 1 , from the unmodified substrate, S 0 . The reverse enzyme, F, catalyzes the removal of M, returning S 1 to S 0 . Background metabolic processes continually replenish D-M from D and M. The substrate, S, can be any molecule, protein or otherwise.Such cycles can function as biological switches, in which the proportion of S 1 at steady state can be varied from low ("off") to high ("on") by altering properties of the cycle, such as the enzyme levels (1, 2). They are regarded as core motifs in cellular information processing (3,4) and have been the subject of much analysis (5-9).Application of these results to specific biological examples has been hampered, however, by the universal assumption that the enzymes E and F follow the Mich...

The Significance of the Bifunctional Kinase/Phosphatase Activities of Diphosphoinositol Pentakisphosphate Kinases (PPIP5Ks) for Coupling Inositol Pyrophosphate Cell Signaling to Cellular Phosphate Homeostasis

“…invariance to quantitative changes of the system's components, including substrate concentration; and (c) increased "parametric sensitivity," that is, a situation in which signaling output is amplified following relatively small changes in the concentration of a particular parameter, such as an enzyme regulator (19,21). However, the significance of these phenomena in vivo is dictated by the catalytic parameters of the mutually antagonistic domains (19,21).…”

“…However, in general, such competing catalytic activities are hosted by separate proteins for the purposes of compartmentalization and for promoting signaling fidelity (20). Only in rare cases have these apparent benefits been selected against in order that the mutually antagonistic catalytic activities co-exist within a single protein (19,21,22). The PPIP5K family is one of these exceptions; representatives from humans, yeasts, and plants contain kinase and phosphatase domains (16), indicating that this bifunctionality has survived at least 1.5 billion years of evolutionary pressure (23).…”

“…1 and 2). Kinase/phosphatase and other covalent modification cycles are a nexus for regulatory inputs into metabolic and signaling pathways (18); in fact this phenomenon is considered a core motif in the field of systems biology (19). However, in general, such competing catalytic activities are hosted by separate proteins for the purposes of compartmentalization and for promoting signaling fidelity (20).…”

Laplacian Dynamics with Synthesis and Degradation

“…The framework computes steady states of Laplacian dynamics associated with a (biological) network, which has applications in many diverse fields of biology such as enzyme kinetics, pharmacology and receptor theory, protein post-translation modification Xu and Gunawardena (2012); Dasgupta et al (2014); Thomson and Gunawardena (2009a, b). The main advantage of the framework is that it can be applied to systems in thermodynamic equilibrium as well as the systems remaining far from thermodynamic equilibrium.…”

MAPK’s networks and their capacity for multistationarity due to toric steady states

“…Computational algebra and algebraic geometry provide powerful tools for studying these solutions [4], and these tools have recently been used to gain new biological insights, for instance in [5,6,21,31,32]. The rate constants can now be treated as symbolic parameters, whose numerical values do not need to be known in advance.…”