Stochasticity and positive feedback enable enzyme kinetics at the membrane to sense reaction size

Abstract

Here, we present detailed kinetic analyses of a panel of soluble lipid kinases and phosphatases, as well as Ras activating proteins, acting on their respective membrane surface substrates. The results reveal that the mean catalytic rate of such interfacial enzymes can exhibit a strong dependence on the size of the reaction system—in this case membrane area. Experimental measurements and kinetic modeling reveal how stochastic effects stemming from low molecular copy numbers of the enzymes alter reaction kinetics based on mechanistic characteristics of the enzyme, such as positive feedback. For the competitive enzymatic cycles studied here, the final product—consisting of a specific lipid composition or Ras activity state—depends on the size of the reaction system. Furthermore, we demonstrate how these reaction size dependencies can be controlled by engineering feedback mechanisms into the enzymes.

A two-component protein condensate of the EGFR cytoplasmic tail and Grb2 regulates Ras activation by SOS at the membrane

“…Thus, in addition to recruitment of more SOS to the condensates (e.g., through multivalent avidity effects), each SOS FL molecule also activated more Ras over the same time compared with uncondensed state of the EGFR TAIL . Also prominent in the fastest overall reaction trajectories from each SOS FL concentration was RasGTP-driven positive feedback, which is evidenced by the positive curvature in the trajectories ( 20 , 41 , 52 ). In these reactions, a constant catalytic rate from SOS FL would have resulted in a Ras activation trajectory with strictly negative curvature as progressively less RasGDP would have been available to be activated.…”

Bimodality in Ras signaling originates from processivity of the Ras activator SOS without deterministic bistability

“…If there were a stable deterministic bistability underlying the bimodal signaling behavior, then this would still be observed in the larger size corrals—appearing as spontaneously separating domains of Ras activity state [see, for example, the PIP 1 /PIP 2 lipid patterns generated from deterministic bistability described in ( 33 )]. Instead, the observation of robust bimodality in small corrals and unimodality in larger corrals indicates a stochastic origin to the bimodal behavior in a system that is intrinsically monostable ( 33 , 34 ). This monostability is further evidenced by the absence of hysteresis in Ras activation during experiments conducted on an unconstrained bilayer, representing the system under deterministic conditions (fig.…”

“…In many cases, such as in T cell activation, signaling reactions are confined to localized signaling clusters on the membrane, further reducing the copy numbers of participating molecules ( 53 , 54 ). Spatial confinement and low molecular copy numbers lead to substantial stochastic variation that effectively changes the laws of chemistry within the cell ( 55 ), sometimes enhancing sensitivity ( 56 ), inducing bistability ( 28 , 57 , 58 ), or even changing the outcome of a competitive signaling reaction ( 33 , 34 ).…”

“…However, this conjecture is based exclusively on computational modeling and indirect measurements in cellular systems: Experimental observation of bimodality in the isolated Ras activation response has not previously been reported (31). One contributing factor to the challenges presented by Ras is the unexpected complexity that can emerge from competitive enzymatic reaction cycles, especially when a membrane is involved and systems are spatially confined (28,(32)(33)(34)(35).…”

Membrane-mediated dimerization potentiates PIP5K lipid kinase activity

“…The membrane-mediated dimerization also amplifies stochastic fluctuations in kinase reaction velocity. In the context of spatial confinement, these magnified fluctuations facilitate mechanisms such as the recently reported stochastic geometry sensing, in which bistability and even the deterministic outcome of a competitive reaction may depend on system size ( Hansen et al, 2019 ; Lee et al, 2021 ). Together, our results highlight a mechanism by which PI(4,5)P 2 binding and membrane-mediated dimerization create a broad dynamic range of PIP5K activities that cells can potentially leverage to tune the concentration and spatial distribution of PI(4,5)P 2 lipids on cellular membranes.…”