Stability Analysis of a Signaling Circuit with Dual Species of GTPase Switches

Abstract

GTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, and function, vesicular transport between organelles, and signal transduction. These hydrolase enzymes operate by toggling between an active "ON") guanosine triphosphate (GTP)-bound state and an inactive ("OFF") guanosine diphosphate (GDP)-bound state; such a toggle is regulated by GEFs (guanine nucleotide exchange factors) and GAPs (GTPase activating proteins).Here we propose a model for a network motif between monomeric (m) and trimeric (t) GTPases assembled exclusively in eukaryotic cells of multicellular organisms. We develop a system of ordinary differential equations in which these two classes of GT-Pases are interlinked conditional to their ON/OFF states within a motif through coupling and feedback loops. We provide explicit formulae for the steady states of the system and perform classical local stability analysis to systematically investigate the role of the different connections between the GTPase switches. Interestingly, a coupling of the active mGTPase to the GEF of the tGTPase was sufficient to provide two locally stable states: one where both active/inactive forms of the mGTPase can be interpreted as having low concentrations and the other where both m-and tGTPase have high concentrations. Moreover, when a feedback loop from the GEF of the tGTPase to the GAP of the mGTPase was added to the coupled system, two other locally stable states emerged, both having the tGTPase inactivated and being interpreted as having low active tGTPase concentrations. Finally, the addition of a second feedback loop, from the active tGT-Pase to the GAP of the mGTPase, gives rise to a family of steady states that can be parametrized by a range of inactive tGTPase concentrations. Our findings reveal that the coupling of these two different GTPase motifs can dramatically change their steady state behaviors and shed light on how such coupling may impact signaling mechanisms in eukaryotic cells.

A Circuit for Secretion-coupled Cellular Autonomy in Multicellular Eukaryotes

“…The net result of this is that the closed loop feedback control allows for a tighter alignment of secretion with respect to EGF by ‘stretching’ out the dose-response curve across series of switches to propagate the signal from the extracellular space to the interior of the cell. Because the stability behavior of a mathematically simpler version of this closed loop system of coupled GTPases showed that coupling afforded a wide range of steady states (Stolerman et al, 2021), it is tempting to speculate that the coupled system allows flexibility in responses over a wide range of stimulus. In fact, follow-up work has now revealed how ranges of activity of the mGTPase Arf1, reaction kinetics, the negative feedback loop (mGAP), and the cascade length affect DoRA (Qiao et al, 2022).…”

Design principles of improving the dose-response alignment in coupled GTPase switches

“…1c). In the presence of epidermal growth factor (EGF), the active Ras-superfamily mGTPases Arf1 on Golgi membrane recruit GIV/Girdin (a protein that is known to fuel aggressive traits in diverse cancers), and the latter works as guanine nucleotide exchange factor (GEF) to turn tGTPases Giαβγ on [41][42][43][44][45] . Subsequently, GIV increases the level of the GAP for mGTPase by molecular scaffolding action, and the activated tGTPase acts as a co-factor to maximally activate the GAP.…”

“…Subsequently, GIV increases the level of the GAP for mGTPase by molecular scaffolding action, and the activated tGTPase acts as a co-factor to maximally activate the GAP. This circuit was subsequently modeled for cell secretion 34 and for stability analysis 45 .…”

Design principles of dose-response alignment in coupled GTPase switches

“…We briefly describe the biochemical circuit that we study here; this circuit was originally described in mammalian cells and experimentally interrogated in (33), (Figure 1A). In the presence of epider mal growth factor (EGF), the active Rassuperfamily mGTPases Arf1 on Golgi membrane recruit GIV/Girdin (a protein that is known to fuel aggressive traits in diverse cancers), and the latter works as guanine nucleotide exchange factor (GEF) to turn tGTPases Gi on (39)(40)(41)(42)(43). Subsequently, GIV increases the level of the GAP for mGTPase by molecular scaffolding action, and the activated tGT Pase acts as a cofactor to maximally activate the GAP.…”

“…Subsequently, GIV increases the level of the GAP for mGTPase by molecular scaffolding action, and the activated tGT-Pase acts as a co-factor to maximally activate the GAP. This circuit was subsequently modeled for cell secretion (44) and for stability analysis (43).…”