  GTPases are molecular switches that regulate a wide range of cellular
processes, such as organelle biogenesis, position, shape, and signal
transduction. These 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
dissect a network motif between monomeric (m) and trimeric (t) GTPases
assembled exclusively in eukaryotic cells of multicellular organisms. To this
end, we develop a system of ordinary differential equations in which these two
classes of GTPases are interlinked conditional to their ON/OFF states within a
motif through feedforward and feedback loops. We provide formulas for the
steady states of the system and perform local stability analysis to investigate
the role of the different connections between the GTPase switches. A
feedforward from 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. When a feedback loop from the GEF
of the tGTPase to the GAP of the mGTPase was added to the feedforward 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 tGTPase to the GAP of the
mGTPase, gives rise to a family of steady states parametrized by the 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 information processing in
eukaryotic cells.
