GTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, 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 GTPases 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. In both states the tGTPase is inactivated and active tGTPase concentrations are low. 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 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.

GTP酶是调节多种细胞过程的分子开关，例如细胞器的生物发生、位置、形状、功能、细胞器之间的囊泡运输和信号转导。这些水解酶通过在活性（“ON”）三磷酸鸟苷（GTP）结合状态和非活性（“OFF”）鸟苷二磷酸（GDP）结合状态之间切换来发挥作用；这种切换由 GEF（鸟嘌呤核苷酸交换因子）和 GAP（GTP 酶激活蛋白）调节。在这里，我们提出了一个仅在多细胞生物的真核细胞中组装的单体（m）和三聚体（t）GTP酶之间的网络基序模型。我们开发了一个常微分方程系统，其中这两类 GTPases 通过耦合和反馈环路以基序内的开/关状态为条件相互关联。我们为系统的稳态提供了明确的公式，并进行经典的局部稳定性分析，以系统地研究 GTPase 开关之间不同连接的作用。有趣的是，活性 mGTPase 与 tGTPase 的 GEF 的偶联足以提供两种局部稳定状态：一种是 mGTPase 的活性/非活性形式都可以解释为具有低浓度，另一种是 mGTPase 和 tGTPase 都具有低浓度。高浓度。此外，当从 tGTPase 的 GEF 到 mGTPase 的 GAP 的反馈回路添加到耦合系统中时，出现了另外两种局部稳定状态。在这两种状态下，tGTP 酶均处于失活状态，并且活性 tGTP 酶浓度较低。最后，添加第二个反馈环路，从活性 tGTPase 到 mGTPase 的 GAP，产生一系列稳态，可以通过一系列非活性 tGTPase 浓度进行参数化。我们的研究结果表明，这两种不同 GTPase 基序的耦合可以显着改变它们的稳态行为，并揭示这种耦合如何影响真核细胞中的信号传导机制。