Design of versatile biochemical switches that respond to amplitude, duration, and spatial cues Azi Lipshtat1, Gomathi Jayaraman, John Cijiang He, and Ravi Iyengar Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, NY 10029 Edited by Robert J. Lefkowitz, Duke University Medical Center, Durham, NC, and approved November 11, 2009 (received for review August 3, 2009) Cells often mount ultrasensitive (switch-like) responses to stimuli. transport by Ran (16). Because of their central role in numerous The design principles underlying many switches are not known. We pathways, small GTPases (GTPases) have been studied exten- computationally studied the switching behavior of GTPases, and sively, both experimentally and computationally (1, 13, 17, 18). found that this first-order kinetic system can show ultrasensitivity. For many GTPases, the intrinsic cycle between the GDP- Analytical solutions indicate that ultrasensitive first-order reactions bound state and GTP-bound state is very slow. Cycling rates are can yield switches that respond to signal amplitude or duration. greatly enhanced by guanine nucleotide exchange factors (GEFs) The three-component GTPase system is analogous to the physical and GTPase activating proteins (GAPs) (19). Signaling pathways fermion gas. This analogy allows for an analytical understanding of that use heterotrimeric G proteins or small GTPases show both the functional capabilities of first-order ultrasensitive systems. graded and switch-like responses. What mechanisms underlie the Experiments show amplitude- and time-dependent Rap GTPase switching behavior? Zero-order ultrasensitivity can be obtained switching in response to Cannabinoid-1 receptor signal. This first- by low enzyme (GEF or GAP) to substrate (GTPase) ratio. order switch arises from relative reaction rates and the concen- However, experimental observations and estimations show that trations ratios of the activator and deactivator of Rap. First-order this is not always the case (8, 20). Although GEF and GAP ultrasensitivity is applicable to many systems where threshold for concentrations are lower than the GTPases levels, the difference transition between states is dependent on the duration, amplitude, is not sufficient. When multiple GEFs or GAPs are simulta- or location of a distal signal. We conclude that the emergence of neously active, the effective concentrations of the regulators can ultrasensitivity from coupled first-order reactions provides a be similar to that of the GTPase, resulting in a first-order system. fi versatile mechanism for the design of biochemical switches. How do rst-order reactions yield ultrasensitive response, and SYSTEMS BIOLOGY why don't we always observe this response? GTPase | signaling | ultrasensitivity GEFs and GAPs are controlled by receptor-regulated intra- cellular events (9, 21). Such regulation is critical for normal fficient regulation of intracellular processes benefits from "all physiology. Abnormal regulation of GEFs or GAPs has been Eor none" response (1), where a cellular component switches implicated in cancer (22), viral and bacterial pathogenesis (23), between two functional states upon crossing a threshold. Often, a vascularization defects during development (24), and mental regulator triggers state change. Near the threshold point, a small retardation (25). Often, regulation of either a GAP or a GEF is fi change in one parameter, such as regulator concentration or signal suf cient for GTPase activation (9, 21, 26). We explored the duration, causes switching of the responding component. Such relationship between different levels of GEF and GAP activity by responses are called ultrasensitive (2). A widely known mechanism numerically simulating receptor-regulated Rap activation, using underlying a steep response curve is the "zero-order ultra- an ordinary differential equations model. The signaling network sensitivity" first proposed by Goldbeter and Koshland (2), who (Fig. S1) includes our prior experimental data (15) and the — regulation of Rap by cAMP (27). Details of the simulations are showed that under zero-order conditions i.e., when one or more SI Text of the enzymes in a coupled system are saturated—the transition described in , and the models are available at the Virtual Cell site. In Fig. 1, we show the formation of GTP-bound Rap in between the active and inactive conformations exhibits high sen- α α sitivity to the concentration ratio of the enzymes. Other mecha- response to signals from activated 2-adrenergic ( 2R) and β-adrenergic (βAR) receptors. The α2R signal leads to degra- nisms that yield ultrasensitivity include cooperativity, multistep β regulation, and stoichiometric inhibitors (3–5). Positive feedback dation of Rap GAP* whereas the AR signal activates the GEF. We observe an abrupt transition from a low activity state to high loops play an important role in producing switching behavior (4) activity as the α2R signal crosses a threshold. Similar behavior is and are often considered necessary for bistability (6, 7). Mecha- observed when signal duration is lengthened while the signal nisms that depend on loops require complex network organization amplitude is fixed (Fig. 1C). Thus, level of active Rap is very such as topological motifs in addition to the enzymatic activity to sensitive to the signal amplitude and duration, with distinct produce switches. However, switching behavior is observed in the subthreshold and above-threshold responses. As opposed to the absence of loops, and the design principles for such switches are high sensitivity to α2R activation, the response to βAR stim- poorly understood. We have used analytical and numerical ulation is slightly slower than a regular Michaelian curve (Fig. methods as well as experiments to describe first-order ultra- 1D). The amplitude of the βAR stimulation affect the Rap sensitivity as the basis for a versatile design of a biochemical switch activation level, but the sensitivity to the exact stimulus charac- that responds to both duration and concentration of stimulus. teristics is low. However, the duration of the signal produces a Ultrasensitivity in GTPases Small GTPases can function as molecular switches in varied Author contributions: A.L conducted all the theoretical analysis; A.L., J.C.H., and R.I. de- cellular processes including signaling networks (8). Their con- signed research; G.J. and J.C.H. performed experiments; and A.L. and R.I. wrote the paper. version from GDP (inactive) to GTP (active) conformations The authors declare no conflict of interest. promotes interaction with downstream effectors to propagate This article is a PNAS Direct Submission. information flow. Rapid responses of GTPases to incoming – 1To whom correspondence should be addressed at: Department of Pharmacology and regulation can turn downstream pathways on and off (9 11). Systems Therapeutics, Mount Sinai School of Medicine, One Gustave L. Levy Place, Box Thus, GTPases play an essential role in controlling many cellular 1215, New York, NY 10029. E-mail: [email protected]. – responses (10 13). Examples include cellular proliferation by This article contains supporting information online at www.pnas.org/cgi/content/full/ Ras (14), neurite growth by Rap1 (15), and nucleocytoplasmic 0908647107/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.0908647107 PNAS Early Edition | 1of6 Downloaded by guest on September 23, 2021 μ 300 [Clonidine] ( M) ½SGÃ A 0.1 ¼ 1 ; [2] 200 0.032 0.01 SGT 1 þ kGAP=kGEF 0.0032 100 0.001 0.00032 ) 0.0001 k k * k k * 2 0 where GEF = on[GEF ] and GAP = off[GAP ] are the effec- m 0 2000 4000 6000 8000 10000 μ time (sec.) tive reaction rates. The activity of GEFs and GAPs may be pos- itively or negatively regulated. We consider the case of negative 200 B C 200 regulation of the GAP* by a signal X (receptor signal), which n =2.9 n =1.7 100 H H 100 targets the GAP* for irreversible deactivation (by degradation or 0 0 −3 −2 −1 0 1 2 fi GTP (molecules/ any other rst-order reaction such as sequestration) (15, 21) ⋅ 10 10 10 10 10 10 [Clonidine] (μM) Clonidine Signal (sec.) (Fig. 2A). The RasGAP neurofibromin undergoes degradation Rap 200 D E 300 upon treatment with various growth factors (29), and p120 Ras- 200 n =0.7 n =2.2 GAP is degraded by caspase (30). The signal triggers the degra- 100 H H 100 dation of GAP* either directly or through a reaction cascade. 0 0 −4 −3 −2 −1 0 1 2 1 2 3 10 10 10 10 10 10 10 10 10 10 The analysis is valid as long as the effective rate of GAP* μ [Isoproterenol] ( M) Isoproterenol Signal (sec.) decrease is proportional to the signal amplitude and depends Fig. 1. Numerical simulations of Rap regulation. A detailed simulation of on the GAP* concentration [GAP*] (see calculation in SI Text). the Rap1 pathways was performed by using Virtual Cell (see Fig. S1 for the Although we assume that the GAP deactivation rate is propor- pathways). α2AR were stimulated for fixed duration and with various tional to [GAP*], in SI Text we show that this assumption is not amplitudes, evenly distributed on a logarithmic scale. Then, Rap was acti- necessary, and that ultrasensitivity can be achieved from any vated by a βAR stimulus. (A) The activation level is clustered into two groups α nonzero positive dependence on [GAP*]. Here, we present of low and high activation. (B and C) 2AR-stimulated steady state Rap the standard case of mass action law. In this regime, the deacti- activity is ultrasensitive with respect to concentration and duration. (D) βAR β vation rate (which is the time derivative of [GAP*]) is propor- stimulation of Rap is subsensitive with respect to signal amplitude. (E) AR X activation of Rap is ultrasensitive with respect to signal duration. tional to [GAP*]. As a result, applying a stimulus for a duration τ causes decay in active [GAP*] that is exponential with respect to both time and X. By the end of the signal dura- tion, GAP* has a new steady state concentration, namely switching response (Fig.