A positive feedback loop that regulates SOS activity results in digital signaling
Stimulated tyrosine kinase receptors (e.g., growth factor receptors, T cell receptors), recruit SOS to the plasma membrane by the adapter molecule, Grb2 (Genot and Cantrell, 2000
). The Rem and Cdc25 domains in SOS are required for its GEF catalytic activity (), and we refer to them together as SOScat
(SOS catalytic domain). SOS itself has very low GEF activity. Crystallographic and biochemical studies as well as experiments with cell lines show that the activity of SOScat
is strongly influenced by a second Ras binding site which is distal to the GEF catalytic site (Margarit et al., 2003
). Binding of RasGDP to this allosteric pocket results in a 5-fold increase in GEF activity, whereas binding of RasGTP effects a much larger (~ 75-fold) increase (Freedman et al., 2006
; Sondermann et al., 2004
). Thus, SOS-mediated Ras activation involves positive feedback regulation by its own catalytic product, RasGTP ().
A minimal model of the catalytic domain of SOS predicts three possible states of Ras activation
The activity of full-length SOS is inhibited by both N-terminal and C-terminal regions that flank SOScat
). Recruitment of SOS to the plasma membrane results in conformational changes that relieve this inhibition and allow RasGDP to bind to SOS′ catalytic site (Corbalan-Garcia et al., 1998
). In agreement, expression of SOS1cat
without these flanking sequences results in Ras signaling without the need for membrane targeting or external stimulus (Roose et al., 2007
). We explored the consequences of positive feedback regulation of SOS by developing a mathematical model for the signaling module in wherein SOScat
We first ignored stochastic fluctuations (Kampen, 1992
) in the number of molecules participating in signaling, and developed a deterministic model describing the temporal evolution of the most probable number (or concentration) of the proteins involved in Ras activation via SOScat
(). summarizes the values of rate parameters that appear in the equations (Procedures). Only the ratios of certain parameters had been measured. Varying the individual parameters by factors of at least ten while keeping the ratio fixed did not affect the qualitative results (Figures S2–S4
Table 1 Parameters used for the equations. Rates are calculated from the catalytic rates and/or the dissociation constants (KD) reported in the literature. For additional information see supplement, section I.
shows the theoretical steady-state dose-response curve for Ras activity as the amount of SOScat
(α) is varied. For low or high levels of SOScat
, there is one possible state characterized by low or high levels of active Ras, respectively. However, for intermediate levels of SOScat
, three states of Ras activity are possible. The states shown in blue are unstable to small perturbations, and these states could exist only fleetingly. Therefore, for intermediate levels of SOScat
, two possible dominant states of Ras activity could be simultaneously observed; i.e., a bistability is predicted. As the amount of SOScat
is increased, the system could follow the lower stable branch until this was no longer possible, and then there would be a large jump in Ras activity (at point A). Thus, the dose-response curve could be very sharp. Importantly, bistability and the concomitant sharp threshold are abrogated if the positive feedback loop regulating SOS′ GEF activity is removed from the model (green line in and S2E
Formulas obtained from a detailed analytical study (Supplement, Section VI
) suggest that, in addition to feedback regulation of SOS, the minimal requirements for bistable Ras activity are: 1] catalytic Ras activation by SOS, with RasGTP bound to the allosteric site and 2] catalytic deactivation of RasGTP by RasGAPs. These features are true. The analytical treatment of simplified models also supports our numerical parameter sensitivity studies which show that our qualitative results are robust to wide variations in parameters as long as the basic ingredients described above are present.
We then investigated the potential effect of Ras activation via RasGRP1 on the bistable Ras activity driven by SOScat
. A GEF, RasGRF, which is structurally related to RasGRP, is not dependent on feedback regulation by Ras (Freedman et al., 2006
). So, we assumed that Ras is activated by RasGRP without feedback, and used the measured rate parameters for RasGRF since those for RasGRP are unknown. As shown in , bistability and sharp responses are predicted to disappear if RasGRP levels (or activity) are very high. This is because RasGRP activity, which is not subject to feedback regulation can convert most Ras molecules to its active form before the SOS feedback loop is engaged. also shows that low levels of RasGRP activity reduce the threshold for SOScat
(α) to induce a sharp response. We show later that this is because absence of RasGRP makes it difficult to ignite the positive feedback loop regulating SOS′ GEF activity. These results suggest that an optimal level of expression or activity of RasGRP, the analog route to Ras activation, enables efficient deployment of feedback regulation of SOS which leads to bistability.
To explore the manifestations of these characteristics of Ras activation in lymphocytes (where stochastic variations between stimulated cells can be important), we carried out stochastic computer simulations of signaling events that might occur in lymphocytes (). The simulations were carried out using the Gillespie algorithm (Gillespie, 1977
), which has been used profitably to study biological systems that exhibit multi-stability (Elf and Ehrenberg, 2004
; McAdams and Arkin, 1997
). Parameters not listed in needed to carry out the simulations are provided in the supplement. The qualitative features of the results are robust to variations in unknown parameters over wide ranges (Tables S6–S8, Figures S5–S12
). The purpose of our in silico
studies was not quantitative recapitulation of known data, but to provide qualitative mechanistic insights that can be tested experimentally.
We carried out stochastic calculations using the amount of SOScat
as a surrogate for the level of receptor stimulation. Many replicate dynamic simulations were carried out and levels of RasGTP at various time points were recorded (see Figure S30
for examples). Each simulation corresponds to assaying an individual lymphocyte. The combined results for all such in silico “cells” at a particular time point are displayed (). For low levels of SOScat
, all simulations result in low levels of RasGTP, resulting in a single corresponding peak in the histogram. As SOScat
is increased, this peak does not gradually move to higher values of RasGTP. Rather, beyond a threshold value of SOScat
, a second peak corresponding to a much higher level of RasGTP emerges; the histogram is bimodal (). Thus, the sharp threshold and bistability shown in are manifested as digital signaling. The prediction is that lymphocytes are either “on” or “off” with regard to Ras activation.
To test these predictions, we used a Jurkat T cell line into which different amounts of SOS1cat
and GFP were transfected together (Roose et al., 2007
). Individual cell assays are required to compare experimental results with the histograms shown in . Analysis of active Ras for individual cells in a population is not possible in this transfection experiment, and so we examined upregulation of a cell surface activation marker CD69 by individual cells using flow cytometry. CD69 levels correlate with the strength of Ras-ERK signaling (Roose et al., 2007
), but activation of signaling molecules downstream of Ras could be influenced by feedback regulation of modules such as the MAPK pathway (Ferrell, 2002
; Kholodenko et al., 2002
). We will address this issue directly below.
Low or high levels of SOS1cat
expression led to unimodal cell populations with low or high levels of CD69 induction ( and S21B
). Intermediate levels of SOS1cat
(red) induced a bimodal CD69 expression pattern in wild-type Jurkat T cells (). SOS1cat
-induced bimodality was not observed for a control marker that is Ras-unresponsive (Figure S21C
). These results in cells mirror the predictions of the computer simulations in that signaling is digital. We next tested the hypothesis emerging from our calculations ( and Figure S2E
) that the origin of digital signaling is feedback regulation of SOS-mediated Ras activation.
Experiments carried out with RasGRP1-deficient JPRM441 cells indicate the importance of this feedback loop. In contrast to wildtype cells (), intermediate levels of SOS1cat
induced high CD69 expression levels in very few JPRM441 cells (13% in , top row). Similarly, intermediate levels of SOScat
did not generate a bimodal response in computer simulations of the RasGRP deficient state (). Basal RasGRP1-mediated activation of Ras is not subject to feedback regulation, but can “ignite” the SOS feedback loop (Roose et al., 2007
) by providing RasGTP which can bind SOS′ allosteric pocket and increase its activity 75-fold. Consistent with our computational results (), in RasGRP-deficient JPRM441 cells, lower basal levels of RasGTP make it more difficult to ignite the SOS feedback loop. Sufficiently high levels of SOScat
can induce bimodal responses without RasGRP1 (, and S22
) because RasGTP produced by the GEF activity of SOScat
with RasGDP bound to the allosteric pocket can ultimately prime SOS′ feedback loop.
A RasGTP mimetic restores efficient SOScat –induced bimodal signals in RasGRP deficient cells
The computer simulation results suggested that a bimodal response would re-emerge in RasGRP-deficient cells for intermediate levels of SOS1cat
if exogenous RasGTP molecules that bind to SOS′ allosteric pocket were added. To test this, we introduced Ras molecules like H-RasV12C40 (Roose et al., 2007
) or H-RasG59E38 (Boykevisch et al., 2006
) that are predominantly GTP loaded (because of the V12 or G59 mutation) and thus bind SOS′ allosteric pocket to increase GEF activity. These molecules also contain a second mutation (C40 or E38) that impairs binding to RAF and so do not directly activate the RAF-MEK-ERK-CD69 pathway; i.e., downstream pathways must be activated by endogenous Ras molecules.
In this type of assay, not all transfected cells start to express SOS1cat
synchronously and SOS1cat
expressing cells transit from low CD69 to high CD69 expression. It is therefore difficult to ascertain whether the response is bimodal or not by visual inspection. We adapted Hartigan’s test (Hartigan, 1985
), which allows for a qualitative determination of whether a response in a population of cells is bimodal or unimodal. The generated histograms were divided into 120 equal portions and the mean fluorescence of CD69 and the number of cells in each portion were determined. Hartigan’s test confirmed that intermediate levels of SOS1cat
when combined with H-RasG59E38 but not wt H-Ras restored bimodal signaling in RasGRP-deficient cells (, bottom row: B with p<0.01). The same level of SOS1cat
or H-RasG59E38 alone also did not result in high CD69 expression (, top row, unimodal; U:p<0.01). Importantly, when the allosteric pocket in SOScat
is mutated (SOS1cat
-W729E), so that it can no longer interact with nucleotide-associated Ras proteins, adding H-RasG59E38 does not result in a bimodal pattern of signaling (, bottom row). Similar results were obtained with H-RasV12C40 (data not shown). Modeling this cell biological experiment is in concurrence with these results (). Therefore, the digital signaling we observe for ERK-CD69 signaling requires feedback regulation of SOS-mediated Ras activation.
There are two possible reasons for why digital signaling in lymphocytes originates in SOS-mediated Ras activation: (i) Ignition of the SOS feedback loop is necessary for generating sufficiently high levels of RasGTP required to prime downstream feedback loops that cause digital signaling (e.g., those associated with the MAPK pathway (Bhalla and Iyengar, 1999
; Ferrell, 2002
; Kholodenko et al., 2002
). (ii) Digital signaling is controlled by feedback regulation of Ras activation by SOS. Whereas signaling is undoubtedly influenced by feedback regulation of downstream signaling modules, results described below suggest that, in lymphocytes, the latter scenario is true.
Receptor stimulation results in digital signaling with SOS and analog responses with RasGRP alone
The strength of lymphocyte receptor stimulation impacts outcomes (e.g., T cell activation, thymocyte development (Starr et al., 2003
)). Therefore, we studied how SOS and RasGRP influence cellular responses as the amount of stimulatory ligands is varied.
We studied a simplified computational model for processes upstream of Ras activation (See section III, supplement
). In short (see ), receptor stimulation and phosphorylation generates activated ZAP-70 molecules. Activated-ZAP-70 phosphorylates the adaptor molecule LAT, which recruits both PLCγ and Grb2/SOS. PLCγ is then phosphorylated, and this generates IP3 and DAG. Induced DAG enhances RasGRP recruitment and activation. We do not incorporate cooperative effects associated with Grb2/SOS recruitment to LAT (Houtman et al., 2006
). Including this feature would lead to sharper cellular responses (Prasad).
For weak receptor stimulation, as might occur under physiologic antigen receptor stimulation (), wildtype systems that have low initial levels of active Ras exhibit a bimodal pattern of signaling after a short time which ultimately becomes a unimodal distribution with high RasGTP (, left column). For very strong stimulation, a unimodal state of high RasGTP is rapidly reached (, left column). Without RasGRP, signaling is inhibited. Importantly, without SOS such systems demonstrate a graded response, indicating the analog character of RasGRP-mediated Ras activation (, middle column). Changing the values of the parameters (e.g., the numbers of RasGRP and SOS molecules) used to obtain the results shown in does not lead to qualitative changes (Tables S12–S13, Figures S13–S20
To test these predictions, we determined the pattern of ERK phosphorylation in individual cells. First, 20,000 Jurkat T cells were either stimulated via the TCR or by PMA. The latter mimics a DAG-PKC-RasGRP pathway, but does not target SOS. Engagement of the TCR generated a unimodal P-ERK response at early timepoints that transitioned to a bimodal response at three minutes after stimulation (). In contrast, even strong stimulation via PMA never induced a bimodal ERK phosphorylation pattern and, instead, exhibited an analog response ().
RasGRP induces analog phospho-ERK signals, whilst SOS induces digital signals in B cell lines and primary T cells
Experiments with cells wherein genes of interest were deleted further support these results. Peripheral T cells do not develop in RasGRP1 deficient mice (Dower et al., 2000
) and a selective SOS1−/−
peripheral T cell model to circumvent lethality due to SOS1 deficiency has not been generated (Wang et al., 1997
). Therefore, we used a chicken DT40 B cell line in which pertinent genes have been genetically inactivated (Roose et al., 2007
). We analyzed the ERK phosphorylation pattern of 20,000 cells (wildtype, SOS1−/−
, and RasGRP1−/−
) that were stimulated with increasing levels of B cell receptor (BCR) crosslinking-M4 monoclonal antibody.
Wildtype cells stimulated by low levels of M4, mimicking physiological lymphocyte stimulation by antigen, exhibited a bimodal pattern of ERK activation at the 3 and 10 minutes time points ( “WEAK” and S24
). Hartigan’s tests (Hartigan, 1985
) confirmed that the response is bimodal. In contrast, SOS1−/−
DT40 B cells do not exhibit bimodal distributions at any time point regardless of stimulus level (, middle column). Thus, without SOS, signaling is analog in character regardless of strength of stimulus. Furthermore, while PMA-induced responses were severely impaired in RasGRP1−/−
cells (, right column), PMA induced very similar analog patterns of ERK phosphorylation in wildtype and SOS1−/−
DT40 B cells (, left and middle columns). These results reveal analog ERK responses from RasGRP-induced Ras activation, and that there is no intrinsic defect preventing SOS1−/−
DT40 B cells from turning on the Ras-ERK pathway.
This behavior in cell lines was mirrored in primary CD4 positive peripheral T cells. Ex vivo TCR stimulation of primary cells results in a digital pattern of ERK phosphorylation (), but PMA stimulation results in analog signaling ().
Thus, in Jurkat T cells, DT40 B cells, and primary lymph node T cells digital signaling requires engagement of the SOS pathway for Ras activation (–). Notably, for all systems, the ERK response to PMA stimulation was analog at all doses tested, including those that generate high levels of RasGTP. This implies that the predicted analog Ras response in the absence of SOS (, middle column) is not translated to digital responses by downstream signaling modules. If ignition of the positive feedback loop associated with SOS-mediated Ras activation only served to generate high levels of RasGTP that can stimulate digital signaling in a downstream module such as the MAPK pathway, a bimodal pattern of ERK activation should have been observed upon strong PMA stimulation. Since this is not so (), our results suggest that the digital signaling we observe for ERK and CD69 is not only predicated on positive feedback regulation of SOS-mediated Ras activation ( and ), but is controlled by it.
Prediction of hysteresis in Ras activation
Due to technical limitations, we are not able to carry out single cell assays of Ras activity. However, another related, but unanticipated characteristic that derives from our model, hysteresis, can be assessed by measuring Ras activation at the population level. Hysteresis is a direct consequence of bistability due to positive feedback regulation of SOS-mediated Ras activation (), and the phenomenon and its biochemical origin is shown in .
Hysteresis at the level of RasGTP depends on SOS
When previously unactivated cells are stimulated, RasGTP levels are low. Hence, the allosteric site of most SOS molecules is occupied by RasGDP and SOS′ GEF activity is low. Increasing stimulus results in more RasGTP production, and an increase in the number of SOS molecules with RasGTP bound to the allosteric pocket, resulting in ignition of the positive feedback loop and a sharp increase in active Ras levels. These processes result in the black dose-response curve in , which is obtained from computer simulations where the initial RasGTP levels were set to zero.
A very different dose-response curve (red curve in ) is predicted by computer simulations where the initial RasGTP level was set to a large value, and then the response to smaller stimulus levels were calculated. This is the predicted dose-response for cells that are first robustly stimulated such that a high RasGTP level is realized, then the stimulus is quickly reduced (as in removal of antigen), and the response assessed after a time period that is sufficient for a new active Ras level to be established. When cells that have been previously robustly activated are exposed to lower stimulus levels, most SOS molecules have RasGTP bound to the allosteric site and are characterized by high GEF activity. So, for the same stimulus level (or SOS targeted to the membrane), previously stimulated cells will exhibit a higher level of active Ras than previously unstimulated cells because in the former situation SOS is a more active enzyme. Concomitantly, the threshold stimulus required for robust Ras activation shifts to lower values () for previously stimulated cells. However, this hysteretic effect will only be manifested for a finite period of time. Ultimately, RasGTP molecules bound to the allosteric site of SOS in previously stimulated cells will be displaced by RasGDP molecules as the amount of RasGTP in the cell declines because of lower stimulus levels. If the second stimulus level falls below a threshold, this process occurs very rapidly, and this is why hysteresis is not predicted for weak receptor stimulation.
SOS-dependent hysteresis in Ras activation
Experimental results for Jurkat T cells and DT40 B cells () demonstrate the predicted hysteresis in Ras activation, and that it is due to the feedback loop associated with SOS and not due to feedback from downstream signaling modules.
Stimulation of Jurkat T cells using a maximal dose of TCR crosslinking antibody results in near maximal Ras activation after 3 minutes of stimulation (Figure S27A
). Cells were also exposed to increasing concentrations of Src kinase inhibitor (PP2) to inhibit Lck (see ) and interrupt signaling events upstream of Ras activation in a dose-dependent manner. PP2 was introduced simultaneously with the stimulus (t=0 min) or after cells reached maximal levels of RasGTP (t=3 min). RasGTP was analyzed at three minutes for PP2 added at t=0 min. If PP2 was added at t=3 min, RasGTP was assayed at seven minutes, thereby allowing a new balance with the reduced stimulus to be established. Computer simulations (Figure S27D
) show that this protocol should allow us to test whether hysteresis occurs at the level of Ras as predicted in .
shows that TCR-induced RasGTP levels in wildtype Jurkat cells decrease when PP2 is added simultaneously with the stimulus, demonstrating a dependence on Src kinases (or stimulus level) for RasGTP generation that is akin to the black curve in for previously unstimulated cells. However, when PP2 is added at three minutes (stimulus lowered after stimulation), RasGTP levels are high at seven minutes even at high doses of PP2. This is akin to the red curve in , and demonstrates hysteresis because, in previously stimulated cells, RasGTP levels are relatively high between three and seven minutes in spite of a lower stimulus. After a sufficiently long time, as predicted, hysteresis is not observed (data not shown).
Importantly, these effects were not determined by feedback loops originating downstream of Ras. Preloading of cells with MEK1/2 inhibitor, U0126, efficiently blocks MEK and ERK phosphorylation but allows for RasGTP generation, albeit with slightly delayed kinetics (Figure S27A
), but hysteresis was still observed ().
We also tested the prediction that SOS-mediated Ras activation underlies hysteresis by using the doubly SOS deficient DT40 cells. Maximal BCR crosslinking leads to similarly high-levels of RasGTP at three minutes in wildtype and SOS1−/−
cells (Figure S27B
). Of note, RasGTP production is clearly impaired in moderately stimulated SOS1−/−
cells (Figure S27C
). RasGTP levels in wildtype DT40 cells were sensitive to PP2 inhibition at the initiation of BCR stimulation. When cells were allowed to generate RasGTP for the first three minutes prior to PP2 addition, hysteresis was observed since RasGTP levels were high when compared to cases where the same dose of PP2 was added at the initiation of BCR stimulation (). In sharp contrast, SOS1−/−
cells do not exhibit hysteresis, and RasGTP levels decrease with increasing amounts of PP2 on the way up (PP2 at t=0) and the way down (PP2 at t=3) ().
Bistability and hysteresis provide Ras signaling memory during serial stimulation
T cell activation may require integration of membrane-proximal signals from sequential contacts (each approximately 3 minutes in duration) that occur between T cells and antigen presenting cells in lymphoid tissues (Bousso and Robey, 2003
; Henrickson et al., 2008
; Skokos et al., 2007
). A molecular mechanism that enables T cells to “remember” past encounters with antigen is not known.
Suppose during a T cell-APC contact the quality and quantity of encountered pMHC ligands is sufficient to stimulate engagement of the SOS feedback loop and robust Ras activation, but insufficient for other events necessary for T cell activation. The T cell disengages from the APC, and is not subject to stimulation until it encounters another APC. During this period the stimulus is “off”, and active Ras levels decline because phosphatases act on pLAT () causing SOS to disengage from the membrane, RasGAPs reduce RasGTP levels during the time that the stimulus is “off”, etc.. Suppose that during the next encounter of this T cell with an APC it encounters a weak stimulus that would not result in robust Ras activation if this T cell had not been previously robustly stimulated. We asked whether the existence of an underlying bistable steady-state structure due to feedback regulation of SOS () would result in restoration of robust Ras activation upon weaker re-stimulation. If so, bistability and hysteresis would be manifested as a molecular memory that enables integration of serially encountered weak signals after exposure to a strong stimulus.
To explore this idea, we carried out calculations with the minimal model shown in . Robust stimulation of active Ras due to high levels of SOScat was followed by suddenly removing the stimulus. We then studied the dynamics of re-stimulation with a weak stimulus (green) after the originally strong stimulus has been “off” for a certain time (). Increasing the duration of the resting phase reduces the RasGTP level at the time of re-stimulation, because of the RasGAPs present in our model. shows that maximal activation is recovered upon re-stimulation with a subsequent weaker stimulus, provided that RasGTP does not decline below the level of the unstable steady state (blue points in ). If RasGTP levels decline to baseline during the duration when the stimulus is “off”, then RasGTP levels are low upon re-stimulation (, 500 sec. rest period). If there is no bistability and hysteresis as when SOScat is not subject to feedback regulation (or Ras is activated via RasGRP), restimulation with a weak stimulus results in low levels of Ras activation regardless of prior stimulation; i.e., there is no memory ().
Stimulation of Jurkat T cells or B cells with the plant lectin Concanavilin A (Con A) results in robust calcium responses that rely on binding of ConA to the TCR or BCR (Weiss et al., 1987
). Importantly, binding of Con A can be relatively rapidly abrogated by addition of α-methyl-mannoside (α-MM), a competitive carbohydrate. We used this protocol to test the predictions in . Because T and B cells respond similarly to this protocol, we used the DT40 system as it enables testing the effects of SOS by genetic deletion ().
ConA stimulation resulted in robust Ras activation in both wildtype and SOS1−/−SOS2−/− DT40 B cells at 3 minutes (). Addition of α-MM treatment to robustly stimulated wildtype cells resulted in a decline in RasGTP levels. It is important to note that at 12 minutes, RasGTP levels still remained moderately above the basal level. Next, we tested the effect of a very weak stimulus of anti-BCR crosslinking antibody given at this 12-minute time point (see ). Priming with ConA followed by α-MM treatment resulted in hyperresponsive RasGTP levels induced by this weak second signal that did not elicit a response when wildtype DT40 B cells were primed with PBS as a negative control (). In contrast, when doubly-deficient SOS1−/−SOS2−/− DT40 B cells were primed through the same regimen, we observed only minimal RasGTP stimulation by the second signal mediated by the BCR (). These data are consistent with the prediction () that the underlying bistability and hysteresis due to feedback regulation of SOS confers memory to the dynamic responses of previously stimulated lymphoid cells.