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Temporal pattern and synergy influence activity of ERK signaling pathways during L-LTP induction

  1. Nadiatou T Miningou Zobon
  2. Joanna Jędrzejewska-Szmek
  3. Kim T Blackwell  Is a corresponding author
  1. Department of Chemistry and Biochemistry, George Mason University, United States
  2. Laboratory of Neuroinformatic, Nencki Institute of Experimental Biology of Polish Academy of Sciences, Poland
  3. Interdisciplinary Program in Neuroscience, Bioengineering Department, George Mason University, United States
  4. Krasnow Institute for Advanced Study, George Mason University, United States
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Cite this article as: eLife 2021;10:e64644 doi: 10.7554/eLife.64644

Abstract

Long-lasting long-term potentiation (L-LTP) is a cellular mechanism of learning and memory storage. Studies have demonstrated a requirement for extracellular signal-regulated kinase (ERK) activation in L-LTP produced by a diversity of temporal stimulation patterns. Multiple signaling pathways converge to activate ERK, with different pathways being required for different stimulation patterns. To answer whether and how different temporal patterns select different signaling pathways for ERK activation, we developed a computational model of five signaling pathways (including two novel pathways) leading to ERK activation during L-LTP induction. We show that calcium and cAMP work synergistically to activate ERK and that stimuli given with large intertrial intervals activate more ERK than shorter intervals. Furthermore, these pathways contribute to different dynamics of ERK activation. These results suggest that signaling pathways with different temporal sensitivities facilitate ERK activation to diversity of temporal patterns.

Introduction

Temporal patterns are a key feature of the environment. The speed of traversing space is indicated by the time between spatial cues. In classical conditioning, adaptive changes in behavior require an animal to respond to a cue in an appropriate time frame to gain a reward or avoid punishment (Delamater and Holland, 2008; Mauk and Ruiz, 1992). In these and other tasks, environmental cues, i.e., sensory inputs, are converted into spatio-temporal patterns of activation. Pattern discrimination requires that neurons are able to discriminate and respond differently to these different temporal input patterns (Bhalla, 2017); conversely, neurons need to be able to learn despite a difference in temporal patterns.

Long-term potentiation (LTP), the activity-dependent and persistent strengthening of synapses, is widely considered to be a cellular mechanism underlying memory storage. The temporal pattern sensitivity of neurons is evident from the wide range of synaptic plasticity induction protocols, with some protocols producing LTP and some producing weakening of synapses (Malenka and Bear, 2004). Memory consolidation is also affected by temporal patterns: it has been shown that theta oscillations, which emerge during learning, and sharp-wave ripples can influence LTP induction (Çalışkan and Stork, 2018; Sadowski et al., 2016; Wang et al., 2020), demonstrating a role for temporal patterns during memory consolidation.

In the hippocampus, two ‘phases’ of LTP are distinguished. Late-phase LTP (L-LTP), induced by repetitive stimulation, can last more than 8 hr and involves de novo protein synthesis (Davis et al., 2000; Sweatt, 2004; Tang and Yasuda, 2017). In contrast, early-phase LTP does not require protein synthesis and typically does not persist for more than 2 hr. It is also important to distinguish between induction and maintenance of L-LTP. Induction of L-LTP refers to the processes occurring during and shortly after the induction stimulation, whereas maintenance of L-LTP refers to the processes occurring tens of minutes to hours after induction.

A critical molecule in induction of L-LTP and memory is extracellular signal-regulated kinase (ERK) (English and Sweatt, 1997). Numerous studies have demonstrated that ERK contributes to L-LTP induction by controlling the transcription and protein translation necessary for L-LTP (for review, see Miningou and Blackwell, 2020; Peng et al., 2010), as well as increasing cell excitability by phosphorylating potassium channels (Schrader et al., 2006). ERK is activated by a cascade of kinases (Buscà et al., 2016; Terrell and Morrison, 2019), which are activated by Ras family GTP binding proteins, which are controlled by diverse Guanine nucleotide Exchange Factors (GEFs) and GTPase-activating proteins (GAPs). Several of these GEFs and GAPs play a pivotal role in synaptic plasticity and neurodevelopmental disorders, but their role in ERK activation during induction of L-LTP has not been demonstrated.

In the hippocampus, synaptic stimulation leads to activation of these GEFs and GAPs. Influx of calcium activates the calcium-sensitive GEF, RasGRF (Feig, 2011; Schwechter et al., 2013), and, via CaMKII, enhances activity of the synaptically localized GAP, SynGap, while dispersing it from the spine (Gamache et al., 2020). The intracellular second messenger cyclic adenosine monophosphate (cAMP) activates two key molecules upstream of ERK activation: protein kinase A (PKA) and the GEF exchange factor activated by cAMP (Epac) (de Rooij et al., 2000; Enserink et al., 2002; Schmitt and Stork, 2002). However, the contribution of calcium and cAMP pathways to ERK activation during L-LTP induction is unclear. A critical question is to what extent those signaling pathways work synergistically to activate ERK, whether they are redundant or whether they operate in different temporal regions.

A second critical question is how patterns of synaptic input determine which set of signaling pathways activate ERK leading to the induction of L-LTP. Key ERK activators, such as PKA and CaMKII, exhibit different temporal sensitivity: cAMP/PKA favors spaced LTP stimulation protocols (Kim et al., 2010; Scharf et al., 2002; Woo et al., 2003), while calcium/CaMKII prefers massed LTP stimulation (Ajay and Bhalla, 2004; Kim et al., 2010). Both of these signaling pathways converge on ERK, allowing the neuron to learn despite a variation in temporal pattern; on the other hand, temporal pattern can still influence the response of the neuron by controlling the temporal pattern of ERK activation. For example, transient ERK leads to proliferation, while sustained ERK leads to differentiation (Santos et al., 2007; Sasagawa et al., 2005; von Kriegsheim et al., 2009).

To answer these questions about temporal pattern and synergy, we developed a single-compartment computational biochemical model of postsynaptic signaling pathway underlying L-LTP induction in hippocampal CA1 pyramidal neurons. Simulations reveal that ERK pathways work synergistically, that the contribution of cAMP increases while the calcium contribution decreases with spaced stimuli, with ERK activity favoring spaced stimuli. The calcium- and cAMP-activated pathways have distinct temporal dynamics, providing a mechanism whereby different temporal patterns can activate different downstream effectors.

Results

Model validation

To investigate how temporal pattern of synaptic activity determines which pathway in the ERK signaling cascade (Figure 1A, Figure 1—source data 15) dominates in dendritic spines of hippocampal CA1 pyramidal neurons, we developed a single-compartment, stochastic reaction–diffusion model of pathways activating ERK. The model included two calcium signaling pathways (RasGRF and SynGap) and three cAMP signaling pathways (Epac, PKA, and the βγ subunit of Gi). The model was built by merging and adapting two existing models of synaptic plasticity in hippocampal neurons (Jain and Bhalla, 2014; Jȩdrzejewska-Szmek et al., 2017). These previously published models were modified by adding SynGap and RasGRF, which are critical for ERK activation.

Schematic representation of signaling pathways activating ERK.

(A) Five pathways are included in the model: calcium activation of (1) RasGRF followed by RasGTP production or (2) CaMKII phosphorylation of SynGap followed by increasing RasGTP and Rap1GTP lifetime; cAMP activation of (3) Epac or (4) PKA phosphorylation of Src family kinase, leading to Rap1GTP production; Gi subtype of GTP binding protein (Giβγ) (5) recruits Src family kinase followed by activation of RasGTP. (B) Four effects of CaMKII on SynGap were evaluated. KCK: No autophosphorylation of CaMKII, KSyn1: No pCaMKII binding to SynGap, KSyn2: SynGap binds to pCaMKII, but cannot be phosphorylated, KSyn3: SynGap phosphorylated, but not dispersed to the dendrite. (C) LTP protocols: four trains of 100 Hz (each 1 s duration) spaced by different intertrial intervals: 3, 20, 40, 80, and 300 s.

Figure 1—source data 1

Reactions and rate constants involved in signaling pathway leading to Ras and Rap1 activation.

https://cdn.elifesciences.org/articles/64644/elife-64644-fig1-data1-v2.docx
Figure 1—source data 2

Reactions and rate constants involved in signaling pathway of SynGap.

https://cdn.elifesciences.org/articles/64644/elife-64644-fig1-data2-v2.docx
Figure 1—source data 3

Reactions and rate constants involved in core ERK signaling pathway.

https://cdn.elifesciences.org/articles/64644/elife-64644-fig1-data3-v2.docx
Figure 1—source data 4

Reactions and rate constants involved in signaling pathways from calcium to CaMKII.

https://cdn.elifesciences.org/articles/64644/elife-64644-fig1-data4-v2.docx
Figure 1—source data 5

Reactions and rate constants involved in signaling pathways leading from cAMP to PKA.

https://cdn.elifesciences.org/articles/64644/elife-64644-fig1-data5-v2.docx
Figure 1—source data 6

Total concentrations of molecule species.

https://cdn.elifesciences.org/articles/64644/elife-64644-fig1-data6-v2.docx

To validate the model, we replicated the results from several published experiments. First, we simulated an experiment measuring RasGTP in response to glutamate uncaging at 0.5 Hz with 0 mM extracellular Mg2+ (Harvey et al., 2008), by delivering a single pulse of 0.5 µM of calcium for 60 s. RasGTP dynamics are qualitatively consistent with experimental measurements of Harvey et al., 2008 (Figure 2A). Second, we mimicked an L-LTP experiment that applied two trains of 100 Hz frequency spaced by 20 s intervals (Kasahara et al., 2001), by injecting 5 µM calcium, 1 µM cAMP, and 0.1 µM Giβγ. The simulation shows qualitative match of ERK activation to the experimental model as ERK peaks around 3 min after stimulation and returns to basal about 30 min after stimulation (Figure 2B). Third, we show that cAMP-bound Epac and phosphorylation of PKA substrates are similar to that measured in hippocampal neurons (Figure 2—figure supplement 1A and B). Fourth, we show that our parameter optimization was successful, allowing us to reproduce CaMKII activation (Figure 2—figure supplement 1C) and CaMKII phosphorylation of SynGap (Figure 2—figure supplement 1D). Additional validations, comparing results to knockout experiments, are shown after the L-LTP results. In summary, the model is based on two, well-constrained, and validated signaling pathway models and is further validated experimentally with several systems level experiments.

Figure 2 with 1 supplement see all
Model validation.

(A) Time course of RasGTP in response to 30 pulses at 0.5 Hz (Harvey et al., 2008). RasGTP dynamics are qualitatively consistent with experimental measurements. (B) Relative increase of ppERK in response to L-LTP stimuli (two bursts of 100 Hz for 1 s, bursts separated by 20 s) (Kasahara et al., 2001). Simulation shows qualitative match of ERK activation to the experimental model as ppERK peaks around 3 min after stimulation and returns to basal about 30 min after stimulation.

Single-pulse stimuli: maximal ERK activation requires multiple pathways

In order to assess whether multiple pathways are required for maximal ERK activation, both single pathway and multi-pathway dynamics were monitored. Simulation experiments used different amplitude ranges (for 1 s) and different durations of the input to evaluate doubly phosphorylated ERK (ppERK) (Table 1). We assessed whether the ERK response is graded or ultrasensitive and whether multiple pathways combine linearly or nonlinearly.

Table 1
Single pathway experiment.
InputAmplitude protocol (µM)Duration protocol (s)
Calcium1 s: 0.2, 0.3, 0.5, 1, 1.5, 2, 50.5 µM: 1, 2, 4, 5, 6, 8, 10, 30, 100
1 µM: 1, 4, 100
cAMP1 s: 0.1, 0.2, 0.5, 1, 1.5, 20.1 µM: 1, 4, 10, 30, 100
0.5 µM: 1, 4, 10, 30, 100
Giβγ1 s: 0.005, 0.03, 0.1, 0.50.03 µM: 1, 4, 10, 30, 100
0.1 µM: 1, 4, 10, 30, 100

Linear activation by cAMP pathway: opposite dynamics of Epac and PKA

cAMP activates ERK through three different pathways: Epac activation of Rap1GTP, PKA phosphorylation of Src, and PKA phosphorylation of β adrenergic receptors (βAR), which switches βAR coupling from Gs to Gi, which is followed by Giβγ recruitment of Src (Lin et al., 2013; Luttrell et al., 1997). To separate the direct action of cAMP (i.e. Epac activation of Rap1GTP or PKA phosphorylation of Src) from its indirect action through the switching pathway, we evaluated the effect of Giβγ separately and in combination with Epac and PKA direct activation.

Model simulations show a linear activation of ppERK with either cAMP duration or concentration (Figure 3, Table 2), through the direct pathway and a slightly non-linear activation with indirect pathway. As observed in Figure 3A,B, as the input duration increases, ppERK amplitude and duration increase. Similarly, the indirect cAMP pathway displays linear activation of ERK with Giβγ input (Figure 3C). Figure 3D shows that increasing the input duration (red traces) or concentration (black trace) is similarly effective in increasing ppERK. Giβγ produces a delayed activation of ERK consistent with experimental data (Koch et al., 1994; Schmitt and Stork, 2002) and a computational model showing a 7 min delay (Khalilimeybodi et al., 2018). cAMP and Giβγ input for these simulations are shown in Figure 3—figure supplement 1. In summary, in response to cAMP input, ppERK total activity is linearly related to the input duration and concentration, with a delayed activation through the indirect pathway.

Figure 3 with 1 supplement see all
Linear activation of ERK by cAMP pathways.

(A) ppERK response to a single pulse of 0.5 μM cAMP is graded with duration. (B) Integral of ppERK concentration over time (AUC) in response to different cAMP concentrations (for 1 s) and different cAMP durations (with a concentration of 0.5 μM). (C) Time course of ppERK in response to single pulses of 0.1 μM Giβγ for different durations. Recruitment of ERK by Giβγ binding protein shows delayed activation. (D) Total activity of ppERK in response to different Giβγ concentrations (for 1 s) and durations (with a concentration of 0.1 μM). Increasing duration or concentration are similarly effective in increasing ppERK. (E) Direct and indirect cAMP pathways combine linearly for all duration inputs and sublinearly, with prolonged duration inputs. Two-way ANCOVA (analysis of covariance) of ppERK AUC versus stimulation characteristics (duration) and type (combination versus summation) as factors (N = 5 in each group) is significant for both duration and type (F (2,47) = 419.5, T < 0.001; P(dur) < 0.0001, T(dur) = 28.61, P(type) < 0.0001, T(type) = 4.54). Combo: response to Giβγ and cAMP, sum: sum of the responses in (A) and (C). (F) Ratio of ppERK to basal ppERK in response to cAMP activation of PKA, Epac or Giβγ (0.5 μM (cAMP) or 0.1 μM (Giβγ) for 30 s). ppERK increases quickly and transiently with Epac and with a delay and more prolonged in response to PKA or Giβγ.

Table 2
Regression analysis results for cAMP pathway.

AIC: Akaike information criteria, lower values indicate better models. If adjusted R2 for linear is less than 0.9, then the best model is determined by AIC.

GiβγcAMPCalcium
DurConcDurConcDurConc
Adjusted R2Linear0.8320.8270.9510.9370.4860.675
log0.8800.7870.9570.8150.9550.604
Hill0.9220.9130.9690.9640.9700.989
AICLinear−1.112−8.266−10.181−52.828166.22599.958
log10.19624.02213.45813.710107.598127.772
Hill−28.406−38.033−48.562−48.911−86.367−101.415
ConclusionNon-linearNon-linearLinearLinearNon-linearNon-linear

To investigate the activation of ERK by Epac and PKA individually, the simulations were repeated while blocking cAMP binding to one of these molecules (Table 3). When cAMP binding to Epac is blocked, the basal quantity of ppERK is dramatically reduced (results not shown), implying that Epac is the main source of basal ppERK. The remaining activity, due to PKA, shows a delayed activation of ERK (Figure 3F). In contrast, Epac produces a fast and transient activation of ERK (Figure 3F). Similarly to PKA activation, Giβγ shows a delayed activation of ERK (Figure 3F). Thus, Epac contributes to ERK activation with different temporal dynamics compared to PKA and Giβγ.

Table 3
Knockout experiment.

Rate constant names are shown in Figure 1A,B. Block lists the rate constant whose value is set to zero.

InputBlockEffect/molecular dependence
Calcium
2000 nM for 1 s
KCKCaMKII is activated but cannot autophosphorylate itself, thus RasGRF is the only contributor
KSyn1pCaMKII is unable to bind to SynGap
KSyn2pCaMKII binds to SynGap but is unable to phosphorylate SynGap
KSyn3SynGap is phosphorylated but is unable to disperse to the dendrite
cAMP
500 nM for 30 s
KEpacEpac binds cAMP but cannot activate Rap1GDP, thus PKA is the only contributor
KPKAFinal step of PKA pathway activation of Rap1GDP is blocked, thus Epac is the only contributor

Direct and indirect cAMP pathways combine linearly for short duration inputs and sublinearly with prolonged duration inputs. Figure 3E shows that the response to stimulating all three cAMP pathways overlaps with the sum of the single pathway responses only at a short duration. As the stimulus duration increases, the ppERK response is slightly lower than the sum of responses to cAMP direct and indirect activation (Figure 3E,F). Sublinear summation is due to two loci of competition. First, competition was observed between the PKA phosphorylation of Src and Giβγ activation of Src. PKA has a higher affinity for Src than does Giβγ; therefore, Src is trapped by PKA, reducing available Src for Giβγ. This sublinear response is observed with 2× and 4× increases in Src quantity (results not shown), demonstrating that the sublinear summation is not due to Src depletion but indeed due to Giβγ and PKA competition with Src. The second competition was observed between Epac and the Giβγ/Crk-C3G for Rap1GDP. Rap1GDP is utilized by Epac, which reduces the Rap1GDP availability for Giβγ/Crk-C3G. Blocking Epac allows more Rap1GDP to bind Crk-C3G, prolonging ppERK activity as observed with Giβγ alone. In conclusion, competition between PKA and Giβγ for Src, and between Epac and Crk-C3G for Rap1GDP, affects summation in the cAMP pathway.

Non-linear activation by calcium pathways: SynGAP dispersion and phosphatase activity control ERK activation by calcium

Model simulations show a non-linear activation with either calcium duration or concentration. Figure 4A reveals that low calcium inputs produce little to no ppERK, whereas with higher calcium inputs, ppERK reaches a plateau and the duration of ppERK is prolonged. Similar results are observed with increasing duration using 0.5 μM calcium concentration. Total activity of ppERK (Figure 4B, Table 2) reveals a supralinear response (also called ultrasensitivity), with a calcium duration threshold of 5 s and an amplitude threshold between 1 and 2 μM. A calcium amplitude or duration above these thresholds induces maximal and sustained ppERK. Calcium input for these simulations is shown in Figure 3—figure supplement 1A.

Nonlinear activation of ERK by calcium pathway.

(A) Time course shows a sustained ppERK when calcium is above amplitude threshold (2 μM) for 1 s duration. (B) Total ppERK activity over time in response to different calcium concentrations (for 1 s) and different calcium durations (with a concentration of 0.5 μM) reveals ultrasensitive response. (C) With CaMKII activity blocked, RasGRF is the sole calcium-activated pathway to ERK activation. ERK activation is no longer ultrasensitive. (D) pCaMKII and ppERK activities in response to 0.5 μM for 30 s of calcium decrease with increased PP1. Similar results were observed with different concentrations or duration. (E) Increasing PP1 quantity decreases the steepness of ppERK vs duration (log10) curve. (F) Total ERK activity changes with SynGap availability. Blocking dispersion of SynGAP reduces ppERK, whereas allowing CaMKII to bind but not phosphorylate SynGAP enhances ppERK. (G) Ratio of ppERK to basal ppERK in response to calcium activation of RasGRF or SynGap alone (0.5 µM calcium for 30 s), compared with control (SynGap + RasGRF).

To determine whether the ultrasensitivity of ppERK was caused by CaMKII, we blocked CaMKII phosphorylation (of itself and SynGap) and assessed ERK activation by RasGRF. Blocking CaMKII significantly reduces ppERK activity, especially for long or high calcium inputs (Figure 4C). We also observed a shift from a sustained and prolonged ppERK to a transient ppERK, which is caused by calmodulin activation of RasGRF (Figure 4G). This shows that RasGRF is responsible for the early calcium activation of ERK.

The ultrasensitivity of CaMKII autophosphorylation has been shown to depend on the quantity of the phosphatase PP1 (Bradshaw et al., 2003; Singh and Bhalla, 2018), and thus might regulate the calcium duration and amplitude thresholds. We used a concentration of 3.6 µM of PP1 (PP1: CaMKII ratio = 18%) based on previous reports (Rangamani et al., 2016). To evaluate whether PP1 quantity controls the ppERK non-linear response, we repeated simulations with different quantities of PP1 (10, 50, and 100% of CaMKII quantity). Model simulations show that both ppERK and phosphorylated CaMKII decrease as PP1 concentration increases (Figure 4D). The calcium duration producing half-maximal ppERK did not change much with increased PP1; however, the sensitivity to calcium duration decreased with an increase in PP1 (Figure 4E, Table 4). Thus, our data demonstrate that PP1 indirectly influences ppERK amplitude and sensitivity to calcium duration through modulation of pCaMKII. Therefore, the ultrasensitivity of both CaMKII and ppERK depends on the ratio of CaMKII to PP1 quantity.

Table 4
PP1 concentration influences ppERK quantity and ultrasensitivity.

The calcium duration producing half-maximal ppERK AUC and the sensitivity to duration were estimated by fitting a hill equation to ppERK AUC vs calcium duration. Values shown are parameter estimates ± standard deviation of the estimate. Width at half max: the calcium duration at half-maximal ppERK.

Pp1 (%)Width at half maxHill coefficient
106.0 ± 1.074.1 ± 1.5
186.7 ± 1.532.5 ± 1.1
509.9 ± 5.281.4 ± 1.1

CaMKII does not directly activate ERK but instead modulates ERK phosphorylation through its phosphorylation of SynGap, a molecule that inactivates Ras family GTPases. The effect of CaMKII phosphorylation is complex, including enhanced SynGap activity (Walkup et al., 2015) and SynGap dispersion from the spine (Araki et al., 2015). We evaluated the contribution of these processes by eliminating them individually. Simulations reveal that persistent activation of ERK requires phosphorylation of SynGap by pCaMKII and dispersion of pSynGap to the dendrite (Figure 4F). A lower ppERK total activity results when pSynGap remains anchored in the spine (Figure 1B, Figure 4F, no pSynGap dispersion trace). Blocking the phosphorylation of SynGap was implemented using two approaches. In one, CaMKII can bind to SynGap but does not phosphorylate it. This reduces the available SynGap, which doubles ppERK concentration compared to control (Figure 4F, pCK bound to SynGap). In the second approach, CaMKII is unable to bind to SynGap. This increases the available SynGap, resulting in a reduction of ppERK below basal (Figure 4F, no pCK bound to SynGap). These data suggest that the quantity of free SynGap in the spine, which is controlled by CaMKII, regulates ERK activation. To verify that the results were not an artifact of the binding affinity implemented in the model, simulations were repeated using 10× and 100× lower affinity of pCaMKII for SynGap. Simulation results show a similar relation of ppERK to pSynGap, reinforcing the hypothesis that CaMKII regulates ppERK total activity through its modulation of SynGap.

Overall ppERK response is a linear combination of response to calcium and cAMP

Simulations reveal that both pathways (calcium, cAMP) combine linearly to activate ERK. Figure 5A shows that the response to stimulating both pathways overlaps with the sum of the single pathway responses. This summation was observed with short and long duration stimuli and with high- and low-amplitude stimuli, regardless of whether calcium was below or above the threshold. When calcium is below threshold (e.g. short duration stimuli), cAMP contributes more to ppERK, whereas when calcium is above the threshold, it provides most of the ppERK (Figure 5B). The contribution of cAMP is transient, occurring briefly after induction while the calcium contribution is delayed and sustained (Figure 5C). The two pathways have distinct temporal dynamics that overlap and switch in their contribution about 3 min after induction. Further subdividing pathway contributions (Figure 5D) reveals that the transient ppERK is produced by Epac, with PKA and Gi contributing to a small sustained ppERK. Most of the sustained ppERK is produced by SynGap, with RasGRF contributing to a small transient ppERK.

Overall ppERK response is a linear combination of response to calcium and cAMP.

(A) Time course of ppERK response to calcium and cAMP. Calcium in combination with cAMP traces overlaps with the sum of the single pathway responses for both short and long duration stimuli. Two-way ANCOVA (analysis of covariance) of ppERK AUC versus stimulation characteristics (duration) and type (combination versus summation) as factors (N=5 in each group) is significant for both stimulation but not type (F (2,47) = 65.55, P(dur) < 0.0001, T(stim) = 11.41, P(type) = 0.35, T(type) = −0.945). (B) Summary of ppERK AUC versus duration shows that the fraction of ppERK produced by calcium pathways increases with duration of the stimulation. (C) Dynamics of ppERK, relative to basal ppERK, in response to cAMP (0.5 µM cAMP and 0.1 µM Giβγ for 30 s), calcium (0.5 µM for 30 s), or combination. ppERK increases transiently with cAMP, with a delay in response to calcium and is higher with combination (calcium and cAMP ). (D) Dynamics of single pathways. Ratio of ppERK to basal ppERK in response to PKA (0.5 µM cAMP), Epac (0.5 µM cAMP), Giβγ (0.1 µM), RasGRF (0.5 µM calcium), and SynGap (pCaMKII feedforward loop; 0.5 µM calcium) for 30 s. Epac and RasGRF produce transient ppERK, whereas PKA, Giβγ, and SynGap produce transient and delayed ppERK. C2 and D2 expand the first 100 s after stimulation of C1 and D1, respectively.

In summary, ppERK exhibits a non-linear response to calcium, a linear response to cAMP pathways, and the response to the combination of pathways also is a linear combination of the single pathway responses. Nevertheless, each pathway exhibits distinct temporal pattern dynamics. However, these simulations used single pulses of stimuli; thus, the next section evaluates the response to stimuli similar to those used for synaptic plasticity experiments.

L-LTP stimuli: ERK signaling pathway temporally integrates input signals

Previous research has shown that different temporal patterns for inducing L-LTP work through different signaling pathways: PKA is needed for spaced stimuli, while CaMKII is greater in response to massed stimuli. Thus, a critical question is whether different temporal patterns select different signaling pathways for activation of ERK. To evaluate that question, we simulated the response to L-LTP inputs. As in L-LTP experiments, the model was activated with four trains of 100 Hz stimuli for 1 s using a range of intertrain intervals (ITIs), including massed (3, 20, 40 s) and spaced (80,300 s) ITI.

Temporal sensitivity of ppERK to cAMP matches that of PKA

Since ppERK increases more with cAMP duration than concentration (either direct action or in combination with Giβγ), as shown above, we predicted that ppERK would be greater for spaced than massed stimulation with cAMP. Model simulations with cAMP input show that ppERK total activity increases as ITI increases (Figure 6). Note that the ppERK amplitude decreases with ITI (Figure 6A), but the increase in ppERK duration more than compensates for the lower amplitude, resulting in greater total activity for the 300 s ITI. The summation is significantly higher than the combination as observed with single-pulse stimuli: ppERK in response to Giβγ plus Epac and PKA pathways is less than the sum of the responses to either pathway alone (Figure 6B). Competition for Src and Rap1GDP, which limits linear summation, is also observed for L-LTP stimuli. Note that the temporal sensitivity of ppERK is similar to that of PKA (Figure 6B). However, the Epac pathway contributes more to ppERK with short ITI while PKA contributes more with spaced stimuli (Figure 6—figure supplement 1), suggesting an Epac-dependent L-LTP for short ITIs. In summary, ERK activated by cAMP exhibits sensitivity to ITI and is greater with spaced stimuli. These data are consistent with experiments showing a requirement for PKA in spaced but not massed stimulation, and simulations showing an increase in PKA activity with spaced stimulation (Kim et al., 2010; Woo et al., 2003).

Figure 6 with 1 supplement see all
ppERK favors spaced stimuli in response to cAMP input.

(A) Time course of ppERK in response to 4 trains of 100 Hz stimuli of cAMP (Epac, PKA, Giβγ pathways). ppERK peak amplitude decreases with ITI, but the AUC increases with ITI. (B) Total kinase activity in response to cAMP shows that ppERK exhibits sublinear response to cAMP stimuli: the sum (dashed line) is higher than ppERK in response to combination (solid black line). PKA and ppERK have similar temporal sensitivity, favoring spaced stimuli. Two-way ANCOVA (analysis of covariance) of ppERK AUC versus stimulation characteristics (ITI) and type (combination versus summation) as factors (N = 5 in each group) is significant for both stimulation ITI and type (F (2,47) = 42.25, T < 0.0001; T(ITI) = 4.67, P(ITI) < 0.0001, T(type) = 7.92, P(type) < 0.0001).

ppERK favors longer ITIs, independent of CaMKII temporal sensitivity

L-LTP simulations using 1 µM amplitude calcium pulses produce similar ppERK traces for ITIs between 3 and 40 s (Figure 7A). Multiple 1 s pulses of 1 µM calcium are similar to a single 5 s pulse, due to the slow decay of pCaMKII; thus, calcium is above the threshold for CaMKII ultrasensitivity and ppERK is sustained for a long duration, consistent with experimental data showing that CaMKII above threshold is enough to induce L-LTP (Shibata et al., 2021). Only with a 300 s ITI does pCaMKII and ppERK decay (though not to basal) between stimuli. The temporal sensitivity of ppERK in response to calcium input tends toward longer ITIs than the temporal sensitivity of CaMKII. The greatest total activity of ppERK (Figure 7B) and pCaMKII (Figure 7C) are observed with 80 s and 3 s ITI, respectively. To test the role of CaMKII ultrasensitivity in the temporal sensitivity of ppERK, we repeated simulations with an increased PP1 quantity (10 µM or 50% ratio). As observed with 18% PP1, the greatest pCaMKII occurs with short ITIs, as reported previously (Ajay and Bhalla, 2004; Kim et al., 2010), but the decrease in pCaMKII with ITI is steeper with 50% PP1. This change shifted ppERK temporal sensitivity slightly to favor middle ITIs but still does not match the temporal sensitivity of CaMKII.

Figure 7 with 2 supplements see all
ppERK favors spaced stimuli in response to calcium input, in contrast to temporal sensitivity of CaMKII.

(A) Time course of ppERK in response to four trains of 100 Hz calcium stimuli (1 μM concentration) shows sustained and prolong ppERK with 3 and 40 s ITI. (B) ppERK AUC changes with PP1 quantity, but still is highest for spaced ITIs. (C) Increasing PP1 quantity or lowering calcium concentration makes CaMKII more sensitive to shorter ITIs.

In addition to varying PP1 quantity, we used lower concentration calcium pulses and an alternative CaMKII model (alt CaMKII) (Dupont et al., 2003; Jȩdrzejewska-Szmek et al., 2017) that does not exhibit the same ultrasensitivity. Simulations with this alternative CaMKII model reveal a small shift in temporal sensitivity toward smaller ITIs, but the temporal sensitivity of ppERK still tends toward longer ITIs than the temporal sensitivity of CaMKII. Similar results were observed with the ultrasensitive CaMKII model when smaller calcium pulses (0.5 µM) were used (Figure 7B,C). In addition, ERK’s temporal sensitivity follows RasGRF (low calcium) and SynGap (high calcium) temporal activity (Figure 7—figure supplement 1). Similar to what was observed with single-pulse experiments, either blocking dispersion of SynGap or blocking pCaMKII binding to SynGap reduces ppERK (Figure 7—figure supplement 2). In summary, though the ultrasensitivity of CaMKII is controlled in part by PP1, ppERK temporal sensitivity does not follow CaMKII temporal sensitivity, and instead follows the temporal sensitivity of CaMKII downstream targets such as SynGap.

ppERK favors long intertrial intervals

To simulate L-LTP in response to four trains of synaptic activation, we used both calcium and cAMP inputs, as would occur with glutamatergic inputs. L-LTP simulations with both calcium and cAMP show an increase of ppERK total activity with longer ITI. Results show that the greatest total ppERK occurs at 80 s (using 18% PP1 and 1 µM calcium) or 300 s (using 50% PP1-1 µM calcium or 18% PP1-0.5 µM calcium) (Figure 8A). Though the change in optimal ITI varies little, the total quantity of ppERK greatly depends on calcium and PP1 concentration. In these simulations, the contribution of the cAMP pathway to ppERK is independent of calcium, in part because cAMP, calcium, and Giβγ are specified independently (Figure 8—figure supplement 1). To address the question of which pathway contributes more to ppERK and whether different temporal patterns use different pathways, we calculated the percent ppERK produced by each pathway. cAMP is responsible for a majority of the ppERK with below threshold calcium, but only responsible for a third of the ppERK for above threshold calcium (Figure 8B). Analyzing the five pathways separately reveals ppERK increases with ITI for all pathways (Figure 8—figure supplement 2). Nonetheless, the relative contribution of SynGap decreases with ITI, as the other pathways increase more with ITI (Figure 8C). As seen with single-pulse stimuli, pSynGap is the main source of prolonged ppERK, whereas Epac and RasGRF are main sources of transient ppERK (Figure 8—figure supplement 3).

Figure 8 with 4 supplements see all
ppERK integration of calcium and cAMP inputs can be linear or supralinear.

(A) ppERK mostly increases with temporal interval, with the greatest quantity occurring at 80 s (above calcium threshold or 18% PP1) or 300 s (below calcium threshold). Supralinear summation occurs at 18% PP1 and linear summation occurs at low calcium or high PP1 – conditions that reduce ultrasensitivity of CaMKII (Figure 3E). Supralinearity is indicated by the response to the combination of cAMP and calcium (Combo) being greater than the sum of responses to calcium and cAMP separately. ANCOVA results are in Table 5. (B) Summary of ppERK total activity in response to 300 s ITI. The contribution of the calcium pathway relative to the cAMP pathway is greatest when calcium is above threshold for an ultrasensitive CaMKII response. (C) Qualitative single pathway contribution to ppERK (ppERK from single pathway divided by ppERK from all pathways; sum of pathways exceeds 100%). The contribution of SynGap decreases with ITI, whereas other pathways increase with ITI.

Table 5
Two-way ANCOVA (analysis of covariance) results for ppERK AUC versus stimulation characteristics (ITI) and type (combination versus summation) as factors (N = 5 in each group).
cAMP+Giβγ+calcium
0.5 µM ca18% PP150% PP1
F (2,47)43.5628.283.99
P (ITI)<0.0001<0.00010.023
T (ITI)9.116.432.36
P (type)0.05<0.00010.13
T (type)−2.04−3.90−1.56
ConclusionSignificant for stim onlySignificant for both type and stimSignificant for stim only

ppERK linearly integrates the calcium and cAMP inputs when calcium is below threshold. Thus, the response to the combined stimuli is similar to the sum of ppERK responses to individual stimuli with 0.5 µM calcium (Figure 8A). Similar results were obtained with 50% PP1. With 18% PP1 and high calcium (above threshold), supralinear summation was observed: the response to the combination is greater than the summation of individual responses (Figure 8A). CaMKII modulation of SynGap with above threshold calcium may be responsible for the supralinear summation as SynGap dispersion enhances RasGTP and Rap1GTP in response to cAMP.

To further investigate responses to synaptic input, we simulated our model with five different L-LTP protocols. Two of them, bath-applied isoproterenol (ISO) followed by either 1 s of 100 Hz stimulation or 180 s of 5 Hz, experimentally elicit LTP, whereas giving 100 Hz, 5 Hz, or ISO alone do not. For these protocols, cAMP, calcium, and Giβγ inputs (Figure 9—figure supplement 1) were determined from a spatial model response to glutamate (Jȩdrzejewska-Szmek et al., 2017); thus, cAMP is produced by Gs and calcium-calmodulin activation of adenylyl cyclase. Simulation results show that isoproterenol followed by either 100 Hz or 5 Hz produce greater ppERK than ISO, 100 Hz, or 5 Hz alone (Figure 9). These results are consistent with experimental observations (Gelinas et al., 2008a; Gelinas et al., 2008b; Winder et al., 1999) that the combination stimuli are needed to produce L-LTP, thus validating the model. In addition, our results show that cAMP provided by ISO is compensating for the strong calcium input provided by four trains of 100 Hz.

Figure 9 with 1 supplement see all
ppERK predicts the occurrence of L-LTP when bath-applied ISO is followed by either 1 s of 100 Hz stimulation or 180 s of 5 Hz.

ppERK in response to isoproterenol (ISO), 1 s of 100 Hz, or 180 s of 5 Hz does not exceed 30 nM (A), whereas ppERK reaches or exceeds 35 nM in response to the combination of isoproterenol and either 100 Hz or 5 Hz stimulation (B).

We performed additional simulations to evaluate the role of Ras and Raf isoforms and to further validate the model. First, we simulated Raf knockout experiments and measured ERK activity in response to four trains of 100 Hz. Simulation results are consistent with experimental data (Chen et al., 2006; Li et al., 2016; Takahashi et al., 2017; York et al., 1998) as bRaf knockout, but not Raf1 knockout, greatly reduces ERK activity (Figure 8—figure supplement 4A). Second, we simulated Ras or Rap knockout and measured ERK activity after LTP induction. Simulation results are consistent with experimental data (Grewal et al., 2000b; Grewal et al., 2000a; Keyes et al., 2020; Li et al., 2016; Takahashi et al., 2013; York et al., 1998; Zhang et al., 2018) as knocking out Rap1 produces a greater ppERK deficit than knocking out Ras (Figure 8—figure supplement 4B). We assessed whether Ras could compensate for Rap and vice versa, by doubling the quantity of the remaining GTPase. Result shows that doubling Ras cannot compensate for the Rap1 knockout, whereas doubling Rap1 increases ppERK above the control (Figure 8—figure supplement 4B2). This shows, for the first time, that overexpression of Rap1 can compensate for Ras activity in ERK activation.

A unique aspect of our model is that full activation of Raf1-RasGTP requires dimerization; thus, we evaluated the impact of dimerization on ERK activation. Dimerization reduces the temporal sensitivity of ppERK (Figure 8—figure supplement 4A), as the difference in ppERK between 3 s and 300 s ITIs is much larger when dimerization does not occur. The biggest effect is a reduction in ppERK at short ITIs; thus, dimerization enhances ppERK mostly for short ITIs.

In summary, these results demonstrate that ERK signaling pathways integrate multiple inputs synergistically. In fact, ppERK activity in response to the combination of calcium and cAMP is always greater than the response to either calcium or cAMP alone. For high calcium inputs, as likely occur during L-LTP induction, these inputs combine supralinearly. Synergy is attributable to CaMKII phosphorylation of SynGap, as dispersion of SynGap from the spine enhances RasGTP and RapGTP in response to both calcium and cAMP inputs. Furthermore, our simulations suggest that Raf dimerization enhances Raf1 activation of ERK in response short ITI, thereby reducing the temporal sensitivity of ERK activation.

Robustness

In computational models, it is critical to ensure the robustness of the results to variation in parameter values. The main result of the model is that ERK signaling pathways, no matter the protocol used, favor spaced stimuli. To assess the robustness of the temporal sensitivity of ERK signaling pathways to small variations in parameters, simulations were repeated using concentrations of ±10% of the control value. The concentrations were changed either individually or collectively with changes drawn from a uniform distribution (between −10% and +10%). These simulations show that total ERK increase with ITI, similar to control results. Table 6 shows that the optimal ITI was 80 or 300 s (spaced) 80% of the time. We also evaluated the mean ppERK (across all ITIs) and the degree of temporal sensitivity, quantified as the difference between maximum ppERK and minimum ppERK (across ITIs). Results show that a 10% change in a single-molecule quantity rarely produced more than 20% change in mean ppERK (Figure 10A), with changes evenly distributed about 0%. In contrast, temporal sensitivity was more sensitive to parameter variations, with most parameter changes increasing temporal sensitivity (Figure 10B). An increase in temporal sensitivity with minimal change in mean ppERK implies that the response to short ITIs decreases while the response to long ITIs increases. As observed with single-molecule changes, small random changes to all molecule quantities increased temporal sensitivity (Figure 10B) with minimal changes in mean ppERK (Figure 10A).

ERK Temporal sensitivity is robust to parameter variations.

Molecule concentrations were changed individually by either +10% (red) or −10% (black) or the set of concentrations was changed randomly, within ±10% (gold). (A) Percent change in mean ppERK, averaged across all 5 ITIs. (B) Percent change in temporal sensitivity. Most variations increased temporal sensitivity.

Table 6
Count of best ITIs.

Count of preferred ITIs in robustness simulations, using either single-molecule changes of ±10% or random changes (between +10% and −10%) to all molecules. 80% of the parameter variations yield optimal ppERK in response to spaced stimulation (ITI = 80 or 300 s).

ITIsRandom10% lower10% higherTotal percent
338004.69
2046015.80
40813110.49
801541125139.14
3001814010239.88

To evaluate which molecule quantities produced the largest effect on ppERK, we used random forest regression to analyze the effect of random changes on the entire set of molecules. Random forest regression is a non-linear method (in contrast to linear regression) to determine which parameters are best for predicting the results. The algorithm creates numerous decision trees, each of which is a hierarchical set of rules, where each rule partitions the data (ppERK in our case) based on a single feature (molecule quantity in our case). The features of each tree are ranked based on their weight in accurately predicting the data. Table 7 ranks the molecules, with the highest weight indicating the molecule that caused the most significant change in ppERK. The observation that most weights are small indicates that no single molecules can explain the change in ppERK. However, calcium pathway molecules such as RasGRF, calmodulin, pmca, and cAMP pathway such as Epac are ranked high, consistent with the contribution illustrated in single pathway simulations. In summary, the temporal sensitivity of ERK is quite robust to variation in parameters and favors spaced ITIs.

Table 7
Random forest analysis.

One hundred random perturbations of all molecule concentrations (between +10% and −10%) were simulated. Features are ranked from most important to least important in predicting the temporal sensitivity. The sum of features’ importance equals 1.

Molecules abbreviationWeightsMolecules full name
RasGRF0.084Ras guanine nucleotide–releasing factor
Sos0.074Son of sevenless
Cam0.068Calmodulin
MEK0.050Mitogen-activated protein kinase kinase
PDE20.050Phosphodiesterase 2
pmca0.048Plasma membrane calcium pump
Epac0.046Exchange protein directly activated by cAMP
Calbin0.046Calbindin
CRKC3G0.044v-CRK Proto-Oncogene/Rap guanine nucleotide exchange factor 1
rasGap0.043Ras GTPase-activating protein
SynGap0.042Synaptic rasGap
PP10.038Protein phosphatase 1
Shc0.035Src homology collagen-like
Grb20.034Growth factor receptor-bound protein 2
PP2A0.033Protein phosphatase 2
MKP10.033Mitogen-activated protein kinase phosphatase 1
Ng0.033Neurogranin
Src0.032Non-receptor tyrosine kinase
Cbl0.030Casitas B-lineage lymphoma
ERK0.027Mitogen-activated protein kinase
PDE40.025Phosphodiesterase 4
PKA0.025Protein kinase A
NCX0.022Sodium calcium exchanger

Discussion

Numerous experiments have demonstrated that ERK is critical in L-LTP induction: ERK phosphorylates transcription factors, molecules involved in protein translation, and regulates cell excitability through ion channel phosphorylation. ERK is activated through numerous pathways; however, it is unclear why so many pathways converge on ERK. Furthermore, some pathways are required, whereas other pathways can be compensated. Due to complicated interactions, models of signaling pathways are crucial for understanding the molecular foundations of L-LTP. Using a computational model of signaling pathways underlying L-LTP in hippocampus CA1, we evaluated temporal sensitivity and synergy between the ERK pathways utilized by different L-LTP stimulation protocols. Our data demonstrate that calcium and cAMP work synergistically to activate ERK, and we show for the first time the role of SynGAP in mediating the synergy between pathways. SynGAP mutations are associated with a variety of syndromes, such as autism and intellectual disability. Our simulations suggest that this phenotype might be in part caused by dynamics of ERK activation following closely the dynamics of SynGAP dispersion from the spine. Our data also show that stimuli spaced in time activate more ERK than stimuli massed in time, a temporal sensitivity similar to PKA but different than CaMKII. These ERK activation pathways are not redundant as each has a distinct dynamic, contributing to different time frames of ERK activation. For example, Epac contributes to an early transient ERK activation, whereas PKA contributes to a later transient ERK activation. With massed stimuli, calcium produces a rapid and sustained ERK activation, whereas with spaced stimuli, calcium only produces small transient ERK responses. The difference in dynamics and contribution of each pathway reinforce how neurons are able to recognize and discriminate different patterns in learning protocols.

The model elucidates that CaMKII contributes to ERK activation through phosphorylation of SynGap. This synaptic RasGap, selectively expressed in the brain, regulates ERK activity by inactivating RasGTP and Rap1GTP (Gamache et al., 2020; Pena et al., 2008). CaMKII phosphorylation of SynGap both increases its activity (Walkup et al., 2015) and causes dispersion to the dendrite (Araki et al., 2015). To investigate the role of dispersion, we repeated simulations without dispersion of pSynGap and observed that the ppERK amplitude was decreased by half. This effect is observed because its activity is doubled in the spine, reducing the available quantity of RasGTP and Rap1GTP. Thus, the dispersion of pSynGap attenuates its activity in the spine, which allows a long-lasting spine enlargement as observed in experiments (Araki et al., 2015). We also showed that blocking CaMKII binding to SynGap greatly reduced ppERK activity, whereas allowing CaMKII to bind but not phosphorylate SynGap greatly increased ppERK activity. This result is consistent with experiments (Rumbaugh et al., 2006) showing that overexpression or depletion of SynGap significantly reduced and enhanced ERK activity, respectively. Thus, CaMKII-dependent SynGAP dispersion from the spine controls ERK recruitment.

One of our main conclusions is that feedforward loops can support ERK activation for L-LTP induction without PKC. Induction refers to the transient events that trigger the formation of L-LTP, while maintenance refers to the persistence of biochemical signaling that supports L-LTP. Our results showed that ppERK decays in less than an hour, suggesting that ERK is required during induction of L-LTP, but not during maintenance, which lasts for multiple hours. These results are consistent with experiments showing that inhibition of ERK 30 min after induction does not block LTP (Kelleher et al., 2004). PKMζ, the atypical form of PKC, participates in a feedforward loop to support L-LTP maintenance (Ajay and Bhalla, 2004Ajay and Bhalla, 2007Tsokas et al., 2016) however, the evidence that PKC is required for L-LTP induction is weak, and thus we did not include it in our model. Similarly, we did not include metabotropic glutamate receptors, which activate PKC, because structural plasticity, a correlate of LTP, is independent of mGluR stimulation (Zhai et al., 2013). An alternative feedforward loop involves PKA inhibiting ERK inactivation mechanisms (Neves et al., 2008), but PKA is not required for all forms of L-LTP induction. Our model reveals an additional feedforward loop, connecting CaMKII to SynGap to ERK, which is activated during L-LTP induction. This pathway may be critical for induction of L-LTP in CA1 for protocols resistant to inhibition of PKA and PKC (Sweatt, 1999). In summary, our study supports prior results showing that feedforward loops are sufficient to activate ERK but reveals a novel feedforward loop involving SynGap.

Temporal selectivity is an important characteristic of learning and memory formation. Animals can learn to respond similarly to a variety of temporal patterns or can respond differently depending on the temporal pattern (Delamater and Holland, 2008; Mauk and Ruiz, 1992). In some cases, synaptic input can produce either LTD or LTP depending on the temporal frequency of the input (Chen et al., 2010; Hawes et al., 2013). In other words, neurons can discriminate and respond differently to these different temporal input patterns (Bhalla, 2017), but also need to be able to learn despite a difference in temporal patterns. We showed that ERK is activated for a wide range of temporal input patterns, but what are the differences allowing temporal pattern discrimination?

One mechanism for temporal pattern discrimination is the temporal pattern of ERK itself, which can determine whether a cell differentiates or divides (Santos et al., 2007; Sasagawa et al., 2005; von Kriegsheim et al., 2009) and whether LTP and LTD occur (Thiels et al., 2002). We have summarized kinase activity as area under the curve, but some downstream molecules may be more sensitive to dynamics or peak activity. Indeed, our data show repeated transients of ppERK with 300 ITI versus a sustained ppERK with 80 and smaller ITIs, and the peak activity of ERK has a different temporal sensitivity than total activity. Total activity increases with ITI while peak decreases with ITI, implying that processes sensitive to peak versus AUC could distinguish these temporal patterns. We predict that these temporal patterns can be decoded by the nucleus to produce different gene expression patterns, as previously suggested (Jain and Bhalla, 2014). Our model prediction of different ERK dynamics could be tested using the new EKAR sensor to image ERK activation in hippocampal slices after L-LTP induction using different ITIs, and the prediction of different gene expression patterns could be tested using some of the newer gene expression techniques, e.g., TRAP-seq (McKeever et al., 2017), to determine whether short ITIs produced different gene expression patterns than long ITIs.

A second mechanism for temporal pattern discrimination is that pathways activating ERK have other targets essential for L-LTP induction. Our results show that the CaMKII and calcium contribution to ERK decreases with ITI, whereas the PKA and cAMP contribution to ERK increases with ITI. The opposite temporal sensitivity of these critical kinases, as previously reported (Ajay and Bhalla, 2004Ajay and Bhalla, 2007; Kim et al., 2010; Woo et al., 2003), can contribute to pattern discrimination by the neuron, through activation of other downstream molecules that are required for LTP. For example, re-organization of the actin cytoskeleton (Borovac et al., 2018; Honkura et al., 2008; Obashi et al., 2019) is required to increase the size of the spine to allow for more glutamate receptors. In particular, both CaMKII and PKA control actin binding proteins, such as cofilin (Havekes et al., 2016; Zhao et al., 2012). Thus, even in cases where ERK activity cannot distinguish temporal patterns, the temporal sensitivity of other key kinases can contribute to temporal pattern sensitivity.

Our results suggest that numerous signaling pathways activate ERK to enhance sensitivity to a range of temporal patterns, but there are other differences between the pathways that suggest they are not redundant. If those pathways were redundant, then, contrary to experimental observations (Gelinas et al., 2008b; Gelinas et al., 2008a; Scharf et al., 2002; Woo et al., 2003), blocking one of them should not block ERK-dependent L-LTP. In addition, our model predicts that Rap1 and Ras are not interchangeable: Rap1 can compensate for Ras, but Ras cannot compensate for Rap1. Instead of redundancy, multiple pathways may be needed to control ERK dynamics and allow it to perform multiple tasks. For example, Sasagawa et al., 2005 demonstrated that there are two distinct dynamics of ERK, transient and sustained, due to the distinct timeframe of Ras and Rap. Similarly, we observed that each ERK activation pathway has a distinct dynamic, each contributing to a different time frame of ERK activation. For example, Epac contributed to an early transient ERK activation, whereas PKA contributed to a later transient ERK activation, and CaMKII produced a sustained ERK activation. Thus, our model predicts that an Epac knockout would lead to slower ERK activation. These different time frames of ERK may phosphorylate different targets (Keyes et al., 2020; Zhai et al., 2013; Zhang et al., 2018). For example, Epac, a molecule of emerging importance in neurodevelopmental disorders, may have a role in disorders in cAMP degradation by enhancing the early activation of ERK. SynGap may be critical for a pool of ERK in the spine, whereas PKA may be essential for a pool of ERK that translocates to the nucleus. In this context, we predict that overexpression of SynGap would not reduce ERK activity in the nucleus but only in the spine. An experimental test of this prediction could use EKAR imaging (Harvey et al., 2008) to quantify ERK expression in the spine versus nucleus or measure gene expression with overexpression of SynGap.

Different temporal patterns may produce different outcomes by activating different pools of ERK. Studies have shown that scaffolding proteins, such as Kinase Suppressor of Ras (KSR) protein (Dougherty et al., 2009; Shalin et al., 2006) and β-arrestins (Bourquard et al., 2015; DeFea et al., 2000), can create multi-protein complexes of ERK, MEK, and Raf and dictate the subcellular location of ERK activity. Thus, a critical question is whether the spatial pool of ERK depends on which signaling pathways are activated during induction of LTP. These different pools of ERK may perform different functions, such as translocating to the nucleus to initiate gene transcription, staying in the cytoplasm to initiate local changes in excitability, or allowing stimulated spines to capture newly synthesized proteins to enable persistence of L-LTP (as in synaptic tagging and capture) (Frey and Morris, 1997; Redondo et al., 2010; Sajikumar et al., 2007; Young et al., 2006). This leads to a second question regarding what limits the spatial spread of molecules involved in marking spines as having been stimulated. In this context, a possible role for SynGAP dispersion would be to limit diffusion of active Ras family proteins to nearby, non-stimulated spines, thereby creating microdomains of ERK. Spatial models (Bhalla, 2017; Kim et al., 2011) have shown that buffering and other inactivation mechanisms can produce spine-sized microdomains of calcium and cAMP, but not PKA or CaMKII, suggesting additional mechanisms may be needed to produce spine-sized microdomains of ERK. Taking those questions together it will be quite interesting to implement a spatial model to investigate mechanisms that govern spatial pools of ERK and spatial and tagging specificity.

Materials and methods

Computational methods

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To investigate how temporal pattern of synaptic activity determines which pathway in the ERK signaling cascade (Figure 1A, Figure 1—source data 15) dominates in dendritic spines of hippocampal CA1 pyramidal neurons, we developed a single-compartment, stochastic reaction–diffusion model of pathways activating ERK. The model was built by merging and adapting two existing models of synaptic plasticity in hippocampal neurons. One of those models (Jȩdrzejewska-Szmek et al., 2017) explains how different temporal patterns activate different kinases such as CaMKII and PKA that are critical for L-LTP induction, and the other model (Jain and Bhalla, 2014) demonstrates that protein synthesis is the result of synergistic activation of different pathways such as ERK and mTOR to generate unique patterns in response to different L-LTP stimuli. These previously published models were modified by adding several molecules and reactions critical for ERK activation.

One major change to the merged model is C-Raf dimerization. Dimerization regulates C-Raf activation and its subcellular localization (Desideri et al., 2015; Garnett et al., 2005). Full activation of C-Raf, but not BRaf, requires dimerization. RasGTP binds to C-Raf to form an inactive complex, C-Raf-RasGTP, which then homodimerizes to become active, thus able to phosphorylate MEK that activates ERK. Another major change is the addition of two important molecules, RasGRF and SynGap, involved in hippocampal LTP (Araki et al., 2015; Darcy et al., 2014; Jin and Feig, 2010; Kim et al., 1998; Li et al., 2006). RasGRF is activated by binding to calcium-calmodulin; once activated, RasGRF binds to RasGDP and allows the exchange of GDP for GTP. SynGap inactivates Rap1GTP and RasGTP with low affinity. Once phosphorylated by CaMKII, SynGAP affinity doubles toward RasGTP and Rap1GTP and causes SynGAP dispersion from synapses to the dendrite.

Initial conditions and rate constants are either taken from previous models (Jain and Bhalla, 2014; Jȩdrzejewska-Szmek et al., 2017) or adjusted to reproduce experimentally measured concentrations of molecules (Figure 1—source data 16) or to match time course data, for example rate constants governing CaMKII autophosphorylation. The concentration of some species was adjusted to produce an intracellular concentration of calcium of ~50 nM and cAMP of ~30 nM, among others. For example, the concentration of PDEs was adjusted to produce a 30 nM basal cAMP. Calcium extrusion mechanisms and the low affinity and immobile calcium buffer were adjusted to obtain a steady state of about 50 nM of internal calcium. To match the in vitro data on basal concentration, we ran the model for about an hour to obtain steady-state concentrations for all molecules.

Several simulations use a compartment with a volume comparable to a spine head (about 0.1–0.8 µm3). To minimize noise inherent in stochastic models, most simulations used a larger compartment, of volume 4 µm3. Other than the level of noise, no differences in temporal sensitivity were observed between the small and large volume models.

Stimulation protocols

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In brain slices, presynaptic stimulation results in calcium influx through NMDA receptors, and norepinephrine (NE) or dopamine, which bind to Gs-coupled metabotropic receptors (Jȩdrzejewska-Szmek et al., 2017) is required for L-LTP (Huang and Kandel, 1995). To investigate the effect of calcium distinct from cAMP produced by NE, the model is activated using three independent inputs leading to ERK activation: calcium (through RasGRF and SynGap), cAMP (through Epac and PKA), and βγ subunit of inhibitory G protein (Gi) (through implicit PKA phosphorylation of βAR). βARs are mostly coupled with stimulatory G protein (Gs). However, when phosphorylated by PKA, βARs decouple from Gs and couple with inhibitory G proteins (Gi). Both Gs-activated and βAR coupled with Gi-activated signaling pathways converge to activate ERK using different pathways. To determine whether maximal ERK activation requires multiple pathways, the contribution of each pathway was tested singly and in combination using either a duration or amplitude protocol (Table 1). Duration protocols used a sustained concentration of calcium, cAMP, and Giβγ. Amplitude protocols used transient (1 s duration) elevations of different concentrations of the inputs. Calcium and cAMP each have several different pathways to ERK activation; thus, to determine the contribution of each of the (sub)pathways, the above simulations were repeated with one of the rates set to zero, as shown in Table 3. To investigate whether different L-LTP temporal patterns select different signaling pathways for ERK activation, simulations were performed using stimulation protocols identical to the experimental protocols used to induce L-LTP. Therefore, we stimulated the model with four trains of 100 Hz for 1 s at five different intertrial intervals: 3, 20, 40 s (massed) or 80 and 300 s (spaced) (Figure 1C). Each stimulation pulse triggered a transient elevation of either calcium, cAMP (direct action and in combination with Giβγ) singly, or in combination.

We also tested different forms of stimulation patterns that induce L-LTP. The additional stimulation protocols are bath-applied ISO followed by 1 train of 100 Hz (ISO+100 Hz) or 5 Hz (ISO+5 Hz). The inputs used to run these simulations are derived from simulations of a spatial model response to glutamate (Jȩdrzejewska-Szmek et al., 2017).

Simulation and analysis

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The model is implemented using a stochastic reaction–diffusion simulator NeuroRD (Jȩdrzejewski-Szmek and Blackwell, 2016), version 3.2.4 (Jędrzejewski-Szmek and Blackwell, 2018), using the adaptive (asynchronous tau-leap) numerical method and tolerance of 0.1. Even though stochastic fluctuations observed using small compartments do not impact the results, the stochastic algorithm is extremely fast, especially for stiff systems; thus, there would be no advantage to switching to a potentially less accurate deterministic simulator. All model files needed to run the simulations, including molecule quantities, reaction rate constants, and stimulation quantities, are available on GitHub (Miningou Zobon et al., 2021) and on modelDB, accession number 267073.

Biochemical experiments assess kinase activity by measuring the change in concentration of the product after a specific time. Thus, in these simulations, the kinase activity is quantified as total activity over simulated time compared to the activity under conditions of no stimulation, also known as area under the curve (AUC). To account for stochastic variation, simulations were repeated five times (each using a different random seed) and results presented are the mean and standard error over the trials. The sample size is based on previous publications (Jȩdrzejewski-Szmek and Blackwell, 2016), which found this sample size sufficient to show differences between conditions. Analysis was done in Python 3, using nrdh5_analV2.py available on GitHub (Blackwell and Miningou Zobon, 2021).

Statistical analysis was done in Python3 (https://github.com/neurord/ERK/tree/master/Analysis), Miningou Zobon and Blackwell, 2021. To assess whether the response was linear, the AUC versus stimulation duration or concentration was fit to a line, a Hill equation, and a logarithmic equation (the latter two selected subjectively as matching the shape of the curve). The response was considered non-linear if both adjusted R2 and Akaike information criteria were better for one of the non-linear equations. To determine whether two pathways combined linearly, analysis of variance was used, with AUC of doubly ppERK as the dependent variable, and intertrial interval and stimulation type (combination or summation) as independent variables (N = 5 in each group). Random forest regression was used to analyze the robustness simulations, to determine which parameter values had the most influence on the change in ppERK AUC. Random forest is a non-linear method of regression that creates multiple decision trees. Each tree is made by randomly selecting features, for example molecule concentration, that best predict the dependent variable, that is ppERK. By using a large number of decision trees (100 for this analysis), the results are quite robust. The outcome of the random forest is a weight for each feature, indicating its usefulness in predicting the dependent variable. By design, the sum of weights for all features equals 1.

Data availability

All model files are freely available on https://github.com/neurord/ERK/releases/tag/1.0.0 (copy archived at https://archive.softwareheritage.org/swh:1:rev:27db0c5f79d5a1a7922b06e2a0b258102dec9670). All programs to analyze simulation output are available on https://github.com/neurord/NeuroRDanal/releases/tag/2.0.0 (copy archived at https://archive.softwareheritage.org/swh:1:rev:4fe66de8f9be91a32109fcd5db862a8bac9371e3). Programs for the statistical analysis and random forest analysis are available on https://github.com/neurord/ERK/tree/master/Analysis (copy archived at https://archive.softwareheritage.org/swh:1:rev:27db0c5f79d5a1a7922b06e2a0b258102dec9670). These URLs are provided in the manuscript methods section. Model files are available from modelDB, accession number 267073.

The following data sets were generated
    1. Miningou ZNT
    2. Blackwell KT
    (2021) modelDB
    ID 267073. Model files for simulating the ERK signaling pathway during L_LTP induction in the hippocampus.

References

Decision letter

  1. Upinder Singh Bhalla
    Reviewing Editor; Tata Institute of Fundamental Research, India
  2. Ronald L Calabrese
    Senior Editor; Emory University, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

It is interesting how a few molecules, such as the protein kinase ERK, act as a convergence points for multiple pathways in synaptic plasticity. In this study the authors show how ERK not only acts like a hub for many inputs, but also selectively responds to different time-patterns of inputs depending on which combination of inputs are active.

Decision letter after peer review:

Thank you for submitting your article "Temporal pattern and synergy influence activity of ERK signaling pathways during L-LTP induction" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Ronald Calabrese as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

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Summary:

This study takes on the question of the roles of the many pathways leading to ERK activation in long-term potentiation. This is an advance since few models consider timing roles of more than a couple of input pathways to ERK or in plasticity. The authors consider two aspects: how pathways sum to give strong responses, and distinct temporal pattern selectivity. They show that both summation linearity, and pattern selectivity, are strongly governed by which pathways are engaged in driving the response.

Essential Revisions:

A key point discussed by the reviewers was whether the temporal pattern selectivity represented sufficient interest and novelty. Could the authors make a strong case for this? In addition the reviewers felt that the following points would be essential to address in a revision:

1. Could the authors provide extensive comparisons to experiment? All the reviewers felt that the parameterization was inadequately validated, specially as the model was a significant change from its original sources.

2. Could the authors bring a more complete account of activation of the chosen pathways by synaptic input? It should be possible to simulate how all the pathways are triggered, presumably in an overlapping way, by different kinds of input.

3. While ERK is important, there are numerous other pathways that play a key role in plasticity. The authors should specify the role of ERK and relate it to other pathways.

4. The analyses of summation and linearity should be done in a more statistically complete manner.

5. The authors should provide better documentation of their reaction system through diagrams and standard formats.

6. What testable predictions does the model make?

In addition, the reviewers brought up other relevant points in their individual reviews.Reviewer #1:

This study takes on the question of the roles of the many pathways leading to ERK activation in long-term potentiation. This is an advance: few models consider more than a couple of input pathways. The authors consider two aspects: how pathways sum to give strong responses, and distinct temporal pattern selectivity.

The model and analysis is potentially interesting, but the paper would be much strengthened if there were more convincing validation of the properties of the model by way of simulations to compare with experiments. I also bring up a couple of points about how better to link synaptically-driven responses to the properties of the model.

1. I was looking to see some model validation before diving into the predictions of the model. Specifically, it would have been useful to compare the model ERK responses to each of the individual stimulation pathways that the authors implement.

Around line 531 the authors describe how parameters were chosen. These seem to rely on previous work or on steady-state levels in the absence of stimulation. Since the model is quite different from the source models, it is important to provide additional validation. Further, time-series responses and dose-response curves give far tighter constraints on system behavior than single-point steady-state readouts. A figure with a range of such validation runs would be very helpful.

1b. There is a nice analysis (Table 2) of effects of KO on responses. Surely there are physiological experiments to compare with this? In the para around line 137 several experiments are mentioned but it would be useful to show simulations to compare with the data.

2. What is the relative strength of contributions by each of the proposed 5 pathways to ERK regulation? How was this ascertained?

3. It is interesting to see differences in linearity between cAMP and Ca pathways. However, these are themselves downstream of the synaptic input. Could the authors explore how these differences would manifest upon synaptic input to a typical synapse having AMPAR, NMDAR, and mGluR? Won't they be rather overlaid on each other?

4. While it is nice to see a model with as many as 5 pathways driving ERKII, I am curious about the choice of these input pathways. From synaptic input one would expect to see an mGluR component. Do the authors envision that this folds into Gbg? Further, one sees other signals such as BDNF as major players in plasticity.

4b. I bring this up also in the context of the reported time-courses. Experimental time-courses of other pathway inputs can be quite different from those explored here, BDNF tending to be quite slow.

Reviewer #2:

There are, however, a couple of points that I feel should be addressed, in order for me to enthusiastically recommend this manuscript for publication.

1. There needs to be additional technical detail on how the original models were expanded. The model presented here was developed by merging Jȩdrzejewska-Szmek et al., 2017 and Jain and Bhalla, 2014 models. These models were developed based on experimental data and validated with independent experimental datasets in a rigorous manner. It is not clear how the combining these two models, and the additional molecules and reactions added have affected the dynamics of ERK activation, and how comparable they are to the original experimental data used for model development in the previous modeling efforts. It is not clear if the model was reparametrized.

2. Beyond the ERK activation traces, it would be useful for clarity sake to also include the simulated traces for the activation of the upstream molecules (PKA, RAS, RAP, etc). Given how additional changes have been made additional information should be provided to ensure that the contribution of each pathway is accurately represented.

Reviewer #3:

This paper is primarily about modeling the ERK pathway during the induction of synaptic plasticity. This pathway has been previously modeled, and this is cited in the paper. The main addition here is the addition of the effect of SynGap which is necessary in some form of LTP. This is a very detailed study, and what it seems to primarily show is that the ERK pathway favored spaced vs. massed stimulation protocols. This is a very detailed paper, but no conceptually new ideas are presented here. The paper adds to an existing foundation, but fails to make the case that this is a very significant addition. What is the significant consequence at a higher level of these added details?

The ERK pathway is just one component of a much larger set of pathways that control synaptic plasticity, how much do we learn from studying this pathway in isolation? Also, the paper cites the importance of this pathway to L-LTP, is it the induction phase of L-LTP? It seems so because ppRRK decays in less than an hour. How then does this pathway contribute to the maintenance of L-LTP, these processes such as a possible upregulation of protein synthesis are not part of this model either.

This paper studies in detail different pathways that influence ERK activation is synapses. This is a very detailed study, but how many details do we actually know? For a detailed paper though it seems that many of the details are missing. Is there a detailed diagram of reactions, or set of equations for all these reactions? Some coefficients are named in figure 1, and this might be sufficient for a schematic description of the model in the paper, however there must be somewhere a detailed description of all reactions. How many species are there here, how many coefficients? How are coefficient values known? How many coefficients are directly estimated? The paper does carry out an extensive robustness analysis, though it is not well explained.

What are the major takeaways from this paper, and what experiments could test this model?

To summarize, the paper is very detailed carefully constructed and executed, it fails to convince that the problem it addresses is very significant, and it makes no conceptual breakthroughs.

The induction protocols seem to include not only calcium pulses, but also cAMP and g-protein coupled pulses, what is the cellular origin of these other pulses? Is the G protein activation due to β-adrenergic activation, is this activation necessary for plasticity? What is the cellular origin of the cAMP and Gi activation in slice? Similarly, what primarily activated cAMP in real synapses?

Is ERK required for all forms of LTP? Some references indicate it might not be. Is ERK necessary for early LTP induced by 100Hz stimulation?

I get lost in the details of the introduction, description of different pathways should be in results and relate to figure 1. It looks like a shopping list, why is this significant?

Why is it important that this is a stochastic diffusion reaction model rather than a deterministic model? Nothing about fluctuations, except for small error bars are mentioned in this paper.

Do not reference Zhang et al. Nature Neuro 2012, its' not a mammalian LTP model, still there are similarities (and differences), especially as ERK pathways are studied and since it relates to spaced learning.

229 – where do we see autophosphorylation in figure 3F?

Figure 6B – hard to see shape of symbols.

No model diagrams or equations here, for example how in CaMKII autophosphorylation implemented? Figure 6C – what is old CaMKII? They give a reference, but we do not know what the new model is.

Narrow picture by looking only at ERK. – For example, increasing PP1 can enhance ppERK, however it might reduce overall LTP due to dephosphorylation of AMPA receptors. What wins?

Figure 7 – what in figure 7 shows super linearity? It's in the title, where else? This applies to paragraph starting in line 368 as well. Where do we see these results. We can try to eyeball it. It would be useful to show a plot of combined model/(sum of individual models). By eyeballing this it seems (but might be wrong) that the super-linearity is minimal.

403 – the first time random-forest was mentioned in line 403, and this method is not explained or defined prior to this or even in this paragraph. For eLife type of readers this needs to be explained in simple terms.

423 – typo – "Molecules were randomly simultaneous(ly)"

What to weights in table 5 mean? This relates to the random forest analysis which is not explained.

Similar problems with figure 8, what is shown here? What is the analysis used here? This is totally unclear. Are molecules here changed one at a time? How much are they changed? Is this the 10% discussed earlier? It would also be more instructive to show relative range changes.

How is this paper related to the recent Maki-Marttunen paper from the same lab which appeared recently (https://www.biorxiv.org/content/10.1101/2020.01.27.921254v1.abstract), it is not referenced here. That is a more general paper but seems to exclude ERK. If ERK is so significant how can it be excluded in one paper and included in another from the same lab?

Discussion starts OK, but again devolves into excessive details.

Does this model possibly explain induction of L-LTP, or its maintenance phase? It seems the prior since ppERK activity returns to baseline; these should be distinguished.

In summary – this paper fails to convince that it is of general interest beyond a narrow community. However, the comments in this section show that there are changes to be made even for the specific community of scientists interested in the signaling pathways of LTP.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Temporal pattern and synergy influence activity of ERK signaling pathways during L-LTP induction" for further consideration by eLife. Your revised article has been evaluated by Ronald Calabrese (Senior Editor) and a Reviewing Editor.

The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:

Summary points from the previous decision:

Point 1: Comparisons to experiments and validation of parameterization.

The authors have partly addressed this point, with comparisons of simulations to several additional experiments. They have also provided tables of data sources but many parameters are linked to previous models rather than to experiments. It would be helpful if the authors could explicitly address the point about _parameter_ validation, and to what extent systems level experiments provide validation for rate terms.

Point 2: Activation of pathways by synaptic input.

Here the authors use the model from their 2017 paper to generate Ca and cAMP waveforms, and report results consistent with experiments. It is just a single figure though, and only reports ppERK. We don't see the upstream pathways and their responses. Since the authors have now added these upstream pathways, it would be good to see the time-courses for upstream key molecules indicated in figure 1. These include Ca, Gbg, cAMP, as well as CaMKII, PKA, synGap, Ras and Rap1. It would be useful to have a figure with these time-courses for the major stimulus patterns used in the figures. In Figure 8 – supplementary Figure 2B the authors provide some time-courses for a few molecules. A complete set would be desirable.

Point 4: Linearity. Here the authors report ANCOVA analysis for figures 3, 5, 6. This addresses the point.

Point 5: Source data now provided. Unfortunately it isn't in SBML. If the authors can apply a conversion program to their model, an SBML version would be valuable.

Point 6: Predictions: These are now provided.

Responses to reviewer 1: OK.

Responses to reviewer 2: OK

Responses to reviewer 3: We recommend that the response to the point about induction protocols would be best addressed with graphs of the time-courses mentioned above in Point 2.

Also, the response to the reviewer's point about the use of a stochastic method would be good to include in the text. We did not see this statement there.

https://doi.org/10.7554/eLife.64644.sa1

Author response

Summary:

This study takes on the question of the roles of the many pathways leading to ERK activation in long-term potentiation. This is an advance since few models consider timing roles of more than a couple of input pathways to ERK or in plasticity. The authors consider two aspects: how pathways sum to give strong responses, and distinct temporal pattern selectivity. They show that both summation linearity, and pattern selectivity, are strongly governed by which pathways are engaged in driving the response.

Essential Revisions:

A key point discussed by the reviewers was whether the temporal pattern selectivity represented sufficient interest and novelty. Could the authors make a strong case for this?

We now begin the manuscript with a general explanation of the importance of temporal pattern (lines 36-43).

“Temporal patterns are a key feature of the environment. The speed of traversing space is indicated by the time between spatial cues. In classical conditioning, adaptive changes in behavior require an animal to respond to a cue in an appropriate time frame to gain a reward or avoid punishment (Delamater and Holland, 2008; Mauk and Ruiz, 1992). In these and other tasks, environmental cues, i.e., sensory inputs, are converted into spatio-temporal patterns of activation. Pattern discrimination requires that neurons are able to discriminate and respond differently to these different temporal input patterns (Bhalla, 2017); conversely, neurons need to be able to learn despite a difference in temporal patterns.”

We also explain the relevance of temporal pattern discrimination for LTP (lines 46-51) and other cell functions (lines 83-88). In summary, temporal pattern of synaptic inputs can influence the response of the neuron by controlling the temporal pattern of ERK activation. Temporal pattern has been shown to affect numerous aspects of neuron function, including whether LTD or LTP occurs. In other word, temporal pattern and timing of the inputs regulate learning and memory.

We discuss the importance of temporal pattern in the discussion, lines 444-492.

1. Could the authors provide extensive comparisons to experiment? All the reviewers felt that the parameterization was inadequately validated, specially as the model was a significant change from its original sources.

We did extensive comparisons to experiments in the first version, but did not report them. We have now added several of those comparisons as well as several new validations.

We have added graphs of RasGTP in response to inputs of 60 sec train of 0.5 μm of calcium and directly compare to Harvey et al., 2008 (lines 108-112, Figure 2A).

We have added graphs of ppERK in response to inputs of 1 sec train of 5 μm and 1 μm of calcium and cAMP respectively and directly compare to Kasahara et al., 2001 (lines 112-116, Figure 2B).

We simulated the L-LTP protocols induced with isoproterenol followed by either 100 Hz or 5 Hz stimulation, and show that both of those protocols produce a higher ppERK than ISO, 100 Hz or 5 Hz alone (lines 309-319, Figure 9).

We simulated knockout experiments of bRaf, Raf1, Ras and Rap (lines 320-339 and Figure 8 – Supplementary Figure 3), and show that our results are consistent with experimental data.

2. Could the authors bring a more complete account of activation of the chosen pathways by synaptic input? It should be possible to simulate how all the pathways are triggered, presumably in an overlapping way, by different kinds of input.

Indeed, these pathways are triggered by both synaptic and neuromodulator input. Neuromodulators such as dopamine and norepinephrine are released during LTP stimulation and activate Gs coupled receptors to produce cAMP. Calcium influx through NMDA receptors not only activates the calcium pathways in our model but also can activate adenylyl cyclases to produce cAMP. To better investigate ERK activation during L-LTP induction, we have generated calcium and cAMP input by simulation of our published model of those pathways (Jȩdrzejewska-Szmek et al., 2017), and then measured the ERK response to calcium and cAMP using several LTP induction protocols. These simulations were done by Joanna Jedrzejewska-Szmek, who has been added as a co-author. These results, lines 309-319 and new Figure 9, show that isoproterenol followed by either 100 Hz or 5 Hz produce greater ppERK than ISO, 100 Hz or 5 Hz alone, consistent with the experimental observation that the combination stimuli are needed to produce L-LTP.

3. While ERK is important, there are numerous other pathways that play a key role in plasticity. The authors should specify the role of ERK and relate it to other pathways.

We have clarified the role of ERK in the introduction (lines 61-62) and we discuss its role further in the discussion, lines 380-382. We have related ERK to other pathways in the context of temporal pattern sensitivity, lines 451-483. Specifically, both PKA and CaMKII phosphorylate molecules involved in cytoskeletal reorganization (lines 465-469).

4. The analyses of summation and linearity should be done in a more statistically complete manner.

We now added statistical analysis of linearity for all graphs of ppERK versus duration and concentration. We do a statistical analysis of whether the combination of molecules produces linear summation for all combinations. The statistics have been added to the captions of figures 3, 5, 6, or as additional tables.

5. The authors should provide better documentation of their reaction system through diagrams and standard formats.

We now provide a table of reactions, reaction rates, and molecule quantities, Figure 1 Source Data 1-6.

6. What testable predictions does the model make?

We have now added several predictions to the discussion.

We predict that these temporal patterns can be decoded by the nucleus to produce different gene expression patterns. Our model prediction of different ERK dynamics could be tested using the new EKAR sensor to image ERK activation in hippocampal slices after L-LTP induction using different ITIs, and the prediction of different gene expression patterns could be tested using some of the newer gene expression techniques, e.g.TRAP-seq (McKeever et al., 2017), to determine whether shorter ITIs produced different gene expression patterns than long ITIs (lines 452-458).

We observed that each ERK activation pathway has a distinct dynamic, each contributing to a different time frame of ERK activation. For example, Epac contributed to an early transient ERK activation, whereas PKA contributed to a later transient ERK activation, and CaMKII produced a sustained ERK activation. Thus, our model predicts that an Epac knockout would lead to a slower ERK activation (lines 480-484).

These different time frames of ERK may phosphorylate different targets (Keyes et al., 2020; Zhai et al., 2013; Zhang et al., 2018). For example, Epac, a molecule of emerging importance in neurodevelopmental disorders, may have a role in disorders in cAMP degradation by enhancing the early activation of ERK. SynGap may be critical for a pool of ERK in the spine, whereas PKA may be essential for a pool of ERK that translocate to the nucleus. In this context, we predict that overexpression of SynGap would not reduce ERK activity in the nucleus but only in the spine. An experimental test of this prediction could use EKAR imaging (Harvey et al., 2008a) to quantify ERK expression in the spine versus nucleus or measure gene expression with overexpression of SynGap (lines 484-492).

Reviewer #1:

1. I was looking to see some model validation before diving into the predictions of the model. Specifically, it would have been useful to compare the model ERK responses to each of the individual stimulation pathways that the authors implement.

As explained above, in essential revisions, we have performed additional simulations to validate the model:

We did extensive comparisons to experiments in the first version, but did not report them. We have now added several of those comparisons as well as several new validations.

We have added graphs of RasGTP in response to inputs of 60 sec train of 0.5 μm of calcium and directly compare to Harvey et al., 2008 (lines 108-112, Figure 2A).

We have added graphs of ppERK in response to inputs of 1 sec train of 5 μm and 1 μm of calcium and cAMP respectively and directly compare to Kasahara et al., 2001 (lines 112-116, Figure 2B).

We simulated the L-LTP protocols induced with isoproterenol followed by either 100 Hz or 5 Hz stimulation, and show that both of those protocols produce a higher ppERK than ISO, 100 Hz or 5 Hz alone (lines 309-319, Figure 9).

We simulated knockout experiments of bRaf, Raf1, Ras and Rap (lines 320-339 and Figure 8 – Supplementary Figure 3), and show that our results are consistent with experimental data.

Around line 531 the authors describe how parameters were chosen. These seem to rely on previous work or on steady-state levels in the absence of stimulation. Since the model is quite different from the source models, it is important to provide additional validation. Further, time-series responses and dose-response curves give far tighter constraints on system behavior than single-point steady-state readouts. A figure with a range of such validation runs would be very helpful.

We have clarified to explain that we do not rely on single steady-state levels for selecting parameters. We do constrain our responses according to time-series data (e.g. for pCaMKII, and for Epac) and dose-response curves (e.g. for CaMKII activation). But we also use basal concentrations as constraint, which is not always done. We now add tables of parameters which shows that most parameters were taken from the two models and identifies the parameters that were newly derived or re-parameterized. We provide the URL to the code on github that implemented parameter optimization for CaMKII and SynGap. In addition, we provide additional validation figures comparing model responses with published data (for ppERK and RasGTP).

1b. There is a nice analysis (Table 2) of effects of KO on responses. Surely there are physiological experiments to compare with this? In the para around line 137 several experiments are mentioned but it would be useful to show simulations to compare with the data.

We agree it would be much better to compare our KO experiments with physiological experiments. We now add these comparisons to data for the SynGap KO, but we cannot find data for the effect of Epac KO. We have also added additional KO experiments, comparing the effect of Raf, Ras and Rap KO with experiments (Figure 8 – Supplementary Figure 3, lines 320-339). The effect of an Epac KO is now a prediction of the model as explained in the discussion on lines 481-486.

2. What is the relative strength of contributions by each of the proposed 5 pathways to ERK regulation? How was this ascertained?

We now present a more complete pathway analysis. Figure 8C shows the contribution of each pathway as the percentage of total activity (the ratio of ppERK AUC for a single pathway divided by ppERK AUC with all pathways), and shows that the sum of the pathways exceeds 100%. We also added additional figures (Figure 7 – Supplementary Figure 2B, Figure 6 – Supplementary Figure 1B) showing ppERK responses to single pathways, which also show that the pathways contribute to different time frames of ERK activation. We also show the dynamics of the pathways in response to single pulse stimulation in Figure 5C and D.

3. It is interesting to see differences in linearity between cAMP and Ca pathways. However, these are themselves downstream of the synaptic input. Could the authors explore how these differences would manifest upon synaptic input to a typical synapse having AMPAR, NMDAR, and mGluR? Won't they be rather overlaid on each other?

The simulations using 4 trains of both calcium and cAMP are meant to represent the response to 4 trains of synaptic activation (line 285-286). In addition, to better evaluate the response to more typical synaptic activation, we added simulations in response to the cAMP and calcium concentration dynamics that occur in response to glutamate plus neuromodulators during L-LTP induction, as determined by our published model of those pathways (Jȩdrzejewska-Szmek et al., 2017). These simulations were done by Joanna Jedrzejewska-Szmek, who has been added as a co-author. These results, new figure 9, shows that isopropanol followed by either 100 Hz or 5 Hz produce greater ppERK than ISO, 100 Hz or 5 Hz alone, which corresponds to experimental data showing that only isopropanol plus 100 Hz or 5 Hz produce L-LTP. The purpose of simulating these pathways separately is to understand their different contributions. Figure 8-supplementary Figure 2 shows that even when these pathways are correlated, they contribute to different time frames of ERK activation.

4. While it is nice to see a model with as many as 5 pathways driving ERKII, I am curious about the choice of these input pathways. From synaptic input one would expect to see an mGluR component. Do the authors envision that this folds into Gbg? Further, one sees other signals such as BDNF as major players in plasticity.

4b. I bring this up also in the context of the reported time-courses. Experimental time-courses of other pathway inputs can be quite different from those explored here, BDNF tending to be quite slow.

mGluR would provide a Gq component leading to activation of PKC. This pathway is quite important for LTP in other systems (striatum, neocortex), and PKC is critical for maintenance of synaptic plasticity; however, this research is focused on induction of LTP, which is generally found to be independent of PKC. In addition, published data (Zhai et al., 2013) shows that structural plasticity, a correlate of LTP, is independent of mGluR stimulation. We now discuss this on lines 426-428.

Regarding BDNF, we agree that it contributes to ERK activation through the canonical pathways. However, as the reviewer points out, this pathway is quite slow, and thus is unlikely to contribute to temporal sensitivity. Because this research is focused on temporal sensitivity, BDNF was excluded from the model. To completely predict whether ppERK is sufficient for plasticity, ideally, we would include the BDNF-TrkB pathway; however, the concentration profile of BDNF is not well characterized, making this aspect of the model problematic.

Reviewer #2:

There are, however, a couple of points that I feel should be addressed, in order for me to enthusiastically recommend this manuscript for publication.

1. There needs to be additional technical detail on how the original models were expanded. The model presented here was developed by merging Jȩdrzejewska-Szmek et al., 2017 and Jain and Bhalla, 2014 models. These models were developed based on experimental data and validated with independent experimental datasets in a rigorous manner. It is not clear how the combining these two models, and the additional molecules and reactions added have affected the dynamics of ERK activation, and how comparable they are to the original experimental data used for model development in the previous modeling efforts. It is not clear if the model was reparametrized.

We now add tables of parameters which includes which parameters taken from the two models and which parameters were newly derived or re-parameterized. In addition, we provide additional validation figures (Figure 2, Figure 9, and Figure 8 – Supplementary figure 3) comparing model responses with published data.

2. Beyond the ERK activation traces, it would be useful for clarity sake to also include the simulated traces for the activation of the upstream molecules (PKA, RAS, RAP, etc). Given how additional changes have been made additional information should be provided to ensure that the contribution of each pathway is accurately represented.

We have added additional graphs showing dynamics of RasGTP (Figure 2A), active Epac (Figure 8 – Supplementary Figure 2B), active RasGRF (Figure 8 – Supplementary Figure 2C), and phosphorylated SynGap (Figure 8– Supplementary Figure 2D), to provide more insight into the pathways and demonstrate their contribution. These molecules were selected as showing contribution to different time frames of activation.

Reviewer #3:

This paper is primarily about modeling the ERK pathway during the induction of synaptic plasticity. This pathway has been previously modeled, and this is cited in the paper. The main addition here is the addition of the effect of SynGap which is necessary in some form of LTP. This is a very detailed study, and what it seems to primarily show is that the ERK pathway favored spaced vs. massed stimulation protocols. This is a very detailed paper, but no conceptually new ideas are presented here. The paper adds to an existing foundation, but fails to make the case that this is a very significant addition. What is the significant consequence at a higher level of these added details?

We have completely rewritten the introduction and the discussion to emphasize the novelty of our results. Aside from demonstrating the role of SynGap, we also show that different signaling pathways contribute to different time frames of ERK activation. Thus, while ERK can respond to either spaced or massed stimulation (though we higher total activity with spaced), two of the pathways (RasGRF and Epac) are active early, SynGap is activated a bit later but prolonged, and the two other pathways are active later but transient (PKA and Gbg). These different time frames of ERK can serve allow temporal pattern discrimination. We now explain the consequence of temporal pattern discrimination in the discussion (444-492).

The ERK pathway is just one component of a much larger set of pathways that control synaptic plasticity, how much do we learn from studying this pathway in isolation? Also, the paper cites the importance of this pathway to L-LTP, is it the induction phase of L-LTP? It seems so because ppRRK decays in less than an hour. How then does this pathway contribute to the maintenance of L-LTP, these processes such as a possible upregulation of protein synthesis are not part of this model either.

We now clarify in the introduction that ERK is involved in induction of L-LTP, which includes triggering the protein synthesis (lines 59-62) The evidence for ERK in maintenance phase has not been demonstrated. In fact, very few molecules, with the exception of atypical forms of PKC, are involved in maintenance. We now explain that our time frame of ERK activation is consistent with experiments, and that ERK is not needed for maintenance (418-426).

This paper studies in detail different pathways that influence ERK activation is synapses. This is a very detailed study, but how many details do we actually know? For a detailed paper though it seems that many of the details are missing. Is there a detailed diagram of reactions, or set of equations for all these reactions? Some coefficients are named in figure 1, and this might be sufficient for a schematic description of the model in the paper, however there must be somewhere a detailed description of all reactions. How many species are there here, how many coefficients? How are coefficient values known? How many coefficients are directly estimated? The paper does carry out an extensive robustness analysis, though it is not well explained.

We now provide table of reactions and rate constants, which also indicate which coefficient values were known, and which were estimated (Figure 1 –Source Data 1-6). As is evident from these tables, very few of the coefficient values were changed.

We have re-worked the explanation of the robustness analysis (lines 366-370 and 604-609).

To summarize, the paper is very detailed carefully constructed and executed, it fails to convince that the problem it addresses is very significant, and it makes no conceptual breakthroughs.

The observation that different signaling pathways contribute to different time frames of ERK activation is a conceptual breakthrough in highlighting that, as observed in other cells, different ERK dynamics may have different functions.

The induction protocols seem to include not only calcium pulses, but also cAMP and g-protein coupled pulses, what is the cellular origin of these other pulses? Is the G protein activation due to β-adrenergic activation, is this activation necessary for plasticity? What is the cellular origin of the cAMP and Gi activation in slice? Similarly, what primarily activated cAMP in real synapses?

The cellular origin of these other pulses are Calcium, norepinephrine and dopamine. Both the locus coeruleus and the ventral tegmental area project to the hippocampus, and electrical stimulation is known to release norepinephrine, as explained in (Jȩdrzejewska-Szmek et al., 2017). Some early publications (Huang and Kandel, 1995) show that blocking dopamine will block L-LTP. Both Dopamine D1 and β-adrenergic activation produces GsGTP in the slice, which synergistically enhances the activation of adenylyl cyclase by calcium-calmodulin, to produce cAMP. I.e., in real synapses, both calcium and GsGTP produce cAMP. Regarding Gi activation, most of the research on Gs-Gi switching has been done in cell cultures (Daaka et al., 1997; Martin et al., 2004) however there is evidence that inactivated β adrenergic receptors can recruit ERK in the hippocampus (Havekes et al., 2012). The switching pathway is explained in Jȩdrzejewska-Szmek et al., 2017, and we summarize this in the methods, (lines 557-560).

Is ERK required for all forms of LTP? Some references indicate it might not be. Is ERK necessary for early LTP induced by 100Hz stimulation?

We have now clarified the difference between E-LTP and L-LTP (lines 52-58). Indeed, ERK is not required for E-LTP (Winder et al., 1999), hence we focus on induction protocols for L-LTP. We have now added simulations of E-LTP using 1 train of 100 Hz, and this shows that ppERK is much lower with these protocols.

I get lost in the details of the introduction, description of different pathways should be in results and relate to figure 1. It looks like a shopping list, why is this significant?

We have completely re-written the introduction and added more emphasis on the goal of our research, especially the importance of multiple pathway to ERK with respect to temporal pattern discrimination. We have removed many signaling pathways details and focus more on the relevant factors.

Why is it important that this is a stochastic diffusion reaction model rather than a deterministic model? Nothing about fluctuations, except for small error bars are mentioned in this paper.

When we began this study, we did not know whether stochastic fluctuations would impact our results. We tested that by doing some simulations in very small compartments, but saw no differences (except for increased noise). Though we could have switched to deterministic, the stochastic algorithm is extremely fast, especially for stiff systems; thus, there would be no advantage to switching to a potentially less accurate deterministic simulator.

Do not reference Zhang et al. Nature Neuro 2012, its' not a mammalian LTP model, still there are similarities (and differences), especially as ERK pathways are studied and since it relates to spaced learning.

We removed this article.

229 – where do we see autophosphorylation in figure 3F?

We clarified the autophosphorylation (now Figure 4F). The figure is not showing the autophosphorylation of ppERK but shows the effect of CaMKII phosphorylation of SynGap on ERK activation. We now state on lines 197-199:

“Simulations reveal that persistent activation of ERK requires phosphorylation of SynGap by pCaMKII and dispersion of pSynGap to the dendrite (Figure 4F)”

Figure 6B – hard to see shape of symbols.

We have made the size of the symbols bigger (now Figure 7B).

No model diagrams or equations here, for example how in CaMKII autophosphorylation implemented? Figure 6C – what is old CaMKII? They give a reference, but we do not know what the new model is.

We now provide a table with all reactions and rate constants. In summary, the new CamKII was created using automatic parameter optimization and fitting to time-course data of DeKoninck and Shulman, 1988. The reaction diagram also was modified slightly because NeuroRDv1 only allowed uni- and bi-molecular reactions, whereas NeuroRDv2 allowed higher-order reactions. In both cases, the higher-order phosphorylation reactions allow a single subunit model of CaMKII to exhibit a phosphorylation response of the dodecameric/hexameric in situ CaMKII. We have renamed this to alt CaMKII for alternative CaMKII model.

Narrow picture by looking only at ERK. – For example, increasing PP1 can enhance ppERK, however it might reduce overall LTP due to dephosphorylation of AMPA receptors. What wins?

We have not explained the effect of PP1 concentration clearly. Increasing PP1 does not enhance ppERK; on the contrary, it reduces ERK activation (Figure 4D), because an increase in PP1 results in less phosphorylated CaMKII. Thus, PP1 would both reduce ppERK and reduce AMPA phosphorylation. This section was meant to show that PP1 concentration changes ppERK temporal sensitivity. We have now clarified that increasing PP1 reduces total ERK activity (Figure 4D), and it decreases the steepness of the ultrasensitivity of ppERK to calcium (Figure 1E).

Figure 7 – what in figure 7 shows super linearity? It's in the title, where else? This applies to paragraph starting in line 368 as well. Where do we see these results. We can try to eyeball it. It would be useful to show a plot of combined model/(sum of individual models). By eyeballing this it seems (but might be wrong) that the super-linearity is minimal.

We now add a statement in the caption (now Figure 8) that “Supralinearity is indicated by the response to the combination of cAMP and calcium (Combo) is greater than the sum of responses to calcium and cAMP separately.” In addition, we now plot contribution of each pathway separately, and show the sum of contributions exceeds 100% of the response to the combination (Figure 8C) to help show the supralinearity. We agree that the supralinearity is not dramatic. We have also enhanced our statistical analysis (Table 5) to provide a more complete picture of linear versus non-linear pathway interactions.

403 – the first time random-forest was mentioned in line 403, and this method is not explained or defined prior to this or even in this paragraph. For eLife type of readers this needs to be explained in simple terms.

We now provide a brief explanation of random forest (lines 366-370 and 604-609).

423 – typo – "Molecules were randomly simultaneous(ly)"

Fixed

What to weights in table 5 mean? This relates to the random forest analysis which is not explained.

We now explain that the weight indicates its usefulness in predicting the dependent variable (lines 373 and 608).

Similar problems with figure 8, what is shown here? What is the analysis used here? This is totally unclear. Are molecules here changed one at a time? How much are they changed? Is this the 10% discussed earlier? It would also be more instructive to show relative range changes.

We now provide better explanation of parameter analysis and changed the presentation of the results. We now show relative change in ppERK, averaged across all ITIs, and the relative change in temporal sensitivity, quantified as the difference between maximum ppERK and minimum ppERK (across ITIs). Instead of showing the change for each parameter, we show a histogram of these values as better representing the robustness to parameter change. Using this presentation, we show that the temporal sensitivity of ppERK is quite robust, and in fact most of the parameter variations would increase, rather than decreasing temporal sensitivity.

How is this paper related to the recent Maki-Marttunen paper from the same lab which appeared recently

(https://www.biorxiv.org/content/10.1101/2020.01.27.921254v1.abstract), it is not referenced here. That is a more general paper but seems to exclude ERK. If ERK is so significant how can it be excluded in one paper and included in another from the same lab?

Maki-Marttunen is studying STDP in the neocortex. There are several major differences between STDP and L-LTP. Protein synthesis dependence of STDP has not been demonstrated. This coupled with the duration of follow-up (1 hour or less due to using whole-cell patch) makes it is difficult to determine whether STDP corresponds to E-LTP or L-LTP. Regardless of whether STDP represents E-LTP or L-LTP, the requirement for ERK has not been shown. Because of the size of the synaptic plasticity field, we tried to limit our references to ERK-dependent plasticity.

Discussion starts OK, but again devolves into excessive details.

We have now re-worked the discussion, removed many details, and focus most on important aspects.

Does this model possibly explain induction of L-LTP, or its maintenance phase? It seems the prior since ppERK activity returns to baseline; these should be distinguished.

We now emphasize that the model is explaining L-LTP induction and not maintenance. (lines 59-62 and 418-426)

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Mauk, M.D., Ruiz, B.P., 1992. Learning-dependent timing of Pavlovian eyelid responses: differential conditioning using multiple interstimulus intervals. Behav. Neurosci. 106, 666–681.

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[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Point 1: Comparisons to experiments and validation of parameterization.

The authors have partly addressed this point, with comparisons of simulations to several additional experiments. They have also provided tables of data sources but many parameters are linked to previous models rather than to experiments. It would be helpful if the authors could explicitly address the point about _parameter_ validation, and to what extent systems level experiments provide validation for rate terms.

Parameter validation is indeed a critical, yet difficult task for signaling pathway models. We have updated out tables to include the experimental data sources used in the previous models, to show that many of the parameters were constrained by experimental data. In addition, we provide supplementary figures (Figure 2- supplementary Figure1) showing the fit of the model to data for CaMKII and SynGap (which are the results of parameter optimization), and cAMP-bound Epac and phosphorylation of PKA substrates (which are systems level validations). Since publication of time course data is not common, we are unable to provide direct validation of additional parameters. As the tables illustrate, most of the parameters come from well-validated models, in which parameters were constrained experimentally (e.g. Sasagawa et al., Nature Cell Biology, 2005) or which made predictions that were experimentally tested. The fact that those published parameters are sufficient to reproduce phosphoERK from additional published experiments (Figure 2B) provides yet another systems level validation for the parameters in the published models. Systems level validation is common with these types of models in part due to the difficulty in accurately measuring on rates (compared to affinity) using biochemical experiments. We have added additional sentences about the parameter validation on 116-123.

Point 2: Activation of pathways by synaptic input.

Here the authors use the model from their 2017 paper to generate Ca and cAMP waveforms, and report results consistent with experiments. It is just a single figure though, and only reports ppERK. We don't see the upstream pathways and their responses. Since the authors have now added these upstream pathways, it would be good to see the time-courses for upstream key molecules indicated in figure 1. These include Ca, Gbg, cAMP, as well as CaMKII, PKA, synGap, Ras and Rap1. It would be useful to have a figure with these time-courses for the major stimulus patterns used in the figures. In Figure 8 – supplementary Figure 2B the authors provide some time-courses for a few molecules. A complete set would be desirable.

We now provide supplementary figures showing the time course of calcium, cAMP and Giβγ for single pulse (line 147, 182-183 and Figure 3- supplementary Figure1). We also provide time course of calcium, Giβγ, cAMP, CaMKII, PKA, synGap, Ras, Rap1, Raf, MEK, pSrc in Figure 8 – supplementary Figure 1 and Figure 9 – supplementary Figure1.

Point 5: Source data now provided. Unfortunately it isn't in SBML. If the authors can apply a conversion program to their model, an SBML version would be valuable.

A neurord XML to SBML program has recently been written, though it does not yet convert a small subset of reactions correctly and it does not convert the stimulation files. We now include the SBML for the main reaction and initial condition file in our github repository, and this will be SBML file will be updated once the conversion program has been debugged.

Also, the response to the reviewer's point about the use of a stochastic method would be good to include in the text. We did not see this statement there.

We now include a statement in the methods (lines 593-596) that “Even though stochastic fluctuations observed using small compartments do not impact the results, the stochastic algorithm is extremely fast, especially for stiff systems; thus, there would be no advantage to switching to a potentially less accurate deterministic simulator.”

https://doi.org/10.7554/eLife.64644.sa2

Article and author information

Author details

  1. Nadiatou T Miningou Zobon

    Department of Chemistry and Biochemistry, George Mason University, Fairfax, United States
    Contribution
    Conceptualization, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5824-7706
  2. Joanna Jędrzejewska-Szmek

    Laboratory of Neuroinformatic, Nencki Institute of Experimental Biology of Polish Academy of Sciences, Warsaw, Poland
    Contribution
    Writing - review and editing, model simulations
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-2336-0848
  3. Kim T Blackwell

    1. Interdisciplinary Program in Neuroscience, Bioengineering Department, George Mason University, Fairfax, United States
    2. Krasnow Institute for Advanced Study, George Mason University, Fairfax, United States
    Contribution
    Conceptualization, Software, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    kblackw1@gmu.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-4711-2344

Funding

National Institutes of Health (R01MH 117964)

  • Kim T Blackwell

National Science Foundation (1515686)

  • Kim T Blackwell

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work was supported through the joint NIH-NSF CRCNS program through NSF grant 1515686 and NIMH grant R01MH 117964.

Senior Editor

  1. Ronald L Calabrese, Emory University, United States

Reviewing Editor

  1. Upinder Singh Bhalla, Tata Institute of Fundamental Research, India

Publication history

  1. Preprint posted: November 4, 2020 (view preprint)
  2. Received: November 5, 2020
  3. Accepted: August 3, 2021
  4. Accepted Manuscript published: August 10, 2021 (version 1)
  5. Version of Record published: August 13, 2021 (version 2)

Copyright

© 2021, Miningou Zobon et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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