The sensory-motor neuron synapse of Aplysia is an excellent model system for investigating the biochemical changes underlying memory formation. In this system, training that is separated by rest periods (spaced training) leads to persistent changes in synaptic strength that depend on biochemical pathways that are different from those that occur when the training lacks rest periods (massed training). Recently, we have shown that in isolated sensory neurons, applications of serotonin, the neurotransmitter implicated in inducing these synaptic changes during memory formation, lead to desensitization of the PKC Apl II response, in a manner that depends on the method of application (spaced versus massed). Here, we develop a mathematical model of this response in order to gain insight into how neurons sense these different training protocols. The model was developed incrementally, and each component was experimentally validated, leading to two novel findings: First, the increased desensitization due to PKA-mediated heterologous desensitization is coupled to a faster recovery than the homologous desensitization that occurs in the absence of PKA activity. Second, the model suggests that increased spacing leads to greater desensitization due to the short half-life of a hypothetical protein, whose production prevents homologous desensitization. Thus, we predict that the effects of differential spacing are largely driven by the rates of production and degradation of proteins. This prediction suggests a powerful mechanism by which information about time is incorporated into neuronal processing.

Memories are among an individual's most cherished possessions. One factor that has been shown to exert a powerful influence on memory formation is the pattern of training. Learning trials distributed over time have been shown to consistently produce longer lasting memories than trials distributed over short intervals, in every organism in which this has been studied. This observation has been investigated particularly well in the marine mollusk Aplysia californica. The nervous system of Aplysia is simple and well characterized, yet capable of forming memories, making it an ideal system for the study of learning and memory. Currently, we have a detailed understanding of memory formation in Aplysia at the cellular level. However, there remain many unanswered questions at the molecular level, particularly concerning how the effects of different patterns of learning are mediated. We have developed a mathematical model of a molecular signaling pathway known to underlie memory formation in Aplysia. Our model suggests that the rates of synthesis and degradation of proteins involved in memory regulation are essential for neurons of Aplysia to respond differentially to spaced and massed training. We were able to experimentally validate these findings, thus providing significant evidence for this model, which might underlie memory formation in more complex animals.

Funding: F.N. was supported by an Alexander Graham Bell Canada Graduate Scholarship from the National Sciences and Engineering Research Council. C.A.F. is a postdoctoral fellow of the Fonds de la Recherche en Santé du Quebec (FRSQ) and a Conrad Harrington fellow. C.C.P. holds a Tier II Canada Research Chair. W.S.S. is a James McGill Professor and an FRSQ Chercheur National. This work was supported by a Canadian Institutes of Health Research (CIHR) grant MOP12046 to W.S.S., and a Canadian Excellence in Commercialization and Research (CECR) grant to the Montreal Neurological Institute. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

In order to better understand the signaling pathway mediating the desensitization of PKC Apl II, we developed a model consisting of a system of integro-differential equations describing the differential desensitization of PKC Apl II activation during massed and spaced training. The model provides predictions about the molecular mechanisms responsible for the differences between massed and spaced training. These predictions were validated with new experiments. Together these results suggest that the sensitivity of neurons to the time between training periods is due to the rates of protein synthesis and degradation.

While massed applications of 5HT are less effective than spaced applications at generating LTF measured at 24 h [7] , both spaced and massed training lead to protein-synthesis dependent intermediate-term facilitation (ITF), measured 30 min to 2 hr after 5HT is removed [11] , [14] , [15] . However, the mechanisms underlying ITF induced by spaced or massed training are distinct; ITF induced by spaced training require PKA but not PKC for induction [16] , [17] , while ITF induced by massed training, even a continuous stimulus as short as 10 min, requires PKC but not PKA [14] ( Figure 1 ). Thus, the differential activation of PKC during massed and spaced training appears critical for the different physiological effects of these two training paradigms.

An important mechanism for the differential activation of PKC during spaced and massed applications of 5HT involves differential desensitization of PKC Apl II translocation to the plasma membrane, where it is activated [13] . Spaced training (5×5 min 5HT with 15 min wash periods in between) leads to more desensitization than one massed 25 min application of 5HT [13] . This differential desensitization is surprising, since spaced applications of 5HT allow the neuron to recover in between exposures; yet they cause a greatly increased amount of desensitization when compared to the massed application of 5HT. This effect was shown to depend on both PKA-mediated desensitization and the downstream effects of protein synthesis [13] . Importantly, protein synthesis inhibitors have opposite effects depending on the training stimulus: massed training produces a protein that prevents desensitization of PKC Apl II translocation while spaced training produces a protein that promotes desensitization of PKC Apl II translocation ( Figure 1 ) [13] . Thus, another important distinction between these two training paradigms is that they activate distinct translational pathways.

Spaced training activates PKA but not PKC and leads to PKA-dependent translation that induces intermediate-term facilitation (ITF) and long-term facilitation (LTF) not dependent on PKC. PKA dependent translation also produces a protein that increases PKC desensitization, which is required for spaced training not to activate PKC. Massed training activates both PKA and PKC and leads to PKC-dependent translation that induces a distinct form of ITF not dependent on PKA. PKC-dependent translation also produces a protein that prevents PKC desensitization, which is required for massed training to continually activate PKC.

5HT acts through at least two distinct G protein coupled receptors (GPCRs) in Aplysia to activate protein kinase A and protein kinase C [8] , [9] . The two kinases are differentially activated based on the type of training; spaced applications of 5HT lead to the persistent activation of PKA in the sensory neuron [10] , [11] , while massed applications of 5HT instead activate both PKA and the novel PKC Apl II in the sensory neuron ( Figure 1 ) [10] , [12] .

One form of behavioral sensitization in Aplysia involves an increase in defensive reflexes after a noxious stimulus. The increase in defensive reflexes is caused in part by an increase, or facilitation, of the strength of the synapse between the mechanoreceptor sensory neurons and withdrawal motor neurons [4] . Facilitation is mediated by release of serotonin (5HT) from interneurons activated by the noxious stimulus [5] , [6] . Spaced noxious stimuli are superior to massed stimuli at generating long-term sensitization in the animal [3] and spaced applications of 5HT are superior to massed applications at generating long-term facilitation (LTF) of cultured sensory-motor neuron synapses [7] . The ability to examine the difference between spaced and massed training in cultured neurons allows the study of the differential signaling events activated by spaced and massed training.

Different patterns of training can lead to different types and strengths of memories. For example, training distributed over time (spaced training) is superior to the equivalent amount of training with no interruptions (massed training) for generating long-term memories for verbal tasks [1] . Spaced and massed training are known to activate different molecular signaling pathways underlying memory formation [2] . Aplysia californica, a marine mollusk, provides an ideal model system for examining the differences in molecular signaling mediated by spaced and massed training [3] .

Results

Describing the model architecture We have previously described PKC Apl II translocation and its desensitization in response to 5HT application in the presence of PKA and protein synthesis inhibitors [13], [18], [19]. We showed that PKC translocation differentially desensitizes to spaced and massed applications of 5HT, and that this differential desensitization was dependent on protein translation and PKA activity. In order to understand the molecular mechanisms underlying desensitization of PKC Apl II translocation we designed a signaling network based on our previous experimental findings and biochemical mechanisms known to underlie G protein-coupled receptor (GPCR) desensitization. Our network consists of the translocation of PKC, the cycling of a GPCR, the translation of two hypothetical proteins, and activity of PKA. We have tried to simplify the network whenever possible, including bundling multiple biochemical reactions into one single rate in order to simplify its architecture. The reasoning behind the network's architecture is given in this section and the model equations are given in the Materials and Methods section. The basic unit of the model is the 5HT GPCR (S) that once activated leads to the production of diacylglycerol (DAG), which is capable of activating and translocating PKC Apl II to the membrane [20], [21]. While this pathway consists of multiple steps, such as G-protein activation of phospholipase C and phospholipase D [18], these are not likely to be important for modeling of desensitization, since in most systems the amount of the activatable GPCR is the rate-limiting quantity that is decreased during desensitization [22], [23], [24]. GPCRs can enter a number of different pathways, such that S can exist in several different states, where the change in concentration of each state with respect to time is modeled. The base component of our model includes the activation and inactivation of S without any desensitization dynamics. This component corresponds to how quickly PKC Apl II translocates to the membrane after 5HT application and how quickly it dissociates from the membrane after 5HT is washed away. It is known that application of 5HT results in a maximal translocation of PKC Apl II within one minute, after which it remains at this maximal level for at least five minutes [18], [19]. Washing off 5HT prompts the complete dissociation of PKC Apl II within one minute [13], [18], [25]. To replicate these findings, we used a simple network architecture, whereby in the presence of 5HT, S OFF becomes S ON , which then transforms to S IN1 . S OFF represents the inactivated receptor that can become activated by 5HT, turning S OFF into S ON , which then produces DAG allowing for the translocation of PKC Apl II. S IN1 is an inactivated receptor that needs to be recycled before it can become activated by 5HT again. At a biochemical level, the transitions from S ON to S IN1 to S OFF involve multiple molecular steps including GPCR phosphorylation by G protein receptor kinases, binding of beta arrestin, possible internalization of the receptor, unbinding of the ligand, and then recycling of the receptor back to its initial state [22], [23], [24]. For simplicity, we have reduced these multiple steps into the two steps (S ON to S IN1 to S OFF ) since (i) this is sufficient to capture the behavior required to understand the questions we are addressing (see below) and (ii) we have no specific knowledge concerning regulation of these pathways in Aplysia. The major constraint from the data is that PKC comes off the membrane in less than one minute after 5HT is washed off. Thus S ON to S IN1 must be fast enough to account for this inactivation. However, in the first 5 min of 5HT activation, there is little desensitization of PKC Apl II translocation. Thus, S IN1 to S OFF must be rapid enough to prevent appreciable desensitization in the first five minutes. The transitions between states of S were modeled using mass action kinetics. These model parameters were fit to the previously described PKC dynamics [13], [18], [25] (equations, parameter values, and parameter estimation methods can be found in the Materials and Methods section). Once an appropriate fit was found these parameters were set and we were able to begin expanding the model and modeling data related to PKC Apl II desensitization. The complete model architecture is presented in Figure 2. The model components (color coded) were developed sequentially, with maroon and black first then blue, red, and finally green. The maroon component represents only the translocation of PKC to the plasma membrane and its subsequent dissociation from the membrane. The black component represents the desensitization pathway in the presence of a protein translation inhibitor and a PKA inhibitor. In the presence of these inhibitors, PKC Apl II translocation desensitizes during exposure to 5HT [13]. Thus, there must be a protein translation-independent and PKA-independent desensitization pathway, or a homologous desensitization pathway, which we model as an alternate recycling pathway from S IN1 to S OFF , passing through S IN2 (Figure 2; black network only, equations can be found in the Materials and Methods section). Here S IN2 acts as a secondary inactivated state that requires a longer processing time than S IN1 before recycling back to S OFF . At the biochemical level, this represents the sorting of the GPCR in the endocytic compartment from a rapid recycling pathway into a slow recycling pathway or degradative pathway. This architecture was chosen because of the abundant literature supporting this mechanism for desensitization of GPCRs [22], [23], [24]. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. Complete model network. The maroon network describes the translocation of PKC to the plasma membrane and its subsequent dissociation from the membrane. The module denoted in black represents the homologous desensitization pathway. The blue network defines the PKA mediated desensitization of PKC Apl II. The red network illustrates the AD pathway responsible for the rescuing PKC from desensitization. Finally the D pathway, which is antagonistic to the AD pathway and causes the increase in desensitization, is specified by the green network. In green are the additional roles of AD needed to counteract D during massed training. https://doi.org/10.1371/journal.pcbi.1002324.g002 PKA, which is activated by 5HT, has been shown to increase desensitization of PKC Apl II translocation in the absence of protein translation [13]. The condition where PKA is active and protein translation is inhibited is modeled by the combination of the black, maroon, and blue components. In order to model PKA-mediated protein synthesis-independent desensitization, we included a reduced and modified version of a previous model of PKA activity [26]. Our modifications to this PKA model are described in the next sections. Activity of PKA is capable of converting S OFF directly into S PKA , where S ON is not immediately attainable and PKC Apl II cannot be activated (Figure 2; black and blue networks, equations can be found in the Materials and Methods section). At the biochemical level, this network would represent phosphorylation of the receptor, or receptor-associated protein, by PKA causing the endocytosis of the GPCR from the plasma membrane to an endocytic compartment distinct from S IN1 and S IN2 , probably representing a regulated recycling endosome [27]. It is important to note that since PKA can convert S OFF to S PKA , conversion to S PKA does not require S to go through the active state, S ON , such as the desensitization mediated by S IN2 . This network architecture is required to account for the observation that PKA activity between pulses of 5HT, when S would not be activated, is capable of desensitizing PKC Apl II translocation [13] and is consistent with data on heterologous desensitization of GPCRs in other systems [28]. This consideration also removed the alternate topology where S PKA would represent alternate sorting from S IN1 , since the receptor is only in the S IN1 state when the receptor goes through the active state. The recycling of S PKA back into S OFF is inhibited by PKA. This inhibition was not initially part of the architecture, but it was not possible to replicate both the massed training and spaced training data sets without including the PKA inhibition of S PKA recycling (see results below). At a biochemical level, this suggests that PKA activity is not only required to induce sorting of the receptor to the regulated recycling endosome but its retention in this compartment as well. The reverse situation, with PKA activity inhibited but protein translation allowed to function is modeled by the combination of the black, maroon, and red components. Protein translation in the absence of PKA activity leads to a reduction in the desensitization of PKC Apl II translocation only during massed 5HT application and not spaced [13]. This observation requires that a protein, which protects PKC Apl II translocation from the constitutive desensitization pathway be translated during massed training. We name this hypothetical protein Anti-Desensitizer (AD) and its effects on the network are represented by the black, maroon and red components combined. We modeled the mechanism of AD mediating this protection by having AD convert S OFF into S AD , a form of S preserved from the desensitization pathways leading to S IN2 or S PKA , but similar to S OFF in its ability to become activated by 5HT and cause the translocation of PKC Apl II (Figure 2, black, maroon and red pathway; equations can be found in the Materials and Methods section). At the biochemical level, this would represent the AD protein binding to the receptor, or receptor associated protein, preventing its inactivation and internalization [29], [30], [31], [32]. Since a protein-synthesis dependent protection from desensitization is seen in massed, but not spaced, training protocols, we would expect AD to be synthesized only after massed training. In order for this differential synthesis to occur, we made production of AD proportional to the mathematical integration of the level of active PKC Apl II. PKC Apl II is constantly active during massed training, but not during spaced training; thus, integrating PKC activity allows for selective activation of AD during massed training. PKC is known to regulate the translational machinery in many systems [33], [34] including Aplysia [35], [36], but the exact mechanism by which PKC regulates translation in this case is not known and is not explicitly modeled here. Finally, allowing both protein translation and PKA activity to proceed normally results in an increase in the desensitization of PKC Apl II translocation during spaced training [13]. This increase in desensitization was observable only when both PKA activity and protein translation are allowed to proceed, meaning a translated protein is mediating this increase in desensitization, and its rate of translation is dependent on PKA activity. We name this hypothetical protein Desensitizer (D), and we model its mechanism of action similarly to that of PKA by transforming S OFF into S PKA and inhibiting its recycling back to S OFF (Figure 2, complete network; equations can be found in the Materials and Methods section). Another possible architecture would have been to generate another state of S (S D ), but there was not a good biochemical rationale for this and the model worked well (see below) without this additional state. At the biochemical level, D would be a protein that promotes endocytosis [29], particularly to the PKA-dependent pathway. The rate of translation of D is dependent on the amount of PKA activity, similar to the dependence of AD translation on PKC Apl II activity. One difference between the translation of D and AD is that D's production is delayed by 10 min after its induction. The use of a delay was necessary to account for the observation that desensitization of PKC Apl II translocation after a 5 min pulse of 5HT did not begin until after a 10 min wash [13]. At a biochemical level, there may be many reasons for a delay, ranging from requirements for post-translational modification, cellular trafficking, or delay in the activation of proteins synthesis. Finally, while trying to model the data we found that for D to cause enough desensitization during spaced training resulted in too powerful an inhibition during massed training. This over-inhibition resulted from the fact that unlike AD, D is synthesized during both spaced and massed training since PKA is active in both scenarios [10]. To diminish the role of D during massed training, we introduced two additional effects of the AD protein. First, AD inhibited the transition from S OFF to S PKA , and second, it could transform not only S OFF to S AD but also S PKA to S AD (Figure 2; complete network). At a biochemical level, this corresponds to the ability of the AD protein to prevent endocytosis to the PKA-dependent pathway, and moreover, to bind to the GPCR in the regulated recycling endosome and enhance its recycling, similar to the mechanism by which decreased PKA activity enhanced recycling from this compartment. We also attempted to model the system with AD preventing the translation of D as opposed to opposing its actions, but were unable to achieve a good fit to the data with this architecture. For simplicity, we made the assumption that during the time course of our experiments an insignificant amount of new S is created. This assumption was also made partially because for S to enter the S OFF state, the GPCR would not only have to be synthesized, but processed through the endoplasmic reticulum, Golgi apparatus, and transported back to the membrane, so new S could only contribute to the later parts of the experimental paradigm. We do not have a term for destruction of S, however, as described below, the S IN2 pathway may be equivalent to a degradation pathway, where the GPCR enters late endosomes and lysosomes.

Modeling the homologous desensitization pathway finds slow rate of recovery from desensitization PKC Apl II translocation still desensitizes during exposure to 5HT even when both protein translation and PKA have been inhibited [13]. Thus, there must be a homologous desensitization pathway (Figure 3A; black network only, equations can be found in the Materials and Methods section). Parameter values were estimated by fitting the model to PKC Apl II translocation measurements taken during a continuous 90 min application of 5HT in the presence of the protein translation inhibitor anisomycin and the PKA inhibitor KT5720 [13]. Several parameter estimation methods were used, and surprisingly, all of them yielded recycling rates of S IN2 back to S OFF (k A5 ) that were near zero (parameter values can be found in Table 1), resulting in an excellent fit to the data as can be seen in Figure 3C (R2>0.99). Note that throughout the paper, data presented in blue represents data obtained from Farah et al. (2009) used to train the model, while data presented in red represents experiments performed to confirm predictions of the model. The model predicted very little recycling of the signaling complex from S IN2 during massed training in the absence of protein translation and PKA activity (Figure 3C, D). This was unexpected, since our earlier experiments showed that the desensitization seen after a 5 min pulse of 5HT recovered completely within 45 min, suggesting efficient recycling of the signaling complex [13]. However, these experiments were not done in the presence of a PKA inhibitor. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 3. Modeling and experimental validation of homologous desensitization pathway. A, Model network pathways of homologous desensitization pathway (black) and PKA-mediated desensitization pathway (black and blue). B, Representative confocal fluorescence images of sensory neurons expressing eGFP-PKC Apl II during a 90 min exposure to 5HT followed by a 45 min wash and then a 5 min 5HT application, all in the presence of anisomycin and KT5720. C, Quantification of PKC Apl II translocation (bars) and modeling output (line). Blue bars are data used from Farah et al. (2009) to fit the model parameters. Red bars are data from the present study (n = 8 cells). Error bars are SEM. D, Modeling of S dynamics in response to experimental protocol from B. Black line represents the ratio of S OFF and S ON to total S and the red line the ratio of S IN2 to total S. The times of addition of 5HT and pharmacological agents are indicated below the figure. https://doi.org/10.1371/journal.pcbi.1002324.g003 PPT PowerPoint slide

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larger image TIFF original image Download: Table 1. Model parameters. https://doi.org/10.1371/journal.pcbi.1002324.t001 To test the prediction of the model that desensitization seen in the absence of PKA activity was not reversible, we conducted a new experiment. The rate of S IN2 recycling was predicted to be slow enough that a wash period after massed training with anisomycin and KT5720 would result in little recovery of translocation to initial values. Thus, in a simulation of a 90 min exposure to 5HT followed by a 45 min wash and then a 5 min pulse of 5HT, all in the presence of anisomycin and KT5720, the 5 min pulse of 5HT should only cause a small amount of PKC Apl II translocation, since a majority of S is held in the inactivated state S IN2 (Figure 3C, D). To test this prediction of the model, we used this protocol in a new imaging experiment using Aplysia sensory neurons expressing eGFP-PKC Apl II. The initial massed training caused a similar amount of translocation to that previously observed by Farah et al. (2009) (Figure 3B, C). Furthermore, the amount of desensitization after the 5 min pulse of 5HT matched the modeling prediction extremely well, demonstrating that recovery from desensitization under these conditions was indeed very slow (Figure 3B, C). This protocol required that the neurons be imaged for a total of 140 min. To ensure that the lengthy exposure to room temperature (20–23°C) and the drugs anisomycin and KT5720 had no effect on the health of the neurons, or their ability to translocate PKC Apl II, two 5 min pulses of 5HT were applied with a 130 min wash in between, all in the presence of both drugs. Recovery from a 5 min pulse of 5HT occurs after 45 min [13], so we expect that a 130 min wash should result in complete recovery and that any depression in PKC Apl II translocation would be caused by injury to the neurons due to prolonged exposure to room temperature and drugs. There was no significant difference in the amount of PKC Apl II translocation between the first and second pulse of 5HT (mean+/−sem; 1.08+/−0.18, n = 5). Thus the persistent desensitization observed in the previous experiment is due only to accumulation of S in S IN2 , as predicted by the model and not due to injury to the neurons.

Modeling desensitization induced by PKA confirms rapid rate of recovery PKA, which is activated by 5HT, has been shown to increase desensitization of PKC Apl II translocation during both massed and spaced training [13]. In order to model PKA mediated desensitization, we included a reduced and modified version of a previous model of PKA activity [26]. We reduced the complexity of this model to only include only the dynamics of cAMP production and the association and dissociation of the subunits of PKA. This simplification was done since our experiments and simulations do not occur over long enough time periods for us to expect a contribution from the persistent activity of PKA, which was a major feature of their model. We modified the Pettigrew et al. model by altering the basal level of cAMP and the association rate of the PKA subunits to refine PKA dynamics to better match published data demonstrating PKA activity persisting for a small period after washout of 5HT [10], [37], [38]. This revision was necessary since PKA activity during the wash period is required for desensitization [13]. The new PKA dynamics to massed and spaced training can be seen in Figure 4A–C. Furthermore, we removed any synthesis or degradation of PKA subunits since, similar to PKC Apl II, we do not expect a significant change in the amount of protein during the time course of our experiments [10]. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 4. PKA dynamics. A, Model network pathway of PKA dynamics. R and C represent the regulatory subunit and catalytic subunit of PKA, respectively, where the amount of PKA activity is considered identical to C activity. B, C, PKA activity in response to a 90 min 5HT application (B) or 5×5 min 5HT application (C). Black line represents the amount of cAMP activity; blue line represents C, and red line RC. R is not shown, as it is identical to C. (Model adapted from [70]). D, PKC Apl II translocation in response to 5×5 min application of 5HT with 15 min washes in between and anisomycin present throughout from Farah et al. (2009) (bars) and modeling output (line). E, Modeling of S dynamics in response to experimental protocol from D. Black line represents the ratio of S OFF and S ON to total S, the red line the ratio of S IN2 to total S, and the blue line represents ratio of S PKA to total S. https://doi.org/10.1371/journal.pcbi.1002324.g004 The black and blue networks (Figure 3A) make use of the previously described PKA activity model to affect the desensitization of PKC translocation. Two data sets were used to estimate the parameters of the blue component of the model: one continuous 90 min application of 5HT in the presence of anisomycin and five pulses of 5HT each lasting 5 min with 15 min washes in between, all in the presence of anisomycin [13]. The parameters were estimated to fit both data sets. The conversion of S OFF into S PKA is modeled using mass action kinetics. The recycling of S PKA back into S OFF is inhibited by PKA and is modeled using a combination of mass action kinetics and an inhibitory Hill function (see Materials and Methods section). This network architecture resulted in an excellent fit to both data sets (R2 = 0.99 for massed training and 0.88 for spaced training) (Figures 4D, 5B). It was not possible to replicate both the massed training and spaced training data sets without including the PKA inhibition of S PKA recycling. Without this inhibition, fitting the massed training data set caused too much desensitization during spaced training and fitting the spaced training data set caused insufficient desensitization during massed training. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 5. Modeling and experimental validation of desensitization mediated by PKA pathway. A, Representative confocal fluorescence images of sensory neurons expressing eGFP-PKC Apl II during a 90 min exposure to 5HT followed by a 45 min wash and then a 5 min 5HT application, all in the presence of anisomycin. B, Quantification of PKC Apl II translocation (bars) and modeling output (line). Blue bars are data used from Farah et al. (2009) to fit the model parameters. Red bars are from the present study (n = 10 cells). C, Modeling of S dynamics in response to experimental protocol. Black line represents the ratio of S OFF and S ON to total S, the red line the ratio of S IN2 to total S, and the blue line represents ratio of S PKA to total S. D, Comparing PKC translocation at 135 min after the second 5HT pulse with PKA inactive (anisomycin and KT5720) and PKA active (anisomycin). Student's unpaired two-tailed T test conducted and statistical significance of p<0.01 illustrated by *. https://doi.org/10.1371/journal.pcbi.1002324.g005 Massed training in the absence of protein synthesis leads to more desensitization of PKC Apl II translocation when PKA is active [13]. However, the model predicts that soon after 5HT is washed away, PKA becomes inactive and S PKA can recycle back to S OFF . This recycling suggests that unlike S IN2 mediated desensitization, PKA induced desensitization recovers quickly. Thus, when we simulate a 90 min exposure to 5HT followed by a 45 min wash and then a 5 min pulse of 5HT (as above, but in the absence of a PKA inhibitor), the model predicts a considerable recovery of PKC translocation (Figure 5B, C). This recovery happens because during the 90 min stimulation, the majority of S is held in S PKA , and during the wash most of S PKA recycles back to S OFF . This recycling allows for a greater amount of PKC translocation compared to when PKA was inhibited and the majority of S is found in S IN1 (Figure 3C). To test this prediction of the model, we conducted a new imaging experiment, measuring the translocation of eGFP-PKC Apl II during the application of the above protocol (Figure 5A). The translocation of PKC Apl II caused by the 5 min pulse of 5HT after the 45 min wash is in agreement with the modeling prediction, thus validating this component of the model (Figure 5B). The amount of desensitization of PKC Apl II translocation during the massed training is equivalent to that observed by Farah et al. (2009) and, as in that study, PKA increases the amount of desensitization during massed training. However, despite this increased desensitization in the presence of PKA, active PKA increases the recovery from desensitization, as predicted by the model. The large difference between the recovery in the presence or absence of the PKA inhibitor, KT5720, is illustrated in Figure 5D.

Rescue from desensitization by Anti-Desensitizer (AD) protein The rescue from desensitization by the AD protein is modeled using the black and red network components in combination (Figure 6A, red pathway). Two data sets were used to estimate the parameters of this component of the model: 90 min application of 5HT in the presence of KT5720 and five 5 min pulses of 5HT with 15 min washes in between, all in the presence of KT5720 [13]. The model produced an excellent fit to both data sets (R2 = 0.95 for spaced training and 0.99 for massed training) (Figure 6B, D). One of the unexpected predictions of the model was both a fast degradation of AD, (with a half-life of ∼5 min) and a slow rate of the S AD →S OFF recycling. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 6. Modeling the rescue from desensitization by Anti-Desensitizer (AD) protein. A, Model network pathways of AD desensitization protection pathway (red network designates AD pathway). B, PKC Apl II translocation in response to 5×5 min application of 5HT with 15 min washes in between and KT5720 present throughout from Farah et al. (2009) (bars) and modeling output (line). C, Top panel represents S dynamics in response to experimental protocol from B. Black line represents the ratio of S OFF and S ON to total S and the red line the ratio of S IN2 to total S, and green line represents the ratio of S AD and S ADON to total S. Bottom panel represents the amount of AD over time. D, PKC Apl II translocation in response to 90 min application of 5HT and KT5720 present throughout from Farah et al. (2009) (bars) and modeling output (line). E, Top panel represents S dynamics in response to experimental protocol from D. Line colours similar to in C. https://doi.org/10.1371/journal.pcbi.1002324.g006 To validate this component of the model, we designed a protocol that would be sensitive to the fast degradation rate of AD. This protocol consisted of exposure to 25 min of 5HT in the presence of KT5720 then 65 min of 5HT in the presence of both KT5720 and anisomycin, with no wash in between. This protocol allows for the indirect observation of the degradation of AD and the recycling of S AD back into S OFF . The addition of anisomycin will terminate the translation of AD. During these last 65 min, the model predicts that AD will decay and thus be less effective at transforming S OFF into S AD (Figure 6C). The model further predicts that the absence of AD will cause the remaining S AD to recycle back into S OFF , where it will lose its protection from the homologous desensitization pathway, which will manifest in decreased PKC Apl II translocation. Thus, by observing the increased amount of desensitization of this protocol in comparison to when AD translation is present throughout, we can validate the model's predicted rate of AD degradation and rate of S AD recycling back into S OFF . To test these predictions of the model, a new imaging experiment was performed by applying this protocol to Aplysia sensory neurons expressing eGFP-PKC Apl II. As expected, the amount of PKC translocation observed in these neurons during the first 25 min of 5HT was equivalent to that observed during the 25 min of massed training in the presence of KT5720, carried out by Farah et al. (2009) (Figure 6A, B). However, the final 65 min of this protocol, where both KT5720 and anisomycin are present, caused a lower amount of PKC Apl II translocation compared to that caused by massed training in the presence of only KT5720, in agreement with the model prediction (R2 = 0.99) confirming the fast degradation rate of AD and the slow rate of S AD to S OFF (Figure 7C). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 7. Experimental validation of AD dynamics. A, Representative confocal fluorescence images of sensory neurons expressing eGFP-PKC Apl II during a 90 min exposure to 5HT where during the first 25 min KT5720 alone was applied, while during the last 40 min both anisomycin and KT5720 was applied. B, Quantification of PKC Apl II translocation (bars) and modeling output (line with square points). 90 min 5HT with KT5720 and anisomycin (light blue bars) is similar to that shown in Figure 1C and 90 min 5HT with anisomycin (dark blue bars) is similar to that shown in Figure 4D. These data points, from Farah et al. (2009), are reproduced here for comparison purposes with the following newly acquired data. Error bars are SEM. Red bars represent quantification of eGFP-PKC Apl II translocation during experimental protocol from A (n = 9 cells) compared to line with triangles for the modeling prediction of this experimental protocol (25 min 5HT with KT5720 followed by 65 min with KT5720 and ansiomycin). F, Top panel represents S dynamics in response to experimental protocol from D. Black line represents the ratio of S OFF and S ON to total S and the red line the ratio of S IN2 to total S, and green line represents the ratio of S AD and S ADON to total S. Bottom panel represents the amount of AD over time. https://doi.org/10.1371/journal.pcbi.1002324.g007

Modeling increase in desensitization by Desensitizer (D) protein During spaced training, the desensitization of PKC Apl II translocation was increased in control cells in comparison to when protein translation was inhibited. This increase in desensitization was observable only when both PKA activity and protein translation are allowed to proceed, meaning a translated protein is mediating this increase and its rate of translation is dependent on PKA activity. We name this hypothetical protein Desensitizer (D), and its effects on PKC Apl II translocation are modeled by the green component of the network (Figure 2). Seven data sets were used to estimate the parameters of this component of the model: one continuous 90 min application of 5HT, five pulses of 5HT each lasting 5 min with 15 min washes in between, and five experiments, each with two pulses of 5HT each lasting 5 min but with a different wash period length (5 min, 10 min, 15 min, 30 min, 45 min,) in between the pulses [13] (Figure 8A, C, E). The resulting model formed an excellent fit to the data (R2 = 0.99 for massed training, 0.99 for spaced training, and 0.75 for two pulses of 5HT with varying wash intervals). One exception is the 5 min pulse followed by a 5 min wash, where there is an increase in PKC Apl II translocation compared to the initial translocation, while our model shows no increase in translocation. We believe fitting this increase would require a more detailed dissection of the pathway between the GPCR and its downstream targets and is beyond the scope of this study. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 8. Fitting complete model to PKC translocation measured during no pharmacological interventions. A, PKC Apl II translocation in response to 5×5 min application of 5HT with 15 min washes in between (bars) and modeling output (line). B, Top panel represents S dynamics in response to experimental protocol from A. Black line represents the ratio of S OFF and S ON to total S, red line the ratio of S IN2 to total S, green line represents the ratio of S AD and S ADON to total S, and blue line represents the ratio of S AD and S ADON to total S. Middle panel is the amount of AD over time and the bottom panel is the amount of D over time. C, PKC Apl II translocation in response to a 90 min application of 5HT (bars) and modeling output (line). D, Top panel represents S dynamics in response to experimental protocol from G, with line colours identical to in B. Middle panel represents the amount of AD over time and the bottom panel the amount of D over time. E, PKC Apl II translocation in response to 2×5 min applications of 5HT with varying wash periods in between (black line) and modeling output (red line). https://doi.org/10.1371/journal.pcbi.1002324.g008

Model successfully predicts the response to new spacing protocols As one of the rationales for generating this model was to gain insight into the role of spacing, our final confirmation of the model tested an alternate spacing protocol. We designed an experiment that would require the functioning of all the model components and that made a specific prediction that was not obvious and could be tested. Interestingly, we found that if 15 min pulses of 5HT were used, the model predicted that longer washes would lead to increased desensitization. While 15 min pulses produce both D and AD, the model predicts that longer washes will reduce the levels of AD compared to D and thus predicts greater desensitization by longer washes (Figure 9B and E). In particular note that the model predicts that with the shorter spacing (Figure 9C), the amount of S complex in S AD is larger than in S PKA immediately before the second pulse, while with longer spacing (Figure 9F), the model predicts that there is more S complex in S PKA , than in S AD . Thus, the second pulse of serotonin during the protocol with longer spacing should be less able to translocate PKC Apl II because of the conversion of S AD to S PKA . To test this prediction, we performed a new imaging experiment where sensory neurons were exposed to three 15 min pulses of 5HT with either 15 min or 25 min washes in between the 5HT pulses. The results of this protocol are also sensitive to the delay and rate of D translation (parameters that had not yet been validated in a separate experiment). Both protocols were applied to Aplysia sensory neurons expressing eGFP-PKC Apl II. The amount of PKC translocation during both protocols matched the modeling prediction (R2>0.99) (Figure 9A, B, D, and E) and thus validates this component of the model as well as the functioning of the completed model. In particular, to highlight the effect of the wash, we calculated the amount of desensitization during the 15 min or 25 min wash (e.g. the amount of translocation at the beginning of pulse 2 compared to the end of pulse 1, or the beginning of pulse 3 compared to the end of pulse 2). The model predicted more desensitization during the longer wash and this was confirmed by the imaging experiment (Figure 10). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 9. Longer wash periods lead to greater desensitization of PKC Apl II translocation. A, Representative confocal fluorescence images of sensory neurons expressing eGFP-PKC Apl II during a 3×15 min application of 5HT with 15 min washes in between. B, Quantification of PKC Apl II translocation (bars, n = 9 cells) and modeling output (line). Error bars are SEM. C, Top panel represents S dynamics in response to experimental protocol from A. Black line represents the ratio of S OFF and S ON to total S, red line the ratio of S IN2 to total S, green line represents the ratio of S AD and S ADON to total S. Middle panel represents the amount of AD over time and the bottom panel the amount of D over time. Dotted line represents time of second and third 5HT application. D, Representative confocal fluorescence images of sensory neurons expressing eGFP-PKC Apl II during a 3×15 min applications of 5HT with 25 min washes in between. E, Quantification of PKC translocation (bars, n = 6 cells) and modeling output (line). Error bars are SEM. F, Top panel represents S dynamics in response to experimental protocol from E. Black line represents the ratio of S OFF and S ON to total S, red line the ratio of S IN2 to total S, green line represents the ratio of S AD and S ADON to total S. Dotted line represents time of second and third 5HT application. Middle panel represents the amount of AD over time and the bottom panel the amount of D over time. https://doi.org/10.1371/journal.pcbi.1002324.g009 PPT PowerPoint slide

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larger image TIFF original image Download: Figure 10. Quantifying the amount of desensitization of PKC Apl II translocation occurring during wash periods. Left pair of bars represent the amount of PKC Apl II translocation at the 5 min point of the second pulse divided by the amount of PKC Apl II translocation at the 15 min point of the first pulse. Right pair of bars represents the amount of PKC Apl II translocation at the 5 min point of the third pulse divided by the amount of PKC Apl II translocation at the 15 min point of the second pulse. Red bars correspond to 15 min 5HT with 15 min washes (n = 9) and Orange to 15 min 5HT with 25 min washes (n = 6). Student's unpaired two-tailed T test conducted and statistical significance of p<0.05 illustrated by *. https://doi.org/10.1371/journal.pcbi.1002324.g010