Coupled feedback loops maintain synaptic long-term. potentiation: A computational model of PKMzeta

Transcription

1 1 Draft version 28, This paper has not been peer reviewed. Please do not opy or ite without author's permission. Coupled feedbak loops maintain synapti long-term potentiation: omputational model of PKMzeta synthesis and MP reeptor traffiking Peter Helfer 1* and Thomas R. Shultz 2 1 Department of Psyhology and Integrated Program in Neurosiene, MGill University, Montreal, Quebe, Canada 2 Department of Psyhology and Shool of Computer Siene, MGill University, Montreal, Quebe, Canada * Corresponding author peter.helfer@mail.mgill.a

2 2 bstrat In long-term potentiation (LTP), one of the most studied types of neural plastiity, synapti strength is persistently inreased in response to stimulation. lthough a number of different proteins have been impliated in the sub-ellular moleular proesses underlying indution and maintenane of LTP, the preise mehanisms remain unknown. partiular hallenge is to demonstrate that a proposed moleular mehanism an provide the level of stability needed to maintain memories for months or longer, in spite of the fat that many of the partiipating moleules have muh shorter life spans. Here we present a omputational model that ombines simulations of several biohemial reations that have been suggested in the LTP literature and show that the resulting system does exhibit the required stability. t the ore of the model are two interlinked feedbak loops of moleular reations, one involving the atypial protein kinase PKMζ and its messenger RN, the other involving PKMζ and Glu2-ontaining MP reeptors. We demonstrate that robust bistability stable equilibria both in the synapse s potentiated and unpotentiated states an arise from a set of simple moleular reations. The model is able to aount for a wide range of empirial results, inluding indution and maintenane of late-phase LTP, ellular memory reonsolidation and the effets of different pharmaeutial interventions. Keywords: LTP, PKMζ, PKMzeta, MPR, synapti stability, reonsolidation, omputational model

3 3 uthor summary The brain stores memories by adjusting the strengths of onnetions between neurons, a phenomenon known as synapti plastiity. Different types of plastiity mehanisms have either a strengthening or a weakening effet and produe synapti modifiations that last from milliseonds to months or more. One of the most studied forms of plastiity, long-term potentiation, is a persistent inrease of synapti strength that results from stimulation and is believed to play an important role in both short-term and longterm memory. Researhers have identified many proteins and other moleules involved in long-term potentiation and formulated different hypotheses about the biohemial proesses underlying its indution and maintenane. growing number of studies support an important role for the protein PKMζ (protein kinase M Zeta) in long-term potentiation. To investigate the explanatory power of this hypothesis, we built a omputational model of the proposed biohemial reations that involve this protein and ran simulations of a number of experiments that have been reported in the literature. We find that our model is able to explain a wide range of empirial results and thus provide insights into the moleular mehanisms of memory. Introdution The brain stores memories by adjusting the strengths of onnetions between neurons. Suh synapti plastiity omes in different forms that strengthen or weaken synapses and range from very short-lived to long-lasting. One of the most well-studied forms of plastiity is long-term potentiation, LTP, a phenomenon whereby synapti strength is

4 4 persistently inreased in response to stimulation. Different forms of LTP are known to play important roles in both short-term and long-term memory. Many different proteins have been identified in the sub-ellular moleular proesses that are involved in LTP. n important question is how these proteins, with lifetimes measured in hours or days, an maintain memories for months or years. We present a omputational model that demonstrates how this problem an be solved by two interonneted feedbak loops of moleular reations. We begin with an overview of LTP with emphasis on the empirial findings that our model aims to explain. This is followed by a desription of the model, an aount of our results, and disussion of their impliations. Bakground In his address to the Royal Soiety in 1894, Santiago Ramon y Cajal hypothesized that the brain stores information by adjusting the strengths of assoiations between neurons, as well as by growing new onnetions [1]. In the years sine, the existene of both of these mehanisms, now known as synapti plastiity and synaptogenesis, respetively, has been well established, and there is ample evidene that synapti plastiity plays an important role in learning and memory [2 4]. Neurons ommuniate by transmitting signals aross hemial synapses, where presynapti axon terminals onnet to postsynapti neurons, most often on their dendrites. When a nerve impulse (ation potential) arrives at the axon terminal, neurotransmitter moleules are released into the synapti left, a narrow gap between the two neurons, where they ativate reeptors in the membrane of the postsynapti

5 5 neuron. This sets in motion a series of biohemial events in the postsynapti neuron, the details of whih depend on the type of reeptor, among other fators. Synapti strength depends both on the amount of transmitter that is released by the arrival of a nerve impulse at the axon terminal and on the number and sensitivity of the reeptors. It may thus be regulated on either the pre- or postsynapti side, and mehanisms of synapti plastiity have been shown to operate in both ompartments [3]. Plastiity may either strengthen or weaken a synapse, and the effet may be short-lived or longlasting. Short-term synapti plastiity, lasting from milliseonds to minutes, is primarily due to presynapti mehanisms that adjust the amount of transmitter release, whereas postsynapti modifiations that adjust the number and sensitivity of reeptors are important for long-term plastiity [4]. In partiular, this is true of long-term potentiation (LTP), a type of persistent strengthening of synapses in response to stimulation [5,6], whih has been studied extensively in the C3-C1 synapses of the rodent hippoampus [4] and is known to depend on an inrease in the number of reeptors inserted in the postsynapti membrane [7]. There are at least two forms of LTP: Moderately strong stimulation indues early-phase LTP (E-LTP), whih persists for at most a few hours. When the stimulation is stronger, E-LTP may be followed by late-phase LTP (L-LTP), whih an last for days, months or longer [7,8] and is believed to be an important mehanism for the storage of long-term memories [9,10]. The establishment of L-LTP, known as synapti or ellular memory onsolidation, is a proess that takes less than an hour [11,12] and requires synthesis of new protein. This has been demonstrated by showing that infusion of proteinsynthesis-inhibiting drugs suh as anisomyin an prevent establishment of L-LTP [12

6 6 15]. On the behavioral level, protein synthesis inhibition (PSI) has been shown to impair the formation of long-term memory, onsistent with the notion of L-LTP as a memory mehanism [16]. One long-term memory is established, it is in general no longer vulnerable to infusion of a protein synthesis inhibitor [16]. However, memory retrieval an indue a state of transient instability, during whih the memory is again suseptible to protein synthesis inhibition [17 19]. This suseptibility of memory to post-retrieval PSI infusion has been shown to orrelate with instability of L-LTP at the neural level [20,21], providing further evidene of the importane of LTP as a mehanism of long-term memory. The synapti destabilization that is triggered by memory retrieval is followed by a period of restabilization whih has similarities with the initial synapti onsolidation that follows memory aquisition. It has therefore beome known as memory reonsolidation [19], more speifially synapti (or ellular) reonsolidation, to avoid onfusion with the related but distint phenomenon systems reonsolidation, a temporary dependene on the hippoampus for restabilization of a memory after reativation (retrieval). For reviews of reonsolidation researh, see [22 24]. For a omputational model of systems onsolidation and reonsolidation, see [25]. Glutamatergi synapses In this report, we fous on L-LTP indution and maintenane at glutamatergi synapses, the most abundant type of synapse in the vertebrate nervous system [26,27]. Glutamatergi synapses ontain several kinds of reeptors that are ativated by the neurotransmitter glutamate. Of partiular interest for LTP are the α-amino-3-hydroxy-5- methyl-4-isoxazolepropioni aid reeptor (MP reeptor or MPR), whih mediates

7 7 synapti transmission [28], and the N-methyl-D-aspartate reeptor (NMD reeptor or NMDR), whih is involved with regulatory funtions inluding the regulation of synapti strength [29,30]. MPRs are ion hannels that open when ativated by the neurotransmitter glutamate. The opening of the hannel allows positively harged ions, mainly sodium and potassium, to flow through the ell membrane [31]. This auses a partial depolarization of the membrane, whih at rest is polarized by a net negative harge inside the ell. The partial depolarization is known as an exitatory postsynapti potential, or EPSP, and the amplitude of the EPSP produed by a single ation potential arriving at a synapse is a measure of synapti strength. mong other fators, the EPSP amplitude depends on the number of MPRs inserted in the postsynapti density (PSD), the area of ell membrane that onstitutes the reeiving side of the synapse [31]. Thus mehanisms that ontrol the traffiking of MPRs into and out of the PSD play an important part in the regulation of synapti strength. MPRs are heterotetramers, i.e. they onsist of four non-idential subunits. The subunits are of four different kinds, named Glu1, Glu2, Glu3 and Glu4, and MPRs an be made up of different ombinations of these [32]. Glu2 is of partiular interest here, beause L-LTP is assoiated with an inrease in the number of Glu2- ontaining MPRs inserted in the PSD [20,33,34]. MP reeptors are not permanently inserted in the PSD, but are onstantly being reyled. Certain proteins transport MPRs into the PSD from pools maintained in adjaent areas, while others remove them (a proess known as internalization or

8 8 endoytosis) and either reyle them to stand-by pools or mark them for degradation [35,36]. Protein kinase M zeta (PKMζ) Many proteins have been impliated in the indution and maintenane of LTP, inluding CaMKII, PK, MPK and several isoforms of PKC (for a review, see [7]). n atypial isoform of PKC, protein kinase Mζ (PKMζ), is believed to play an important role for L-LTP. The level of PKMζ has been shown to inrease as the result of NMD reeptor stimulation [37,38], onsistent with its proposed role in L-LTP indution. Inhibition of PKMζ ativity results in disruption of established L-LTP [39 41], and perfusion of PKMζ into a neuron an indue L-LTP [39]. PKMζ ativity is believed to inrease the number of inserted Glu2-ontaining MPRs at the synapse both by failitating the traffiking of these reeptors into the PSD and by inhibiting their removal [42]. Glu2-ontaining MPRs are held at extrasynapti pools by the protein PICK1 whih binds to the Glu2 subunit [34]. PKMζ failitates interation between the traffiking protein NSF and the Glu2 subunit, whih results in its release from PICK1, freeing the MPRs to diffuse laterally into the PSD [34]. Furthermore, one Glu2-ontaining MPRs are inserted in the PSD membrane, PKMζ prevents their removal by inhibiting the interation between the protein BRG2 and the Glu2 subunit [43], an interation that plays a key part in endoytosis of Glu2-ontaining MPRs [42,44]. While Glu2-ontaining MPRs are important for the stabilization of L-LTP, there is evidene that Glu2-laking MPRs play an important role in the indution of earlyphase LTP (E-LTP), and also in reonsolidation. Several studies have shown that Glu2-laking MPRs are initially inserted at the time of memory aquisition or LTP

9 9 indution, and then gradually replaed by Glu2-ontaining MPRs during onsolidation [45 47]. Hong et al. [20] showed that memory reativation triggers an abrupt replaement of Glu2-ontaining MPRs by Glu2-laking MPRs. This is followed by a gradual reversal, i.e. the Glu2-ontaining MPRs are restored and the number of Glu2-laking MPRs delines, as the potentiated state of the synapse is restabilized [20]. Beause the temporary removal of Glu2-ontaining MPRs is ompensated for by an inrease in Glu2-laking MPRs, the synapti strength remains more or less onstant during the period of instability [20]. Rao-Ruiz et al. [21] reported similar results, although they observed a brief period of redued synapti strength between the Glu2-ontaining MPR removal and Glu2-laking MPR insertion. Taken together, these results suggest that the stabilization of LTP, both initially during onsolidation, and after reativation-indued destabilization, requires insertion of Glu2-ontaining MPRs, and that PKMζ plays an important role in maintaining the Glu2-ontaining MPRs at the synapse. n important question is how L-LTP, whih an last for months or longer [8], an be maintained by a protein like PKMζ, with a half-life that probably does not exeed several hours or at most a few days [48 51]. proposed answer to this question involves loal translation of messenger RN (mrn) in or near dendriti spines. Most synapses are formed at dendriti spine heads, with one synapse per spine [52]. It has been shown that PKMζ mrn is transported from the ell body to dendrites [53,54], but the mrn in its basal state is translationally repressed by moleules that bind to it, or to the omplex of proteins required to initiate translation [50,53,55]. There is evidene that PKMζ atalyzes reations that lift this translational blok [49,56], possibly through

10 10 inhibition of the PIN1 protein [42], resulting in a positive feedbak loop [49]. By promoting its own synthesis in this manner, PKMζ may be able to remain at an inreased level, and thus maintain L-LTP, for a long time, perhaps indefinitely. It has also been suggested that the inreased amount of inserted Glu2-ontaining MPRs at a potentiated synapse aptures the PKMζ moleules and keeps them from dissipating away from the synapti ompartment [42]. This hypothesis is supported by several studies that show that bloking endoytosis of Glu2-ontaining MPRs an prevent depotentiation under protools that otherwise ause disruption of L-LTP [21,33,57]. Together with PKMζ s inhibiting effet on MPR endoytosis this onstitutes a seond feedbak loop, a reiproal relationship in whih PKMζ and Glu2- ontaining MPRs prevent eah other s removal from the synapse. s we shall see, the interation between these two feedbak loops plays a entral role in our explanation of synapti bistability, that is that synapses have two stable equilibrium states, unpotentiated and potentiated. Transient stimuli an ause a synapse to transition between these two states, but in the absene of suh signals it tends to remain in one state or the other. L-LTP, LTM and pharmaologial interventions The notion that L-LTP is an important neural orrelate of long-term memory (LTM) has been supported experimentally by demonstrating that pharmaologial interventions that blok L-LTP indution also interfere with the establishment of LTM [58], and that interventions that disrupt established L-LTP also impair onsolidated memories [59]. Here we onsider three types of pharmaeutials that have been shown to produe

11 11 signifiant results with respet to both L-LTP indution and maintenane, and to related behavior-level memory phenomena. Protein synthesis inhibitors. Infusion of protein synthesis inhibitors (PSIs) suh as anisomyin into brain tissue an prevent the indution of L-LTP [58], and also interferes with memory onsolidation, the establishment of LTM [60,61]. One L-LTP is established, it beomes resistant to infusion of anisomyin [11,12]. This does not mean that L-LTP an be maintained indefinitely without ongoing protein synthesis, but rather that it an tolerate an interruption of protein synthesis for the amount of time that anisomyin remains ative after infusion. Reativation of a onsolidated memory, e.g. by a reminder, an temporarily return it to a labile state in whih it is again vulnerable to PSI infusion [18,60]. The putative moleular proess underlying this phenomenon has been termed ellular or synapti memory reonsolidation [18,62]. Conordant with the hypothesis that L-LTP is the neural orrelate of LTM, the temporary post-reativation vulnerability of LTM to PSI infusion an be explained as destabilization of L-LTP, followed by a restabilization phase that requires protein synthesis, hene the suseptibility to PSI. The destabilization has been shown to require the ativity of NMD reeptors [29], and to depend ritially on endoytosis of Glu2-ontaining MPRs [57,63]. Thus protein synthesis inhibition is known to both prevent establishment of L-LTP and to blok reonsolidation, i.e. blok restabilization of L-LTP after retrieval-indued destabilization. ZIP. Muh of the work demonstrating the role of PKMζ in L-LTP is based on administration of the syntheti peptide ZIP (zeta-inhibitory peptide), whih binds to the

12 12 atalyti region of the PKMζ moleule, thus bloking its enzymati ativity [41]. On the behavioral level, infusion of ZIP into brain tissue has been shown to impair onsolidated LTM [59]. On the neural level, ZIP is known to disrupt established L-LTP when applied during the maintenane phase [39 41,64]. These results are onsistent with the notion of a positive feedbak loop: Inhibiting PKMζ s enzymati ativity prevents it from atalyzing its own synthesis; the PKMζ onentration then drops, the MPR endoytosis rate inreases, and the synapse returns to its basal state. On the other hand, ZIP does not prevent L-LTP indution when applied only during or immediately after stimulation. This was demonstrated by Ren et al. [65] in an in-vitro experiment where onset and duration of ZIP appliation were preisely ontrolled. Glu23Y. Glu23Y is a syntheti peptide that bloks regulated endoytosis of Glu2- ontaining MPRs [66,67]. Infusion of Glu23Y has been shown to blok both the destabilizing effet of PSI infusion after memory reativation [20,57] and the depotentiating effet of ZIP during L-LTP maintenane [33]. The Glu23Y peptide is modeled on a sequene of the Glu2 subunit s arboxyl tail and its endoytosisinhibiting effet is believed to be due to ompetitive disruption of the binding of endoytosis-related proteins to this sequene on Glu2 subunits [68]. Computational model The findings desribed above suggest a model of L-LTP maintenane with two onneted feedbak loops: (1) PKMζ maintains its own mrn in a translatable state and translation of the mrn in turn replenishes PKMζ. (2) PKMζ maintains Glu2- ontaining MPRs at the synapse, and these in turn keep PKMζ moleules from dissipating away from the synapti ompartment. Below we desribe a omputational

13 13 model that inorporates these relationships and investigate its ability to aount for results reported in the empirial literature. Methods Deterministi vs. stohasti simulation Systems of hemial reations an be modeled either by deterministi methods based on ordinary differential equations (ODEs) or by stohasti simulation. When the numbers of moleules are small, stohasti simulation is the better hoie, beause random flutuations then have signifiant effets that are not aptured by deterministi methods [69]. In partiular, random flutuations an ause a small system to spontaneously transition from one steady state to another; the resulting impat on system stability an be studied in a stohasti simulation, but not in a deterministi model [70], beause the latter only aounts for average reation rates over a large number of moleules. The moleules of interest for our simulation are present in small numbers in a dendriti spine head, e.g. fewer than a hundred PKMζ moleules (see S1 Text) and at most a 150 MPRs [71,72]. This is well below the size of system that an be realistially simulated by deterministi methods [70,73]. We therefore base our simulation on the Gillespie algorithm [74], a well-established and widely used approah to disrete and stohasti simulation of reation systems [69,70,73]. Model desription The model onsists of four inter-dependent pairs of proesses (see Fig 1):

14 14 Fig 1: Proess diagram. a) tivation/deativation of PKMζ mrn (blue). Translational repression of mrn is lifted by atalyti ativity of PKMζ, possibly by phosphorylation of mrn-binding proteins. phosphatase (pink) dephosphorylates the same proteins, returning mrn to its repressed state. b) Synthesis and degradation/dissipation of PKMζ (yan). Synthesis onsists in loal translation of PKMζ mrn. Degradation and/or dissipation away from the synapti ompartment is inhibited by inserted Glu2-ontaining MPRs. ) Traffiking of Glu2-ontaining MPRs (green) into and out of the PSD. Insertion is failitated by PKMζ, and removal (endoytosis) by the BRG2 protein. d) Inhibition/disinhibition of BRG2-Glu2 interation. Inhibition is modeled as phosphorylation of BRG2 (orange) atalyzed by PKMζ, and disinhibition as dephosphorylation atalyzed by a phosphatase. E1 and E2 (dark green) are enzymes ativated by NMDR stimulation at L-LTP indution and memory reativation, respetively. The effets of PSI, ZIP and Glu23Y (red) are

15 15 modeled by disabling the indiated atalyti reations. Solid arrows represent hemial reations and reeptor traffiking. Dashed lines with filled irles represent atalyti ativity. Dashed lines with rossbars represent inhibition. tivation/deativation of PKMζ mrn. PKMζ lifts the onstitutive translational repression of PKMζ mrn by phosphorylating some substrate, possibly mrn-binding proteins attahed to the mrn. The mrn moleule with attahed proteins and ribosomes (polysome) is represented as a single moleule in the model, and derepression is modeled as phosphorylation of (some omponent of) this moleule by PKMζ. The opposite reation, dephosphorylation by a phosphatase assumed to be present at fixed onentration, returns the mrn to its repressed state. Synthesis and degradation/dissipation of PKMζ. Synthesis onsists in loal translation of PKMζ mrn. (This is somewhat speulative: PKMζ mrn has been shown to be present in dendrites [53,54], but not speifially in dendriti spines.) Inserted Glu2-ontaining MPRs inhibit degradation and/or dissipation of PKMζ away from the synapti ompartment by binding PKMζ moleules [42], probably via a saffold protein suh as PICK1 or KIBR [75]. This is modeled as an affinity of PKMζ for inserted Glu2-ontaining MPRs, with a redued dissipation/degradation rate while so attahed. Glu2-ontaining MPR traffiking into and out of the PSD. The model inludes a fixed-size population of Glu2-ontaining MPRs. t any time, a subset of the MPRs are inserted in the PSD while the remainder are maintained in extrasynapti pools. Transport of MPRs into the PSD is failitated by PKMζ and removal (endoytosis) is enabled by the protein BRG2. In addition to these two regulated

16 16 proesses, onstitutive proesses traffi MPRs into and out of the synapse at lower rates. Inhibition and disinhibition of BRG2-Glu2 interation. The mehanism by whih PKMζ inhibits the interation between BRG2 and the Glu2 subunit to blok MPR removal from the PSD is not known, but presumably involves phosphorylation of some substrate. We model the inhibition as phosphorylation of the BRG2 moleule itself; other possibilities inlude phosphorylation of a site on the Glu2 subunit or of another partiipating protein. The BRG2-Glu2 interation is restored through dephosphorylation of the same substrate by a phosphatase, whih is assumed to be present in fixed onentration. lthough the inrease in PKMζ level that is assoiated with L-LTP indution is known to depend on NMDR ativation [38], the underlying biohemial pathways are unknown. In the model this mehanism is represented by an unspeified enzyme that we all E1 whih, when ativated by a reation asade triggered by NMDR ativation, has the ability to lift the translational blok on PKMζ mrn, thereby enabling PKMζ synthesis. Similarly, the destabilizing effet of memory reativation has been shown to depend on NMDR ativity and on endoytosis of Glu2-ontaining MPRs [20,57,76], but the biohemial asades that onnet these event have not yet been identified. In our model, reativation is simulated as an inrease in the level of a seond unspeified enzyme E2 with the ability to atalyze endoytosis of Glu2-ontaining MPR. In addition to these proesses, the model inludes simulation of the effets of the three pharmaeutials desribed in the introdution. The time intervals that these drugs remain at a high enough onentration to inhibit their targets depend on the doses

17 17 infused and also on their speifi rates of deay or metabolism. The intervals used here are based on ativity periods reported in the ited referenes: PSI: Infusion of a protein synthesis inhibitor is simulated by disabling PKMζ synthesis for nine hours, the amount of time that the protein synthesis inhibitor anisomyin remains ative after infusion into brain tissue [77]. ZIP: dministration of the ZIP peptide is simulated by disabling PKMζ s enzymati ativity atalysis of mrn ativation, failitation of Glu2-ontaining MPR traffiking into the PSD and inhibition of BRG2-Glu2 interation for twelve hours [78]. Glu23Y: Perfusion of Glu23Y is simulated by disabling regulated endoytosis of Glu2-ontaining MPR for twelve hours [76]. (Glu23Y does not affet onstitutive endoytosis of Glu2-ontaining MPR [67].) Table 1 lists the moleule speies inluded in the model, inluding omplexes formed during enzymati reations. ll simulations begin in the lower (unpotentiated) steady state with the indiated initial moleule ounts. Table 1: Moleule speies Symbol Desription Initial ount P Unbound PKMζ 0 RI unphosphorylated PKMζ mrn (inative) 100

18 18 R phosphorylated PKMζ mrn (ative) 0 PP phosphatase 100 PP R PP + R omplex 0 E1 E1 enzyme, ative 0 E1I E1 enzyme, inative 100 E1 RI E1 + RI omplex 0 U Uninserted Glu2-ontaining MPR 100 I Inserted Glu2-ontaining MPR 0 I P PKMζ bound to inserted MPR 0 P RI P + RI omplex 0 I P RI I + P + RI omplex 0 B tive BRG2 100 BI Inative BRG2 0 PP BI PP + BI omplex 0 P B P + B omplex 0 I P B I + P + B omplex 0 B I B + I omplex 0 B I P B + I + P omplex 0

19 19 E2 E2 enzyme, ative 0 E2I E2 enzyme, inative 100 Simulated Reations tivation of PKMζ mrn. PKMζ mrn is present in dendriti spines, but is translationally repressed in its basal state [42,53] due to mrn-binding proteins that prevent translation from being initiated [55]. PKMζ is able to lift the repression, possibly by phosphorylating these proteins, thus atalyzing its own synthesis in a positive feedbak loop. We model mrn with its assoiated proteins as a single moleule, represented by R I in its inative repressed state, and by R when ativated. tivation is modeled using Mihaelis-Menten kinetis [73], i.e. a PKMζ moleule (P) and an inative mrn moleule (R I ) form a omplex P R I. The omplex may then either dissoiate (reation 2) or the atalyti reation (3) may take plae, produing ative mrn (R ): P R 1 I P RI 2 P RI P RI 3 P RI P R (1) (2) (3) Deativation of PKMζ mrn. The PKMζ mrn returns to its repressed state when the mrn-binding proteins are dephosphorylated by a phosphatase whih we denote by PP. This is also modeled with Mihaelis-Menten kinetis (as are all enzymati reations in the model): PP R 4 PP R (4) PP R 5 PP R (5) PP R 6 PP R (6) I

20 20 PKMζ synthesis and degradation/dissipation. PKMζ is synthesized by loal translation of ative mrn (reation 7). Over time PKMζ degrades or diffuses away from the synapti ompartment. Reation 8 represents the ombined effet of these two proesses. The model is unspeifi with respet to their relative importane for PKMζ turnover. R 7 R P (7) P 8 0 Inhibition/disinhibition of BRG2. BRG2 is inhibited by PKMζ and reativated by (8) phosphatase. Both proesses are desribed by Mihaelis-Menten kinetis. B and B I denote ative and inhibited BRG2, respetively: P B 9 P B (9) P B 10 P B P B 11 P BI (10) (11) PP B 12 PP B (12) I PP B 13 I PP BI 14 I I (13) PP B PP B (14) MP reeptor traffiking. Transport of Glu2-ontaining MPRs into the PSD has been shown to involve a traffiking proess that is failitated by PKMζ [34]. Beause the details of this proess are unknown, inluding whih substrate of PKMζ mediates it, we model it as a simple enzymati reation wherein PKMζ atalyzes the onversion of an uninserted Glu2-ontaining MPR, U, to an inserted one, I. P 15 P (15) U U 16. P P U (16) 17. P P U U (17) I

21 21 The protein BRG2 atalyzes endoytosis of Glu2-ontaining MPRs, removal from the PSD. B 18 B (18) I I B 19 I B Ì B 20 B (19) I (20) U pair of unregulated proesses maintain bakground yling of Glu2-ontaining MPRs into and out of the PSD: 21 U I (21) 22 I U (22) Sequestering of PKMζ in the synapti ompartment. Our model implements the notion suggested by Saktor [42] and supported by empirial results [20,33,57], that Glu2-ontaining MPRs, when inserted in the PSD, prevent diffusion of PKMζ moleules away from the synapse and/or slows down degradation of PKMζ. We model this as a PKMζ moleule binding to an inserted Glu2-ontaining MPR to form a omplex I P (reation 23) and by bound PKMζ having a muh lower rate of dissipation/degradation than free PKMζ ( 24 << 8 ): P 23 P I (23) P I I 24 (24) I The I P omplex is dissolved if the Glu2-ontaining MPR is removed from the membrane by BRG2 or onstitutively: B P 25 B P (25) I I B P 26 B P (26) I I B P 27 B P (27) I U 28 I P u P (28)

22 22 PKMζ remains atalytially ative while sequestered by Glu2-ontaining MPRs, thus the reations atalyzed by free PKMζ (reations 1-3 and 9-11) are also atalyzed by PKMζ when it is bound to I : P R 29 P R (29) I I I I P R 30 P R (30) I I I I P R P R (31) 31 I I I P B 32 P B (32) I I 33 I P B I P B (33) P B 34 P B (34) I I I NMDR stimulation. The mehanism by whih NMDR ativation auses an inrease in PKMζ is unknown. We model the effet of strong NMDR stimulation as a rapid inrease in the number of ative moleules of an unspeified enzyme E1 whih, like PKMζ, ativates PKMζ mrn. E1 I and E1 represent the E1 enzyme in its ative and inative states, respetively: 35 E1 R E1 R (35) I I 36 I I 37 I E1 R E1 R (36) E1 R E1 R (37) The E1 enzyme spontaneously deativates at a rate that is speified by the reation onstant 38 : E 38 1 E1 (38) I Reativation. Reativation of a onsolidated memory auses it to beome destabilized [18,79,80]. The moleular mehanism underlying this destabilization is not well understood, but has been showed to depend ritially on endoytosis of Glu2- ontaining MPR [20,57,63]. We model the destabilizing effet of reativation as an

23 23 inrease in the number of moleules of a seond unspeified enzyme, E2, whih atalyzes MPR endoytosis: 39 E2 E2 (39) I U 40 I U E2 P E2 P (40) s in the ase of BRG2-atalyzed endoytosis (reation 27), the MPR/PKMζ omplex dissolves when the MPR is endoytosed (reation 40). The E 2 enzyme spontaneously deativates at a rate that is speified by the reation onstant 41 : E 41 2 E2 (41) I Protein synthesis inhibition. The effet of PSI infusion is simulated by disabling synthesis of PKMζ (reation 7). Inhibition of PKMζ by ZIP. The effet of ZIP infusion is simulated by disabling all PKMζ enzymati ativity (reations 1, 9, 15, 29 and 32). Inhibition of MPR endoytosis by Glu23Y. The effet of Glu23Y infusion is simulated by disabling regulated MPR endoytosis, whether atalyzed by BRG2 (reations 18 and 25) or by the E2 enzyme (reations 39 and 40). The simulated reations are summarized in Table 2. Reation rates are ontrolled by Gillespie reation onstant, 1, 2, et., suh that i dt is the average probability that a partiular ombination of the reatant moleules of reation i will reat during the next infinitesimal time interval dt [74]. The values for the reation onstants have been seleted so that the model s behavior approximates the observed time ourses of the simulated experiments; see ited referenes in the desription of eah simulation.

24 24 Table 2: Simulated reations Reation Desription i (s -1 ) 1 1 P RI P RI Formation of P RI omplex P RI P RI Dissolution of P RI omplex P RI P R tivation of PKMζ mrn, atalyzed by PKMζ PP R PP R Formation of PP R omplex PP R PP R Dissolution of PP R omplex PP R PP R Deativation of PKMζ mrn, atalyzed by I phosphatase R R P Translation of PKMζ mrn P PKMζ degradation or dissipation 0.65 P B P B Formation of P B omplex P B P B Dissolution of P B omplex I P B P B Inhibition of BRG2, atalyzed by PKMζ PP B PP B Formation of PP BI omplex I I I PP B PP B Dissolution of PP BI omplex I PP BI PP B Disinhibition of BRG2, atalyzed by 0.06 phosphatase P P Formation of P U omplex U U. P P Dissolution of P U omplex U U U. P P PKMZ-atalyzed traffiking of Glu2- I 20.0 ontaining MPR into the PSD B B Formation of B I omplex I I B B Dissolution of B I omplex I Ì B I B BRG2-atalyzed endoytosis of Glu2- U ontaining MPR 4.0 U Unregulated traffiking of Glu2-ontaining I MPR into the PSD 0.05 I Unregulated removal Glu2-ontaining U MPR from the PSD P I I P Inserted Glu2-ontaining MPR binds PKMζ 1.0 I P Degradation of PKMζ bound to inserted I MPR B P B P Formation of B I P omplex I I

25 B P B P Dissolution of B I P omplex I I B I P B U P BRG2-atalyzed endoytosis of Glu2- ontaining MPR with bound PKMζ. 4.0 I P u P Unregulated endoytosis of Glu2-ontaining MPR with bound PKMζ P R P R Formation of I P RI omplex I I I I P R P R Dissolution of I P RI omplex I I I I I P RI I P R tivation of PKMζ mrn, atalyzed by MPR-bound PKMζ P B P B Formation of I P B omplex I I I P B I P B I P B I P BI Dissolution of I P B omplex Inhibition of BRG2, atalyzed by MPRbound PKMζ 20.0 E1 R E1 R Formation of E1 RI omplex I I E1 R E1 R Dissolution of E1 RI omplex I I E1 RI E1 R tivation of PKMζ mrn, atalyzed by E enzyme E1 E1 Spontaneous deativation of E1 enzyme I E2 I E2 Endoytosis of Glu2-ontaining MPR, U atalyzed by E2 enzyme 0.1 E2 I P E2 U P E2-atalyzed endoytosis of Glu2- ontaining MPR with bound PKMζ 0.1 E2 E2 Spontaneous deativation of E2 enzyme I Simulation environment The model is implemented as a C++ program and all simulations were exeuted on an Intel i omputer running the Debian Linux 8.4 operating system. Objetives Our omputational model simulates the regulation of PKMζ onentration at the postsynapti density and its role in the indution and maintenane of L-LTP. The goal for the model is to simulate the empirial results desribed in the introdution and summarized in Table 3 below. Most of the ited results are from studies of Shaffer

26 26 ollateral synapses on C1 pyramidal neurons in the rat or mouse hippoampus, a few refer to unspeified hippoampal regions or amygdala of rat or mouse. Table 3: Simulation objetives Result Desription Citations 1 Indution by NMDR stimulation Strong NMDR stimulation indues L-LTP [40,81] 2 PSI bloks NMDRtriggered L-LTP indution Infusion of protein synthesis inhibitors prevents L-LTP indution by NMDR stimulation [9,82] 3 ZIP during stimulation does not prevent L-LTP indution ZIP treatment during and immediately after stimulation does not prevent establishment of L-LTP [65] 4 Indution by PKMζ perfusion Perfusion of PKMζ into a neuron indues L-LTP [39,83] 5 PSI does not disrupt established L- LTP/LTM ppliation of a protein synthesis inhibitor during L-LTP maintenane (without preeding reativation) does not ause disruption of L- LTP [12,18,79]

27 27 6 Reativation does not disrupt LTM Memory reativation does not by itself disrupt LTM [18,79] 7 Reativation followed by PSI infusion does disrupt LTM PSI administered within a time window after reativation disrupts LTM [18,79] 8 Glu23Y bloks the LTM-disrupting effet of PSI Glu23Y administered together with PSI after reativation bloks the LTMdisrupting effet of PSI [20,57,63] 9 ZIP disrupts established L-LTP Infusion of ZIP during the maintenane phase disrupts L-LTP [39 41] 10 Glu23Y bloks the depotentiating effet of ZIP Glu23Y infused together with ZIP prevents depotentiation of established L-LTP [33] Results In the following plots of simulation results, P denotes the total number of PKMζ moleules in the synapti ompartment, whether free or bound to a substrate or to an MPR (see Table 1), and I denotes the number of MPRs inserted in the PSD, with

28 28 and without bound PKMζ moleules. Reation numbers refer to the reations desribed in Table 2. NMDR stimulation indues L-LTP We model the result of strong NMDR stimulation as a rapid inrease of the population of ative E1 enzyme moleules. This auses the translational repression of PKMζ mrn to be lifted (reations 35-37) and synthesis of PKMζ to start (reation 7). Fig 2 shows a trae of the number of PKMζ moleules, ative PKMζ mrn moleules and Glu2-ontaining MPRs inserted in the PSD during a single simulation run. Fig 2: L-LTP indution, single simulation trae. NMDR stimulation is simulated by instantaneous ativation of 100 E1 moleules at Stim. E1 lifts the translational inhibition of PKMζ mrn, synthesis of PKMζ starts, PKMζ drives up the number of inserted Glu2-ontaining MPRs, and the synapse swithes to its potentiated steady

29 29 state. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2-ontaining MPRs, E1: ativated E1 enzyme. The model has two stable states: an unpotentiated state in whih there are very few ative mrn moleules, PKMζ moleules and inserted Glu2-ontaining MPRs, and a potentiated state with signifiantly higher levels of eah of these moleules. The brief spike of E1 enzyme lifts the translational repression of enough PKMζ mrn moleules to trigger a transition to the potentiated state. lthough the moleule numbers flutuate in the potentiated state, it is in fat very stable: No spontaneous depotentiation events are observed even when the model is allowed to run for a full year of simulated time. Fig 3 shows mean moleule ounts for 100 simulations of L-LTP indution. It takes the model between 30 and 60 minutes of simulated time to omplete the swith to its upper (potentiated) steady state in whih there is a high number of inserted Glu2-ontaining MPRs. This is onsistent with the observed duration of the ellular onsolidation window [16,58].

30 30 Fig 3: L-LTP indution. The same simulation as in Fig 2, but here solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. NMD stimulation triggers a brief spike of E1 ativity that ativates PKMζ mrn. This is followed by a slight deline in the number of ative mrn moleules, until the growing amount of PKMζ drives it bak up and an equilibrium is reahed. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2-ontaining MPRs, E1: ativated E1 enzyme. PSI prevents L-LTP indution Simulated PSI infusion prevents NMDR stimulation from induing L-LTP, (Fig 4).

31 31 Fig 4: PSI prevents NMDR stimulation from induing L-LTP. E1 enzyme ativates PKMζ mrn, but PSI prevents PKMζ synthesis and when the E1 enzyme beomes inativate, phosphatase returns the mrn to its inhibited state. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2-ontaining MPRs, E1: ativated E1 enzyme. lthough the spike of ativated E1 enzyme releases the translational blok of mrn, resulting in a high level of ativated PKMζ mrn (R in the model), translation is prevented by the protein synthesis inhibitor, and PKMζ synthesis is not initiated [9,37]. When the E1 enzyme returns to its inative form the mrn beomes repressed again, and the model remains in its unpotentiated state. Like the potentiated state, the unpotentiated state is very stable: No spontaneous potentiation events are observed even when running the model for a year of simulated time.

32 32 By introduing a variable delay between stimulation and PSI infusion, we an study the model s onsolidation window, the time interval after indution during whih PSI prevents establishment of L-LTP. s shown in Fig 5, when the delay before PSI infusion is 20 minutes or less, the model onsistently settles in the lower (unpotentiated) steady state with zero or very few inserted Glu2-ontaining MPRs. When the delay is 50 minutes or more, the model settles in the upper (potentiated) state where the number of inserted Glu2-ontaining MPRs flutuates between a 60 and 100 (f. Fig 2). With intermediate delays, the probability of settling in the upper state gradually inreases with inreasing delay. The model s onsolidation window is thus in the range 30 to 45 minutes, onsistent with empirial results [11,12]. Fig 5 illustrates the model's bistable harater: It settles either in the unpotentiated or potentiated state, never in the region with intermediate numbers of inserted Glu2-ontaining MPRs. See also Fig 3 and Fig 4.

33 33 Fig 5: Consolidation window. Results of simulated NMDR stimulation followed by PSI infusion after a delay varying from 0 to 60 minutes in 5-minute steps. One hundred simulations were run with eah value for the delay. The number of inserted Glu2- ontaining MPRs was reorded twenty hours after stimulation. For eah value of the delay, the heights of the olumns indiate the number of simulations that terminated with the orresponding numbers of inserted Glu2-ontaining MPRs. ZIP during and immediately after stimulation does not prevent L-LTP indution ZIP appliation during stimulation and the first 10 minutes thereafter after does not prevent L-LTP indution, (Fig 6).

34 34 Fig 6: ZIP immediately after stimulation does not prevent L-LTP indution. In this simulation, ZIP inhibits PKMζ ativity during the first 10 minutes after stimulation. L-LTP indution is delayed somewhat ompared to Fig 3, but enough ative PKMζ mrn remains when the ZIP is removed to trigger a transition to the potentiation state. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2- ontaining MPRs, E1: ativated E1 enzyme. Presene of ZIP during the first ten minutes after stimulation does not prevent L-LTP indution [65]. The stimulation lifts the translational blok and PKMζ prodution gets started. Even though PKMζ s enzymati ativity is inhibited, the mrn stays ativated long enough to ride out the ZIP ativity. When the ZIP is washed out, PKMζ beomes ative and drives the synapse into its potentiated state.

35 35 PKMζ infusion indues L-LTP L-LTP an be indued by diffusion of PKMζ into a neuron [39,41]. We simulate infusion by rapidly inreasing the number of PKMζ moleules in the synapti ompartment to 100. This auses the model to settle into its potentiated state, (Fig 7). Fig 7: PKMζ infusion indues L-LTP. Infusion is simulated by stepping the PKMζ moleule ount to 100 at Inf. The PKMζ lifts the translational inhibition of PKMζ mrn, synthesis starts and the synapse swithes to its potentiated state. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2-ontaining MPRs. PSI bloks PKMζ-infusion-indued potentiation The same level of PKMζ infusion that indues L-LTP in the previous experiment (100 moleules) fails to do so in the presene of PSI (Fig 8). lthough the PKMζ infusion initially auses a temporary inrease in the number of inserted Glu2-ontaining

36 36 MPRs, the PSI prevents replenishment to ompensate for PKMζ degradation and dissipation and the model returns to its unpotentiated state. This result, though plausible, has not been demonstrated in a published experiment. It thus onstitutes a predition of the model. Fig 8: PSI bloks L-LTP indution by PKMζ infusion. s in Fig 7, infusion of PKMζ is simulated at Inf. PKMζ triggers ativation of PKMζ mrn as well as an inrease of inserted Glu2-ontaining MPRs, but in the absene of PKMζ synthesis (bloked by PSI), the PKMζ level delines and the synapse settles bak into its unpotentiated state. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2- ontaining MPRs.

37 37 PSI does not disrupt established L-LTP Fonsea et al. [12] demonstrated that suppressing protein synthesis for 100 minutes by bath appliation of anisomyin did not disrupt established L-LTP. Fig 9 shows the results of simulating this experiment in our model. The interruption of protein synthesis auses the number of PKMζ moleules to drop, whih in turn leads to a transient deline in the number of inserted Glu2-ontaining MPRs, but the system reovers when the PSI is removed. Fig 9: PSI infusion during the maintenane phase does not disrupt established L- LTP. L-LTP is indued by NMDR stimulation at Stim. One L-LTP is established (100 minutes after indution), protein synthesis inhibition is applied for 100 minutes. The interruption of kinase synthesis auses a deline in the levels of PKMζ and inserted Glu2-ontaining MPRs, but the synapse reovers when the PSI is removed. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands

38 38 indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2- ontaining MPRs, E1: ativated E1 enzyme. If the model is orret, then the transient derease in the number of Glu2-ontaining MPRs may be detetable as a redued EPSP urrent after PSI appliation. However, it is possible that the temporary removal of Glu2-ontaining MPRs is ompensated for by insertion of Glu2-laking MPRs, similarly to what has been shown to happen during retrieval-indued destabilization [45], in whih ase the synapti strength would be maintained. If this is the ase, then it may instead be possible to detet a transient inrease in retifiation index, beause Glu2-laking MPRs, but not Glu2- ontaning ones, are haraterized by a slight inward retifiation [20,45]. Our model thus predits that one or the other of these two effets (EPSP redution or retifiation) should be detetable after PSI appliation during L-LTP maintenane. Reativation destabilizes, but does not disrupt, L-LTP The effet of memory reativation is simulated as a brief spike in the amount of ative E2 enzyme (Fig 10). This results in rapid endoytosis of the inserted Glu2-ontaining MPRs [20,21] and release of the bound PKMζ moleules whih then start to dissipate. However, due to ontinued synthesis, the PKMζ level is kept from dropping below threshold and the model settles bak into the potentiated steady state [18,79].

39 39 Fig 10: Reativation. NMDR stimulation is simulated by a pulse of ative E1 enzyme at Stim, and reativation by a pulse of ative E2 enzyme at Reat. E2 auses rapid endoytosis of Glu2-ontaining MPRs, whih in turn leads to PKMζ depletion. PKMζ mrn only delines slowly, however, and the synapse returns to its potentiated state when the E2 enzyme deativates. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2-ontaining MPRs, E1: ativated E1 enzyme, E2: ativated E2 enzyme. lthough the population of inserted Glu2-ontaining MPRs is almost ompletely depleted after reativation, the levels of PKMζ and ative PKMζ mrn stay well above their depotentiation thresholds and the model reliably reovers from post-reativation instability (reonsolidation), unless hallenged by simulated pharmaologial interventions (see below). s mentioned earlier, Hong et al. demonstrated this abrupt

40 40 derease of inserted Glu2-ontaining MPRs after memory retrieval, as well as a orresponding transient inrease of Glu2-laking MPRs, whih maintained the synapti strength during the labile period [20]. Reativation followed by PSI disrupts L-LTP Simulation of PSI infusion simultaneously with reativation, or shortly thereafter, auses disruption of L-LTP (Fig 11). Fig 11: Reativation with simultaneous PSI infusion. s in Fig 10, reativation is simulated as a pulse of ative E2 enzyme at Reat, but here the presene of PSI prevents reovery and L-LTP is disrupted. Solid lines represent mean moleule ounts for 100 simulations. Lightly olored bands indiate standard deviation. R: ative PKMζ mrn, P: PKMζ, I: inserted Glu2-ontaining MPRs, E1: ativated E1 enzyme, E2: ativated E2 enzyme.

41 41 In the absene of new protein synthesis, the PKMζ level drops below threshold and the model settles into its unpotentiated state [18,79]. By varying the delay between reativation and PSI infusion, we an establish the model s reonsolidation window, the time interval after reativation during whih L-LTP is vulnerable to PSI. s shown in Fig 12, if PSI infusion is applied 15 minutes or less after reativation, then the model reliably swithes to its lower (unpotentiated) steady state with few inserted Glu2- ontaining MPRs, but with a delay of 30 minutes or more, L-LTP disruption does not result: the model remains in its potentiated state where the number of inserted Glu2- ontaining MPRs flutuates in the range. The model s reonsolidation window is thus in the range 20 to 30 minutes, onsistent with empirial results [18,84].

42 42 Fig 12: Reonsolidation window. Results of simulated reativation followed by PSI infusion. The delay between reativation and PSI infusion is varied from 0 to 60 minutes in 5-minute steps. One hundred simulations were run with eah value for the delay. The number of inserted Glu2-ontaining MPRs was reorded twenty hours after stimulation. For eah value of the delay, the heights of the olumns indiate the number of simulations that terminated with the orresponding numbers of inserted MPRs. Glu23Y bloks post-reativation PSI-infusion from ausing depotentiation When the Glu23Y peptide is infused together with PSI after reativation, it prevents the disruption of L-LTP that PSI otherwise auses [57,63]. s before, reativation triggers ativation of the E2 enzyme, but here the Glu23Y peptide bloks its endoytoti effet. s a result, the Glu2-ontaining MPRs remain