A model of the roles of essential kinases in the induction and expression of late long-term potentiation.

The induction of late long-term potentiation (L-LTP) involves complex interactions among second-messenger cascades. To gain insights into these interactions, a mathematical model was developed for L-LTP induction in the CA1 region of the hippocampus. The differential equation-based model represents actions of protein kinase A (PKA), MAP kinase (MAPK), and CaM kinase II (CAMKII) in the vicinity of the synapse, and activation of transcription by CaM kinase IV (CAMKIV) and MAPK. L-LTP is represented by increases in a synaptic weight. Simulations suggest that steep, supralinear stimulus-response relationships between stimuli (e.g., elevations in [Ca(2+)]) and kinase activation are essential for translating brief stimuli into long-lasting gene activation and synaptic weight increases. Convergence of multiple kinase activities to induce L-LTP helps to generate a threshold whereby the amount of L-LTP varies steeply with the number of brief (tetanic) electrical stimuli. The model simulates tetanic, -burst, pairing-induced, and chemical L-LTP, as well as L-LTP due to synaptic tagging. The model also simulates inhibition of L-LTP by inhibition of MAPK, CAMKII, PKA, or CAMKIV. The model predicts results of experiments to delineate mechanisms underlying L-LTP induction and expression. For example, the cAMP antagonist RpcAMPs, which inhibits L-LTP induction, is predicted to inhibit ERK activation. The model also appears useful to clarify similarities and differences between hippocampal L-LTP and long-term synaptic strengthening in other systems.

A model of late long-term potentiation simulates aspects of memory maintenance.

Late long-term potentiation (L-LTP) denotes long-lasting strengthening of synapses between neurons. L-LTP appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing ongoing activity and biochemical pathways important for L-LTP. In this study, ongoing activity was incorporated into two such models - a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction simply and intuitively, and the detailed model adds activation of essential kinases by Ca(2+). Ongoing activity was modeled as continual brief elevations of Ca(2+). In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca(2+) transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low basal weight to a high weight that is stabilized by ongoing activity. Bistability was robust to parameter variations in both models. Simulations illustrated that prolonged periods of decreased activity reset synaptic strengths to low values, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength. Further investigations that examine the dynamics of activity and synaptic maintenance can be expected to help in understanding how memories are preserved for up to a lifetime in animals including humans.

Glutamate iontophoresis induces long-term potentiation in the absence of evoked presynaptic activity

$\rm\underline{L}$ong-$\rm\underline{t}$erm $\rm\underline{p}$otentiation (LTP) is a candidate cellular mechanism underlying mammalian learning and memory. Protocols that induce LTP typically involve afferent stimulation. The experiments described in this dissertation tested the hypothesis that LTP induction does not require presynaptic activity. The significance of this hypothesis is underscored by results suggesting that LTP expression may involve activity-dependent presynaptic changes. An induction protocol using glutamate iontophoresis was developed that reliably induces LTP in hippocampal slices without afferent stimulation (ionto-LTP). Ionto-LTP is induced when excitatory postsynaptic potentials are completely blocked with adenosine and $\rm\underline{t}$etrodo$\rm\underline{t}$o$\rm\underline{x}$in (TTX). These results suggest constraints on the involvement of presynaptic mechanisms and putative retrograde messengers in LTP induction and expression; namely, these processes must function without many forms of activity-dependent presynaptic processes.^ In testing the role of pre-and postsynaptic mechanisms in LTP expression whole-cell recordings were used to examine the frequency and amplitude of $\rm\underline{s}$pontaneous $\rm\underline{e}$xcitatory $\rm\underline{p}$o$\rm\underline{s}$ynaptic $\rm\underline{c}$urrents (sEPSCs) in CA1 pyramidal neurons. sEPSCs where comprised of an equal mixture of TTX insensitive miniature EPSCs and sEPSCs that appeared to result from spontaneous action potentials (i.e., TTX sensitive EPSCs). The detection of all sEPSCs was virtually eliminated by CNQX, suggesting that sEPSCs were glutamate mediated synaptic events. Changes in the amplitude and frequency sEPSCs were examined during the expression of ionto-LTP to obtain new information about the cellular location of mechanisms involved in synaptic plasticity. The findings of this dissertation show that ionto-LTP expression results from increased sEPSC amplitude in the absence of lasting increases in sEPSC frequency. Potentiation of sEPSC amplitude without changes in sEPSC frequency has been previously interpreted to be due to postsynaptic mechanisms. Although this interpretation is supported by findings from peripheral synapses, its application to the central nervous system is unclear. Therefore, alternative mechanisms are also considered in this dissertation. Models based on increased release probability for action potential dependent transmitter release appear insufficient to explain our results. The most straightforward interpretation of the results in this dissertation is that LTP induced by glutamate iontophoresis on dendrites of CA1 pyramidal neurons is mediated by postsynaptic mechanisms. ^

Calcium-dependent mechanisms and long-term potentiation: Role of NMDA receptors, voltage -dependent calcium channels and persistent protein kinase activity

Long-term potentiation (LTP) is a rapidly induced and long lasting increase in synaptic strength and is the leading cellular model for learning and memory in the mammalian brain. LTP was first identified in the hippocampus, a structure implicated in memory formation. LTP induction is dependent on postsynaptic Ca2+ increases mediated by N-methyl-D-aspartate (NMDA) receptors. Activation of other postsynaptic routes of Ca2+ entry, such as voltage-dependent Ca2+ channels (VDCCs) have subsequently been shown to induce a long-lasting increase in synaptic strength. However, it is unknown if VDCC-induced LTP utilized similar cellular mechanisms as the classical NMDA receptor-dependent LTP and if these two forms of LTP display similar properties. This dissertation determines the similarities and differences in VDCC and NMDA receptor-dependent LTP in area CA1 of hippocampal slices and demonstrates that VDCCs and NMDA receptors activate similar cellular mechanisms, such as protein kinases, to induce LTP. However, VDCC and NMDA receptor activated LTP induction mechanisms are compartmentalized in the postsynaptic neuron, such that they do not interact. Consistent with activation properties of NMDA receptors and VDCCs, NMDA receptor and VDCC-dependent LTP have different induction properties. In contrast to NMDA-dependent LTP, VDCC-induced potentiation does not require evoked presynaptic stimulation or display input specificity. These results indicate that there are two different routes of postsynaptic Ca2+ which can induce LTP and the compartmentation of VDCCs and NMDA receptors and/or their resulting Ca2+ increases may account for the distinction between these LTP induction mechanisms.^ One of the molecular targets for postsynaptic Ca2+ that is required for the induction of LTP is protein kinases. Evidence for the role of protein kinase activity in LTP expression is either correlational or controversial. We have utilized a broad range and potent inhibitors of protein kinases to systematically examine the temporal requirement for protein kinases in the induction and expression of LTP. Our results indicate that there is a critical period of persistent protein kinase activity required for LTP induction activated by tetanic stimulation and extending until 20 min after HFS. In addition, our results suggest that protein kinase activity during and immediately after HFS is not sufficient for LTP induction. These results provide evidence for persistent and/or Ca2+ independent protein kinase activity involvement in LTP induction. ^

Post-translational regulation of an Aplysia glutamate transporter during long-term facilitation.

Regulation of glutamate transporters accompanies plasticity of some glutamatergic synapses. The regulation of glutamate uptake at the Aplysia sensorimotor synapse during long-term facilitation (LTF) was investigated. Previously, increases in levels of ApGT1 (Aplysia glutamate transporter 1) in synaptic membranes were found to be related to long-term increases in glutamate uptake. In this study, we found that regulation of ApGT1 during LTF appears to occur post-translationally. Serotonin (5-HT) a transmitter that induces LTF did not increase synthesis of ApGT1. A pool of ApGT1 appears to exist in sensory neuron somata, which is transported to the terminals by axonal transport. Blocking the rough endoplasmic reticulum-Golgi-trans-Golgi network (TGN) pathway with Brefeldin A prevented the 5-HT-induced increase of ApGT1 in terminals. Also, 5-HT produced changes in post-translational modifications of ApGT1 as well as changes in the levels of an ApGT1-co-precipitating protein. These results suggest that regulation of trafficking of ApGT1 from the vesicular trafficking system (rough endoplasmic reticulum-Golgi-TGN) in the sensory neuron somata to the terminals by post-translational modifications and protein interactions appears to be the mechanism underlying the increase in ApGT1, and thus, glutamate uptake during memory formation.

Bifurcation and singularity analysis of a molecular network for the induction of long-term memory.

Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis.

Long-lasting synaptic potentiation induced by depolarization under conditions that eliminate detectable Ca2+ signals.

Activity-dependent alterations of synaptic transmission important for learning and memory are often induced by Ca(2+) signals generated by depolarization. While it is widely assumed that Ca(2+) is the essential transducer of depolarization into cellular plasticity, little effort has been made to test whether Ca(2+)-independent responses to depolarization might also induce memory-like alterations. It was recently discovered that peripheral axons of nociceptive sensory neurons in Aplysia display long-lasting hyperexcitability triggered by conditioning depolarization in the absence of Ca(2+) entry (using nominally Ca(2+)-free solutions containing EGTA, "0Ca/EGTA") or the absence of detectable Ca(2+) transients (adding BAPTA-AM, "0Ca/EGTA/BAPTA-AM"). The current study reports that depolarization of central ganglia to approximately 0 mV for 2 min in these same solutions induced hyperexcitability lasting >1 h in sensory neuron processes near their synapses onto motor neurons. Furthermore, conditioning depolarization in these solutions produced a 2.5-fold increase in excitatory postsynaptic potential (EPSP) amplitude 1-3 h afterward despite a drop in motor neuron input resistance. Depolarization in 0 Ca/EGTA produced long-term potentiation (LTP) of the EPSP lasting > or = 1 days without changing postsynaptic input resistance. When re-exposed to extracellular Ca(2+) during synaptic tests, prior exposure to 0Ca/EGTA or to 0Ca/EGTA/BAPTA-AM decreased sensory neuron survival. However, differential effects on neuronal health are unlikely to explain the observed potentiation because conditioning depolarization in these solutions did not alter survival rates. These findings suggest that unrecognized Ca(2+)-independent signals can transduce depolarization into long-lasting synaptic potentiation, perhaps contributing to persistent synaptic alterations following large, sustained depolarizations that occur during learning, neural injury, or seizures.

Beta 1-integrins are required for hippocampal AMPA receptor-dependent synaptic transmission, synaptic plasticity, and working memory.

Integrins comprise a large family of cell adhesion receptors that mediate diverse biological events through cell-cell and cell-extracellular matrix interactions. Recent studies have shown that several integrins are localized to synapses with suggested roles in synaptic plasticity and memory formation. We generated a postnatal forebrain and excitatory neuron-specific knock-out of beta1-integrin in the mouse. Electrophysiological studies demonstrated that these mutants have impaired synaptic transmission through AMPA receptors and diminished NMDA receptor-dependent long-term potentiation. Despite the impairment in hippocampal synaptic transmission, the mutants displayed normal hippocampal-dependent spatial and contextual memory but were impaired in a hippocampal-dependent, nonmatching-to-place working memory task. These phenotypes parallel those observed in animals carrying knock-outs of the GluR1 (glutamate receptor subunit 1) subunit of the AMPA receptor. These observations suggest a new function of beta1-integrins as regulators of synaptic glutamate receptor function and working memory.

Lobe specific Ca2+-calmodulin nano-domain in neuronal spines: a single molecule level analysis.

Calmodulin (CaM) is a ubiquitous Ca(2+) buffer and second messenger that affects cellular function as diverse as cardiac excitability, synaptic plasticity, and gene transcription. In CA1 pyramidal neurons, CaM regulates two opposing Ca(2+)-dependent processes that underlie memory formation: long-term potentiation (LTP) and long-term depression (LTD). Induction of LTP and LTD require activation of Ca(2+)-CaM-dependent enzymes: Ca(2+)/CaM-dependent kinase II (CaMKII) and calcineurin, respectively. Yet, it remains unclear as to how Ca(2+) and CaM produce these two opposing effects, LTP and LTD. CaM binds 4 Ca(2+) ions: two in its N-terminal lobe and two in its C-terminal lobe. Experimental studies have shown that the N- and C-terminal lobes of CaM have different binding kinetics toward Ca(2+) and its downstream targets. This may suggest that each lobe of CaM differentially responds to Ca(2+) signal patterns. Here, we use a novel event-driven particle-based Monte Carlo simulation and statistical point pattern analysis to explore the spatial and temporal dynamics of lobe-specific Ca(2+)-CaM interaction at the single molecule level. We show that the N-lobe of CaM, but not the C-lobe, exhibits a nano-scale domain of activation that is highly sensitive to the location of Ca(2+) channels, and to the microscopic injection rate of Ca(2+) ions. We also demonstrate that Ca(2+) saturation takes place via two different pathways depending on the Ca(2+) injection rate, one dominated by the N-terminal lobe, and the other one by the C-terminal lobe. Taken together, these results suggest that the two lobes of CaM function as distinct Ca(2+) sensors that can differentially transduce Ca(2+) influx to downstream targets. We discuss a possible role of the N-terminal lobe-specific Ca(2+)-CaM nano-domain in CaMKII activation required for the induction of synaptic plasticity.

Neurogranin controls the spatiotemporal pattern of postsynaptic Ca2+/CaM signaling.

Neurogranin (Ng) is a postsynaptic IQ-motif containing protein that accelerates Ca(2+) dissociation from calmodulin (CaM), a key regulator of long-term potentiation and long-term depression in CA1 pyramidal neurons. The exact physiological role of Ng, however, remains controversial. Two genetic knockout studies of Ng showed opposite outcomes in terms of the induction of synaptic plasticity. To understand its function, we test the hypothesis that Ng could regulate the spatial range of action of Ca(2+)/CaM based on its ability to accelerate the dissociation of Ca(2+) from CaM. Using a mathematical model constructed on the known biochemistry of Ng, we calculate the cycle time that CaM molecules alternate between the fully Ca(2+) saturated state and the Ca(2+) unbound state. We then use these results and include diffusion of CaM to illustrate the impact that Ng has on modulating the spatial profile of Ca(2+)-saturated CaM within a model spine compartment. Finally, the first-passage time of CaM to transition from the Ca(2+)-free state to the Ca(2+)-saturated state was calculated with or without Ng present. These analyses suggest that Ng regulates the encounter rate between Ca(2+) saturated CaM and its downstream targets during postsynaptic Ca(2+) transients.

Spike timing dependent plasticity: a consequence of more fundamental learning rules.

Spike timing dependent plasticity (STDP) is a phenomenon in which the precise timing of spikes affects the sign and magnitude of changes in synaptic strength. STDP is often interpreted as the comprehensive learning rule for a synapse - the "first law" of synaptic plasticity. This interpretation is made explicit in theoretical models in which the total plasticity produced by complex spike patterns results from a superposition of the effects of all spike pairs. Although such models are appealing for their simplicity, they can fail dramatically. For example, the measured single-spike learning rule between hippocampal CA3 and CA1 pyramidal neurons does not predict the existence of long-term potentiation one of the best-known forms of synaptic plasticity. Layers of complexity have been added to the basic STDP model to repair predictive failures, but they have been outstripped by experimental data. We propose an alternate first law: neural activity triggers changes in key biochemical intermediates, which act as a more direct trigger of plasticity mechanisms. One particularly successful model uses intracellular calcium as the intermediate and can account for many observed properties of bidirectional plasticity. In this formulation, STDP is not itself the basis for explaining other forms of plasticity, but is instead a consequence of changes in the biochemical intermediate, calcium. Eventually a mechanism-based framework for learning rules should include other messengers, discrete change at individual synapses, spread of plasticity among neighboring synapses, and priming of hidden processes that change a synapse's susceptibility to future change. Mechanism-based models provide a rich framework for the computational representation of synaptic plasticity.

Structural plasticity can produce metaplasticity.

BACKGROUND: Synaptic plasticity underlies many aspect of learning memory and development. The properties of synaptic plasticity can change as a function of previous plasticity and previous activation of synapses, a phenomenon called metaplasticity. Synaptic plasticity not only changes the functional connectivity between neurons but in some cases produces a structural change in synaptic spines; a change thought to form a basis for this observed plasticity. Here we examine to what extent structural plasticity of spines can be a cause for metaplasticity. This study is motivated by the observation that structural changes in spines are likely to affect the calcium dynamics in spines. Since calcium dynamics determine the sign and magnitude of synaptic plasticity, it is likely that structural plasticity will alter the properties of synaptic plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In this study we address the question how spine geometry and alterations of N-methyl-D-aspartic acid (NMDA) receptors conductance may affect plasticity. Based on a simplified model of the spine in combination with a calcium-dependent plasticity rule, we demonstrated that after the induction phase of plasticity a shift of the long term potentiation (LTP) or long term depression (LTD) threshold takes place. This induces a refractory period for further LTP induction and promotes depotentiation as observed experimentally. That resembles the BCM metaplasticity rule but specific for the individual synapse. In the second phase, alteration of the NMDA response may bring the synapse to a state such that further synaptic weight alterations are feasible. We show that if the enhancement of the NMDA response is proportional to the area of the post synaptic density (PSD) the plasticity curves most likely return to the initial state. CONCLUSIONS/SIGNIFICANCE: Using simulations of calcium dynamics in synaptic spines, coupled with a biophysically motivated calcium-dependent plasticity rule, we find under what conditions structural plasticity can form the basis of synapse specific metaplasticity.

Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory.

Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular Ca2+ release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. This dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that (1) the dual-time structure similarly confers resistance to internal noise due to molecule number fluctuations, and (2) model variants with altered coupling, which better represent some specific biochemical systems, share all the above advantages. We also develop a similar bistable model with coupling of a fast autoactivation loop to a slow loop. This model's topology was suggested by positive feedback proposed to play a role in long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance are also present in this autoactivation model. Empirically, LTP develops resistance to reversal over approximately 1h . The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback.

Short-Term Plasticity in a Computational Model of the Tail-Withdrawal Circuit in Aplysia.

The tail-withdrawal circuit of Aplysia provides a useful model system for investigating synaptic dynamics. Sensory neurons within the circuit manifest several forms of synaptic plasticity. Here, we developed a model of the circuit and investigated the ways in which depression (DEP) and potentiation (POT) contributed to information processing. DEP limited the amount of motor neuron activity that could be elicited by the monosynaptic pathway alone. POT within the monosynaptic pathway did not compensate for DEP. There was, however, a synergistic interaction between POT and the polysynaptic pathway. This synergism extended the dynamic range of the network, and the interplay between DEP and POT made the circuit responded preferentially to long-duration, low-frequency inputs.

Short-Term Plasticity in a Computational Model of the Tail-Withdrawal Circuit in Aplysia.

The tail-withdrawal circuit of Aplysia provides a useful model system for investigating synaptic dynamics. Sensory neurons within the circuit manifest several forms of synaptic plasticity. Here, we developed a model of the circuit and investigated the ways in which depression (DEP) and potentiation (POT) contributed to information processing. DEP limited the amount of motor neuron activity that could be elicited by the monosynaptic pathway alone. POT within the monosynaptic pathway did not compensate for DEP. There was, however, a synergistic interaction between POT and the polysynaptic pathway. This synergism extended the dynamic range of the network, and the interplay between DEP and POT made the circuit responded preferentially to long-duration, low-frequency inputs.