Coupled phosphatase and kinase switches produce the tristability required for long-term potentiation and long-term depression

The Rise and Fall of Memory in a Model of Synaptic Integration

Plasticity-inducing stimuli must typically be presented many times before synaptic plasticity is expressed, perhaps because induction signals gradually accumulate before overt strength changes occur. We consider memory dynamics in a mathematical model with synapses that integrate plasticity induction signals before expressing plasticity. We find that the memory trace initially rises before reaching a maximum and then falling. The memory signal dissociates into separate oblivescence and reminiscence components, with reminiscence initially dominating recall. In radical contrast, related but nonintegrative models exhibit only a highly problematic oblivescence. Synaptic integration mechanisms possess natural timescales, depending on the statistics of the induction signals. Together with neuromodulation, these timescales may therefore also begin to provide a natural account of the well-known spacing effect in the transition to late-phase plasticity. Finally, we propose experiments that could distinguish between integrative and nonintegrative synapses. Such experiments should further elucidate the synaptic signal processing mechanisms postulated by our model.

Post-translational modification: nature's escape from genetic imprisonment and the basis for dynamic information encoding

We discuss protein post-translational modification (PTM) from an information processing perspective. PTM at multiple sites on a protein creates a combinatorial explosion in the number of potential 'mod-forms', or global patterns of modification. Distinct mod-forms can elicit distinct downstream responses, so that the overall response depends partly on the effectiveness of a particular mod-form to elicit a response and partly on the stoichiometry of that mod-form in the molecular population. We introduce the 'mod-form distribution'-the relative stoichiometries of each mod-form-as the most informative measure of a protein's state. Distinct mod-form distributions may summarize information about distinct cellular and physiological conditions and allow downstream processes to interpret this information accordingly. Such information 'encoding' by PTMs may facilitate evolution by weakening the need to directly link upstream conditions to downstream responses. Mod-form distributions provide a quantitative framework in which to interpret ideas of 'PTM codes' that are emerging in several areas of biology, as we show by reviewing examples of ion channels, GPCRs, microtubules, and transcriptional co-regulators. We focus particularly on examples other than the well-known 'histone code', to emphasize the pervasive use of information encoding in molecular biology. Finally, we touch briefly on new methods for measuring mod-form distributions.

The role of tonic and phasic dopamine for long-term synaptic plasticity in the prefrontal cortex: a computational model

This work presents a computational model of dopamine (DA) influence on long-term potentiation (LTP) and long-term depression (LTD) in the prefrontal cortex. Distinct properties of the model are a DA-concentration-dependent switch from depression to potentiation during induction of plasticity, and an inverted-U-shaped dependence of protein synthesis on the level of background DA. Protein synthesis is responsible for the maintenance of LTP/LTD in the model. Our simulations suggest that in vitro experimental data on prefrontal plasticity, induced by high-frequency stimulation, may be accounted for by a single synaptic mechanism that is slowly (on the timescale of minutes) activated in the presence of DA in a concentration-dependent manner. The activation value determines the direction of plasticity during induction, while it also modulates the magnitude of plasticity during maintenance. More generally, our results support the hypothesis that phasic release of endogenous DA is necessary for the maintenance of long-term changes in synaptic efficacy, while the concentration of tonic DA determines the direction and magnitude of these changes in the PFC.

Calcium/calmodulin-dependent protein kinase II activity regulates the proliferative potential of growth plate chondrocytes

For tissues that develop throughout embryogenesis and into postnatal life, the generation of differentiated cells to promote tissue growth is at odds with the requirement to maintain the stem cell/progenitor cell population to preserve future growth potential. In the growth plate cartilage, this balance is achieved in part by establishing a proliferative phase that amplifies the number of progenitor cells prior to terminal differentiation into hypertrophic chondrocytes. Here, we show that endogenous calcium/calmodulin-dependent protein kinase II (CamkII, also known as Camk2) activity is upregulated prior to hypertrophy and that loss of CamkII function substantially blocks the transition from proliferation to hypertrophy. Wnt signaling and Pthrp-induced phosphatase activity negatively regulate CamkII activity. Release of this repression results in activation of multiple effector pathways, including Runx2- and β-catenin-dependent pathways. We present an integrated model for the regulation of proliferation potential by CamkII activity that has important implications for studies of growth control and adult progenitor/stem cell populations.

The Mean Time to Express Synaptic Plasticity in Integrate-and-Express, Stochastic Models of Synaptic Plasticity Induction

Stochastic models of synaptic plasticity propose that single synapses perform a directed random walk of fixed step sizes in synaptic strength, thereby embracing the view that the mechanisms of synaptic plasticity constitute a stochastic dynamical system. However, fluctuations in synaptic strength present a formidable challenge to such an approach. We have previously proposed that single synapses must interpose an integration and filtering mechanism between the induction of synaptic plasticity and the expression of synaptic plasticity in order to control fluctuations. We analyze a class of three such mechanisms in the presence of possibly non-Markovian plasticity induction processes, deriving expressions for the mean expression time in these models. One of these filtering mechanisms constitutes a discrete low-pass filter that could be implemented on a small collection of molecules at single synapses, such as CaMKII, and we analyze this discrete filter in some detail. After considering Markov induction processes, we examine our own stochastic model of spike-timing-dependent plasticity, for which the probability density functions of the induction of plasticity steps have previously been derived. We determine the dependence of the mean time to express a plasticity step on pre- and postsynaptic firing rates in this model, and we also consider, numerically, the long-term stability against fluctuations of patterns of neuronal connectivity that typically emerge during neuronal development.

Postsynaptic signal transduction models for long-term potentiation and depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

Interplay of the magnitude and time-course of postsynaptic Ca2+ concentration in producing spike timing-dependent plasticity

Synaptic strength can be modified by the relative timing of pre- and postsynaptic activity, a phenomenon termed spike timing-dependent plasticity (STDP). Studies of neurons in the hippocampus and in other regions have found that when presynaptic activity occurs within a narrow time window, typically 10 or 20 ms, before postsynaptic activity, long-term potentiation (LTP) is induced, while if presynaptic activity occurs within a similar time window after postsynaptic activity, long-term depression (LTD) results. The mechanisms underlying these modifications are not completely understood, although there is strong evidence that the postsynaptic Ca (2+) concentration plays a central role. Some previous modeling of STDP has focused on the dynamics of the postsynaptic Ca (2+) concentration, while other work has studied biophysical mechanisms of how a synapse can exist in, and switch between, different states corresponding to LTP and LTD. Building on previous work in these two areas we have developed the first low level STDP model of a tristable biochemical system that incorporates induction and maintenance of both LTP and LTD. Our model is able to explain the STDP observed in hippocampal neurons in response to pre- and postsynaptic pulse pairs, using only parameters derived from previous work and without the need for parameter fine-tuning. Our results also give insight into how and why the time course of the postsynaptic Ca (2+) concentration can lead to either LTP or LTD, and suggest that voltage dependent calcium channels play a key role.

Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models

We review biophysical models of synaptic plasticity, with a focus on spike-timing dependent plasticity (STDP). The common property of the discussed models is that synaptic changes depend on the dynamics of the intracellular calcium concentration, which itself depends on pre- and postsynaptic activity. We start by discussing simple models in which plasticity changes are based directly on calcium amplitude and dynamics. We then consider models in which dynamic intracellular signaling cascades form the link between the calcium dynamics and the plasticity changes. Both mechanisms of induction of STDP (through the ability of pre/postsynaptic spikes to evoke changes in the state of the synapse) and of maintenance of the evoked changes (through bistability) are discussed.

The sensitivity of memory consolidation and reconsolidation to inhibitors of protein synthesis and kinases: computational analysis

Memory consolidation and reconsolidation require kinase activation and protein synthesis. Blocking either process during or shortly after training or recall disrupts memory stabilization, which suggests the existence of a critical time window during which these processes are necessary. Using a computational model of kinase synthesis and activation, we investigated the ways in which the dynamics of molecular positive-feedback loops may contribute to the time window for memory stabilization and memory maintenance. In the models, training triggered a transition in the amount of kinase between two stable states, which represented consolidation. Simulating protein synthesis inhibition (PSI) from before to 40 min after training blocked or delayed consolidation. Beyond 40 min, substantial (>95%) PSI had little effect despite the fact that the elevated amount of kinase was maintained by increased protein synthesis. However, PSI made established memories labile to perturbations. Simulations of kinase inhibition produced similar results. In addition, similar properties were found in several other models that also included positive-feedback loops. Even though our models are based on simplifications of the actual mechanisms of molecular consolidation, they illustrate the practical difficulty of empirically measuring "time windows" for consolidation. This is particularly true when consolidation and reconsolidation of memory depends, in part, on the dynamics of molecular positive-feedback loops.

DMob4/Phocein regulates synapse formation, axonal transport, and microtubule organization

The monopolar spindle-one-binder (Mob) family of kinase-interacting proteins regulate cell cycle and cell morphology, and their dysfunction has been linked to cancer. Models for Mob function are primarily based on studies of Mob1 and Mob2 family members in yeast. In contrast, the function of the highly conserved metazoan Phocein/Mob3 subfamily is unknown. We identified the Drosophila Phocein homolog (DMob4) as a regulator of neurite branching in a genome-wide RNA interference screen for neuronal morphology mutants. To further characterize DMob4, we generated null and hypomorphic alleles and performed in vivo cell biological and physiological analysis. We find that DMob4 plays a prominent role in neural function, regulating axonal transport, membrane excitability, and organization of microtubule networks. DMob4 mutant neuromuscular synapses also show a profound overgrowth of synaptic boutons, similar to known Drosophila endocytotic mutants. DMob4 and human Phocein are >80% identical, and the lethality of DMob4 mutants can be rescued by a human phocein transgene, indicating a conservation of function across evolution. These findings suggest a novel role for Phocein proteins in the regulation of axonal transport, neurite elongation, synapse formation, and microtubule organization.

A Non-Markovian Random Walk Underlies a Stochastic Model of Spike-Timing-Dependent Plasticity

A stochastic model of spike-timing-dependent plasticity (STDP) proposes that spike timing influences the probability but not the amplitude of synaptic strength change at single synapses. The classic, biphasic STDP profile emerges as a spatial average over many synapses presented with a single spike pair or as a temporal average over a single synapse presented with many spike pairs. We have previously shown that the model accounts for a variety of experimental data, including spike triplet results, and has a number of desirable theoretical properties, including being entirely self-stabilizing in all regions of parameter space. Our earlier analyses of the model have employed cumbersome spike-to-spike averaging arguments to derive results. Here, we show that the model can be reformulated as a non-Markovian random walk in synaptic strength, the step sizes being fixed as postulated. This change of perspective greatly simplifies earlier calculations by integrating out the proposed switch mechanism by which changes in strength are driven and instead concentrating on the changes in strength themselves. Moreover, this change of viewpoint is generative, facilitating further calculations that would be intractable, if not impossible, with earlier approaches. We prepare the machinery here for these later calculations but also briefly indicate how this machinery may be used by considering two particular applications.

Regulation of AMPA receptor trafficking in the nucleus accumbens by dopamine and cocaine

Nucleus accumbens (NAc) neurons are excited primarily by AMPA-type glutamate receptors (AMPAR). This is required for cocaine seeking in animal models of cocaine addiction, suggesting AMPAR transmission in the NAc as a key control point for cocaine-related behaviors. This review will briefly describe AMPAR properties and trafficking, with a focus on studies in NAc neurons, and then consider mechanisms by which cocaine may alter AMPAR transmission. Two examples will be discussed that may be important in two different stages of addiction: learning about drugs and drug-related cues during the period of drug exposure, and persistent vulnerability to craving and relapse after abstinence is achieved. The first example is drawn from studies of cultured NAc neurons. Elevation of dopamine levels (as would occur following cocaine exposure) facilitates activity-dependent strengthening of excitatory synapses onto medium spiny neurons, the main cell type and projection neuron of the NAc. This occurs because activation of D1-class dopamine receptors primes AMPAR for synaptic insertion. This may create a temporal window in which stimuli related to cocaine-taking are more efficacious at eliciting synaptic plasticity and thus being encoded into memory. The second example involves rat models of cocaine addiction. Cell surface and synaptic expression of AMPAR on NAc neurons is persistently increased after withdrawal from repeated cocaine exposure. We hypothesize that this increases the reactivity of NAc neurons to glutamate inputs from cortex and limbic structures, facilitating the ability of these inputs to trigger cocaine seeking and thus contributing to the persistent vulnerability to relapse that characterizes addiction.

Co-induction of LTP and LTD and its regulation by protein kinases and phosphatases

The cellular properties of long-term potentiation (LTP) following pairing of pre- and postsynaptic activity were examined at a known glutamatergic synapse in the leech, specifically between the pressure (P) mechanosensory and anterior pagoda (AP) neurons. Stimulation of the presynaptic P cell (25 Hz) concurrent with a 2 nA depolarization of the postsynaptic AP cell significantly potentiated the P-to-AP excitatory postsynaptic potential (EPSP) in an N-methyl-d-aspartate receptor (NMDAR)-dependent manner based on inhibitory effects of the NMDAR antagonist MK801 and inhibition of the NMDAR glycine binding site by 7-chlorokynurenic acid. LTP was blocked by injection of bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA) into the postsynaptic (AP) cell, indicating a requirement for postsynaptic elevation of intracellular Ca(2+). Autocamtide-2-related inhibitory peptide (AIP), a specific inhibitor of Ca(2+)/calmodulin-dependent kinase II (CaMKII), and Rp-cAMP, an inhibitor of protein kinase A (PKA), also blocked pairing-induced potentiation, indicating a requirement for activation of CaMKII and PKA. Interestingly, application of AIP during pairing resulted in significantly depressed synaptic transmission. Co-application of AIP with the protein phosphatase inhibitor okadaic acid restored synaptic transmission to baseline levels, suggesting an interaction between CaMKII and protein phosphatases during induction of activity-dependent synaptic plasticity. When postsynaptic activity preceded presynaptic activity, NMDAR-dependent long-term depression (LTD) was observed that was blocked by okadaic acid. Postsynaptic injection of botulinum toxin blocked P-to-AP potentiation while postsynaptic injection of pep2-SVKI, an inhibitor of AMPA receptor endocytosis, inhibited LTD, supporting the hypothesis that glutamate receptor trafficking contributes to both LTP and LTD at the P-to-AP synapse in the leech.

Low-frequency electrical stimulation induces long-term depression in patients with chronic tension-type headache

Repetitive low-frequency electrical stimulation (LFS) induces pain inhibition in healthy volunteers and in animals, but it is unknown whether it has an analgesic effect in patients with headache. The aim of this study was to investigate if LFS could induce prolonged pain inhibition, called long-term depression (LTD), in patients with chronic tension-type headache (CTTH). Twenty CTTH patients and 20 healthy volunteers were exposed to 20 min LFS (1 Hz) to the forehead. LTD was measured as a decrease in pain response to electrical stimulation in a 1-h post-LFS period following LFS. The LFS induced a significant and stable inhibition of pain (LTD) both in patients with CTTH (post-LFS average decrease in pain rating: 19.6 +/- 3.9%, all P < 0.005, Holm-Sidak) and in healthy controls (30.1 +/- 5.0%, all P < 0.001, Holm-Sidak). During the LFS period, the pain ratings decreased consistently in both groups. In conclusion, a significant and stable pain inhibition (LTD) can be induced in CTTH patients by LFS.

Orexins/hypocretins control bistability of hippocampal long-term synaptic plasticity through co-activation of multiple kinases

AIM

Orexins/hypocretins (OX/Hcrt) are hypothalamic neuropeptides linking sleep-wakefulness, appetite and neuroendocrine control. Their role and mechanisms of action on higher brain functions, such as learning and memory, are not clear.

METHODS

We used field recordings of excitatory post-synaptic potentials (fEPSP) in acute mouse brain slice preparations to study the effects of orexins and pharmacological inhibitors of multiple kinases on long-term synaptic plasticity in the hippocampus.

RESULTS

Orexin-A (OX-A) but not orexin-B (OX-B) induces a state-dependent long-term potentiation of synaptic transmission (LTP(OX)) at Schaffer collateral-CA1 synapses in hippocampal slices from adult (8- to 12-week-old) mice. In contrast, OX-A applied to slices from juvenile (3- to 4-week-old) animals causes a long-term depression (LTD(OX)) in the same pathway. LTP(OX) is blocked by pharmacological inhibition of orexin receptor-1 (OX1R) and plasticity-related kinases, including serine/threonine- (CaMKII, PKC, PKA, MAPK), lipid- (PI3K), and receptor tyrosine kinases (Trk). Inhibition of OX1R, CaMKII, PKC, PKA and Trk unmasks LTD(OX) in adult animals.

CONCLUSION

Orexins control not only the bistability of arousal states and threshold for appetitive behaviours but, in an age- and kinase-dependent manner, also bidirectional long-term synaptic plasticity in the hippocampus, providing a possible link between behavioural state and memory functions.

Toward a microscopic model of bidirectional synaptic plasticity

We show that a 2-step phospho/dephosphorylation cycle for the alpha-amino-3-hydroxy-5-methyl-4-isoxazole proprionic acid receptor (AMPAR), as used in in vivo learning experiments to assess long-term potentiation (LTP) induction and establishment, exhibits bistability for a wide range of parameters, consistent with values derived from biological literature. The AMPAR model we propose, hence, is a candidate for memory storage and switching behavior at a molecular-microscopic level. Furthermore, the stochastic formulation of the deterministic model leads to a mesoscopic interpretation by considering the effect of enzymatic fluctuations on the Michelis-Menten average dynamics. Under suitable hypotheses, this leads to a stochastic dynamical system with multiplicative noise whose probability density evolves according to a Fokker-Planck equation in the Stratonovich sense. In this approach, the probability density associated with each AMPAR phosphorylation state allows one to compute the probability of any concentration value, whereas the Michaelis-Menten equations consider the average concentration dynamics. We show that bistable dynamics are robust for multiplicative stochastic perturbations and that the presence of both noise and bistability simulates LTP and long-term depression (LTD) behavior. Interestingly, the LTP part of this model has been experimentally verified as a result of in vivo, one-trial inhibitory avoidance learning protocol in rats, that produced the same changes in hippocampal AMPARs phosphorylation state as observed with in vitro induction of LTP with high-frequency stimulation (HFS). A consequence of this model is the possibility of characterizing a molecular switch with a defined biochemical set of reactions showing bistability and bidirectionality. Thus, this 3-enzymes-based biophysical model can predict LTP as well as LTD and their transition rates. The theoretical results can be, in principle, validated by in vitro and in vivo experiments, such as fluorescence measurements and electrophysiological recordings at multiple scales, from molecules to neurons. A further consequence is that the bistable regime occurs only within certain parametric windows, which may simulate a "history-dependent threshold". This effect might be related to the Bienenstock-Cooper-Munro theory of synaptic plasticity.

Experimental and computational aspects of signaling mechanisms of spike-timing-dependent plasticity

STDP (spike-timing-dependent synaptic plasticity) is thought to be a synaptic learning rule that embeds spike-timing information into a specific pattern of synaptic strengths in neuronal circuits, resulting in a memory. STDP consists of bidirectional long-term changes in synaptic strengths. This process includes long-term potentiation and long-term depression, which are dependent on the timing of presynaptic and postsynaptic spikings. In this review, we focus on computational aspects of signaling mechanisms that induce and maintain STDP as a key step toward the definition of a general synaptic learning rule. In addition, we discuss the temporal and spatial aspects of STDP, and the requirement of a homeostatic mechanism of STDP in vivo.