Translational switch for long-term maintenance of synaptic plasticity

Maintenance of synaptic plasticity by negative-feedback of synaptic protein elimination: Dynamic modeling of KIBRA- PKM ζ interactions in LTP and memory

Activity-dependent modifications of synaptic efficacies are a cellular substrate of learning and memory. Current theories propose that the long-term maintenance of synaptic efficacies and memory is accomplished via a positive-feedback loop at the level of production of a protein species or a protein state. Here we propose a qualitatively different theoretical framework based on negative-feedback at the level of protein elimination. This theory is motivated by recent experimental findings regarding the binding of P K M ζ and KIBRA, two synaptic proteins involved in maintenance of memory, and on how this binding affects the proteins' degradation. We demonstrate this theoretical framework with two different models, a simple abstract model to explore generic features of such a process, and an experimentally motivated phenomenological model. The results of these models are qualitatively consistent with existing data, and generate novel predictions that could be experimentally tested to further validate or reject the negative-feedback theory.

Network motifs exhibiting a differential response to spaced and massed inputs

One characteristic of long-term memory is the existence of an inverted U-shaped response to increasing intervals between training sessions, and consequently, an optimal spacing that maximizes memory formation. Current models of this spacing effect focus on specific molecular components and their interactions. Here, we computationally study the underlying network architecture, in particular, the potential of motif dynamics in qualitatively capturing the spacing effect in a manner that is independent of the animal model, biomolecular components, and the timescales involved. We define a common training and test protocol, and computationally identify network topologies that can qualitatively replicate the experimentally observed characteristics of the spacing effect. For 41 motifs derived from fundamental network architectures such as autoregulation, feedback, and feedforward motifs, we tested their capacity to manifest the spacing effect in terms of an inverted U-shaped response curve, using different combinations of stimulation protocols, response metrics, and kinetic parameters. Our findings indicate that positive feedback motifs where the stimulus enhances conversion reaction in the loop replicate the spacing effect across all response metrics, while feedforward motifs exhibit a metric-specific spacing effect. For some parameter combinations, linear cascades of activation and conversion reactions were found sufficient to qualitatively exhibit spacing effect characteristics.

RNA epitranscriptomics dysregulation: A major determinant for significantly increased risk of ASD pathogenesis

Autism spectrum disorders (ASDs) are perhaps the most severe, intractable and challenging child psychiatric disorders. They are complex, pervasive and highly heterogeneous and depend on multifactorial neurodevelopmental conditions. Although the pathogenesis of autism remains unclear, it revolves around altered neurodevelopmental patterns and their implications for brain function, although these cannot be specifically linked to symptoms. While these affect neuronal migration and connectivity, little is known about the processes that lead to the disruption of specific laminar excitatory and inhibitory cortical circuits, a key feature of ASD. It is evident that ASD has multiple underlying causes and this multigenic condition has been considered to also dependent on epigenetic effects, although the exact nature of the factors that could be involved remains unclear. However, besides the possibility for differential epigenetic markings directly affecting the relative expression levels of individual genes or groups of genes, there are at least three mRNA epitranscriptomic mechanisms, which function cooperatively and could, in association with both genotypes and environmental conditions, alter spatiotemporal proteins expression patterns during brain development, at both quantitative and qualitative levels, in a tissue-specific, and context-dependent manner. As we have already postulated, sudden changes in environmental conditions, such as those conferred by maternal inflammation/immune activation, influence RNA epitranscriptomic mechanisms, with the combination of these processes altering fetal brain development. Herein, we explore the postulate whereby, in ASD pathogenesis, RNA epitranscriptomics might take precedence over epigenetic modifications. RNA epitranscriptomics affects real-time differential expression of receptor and channel proteins isoforms, playing a prominent role in central nervous system (CNS) development and functions, but also RNAi which, in turn, impact the spatiotemporal expression of receptors, channels and regulatory proteins irrespective of isoforms. Slight dysregulations in few early components of brain development, could, depending upon their extent, snowball into a huge variety of pathological cerebral alterations a few years after birth. This may very well explain the enormous genetic, neuropathological and symptomatic heterogeneities that are systematically associated with ASD and psychiatric disorders at large.

Conditions for Synaptic Specificity during the Maintenance Phase of Synaptic Plasticity

Activity-dependent modifications of synaptic efficacies are a cellular substrate of learning and memory. Experimental evidence shows that these modifications are synapse specific and that the long-lasting effects are associated with the sustained increase in concentration of specific proteins like PKMζ However, such proteins are likely to diffuse away from their initial synaptic location and spread out to neighboring synapses, potentially compromising synapse specificity. In this article, we address the issue of synapse specificity during memory maintenance. Assuming that the long-term maintenance of synaptic plasticity is accomplished by a molecular switch, we carry out analytical calculations and perform simulations using the reaction-diffusion package in NEURON to determine the limits of synapse specificity during maintenance. Moreover, we explore the effects of the diffusion and degradation rates of proteins and of the geometrical characteristics of dendritic spines on synapse specificity. We conclude that the necessary conditions for synaptic specificity during maintenance require that molecular switches reside in dendritic spines. The requirement for synaptic specificity when the molecular switch resides in spines still imposes strong limits on the diffusion and turnover of rates of maintenance molecules, as well as on the morphologic properties of synaptic spines. These constraints are quite general and apply to most existing models suggested for maintenance. The parameter values can be experimentally evaluated, and if they do not fit the appropriate predicted range, the validity of this class of maintenance models would be challenged.

Comparing Theories for the Maintenance of Late LTP and Long-Term Memory: Computational Analysis of the Roles of Kinase Feedback Pathways and Synaptic Reactivation

A fundamental neuroscience question is how memories are maintained from days to a lifetime, given turnover of proteins that underlie expression of long-term synaptic potentiation (LTP) or “tag” synapses as eligible for LTP. A likely solution relies on synaptic positive feedback loops, prominently including persistent activation of Ca²⁺/calmodulin kinase II (CaMKII) and self-activated synthesis of protein kinase M ζ (PKMζ). Data also suggest positive feedback based on recurrent synaptic reactivation within neuron assemblies, or engrams, is necessary to maintain memories. The relative importance of these mechanisms is controversial. To explore the likelihood that each mechanism is necessary or sufficient to maintain memory, we simulated maintenance of LTP with a simplified model incorporating persistent kinase activation, synaptic tagging, and preferential reactivation of strong synapses, and analyzed implications of recent data. We simulated three model variants, each maintaining LTP with one feedback loop: autonomous, self-activated PKMζ synthesis (model variant I); self-activated CamKII (model variant II); and recurrent reactivation of strengthened synapses (model variant III). Variant I predicts that, for successful maintenance of LTP, either 1) PKMζ contributes to synaptic tagging, or 2) a low constitutive tag level persists during maintenance independent of PKMζ, or 3) maintenance of LTP is independent of tagging. Variant II maintains LTP and suggests persistent CaMKII activation could maintain PKMζ activity, a feedforward interaction not previously considered. However, we note data challenging the CaMKII feedback loop. In Variant III synaptic reactivation drives, and thus predicts, recurrent or persistent activation of CamKII and other necessary kinases, plausibly contributing to persistent elevation of PKMζ levels. Reactivation is thus predicted to sustain recurrent rounds of synaptic tagging and incorporation of plasticity-related proteins. We also suggest (model variant IV) that synaptic reactivation and autonomous kinase activation could synergistically maintain LTP. We propose experiments that could discriminate these maintenance mechanisms.

The mTORC1 inhibitor rapamycin and the mTORC1/2 inhibitor AZD2014 impair the consolidation and persistence of contextual fear memory

RATIONALE

The mechanistic target of rapamycin (mTOR) kinase mediates various long-lasting forms of synaptic and behavioural plasticity. However, there is little information concerning the temporal pattern of mTOR activation and susceptibility to pharmacological intervention during consolidation of contextual fear memory. Moreover, the contribution of both mTOR complex 1 and 2 together or the mTOR complex 1 downstream effector p70S6K (S6K1) to consolidation of contextual fear memory is unknown.

OBJECTIVE

Here, we tested whether different timepoints of vulnerability to rapamycin, a first generation mTOR complex 1 inhibitor, exist for contextual fear memory consolidation and persistence. We also sought to characterize the effects of dually inhibiting mTORC1/2 as well as S6K1 on fear memory formation and persistence.

METHODS

Rapamycin was injected systemically to mice immediately, 3 h, or 12 h after contextual fear conditioning, and retention was measured at different timepoints thereafter. To determine the effects of a single injection of the dual mTROC1/2 inhibitor AZD2014 after learning on memory consolidation and persistence, a dose-response experiment was carried out. Memory formation and persistence was also assessed in response to the S6K1 inhibitor PF-4708671.

RESULTS

A single systemic injection of rapamycin immediately or 3 h, but not 12 h, after learning impaired the formation and persistence of contextual fear memory. AZD2014 was found, with limitations, to dose-dependently attenuate memory consolidation and persistence at the highest dose tested (50 mg/kg). In contrast, PF-4708671 had no effect on consolidation or persistence.

CONCLUSION

Our results indicate the need to further understand the role of mTORC1/2 kinase activity in the molecular mechanisms underlying memory processing and also demonstrate that the effects of mTORC1 inhibition at different timepoints well after learning on memory consolidation and persistence.

How can memories last for days, years, or a lifetime? Proposed mechanisms for maintaining synaptic potentiation and memory

With memory encoding reliant on persistent changes in the properties of synapses, a key question is how can memories be maintained from days to months or a lifetime given molecular turnover? It is likely that positive feedback loops are necessary to persistently maintain the strength of synapses that participate in encoding. Such feedback may occur within signal-transduction cascades and/or the regulation of translation, and it may occur within specific subcellular compartments or within neuronal networks. Not surprisingly, numerous positive feedback loops have been proposed. Some posited loops operate at the level of biochemical signal-transduction cascades, such as persistent activation of Ca²⁺/calmodulin kinase II (CaMKII) or protein kinase Mζ. Another level consists of feedback loops involving transcriptional, epigenetic and translational pathways, and autocrine actions of growth factors such as BDNF. Finally, at the neuronal network level, recurrent reactivation of cell assemblies encoding memories is likely to be essential for late maintenance of memory. These levels are not isolated, but linked by shared components of feedback loops. Here, we review characteristics of some commonly discussed feedback loops proposed to underlie the maintenance of memory and long-term synaptic plasticity, assess evidence for and against their necessity, and suggest experiments that could further delineate the dynamics of these feedback loops. We also discuss crosstalk between proposed loops, and ways in which such interaction can facilitate the rapidity and robustness of memory formation and storage.

A continuous model of physiological prion aggregation suggests a role for Orb2 in gating long-term synaptic information

The regulation of mRNA translation at the level of the synapse is believed to be fundamental in memory and learning at the cellular level. The family of cytoplasmic polyadenylation element binding (CPEB) proteins emerged as an important RNA-binding protein family during development and in adult neurons. Drosophila Orb2 (homologue of mouse CPEB3 protein and of the neural isoform of Aplysia CPEB) has been found to be involved in the translation of plasticity-dependent mRNAs and has been associated with long-term memory. Orb2 protein presents two main isoforms, Orb2A and Orb2B, which form an activity-induced amyloid-like functional aggregate, thought to be the translation-inducing state of the RNA-binding protein. Here we present a first two-states continuous differential model for Orb2A-Orb2B aggregation. This model provides new working hypotheses for studying the role of prion-like CPEB proteins in long-term synaptic plasticity. Moreover, this model can be used as a first step to integrate translation- and protein aggregation-dependent phenomena in synaptic facilitation rules.

Subunit exchange enhances information retention by CaMKII in dendritic spines

Molecular bistables are strong candidates for long-term information storage, for example, in synaptic plasticity. Calcium/calmodulin-dependent protein Kinase II (CaMKII) is a highly expressed synaptic protein which has been proposed to form a molecular bistable switch capable of maintaining its state for years despite protein turnover and stochastic noise. It has recently been shown that CaMKII holoenzymes exchange subunits among themselves. Here, we used computational methods to analyze the effect of subunit exchange on the CaMKII pathway in the presence of diffusion in two different micro-environments, the post synaptic density (PSD) and spine cytosol. We show that CaMKII exhibits multiple timescales of activity due to subunit exchange. Further, subunit exchange enhances information retention by CaMKII both by improving the stability of its switching in the PSD, and by slowing the decay of its activity in the spine cytosol. The existence of diverse timescales in the synapse has important theoretical implications for memory storage in networks.

Computational principles of memory

The ability to store and later use information is essential for a variety of adaptive behaviors, including integration, learning, generalization, prediction and inference. In this Review, we survey theoretical principles that can allow the brain to construct persistent states for memory. We identify requirements that a memory system must satisfy and analyze existing models and hypothesized biological substrates in light of these requirements. We also highlight open questions, theoretical puzzles and problems shared with computer science and information theory.

Atypical PKCs in memory maintenance: the roles of feedback and redundancy

Memories that last a lifetime are thought to be stored, at least in part, as persistent enhancement of the strength of particular synapses. The synaptic mechanism of these persistent changes, late long-term potentiation (L-LTP), depends on the state and number of specific synaptic proteins. Synaptic proteins, however, have limited dwell times due to molecular turnover and diffusion, leading to a fundamental question: how can this transient molecular machinery store memories lasting a lifetime? Because the persistent changes in efficacy are synapse-specific, the underlying molecular mechanisms must to a degree reside locally in synapses. Extensive experimental evidence points to atypical protein kinase C (aPKC) isoforms as key components involved in memory maintenance. Furthermore, it is evident that establishing long-term memory requires new protein synthesis. However, a comprehensive model has not been developed describing how these components work to preserve synaptic efficacies over time. We propose a molecular model that can account for key empirical properties of L-LTP, including its protein synthesis dependence, dependence on aPKCs, and synapse-specificity. Simulations and empirical data suggest that either of the two aPKC subtypes in hippocampal neurons, PKMζ and PKCι/λ, can maintain L-LTP, making the system more robust. Given genetic compensation at the level of synthesis of these PKC subtypes as in knockout mice, this system is able to maintain L-LTP and memory when one of the pathways is eliminated.

Memory maintenance in synapses with calcium-based plasticity in the presence of background activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.

Synaptic plasticity is widely believed to be the main mechanism underlying learning and memory. In recent years, several mathematical plasticity rules have been shown to fit satisfactorily a wide range of experimental data in hippocampal and neocortical in vitro preparations. In particular, a model in which plasticity is driven by the postsynaptic calcium concentration was shown to reproduce successfully how synaptic changes depend on spike timing, specific spike patterns, and firing rate. The advantage of calcium-based rules is the possibility of predicting how changes in extracellular concentrations will affect plasticity. This is particularly significant in the view that in vitro studies are typically done at higher concentrations than the ones measured in vivo. Using such a rule, with parameters fitting in vitro data, we explore how long the memory of a particular synaptic change can be maintained in the presence of background neuronal activity, ubiquitously observed in cortex. We find that the memory time scales increase by several orders of magnitude when calcium concentrations are lowered from typical in vitro experiments to in vivo. Furthermore, we find that synaptic bistability further extends the memory time scale, and estimate that synaptic changes in vivo could be stable on the scale of weeks to months.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

Molecular mechanisms underlying neuronal synaptic plasticity: systems biology meets computational neuroscience in the wilds of synaptic plasticity

Interactions among signaling pathways that are activated by transmembrane receptors produce complex networks and emergent dynamical behaviors that are implicated in synaptic plasticity. Temporal dynamics and spatial aspects are critical determinants of cell responses such as synaptic plasticity, although the mapping between spatiotemporal activity pattern and direction of synaptic plasticity is not completely understood. Computational modeling of neuronal signaling pathways has significantly contributed to understanding signaling pathways underlying synaptic plasticity. Spatial models of signaling pathways in hippocampal neurons have revealed mechanisms underlying the spatial distribution of extracellular signal-related kinase (ERK) activation in hippocampal neurons. Other spatial models have demonstrated that the major role of anchoring proteins in striatal and hippocampal synaptic plasticity is to place molecules near their activators. Simulations of yet other models have revealed that the spatial distribution of synaptic plasticity may differ for potentiation versus depression. In general, the most significant advances have been made by interactive modeling and experiments; thus, an interdisciplinary approach should be applied to investigate critical issues in neuronal signaling pathways. These issues include identifying which transmembrane receptors are key for activating ERK in neurons, and the crucial targets of kinases that produce long-lasting synaptic plasticity. Although the number of computer programs for computationally efficient simulation of large reaction-diffusion networks is increasing, parameter estimation and sensitivity analysis in these spatial models remain more difficult than in single compartment models. Advances in live cell imaging coupled with further software development will continue to accelerate the development of spatial models of synaptic plasticity.

Mathematical modeling of sustainable synaptogenesis by repetitive stimuli suggests signaling mechanisms in vivo

The mechanisms of long-term synaptic maintenance are a key component to understanding the mechanism of long-term memory. From biological experiments, a hypothesis arose that repetitive stimuli with appropriate intervals are essential to maintain new synapses for periods of longer than a few days. We successfully reproduce the time-course of relative numbers of synapses with our mathematical model in the same conditions as biological experiments, which used Adenosine-3', 5'-cyclic monophosphorothioate, Sp-isomer (Sp-cAMPS) as external stimuli. We also reproduce synaptic maintenance responsiveness to intervals of Sp-cAMPS treatment accompanied by PKA activation. The model suggests a possible mechanism of sustainable synaptogenesis which consists of two steps. First, the signal transduction from an external stimulus triggers the synthesis of a new signaling protein. Second, the new signaling protein is required for the next signal transduction with the same stimuli. As a result, the network component is modified from the first network, and a different signal is transferred which triggers the synthesis of another new signaling molecule. We refer to this hypothetical mechanism as network succession. We build our model on the basis of two hypotheses: (1) a multi-step network succession induces downregulation of SSH and COFILIN gene expression, which triggers the production of stable F-actin; (2) the formation of a complex of stable F-actin with Drebrin at PSD is the critical mechanism to achieve long-term synaptic maintenance. Our simulation shows that a three-step network succession is sufficient to reproduce sustainable synapses for a period longer than 14 days. When we change the network structure to a single step network, the model fails to follow the exact condition of repetitive signals to reproduce a sufficient number of synapses. Another advantage of the three-step network succession is that this system indicates a greater tolerance of parameter changes than the single step network.

Dendritic protein synthesis in the normal and diseased brain

Synaptic activity is a spatially limited process that requires a precise, yet dynamic, complement of proteins within the synaptic micro-domain. The maintenance and regulation of these synaptic proteins is regulated, in part, by local mRNA translation in dendrites. Protein synthesis within the postsynaptic compartment allows neurons tight spatial and temporal control of synaptic protein expression, which is critical for proper functioning of synapses and neural circuits. In this review, we discuss the identity of proteins synthesized within dendrites, the receptor-mediated mechanisms regulating their synthesis, and the possible roles for these locally synthesized proteins. We also explore how our current understanding of dendritic protein synthesis in the hippocampus can be applied to new brain regions and to understanding the pathological mechanisms underlying varied neurological diseases.

Translational control by changes in poly(A) tail length: recycling mRNAs

Beyond the well-known function of poly(A) tail length in mRNA stability, recent years have witnessed an explosion of information about how changes in tail length and the selection of alternative polyadenylation sites contribute to the translational regulation of a large portion of the genome. The mechanisms and factors mediating nuclear and cytoplasmic changes in poly(A) tail length have been studied in great detail, the targets of these mechanisms have been identified--in some cases by genome-wide screenings--and changes in poly(A) tail length are now implicated in a number of physiological and pathological processes. However, in very few cases have all three levels--mechanisms, targets and functions--been studied together.

Memory-enhancing intra-basolateral amygdala infusions of clenbuterol increase Arc and CaMKIIα protein expression in the rostral anterior cingulate cortex

Activation of β-adrenoceptors in the basolateral complex of the amygdala (BLA) modulates memory through interactions with multiple memory systems. The cellular mechanisms for this interaction remain unresolved. Memory-modulating BLA manipulations influence expression of the protein product of the immediate early gene activity-regulated cytoskeletal-associated protein (Arc) in the dorsal hippocampus, and hippocampal expression of Arc protein is critically involved in memory consolidation and long-term potentiation. The present studies examined whether this influence of the BLA is specific to the hippocampus and to Arc protein. Like the hippocampus, the rostral portion of the anterior cingulate cortex (rACC) is involved in the consolidation of inhibitory avoidance (IA) memory, and IA training increases Arc protein in the rACC. Because the BLA interacts with the rACC in the consolidation of IA memory, the rACC is a potential candidate for further studies of BLA modulation of synaptic plasticity. The alpha isoform of the Calcium/Calmodulin-dependent protein kinase II (CaMKIIα) and the immediate early gene c-Fos are involved in long-term potentiation and memory. Both Arc and CaMKIIα proteins can be translated in isolated synapses, where the mRNA is localized, but c-Fos protein remains in the soma. To examine the influence of memory-modulating manipulations of the BLA on expression of these memory and plasticity-associated proteins in the rACC, male Sprague-Dawley rats were trained on an IA task and given intra-BLA infusions of either clenbuterol or lidocaine immediately after training. Findings suggest that noradrenergic stimulation of the BLA may modulate memory consolidation through effects on both synaptic proteins Arc and CaMKIIα, but not the somatic protein c-Fos. Furthermore, protein changes observed in the rACC following BLA manipulations suggest that the influence of the BLA on synaptic proteins is not limited to those in the dorsal hippocampus.

A mathematical model for astrocytes mediated LTP at single hippocampal synapses

Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which elucidate the role of astrocyte over Long-term Potentiation (LTP). Recently, Perea and Araque (Science 317:1083-1086, 2007) demonstrated a role of astrocytes in induction of LTP at single hippocampal synapses. They suggested a purely pre-synaptic basis for induction of this N-methyl-D-Aspartate (NMDA) Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic induction were not investigated. Here, in this article, we propose a mathematical model for astrocyte modulated LTP which successfully imitates the experimental findings of Perea and Araque (Science 317:1083-1086, 2007). Our study suggests the role of retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically modulated LTP.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity.

Trafficking motifs as the basis for two-compartment signaling systems to form multiple stable states

Transport of molecules in cells is a central part of cell biology. Frequently such trafficking is not just for material transport, but also for information propagation, and serves to couple signaling circuits across cellular compartments. Here, I show that trafficking transforms simple local signaling pathways into self-organizing systems that span compartments and confer distinct states and identities to these compartments. I find that three motifs encapsulate the responses of most single-compartment signaling pathways in the context of trafficking. These motifs combine with different trafficking reactions to generate a diverse set of cellular functions. For example, trafficked bistable switches can oscillate or become quad- or tristable, depending on trafficking mechanisms and rates. Furthermore, the analysis shows how compartments participating in traffic can settle to distinct molecular compositions characteristic of distinct organelle identities. This general framework shows how the interplay between molecular movement and local reactions can generate many system functions, and give distinct identities to different parts of the cell.

Cerebellar supervised learning revisited: biophysical modeling and degrees-of-freedom control

The biophysical models of spike-timing-dependent plasticity have explored dynamics with molecular basis for such computational concepts as coincidence detection, synaptic eligibility trace, and Hebbian learning. They overall support different learning algorithms in different brain areas, especially supervised learning in the cerebellum. Because a single spine is physically very small, chemical reactions at it are essentially stochastic, and thus sensitivity-longevity dilemma exists in the synaptic memory. Here, the cascade of excitable and bistable dynamics is proposed to overcome this difficulty. All kinds of learning algorithms in different brain regions confront with difficult generalization problems. For resolution of this issue, the control of the degrees-of-freedom can be realized by changing synchronicity of neural firing. Especially, for cerebellar supervised learning, the triangle closed-loop circuit consisting of Purkinje cells, the inferior olive nucleus, and the cerebellar nucleus is proposed as a circuit to optimally control synchronous firing and degrees-of-freedom in learning.

Calcium messenger heterogeneity: a possible signal for spike timing-dependent plasticity

Calcium concentrations as well as time courses have been used to model the signaling cascades leading to changes in the strength of synaptic connections. Previous models consider the dendritic spines as uniform compartments regarding calcium signaling. However, calcium concentrations can vary drastically on distances much smaller than typical spine sizes, and downstream targets of calcium signals are often found exactly in these calcium nanodomains. Even though most downstream targets are activated by calcium via calmodulin, which is a diffusive molecule, the capacity of calmodulin to bind to its targets even when it is not fully loaded with calcium allows its downstream cascade to be highly local. In this study, a model is proposed which uses the heterogeneity of calcium concentrations as a signal for spike-timing-dependent plasticity (STDP). The model is minimalistic and includes three sources of calcium in spines: NMDA receptors (NMDARs), voltage gated calcium channels (VGCCs) and IP3 receptors (IP3Rs). It is based on the biochemical cascades and assumption of spatial locations of four calcium-dependent enzymes: calcium/calmodulin-dependent protein kinase II located near NMDARs, calcineurin located near VGCCs, cyclic nucleotide phosphodiesterase (PDE) located near IP3Rs or NMDARs and adenylyl cyclase, located between VDCCs and NMDARs. To quantify the changes in synaptic weights the model also includes a simple description of AMPA receptor insertion in the membrane and docking to the postsynaptic density. Two parameters of the model are tuned such that weight changes produced by either pre or postsynaptic firing alone are minimal. The model reproduces the typical shape of STDP for spike doublets. If PDE is located near IP3Rs, the behavior for spike triplets is consistent with that observed in hippocampal cell culture; if near NMDAR, the behavior is similar to that observed in cortical L2/3 slices.

The protein kinase Mζ network as a bistable switch to store neuronal memory

Background

Protein kinase Mζ (PKMζ), the brain-specific, atypical protein kinase C isoform, plays a key role in long-term maintenance of memory. This molecule is essential for long-term potentiation of the neuron and various modalities of learning such as spatial memory and fear conditioning. It is unknown, however, how PKMζ stores information for long periods of time despite molecular turnover.

Results

We hypothesized that PKMζ forms a bistable switch because it appears to constitute a positive feedback loop (PKMζ induces its local synthesis) part of which is ultrasensitive (PKMζ stimulates its synthesis through dual pathways). To examine this hypothesis, we modeled the biochemical network of PKMζ with realistic kinetic parameters. Bifurcation analyses of the model showed that the system maintains either the up state or the down state according to previous inputs. Furthermore, the model was able to reproduce a variety of previous experimental results regarding synaptic plasticity and learning, which suggested that it captures the essential mechanism for neuronal memory. We proposed in vitro and in vivo experiments that would critically examine the validity of the model and illuminate the pivotal role of PKMζ in synaptic plasticity and learning.

Conclusions

This study revealed bistability of the PKMζ network and supported its pivotal role in long-term storage of memory.

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.

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.

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.

Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches

Synaptic plasticity is thought to underlie learning and memory, but the complexity of the interactions between the ion channels, enzymes and genes that are involved in synaptic plasticity impedes a deep understanding of this phenomenon. Computer modelling has been used to investigate the information processing that is performed by the signalling pathways involved in synaptic plasticity in principal neurons of the hippocampus, striatum and cerebellum. In the past few years, new software developments that combine computational neuroscience techniques with systems biology techniques have allowed large-scale, kinetic models of the molecular mechanisms underlying long-term potentiation and long-term depression. We highlight important advancements produced by these quantitative modelling efforts and introduce promising approaches that use advancements in live-cell imaging.

Pin1 and PKMzeta sequentially control dendritic protein synthesis

Some forms of learning and memory and their electrophysiologic correlate, long-term potentiation (LTP), require dendritic translation. We demonstrate that Pin1 (protein interacting with NIMA 1), a peptidyl-prolyl isomerase, is present in dendritic spines and shafts and inhibits protein synthesis induced by glutamatergic signaling. Pin1 suppression increased dendritic translation, possibly through eukaryotic translation initiation factor 4E (eIF4E) and eIF4E binding proteins 1 and 2 (4E-BP1/2). Consistent with increased protein synthesis, hippocampal slices from Pin(-/-) mice had normal early LTP (E-LTP) but significantly enhanced late LTP (L-LTP) compared to wild-type controls. Protein kinase C zeta (PKCzeta) and protein kinase M zeta (PKMzeta) were increased in Pin1(-/-) mouse brain, and their activity was required to maintain dendritic translation. PKMzeta interacted with and inhibited Pin1 by phosphorylating serine 16. Therefore, glutamate-induced, dendritic protein synthesis is sequentially regulated by Pin1 and PKMzeta signaling.