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

Synaptic Plasticity in the Injured Brain Depends on the Temporal Pattern of Stimulation

Neurostimulation protocols are increasingly used as therapeutic interventions, including for brain injury. In addition to the direct activation of neurons, these stimulation protocols are also likely to have downstream effects on those neurons' synaptic outputs. It is well known that alterations in the strength of synaptic connections (long-term potentiation, LTP; long-term depression, LTD) are sensitive to the frequency of stimulation used for induction; however, little is known about the contribution of the temporal pattern of stimulation to the downstream synaptic plasticity that may be induced by neurostimulation in the injured brain. We explored interactions of the temporal pattern and frequency of neurostimulation in the normal cerebral cortex and after mild traumatic brain injury (mTBI), to inform therapies to strengthen or weaken neural circuits in injured brains, as well as to better understand the role of these factors in normal brain plasticity. Whole-cell (WC) patch-clamp recordings of evoked postsynaptic potentials in individual neurons, as well as field potential (FP) recordings, were made from layer 2/3 of visual cortex in response to stimulation of layer 4, in acute slices from control (naive), sham operated, and mTBI rats. We compared synaptic plasticity induced by different stimulation protocols, each consisting of a specific frequency (1 Hz, 10 Hz, or 100 Hz), continuity (continuous or discontinuous), and temporal pattern (perfectly regular, slightly irregular, or highly irregular). At the individual neuron level, dramatic differences in plasticity outcome occurred when the highly irregular stimulation protocol was used at 1 Hz or 10 Hz, producing an overall LTD in controls and shams, but a robust overall LTP after mTBI. Consistent with the individual neuron results, the plasticity outcomes for simultaneous FP recordings were similar, indicative of our results generalizing to a larger scale synaptic network than can be sampled by individual WC recordings alone. In addition to the differences in plasticity outcome between control (naive or sham) and injured brains, the dynamics of the changes in synaptic responses that developed during stimulation were predictive of the final plasticity outcome. Our results demonstrate that the temporal pattern of stimulation plays a role in the polarity and magnitude of synaptic plasticity induced in the cerebral cortex while highlighting differences between normal and injured brain responses. Moreover, these results may be useful for optimization of neurostimulation therapies to treat mTBI and other brain disorders, in addition to providing new insights into downstream plasticity signaling mechanisms in the normal brain.

A multifarious exploration of synaptic tagging and capture hypothesis in synaptic plasticity: Development of an integrated mathematical model and computational experiments

The synaptic tagging and capture (STC) hypothesis not only explain the integration and association of synaptic activities, but also the formation of learning and memory. The synaptic pathways involved in the synaptic tagging and capture phenomenon are called STC pathways. The STC hypothesis provides a potential explanation of the neuronal and synaptic processes underlying the synaptic consolidation of memories. Several mechanisms and molecules have been proposed to explain the process of memory allocation and synaptic tags, respectively. However, a clear link between the STC hypothesis and memory allocation is still missing because the encoding of memories in neural circuits is mainly associated with strongly recurrently connected groups of neurons. To explore the mechanisms of potential synaptic tagging candidates and their involvement in the process of memory allocation, we develop a mathematical model for a single dendritic spine based on five essential criteria of a synaptic tag. By developing a mathematical model, we attempt to understand the roles of the potentially critical molecular networks underlying the STC and the essential attributes of a synaptic tag. We include essential memory molecules in the STC model that have been identified in earlier studies as crucial for STC pathways. CaMKII activation is critical for the setting of the initial tag; however, coordinated activities with other kinases and the biochemical pathways are necessary for the tag to be stable. PKA modulates NMDAR-mediated Ca²⁺ signalling. Similarly, PKA and ERK crosstalk is essential for Ca²⁺ - mediated protein synthesis during l-LTP. Our theoretical model explains the quantitative contribution of Tags and protein synthesis during l-LTP in synaptic strength.

Computational analysis of memory consolidation following inhibitory avoidance (IA) training in adult and infant rats: Critical roles of CaMKIIα and MeCP2

Key features of long-term memory (LTM), such as its stability and persistence, are acquired during processes collectively referred to as consolidation. The dynamics of biological changes during consolidation are complex. In adult rodents, consolidation exhibits distinct periods during which the engram is more or less resistant to disruption. Moreover, the ability to consolidate memories differs during developmental periods. Although the molecular mechanisms underlying consolidation are poorly understood, the initial stages rely on interacting signaling pathways that regulate gene expression, including brain-derived neurotrophic factor (BDNF) and Ca2+/calmodulin-dependent protein kinase II α (CaMKIIα) dependent feedback loops. We investigated the ways in which these pathways may contribute to developmental and dynamical features of consolidation. A computational model of molecular processes underlying consolidation following inhibitory avoidance (IA) training in rats was developed. Differential equations described the actions of CaMKIIα, multiple feedback loops regulating BDNF expression, and several transcription factors including methyl-CpG binding protein 2 (MeCP2), histone deacetylase 2 (HDAC2), and SIN3 transcription regulator family member A (Sin3a). This model provides novel explanations for the (apparent) rapid forgetting of infantile memory and the temporal progression of memory consolidation in adults. Simulations predict that dual effects of MeCP2 on the expression of bdnf, and interaction between MeCP2 and CaMKIIα, play critical roles in the rapid forgetting of infantile memory and the progress of memory resistance to disruptions. These insights suggest new potential targets of therapy for memory impairment.

Differentiation of adipose-derived stem cells to chondrocytes using electrospraying

An important challenge in the fabrication of tissue engineered constructs for regenerative medical applications is the development of processes capable of delivering cells and biomaterials to specific locations in a consistent manner. Electrospraying live cells has been introduced in recent years as a cell seeding method, but its effect on phenotype nor genotype has not been explored. A promising candidate for the cellular component of these constructs are human adipose-derived stem cells (hASCs), which are multipotent stem cells that can be differentiated into fat, bone, and cartilage cells. They can be easily and safely obtained from adipose tissue, regardless of the age and sex of the donor. Moreover, these cells can be maintained and expanded in culture for long periods of time without losing their differentiation capacity. In this study, hASCs directly incorporated into a polymer solution were electrosprayed, inducing differentiation into chondrocytes, without the addition of any exogenous factors. Multiple studies have demonstrated the effects of exposing hASCs to biomolecules—such as soluble growth factors, chemokines, and morphogens—to induce chondrogenesis. Transforming growth factors (e.g., TGF-β) and bone morphogenetic proteins are particularly known to play essential roles in the induction of chondrogenesis. Although growth factors have great therapeutic potential for cell-based cartilage regeneration, these growth factor-based therapies have presented several clinical complications, including high dose requirements, low half-life, protein instability, higher costs, and adverse effects in vivo. The present data suggests that electrospraying has great potential as hASCs-based therapy for cartilage regeneration.

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.

Modeling suggests combined-drug treatments for disorders impairing synaptic plasticity via shared signaling pathways

Genetic disorders such as Rubinstein-Taybi syndrome (RTS) and Coffin-Lowry syndrome (CLS) cause lifelong cognitive disability, including deficits in learning and memory. Can pharmacological therapies be suggested that improve learning and memory in these disorders? To address this question, we simulated drug effects within a computational model describing induction of late long-term potentiation (L-LTP). Biochemical pathways impaired in these and other disorders converge on a common target, histone acetylation by acetyltransferases such as CREB binding protein (CBP), which facilitates gene induction necessary for L-LTP. We focused on four drug classes: tropomyosin receptor kinase B (TrkB) agonists, cAMP phosphodiesterase inhibitors, histone deacetylase inhibitors, and ampakines. Simulations suggested each drug type alone may rescue deficits in L-LTP. A potential disadvantage, however, was the necessity of simulating strong drug effects (high doses), which could produce adverse side effects. Thus, we investigated the effects of six drug pairs among the four classes described above. These combination treatments normalized impaired L-LTP with substantially smaller individual drug 'doses'. In addition three of these combinations, a TrkB agonist paired with an ampakine and a cAMP phosphodiesterase inhibitor paired with a TrkB agonist or an ampakine, exhibited strong synergism in L-LTP rescue. Therefore, we suggest these drug combinations are promising candidates for further empirical studies in animal models of genetic disorders that impair histone acetylation, L-LTP, and learning.

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.

FindSim: A Framework for Integrating Neuronal Data and Signaling Models

Current experiments touch only small but overlapping parts of very complex subcellular signaling networks in neurons. Even with modern optical reporters and pharmacological manipulations, a given experiment can only monitor and control a very small subset of the diverse, multiscale processes of neuronal signaling. We have developed FindSim (Framework for Integrating Neuronal Data and SIgnaling Models) to anchor models to structured experimental datasets. FindSim is a framework for integrating many individual electrophysiological and biochemical experiments with large, multiscale models so as to systematically refine and validate the model. We use a structured format for encoding the conditions of many standard physiological and pharmacological experiments, specifying which parts of the model are involved, and comparing experiment outcomes with model output. A database of such experiments is run against successive generations of composite cellular models to iteratively improve the model against each experiment, while retaining global model validity. We suggest that this toolchain provides a principled and scalable way to tackle model complexity and diversity of data sources.

AMPA receptor trafficking and its role in heterosynaptic plasticity

Historically, long-term potentiation (LTP) and long-term depression (LTD), the best-characterized forms of long-term synaptic plasticity, are viewed as experience-dependent and input-specific processes. However, cumulative experimental and theoretical data have demonstrated that LTP and LTD can promote compensatory alterations in non-stimulated synapses. In this work, we have developed a computational model of a tridimensional spiny dendritic segment to investigate the role of AMPA receptor (AMPAR) trafficking during synaptic plasticity at specific synapses and its consequences for the populations of AMPAR at nearby synapses. Our results demonstrated that the mechanisms of AMPAR trafficking involved with LTP and LTD can promote heterosynaptic plasticity at non-stimulated synapses. These alterations are compensatory and arise from molecular competition. Moreover, the heterosynaptic changes observed in our model can modulate further activity-driven inductions of synaptic plasticity.

Synaptic input sequence discrimination on behavioral timescales mediated by reaction-diffusion chemistry in dendrites

Sequences of events are ubiquitous in sensory, motor, and cognitive function. Key computational operations, including pattern recognition, event prediction, and plasticity, involve neural discrimination of spatio-temporal sequences. Here, we show that synaptically-driven reaction-diffusion pathways on dendrites can perform sequence discrimination on behaviorally relevant time-scales. We used abstract signaling models to show that selectivity arises when inputs at successive locations are aligned with, and amplified by, propagating chemical waves triggered by previous inputs. We incorporated biological detail using sequential synaptic input onto spines in morphologically, electrically, and chemically detailed pyramidal neuronal models based on rat data. Again, sequences were recognized, and local channel modulation downstream of putative sequence-triggered signaling could elicit changes in neuronal firing. We predict that dendritic sequence-recognition zones occupy 5 to 30 microns and recognize time-intervals of 0.2 to 5 s. We suggest that this mechanism provides highly parallel and selective neural computation in a functionally important time range.

Potential of GPCRs to modulate MAPK and mTOR pathways in Alzheimer's disease

Despite efforts to understand the mechanism of neuronal cell death, finding effective therapies for neurodegenerative diseases is still a challenge. Cognitive deficits are often associated with neurodegenerative diseases. Remarkably, in the absence of consensus biomarkers, diagnosis of diseases such as Alzheimer's still relies on cognitive tests. Unfortunately, all efforts to translate findings in animal models to the patients have been unsuccessful. Alzheimer's disease may be addressed from two different points of view, neuroprotection or cognitive enhancement. Based on recent data, the mammalian target of rapamycin (mTOR) pathway arises as a versatile player whose modulation may impact on mechanisms of both neuroprotection and cognition. Whereas direct targeting of mTOR does not seem to constitute a convenient approach in drug discovery, its indirect modulation by other signaling pathways seems promising. In fact, G-protein-coupled receptors (GPCRs) remain the most common 'druggable' targets and as such pharmacological manipulation of GPCRs with selective ligands may modulate phosphatidylinositol-4,5-bisphosphate 3-kinase (PI3K), mitogen-activated protein (MAP) kinase and mTOR signaling pathways. Thus, GPCRs become important targets for potential drug treatments in different neurodegenerative disorders including, but not limited to, Alzheimer's disease. GPCR-mediated modulation of mTOR may take advantage of different GPCRs coupled to different G-dependent and G-independent signal transduction routes, of functional selectivity and/or of biased agonism. Signals mediated by GPCRs may act as coincidence detectors to achieve different benefits in different stages of the neurodegenerative disease.

Linking Memories across Time via Neuronal and Dendritic Overlaps in Model Neurons with Active Dendrites

Memories are believed to be stored in distributed neuronal assemblies through activity-induced changes in synaptic and intrinsic properties. However, the specific mechanisms by which different memories become associated or linked remain a mystery. Here, we develop a simplified, biophysically inspired network model that incorporates multiple plasticity processes and explains linking of information at three different levels: (1) learning of a single associative memory, (2) rescuing of a weak memory when paired with a strong one, and (3) linking of multiple memories across time. By dissecting synaptic from intrinsic plasticity and neuron-wide from dendritically restricted protein capture, the model reveals a simple, unifying principle: linked memories share synaptic clusters within the dendrites of overlapping populations of neurons. The model generates numerous experimentally testable predictions regarding the cellular and sub-cellular properties of memory engrams as well as their spatiotemporal interactions.

The Contribution of Spatial and Temporal Molecular Networks in the Induction of Long-term Memory and Its Underlying Synaptic Plasticity

The ability to form long-lasting memories is critical to survival and thus is highly conserved across the animal kingdom. By virtue of its complexity, this same ability is vulnerable to disruption by a wide variety of neuronal traumas and pathologies. To identify effective therapies with which to treat memory disorders, it is critical to have a clear understanding of the cellular and molecular mechanisms which subserve normal learning and memory. A significant challenge to achieving this level of understanding is posed by the wide range of distinct temporal and spatial profiles of molecular signaling induced by learning-related stimuli. In this review we propose that a useful framework within which to address this challenge is to view the molecular foundation of long-lasting plasticity as composed of unique spatial and temporal molecular networks that mediate signaling both within neurons (such as via kinase signaling) as well as between neurons (such as via growth factor signaling). We propose that evaluating how cells integrate and interpret these concurrent and interacting molecular networks has the potential to significantly advance our understanding of the mechanisms underlying learning and memory formation.

Pancreatic Beta Cell G-Protein Coupled Receptors and Second Messenger Interactions: A Systems Biology Computational Analysis

Insulin secretory in pancreatic beta-cells responses to nutrient stimuli and hormonal modulators include multiple messengers and signaling pathways with complex interdependencies. Here we present a computational model that incorporates recent data on glucose metabolism, plasma membrane potential, G-protein-coupled-receptors (GPCR), cytoplasmic and endoplasmic reticulum calcium dynamics, cAMP and phospholipase C pathways that regulate interactions between second messengers in pancreatic beta-cells. The values of key model parameters were inferred from published experimental data. The model gives a reasonable fit to important aspects of experimentally measured metabolic and second messenger concentrations and provides a framework for analyzing the role of metabolic, hormones and neurotransmitters changes on insulin secretion. Our analysis of the dynamic data provides support for the hypothesis that activation of Ca²⁺-dependent adenylyl cyclases play a critical role in modulating the effects of glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP) and catecholamines. The regulatory properties of adenylyl cyclase isoforms determine fluctuations in cytoplasmic cAMP concentration and reveal a synergistic action of glucose, GLP-1 and GIP on insulin secretion. On the other hand, the regulatory properties of phospholipase C isoforms determine the interaction of glucose, acetylcholine and free fatty acids (FFA) (that act through the FFA receptors) on insulin secretion. We found that a combination of GPCR agonists activating different messenger pathways can stimulate insulin secretion more effectively than a combination of GPCR agonists for a single pathway. This analysis also suggests that the activators of GLP-1, GIP and FFA receptors may have a relatively low risk of hypoglycemia in fasting conditions whereas an activator of muscarinic receptors can increase this risk. This computational analysis demonstrates that study of second messenger pathway interactions will improve understanding of critical regulatory sites, how different GPCRs interact and pharmacological targets for modulating insulin secretion in type 2 diabetes.

The right time to learn: mechanisms and optimization of spaced learning

For many types of learning, spaced training, which involves repeated long inter-trial intervals, leads to more robust memory formation than does massed training, which involves short or no intervals. Several cognitive theories have been proposed to explain this superiority, but only recently have data begun to delineate the underlying cellular and molecular mechanisms of spaced training, and we review these theories and data here. Computational models of the implicated signalling cascades have predicted that spaced training with irregular inter-trial intervals can enhance learning. This strategy of using models to predict optimal spaced training protocols, combined with pharmacotherapy, suggests novel ways to rescue impaired synaptic plasticity and learning.

Nicotinic Acetylcholine Receptors Sensitize a MAPK-linked Toxicity Pathway on Prolonged Exposure to β-Amyloid

Among putative downstream synaptic targets of β-amyloid (Aβ) are signaling molecules involved in synaptic function, memory formation and cognition, such as the MAP kinases, MKPs, CaMKII, CREB, Fyn, and Tau. Here, we assessed the activation and interaction of signaling pathways upon prolonged exposure to Aβ in model nerve cells expressing nicotinic acetylcholine receptors (nAChRs). Our goal was to characterize the steps underlying sensitization of the nerve cells to neurotoxicity when Aβ-target receptors are present. Of particular focus was the connection of the activated signaling molecules to oxidative stress. Differentiated neuroblastoma cells expressing mouse α4β2-nAChRs were exposed to Aβ1-42 for intervals from 30 min to 3 days. The cells and cell-derived protein extracts were then probed for activation of signaling pathway molecules (ERK, JNK, CaMKII, CREB, MARCKS, Fyn, tau). Our results show substantial, progressive activation of ERK in response to nanomolar Aβ exposure, starting at the earliest time point. Increased ERK activation was followed by JNK activation as well as an increased expression of PHF-tau, paralleled by increased levels of reactive oxygen species (ROS). The impact of prolonged Aβ on the levels of pERK, pJNK, and ROS was attenuated by MEK-selective and JNK-selective inhibitors. In addition, the MEK inhibitor as well as a JNK inhibitor attenuated Aβ-induced nuclear fragmentation, which followed the changes in ROS levels. These results demonstrate that the presence of nAChRs sensitizes neurons to the neurotoxic action of Aβ through the timed activation of discrete intracellular signaling molecules, suggesting pathways involved in the early stages of Alzheimer disease.

Simulations suggest pharmacological methods for rescuing long-term potentiation

Congenital cognitive dysfunctions are frequently due to deficits in molecular pathways that underlie the induction or maintenance of synaptic plasticity. For example, Rubinstein-Taybi syndrome (RTS) is due to a mutation in cbp, encoding the histone acetyltransferase CREB-binding protein (CBP). CBP is a transcriptional co-activator for CREB, and induction of CREB-dependent transcription plays a key role in long-term memory (LTM). In animal models of RTS, mutations of cbp impair LTM and late-phase long-term potentiation (LTP). As a step toward exploring plausible intervention strategies to rescue the deficits in LTP, we extended our previous model of LTP induction to describe histone acetylation and simulated LTP impairment due to cbp mutation. Plausible drug effects were simulated by model parameter changes, and many increased LTP. However no parameter variation consistent with a effect of a known drug class fully restored LTP. Thus we examined paired parameter variations consistent with effects of known drugs. A pair that simulated the effects of a phosphodiesterase inhibitor (slowing cAMP degradation) concurrent with a deacetylase inhibitor (prolonging histone acetylation) restored normal LTP. Importantly these paired parameter changes did not alter basal synaptic weight. A pair that simulated the effects of a phosphodiesterase inhibitor and an acetyltransferase activator was similarly effective. For both pairs strong additive synergism was present. The effect of the combination was greater than the summed effect of the separate parameter changes. These results suggest that promoting histone acetylation while simultaneously slowing the degradation of cAMP may constitute a promising strategy for restoring deficits in LTP that may be associated with learning deficits in RTS. More generally these results illustrate how the strategy of combining modeling and empirical studies may provide insights into the design of effective therapies for improving long-term synaptic plasticity and learning associated with cognitive disorders.

Deficit in long-term synaptic plasticity is rescued by a computationally predicted stimulus protocol

Mutations in the gene encoding CREB-binding protein (CBP) cause deficits in long-term plasticity, learning, and memory. Here, long-term synaptic facilitation (LTF) at Aplysia sensorimotor synapses in cell culture was used as a model system to investigate methods for overcoming deficits in LTF produced by a CBP knockdown. Injecting CBP-siRNA into individual sensory neurons reduced CBP levels and impaired LTF produced by a standard protocol of five 5-min pulses of serotonin (5-HT) delivered at 20 min interstimulus intervals. A computational model, which simulated molecular processes underlying LTF induction, predicted a rescue protocol of five pulses of 5-HT at non-uniform interstimulus intervals that overcame the consequences of reduced CBP and restored LTF. These results suggest that complementary empirical and computational studies can identify methods for ameliorating impairments of learning attributable to molecular lesions.

Molecular constraints on synaptic tagging and maintenance of long-term potentiation: a predictive model

Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of protein kinase M ζ (PKMζ) is thought essential for maintaining LTP. Additional spatial and temporal features that govern LTP and LTD induction are embodied in the synaptic tagging and capture (STC) and cross capture hypotheses. Only synapses that have been “tagged” by a stimulus sufficient for LTP and learning can “capture” PKMζ. A model was developed to simulate the dynamics of key molecules required for LTP and LTD. The model concisely represents relationships between tagging, capture, LTD, and LTP maintenance. The model successfully simulated LTP maintained by persistent synaptic PKMζ, STC, LTD, and cross capture, and makes testable predictions concerning the dynamics of PKMζ. The maintenance of LTP, and consequently of at least some forms of long-term memory, is predicted to require continual positive feedback in which PKMζ enhances its own synthesis only at potentiated synapses. This feedback underlies bistability in the activity of PKMζ. Second, cross capture requires the induction of LTD to induce dendritic PKMζ synthesis, although this may require tagging of a nearby synapse for LTP. The model also simulates the effects of PKMζ inhibition, and makes additional predictions for the dynamics of CaM kinases. Experiments testing the above predictions would significantly advance the understanding of memory maintenance.

A fundamental problem in neurobiology is to understand how memories are maintained for up to years. Long-term potentiation (LTP), an enduring increase in the strength of specific connections (synapses) between neurons, is thought to comprise, at least in part, the substrate of learning and memory. What processes transduce brief stimuli into persistent LTP? Persistent increased activity of an enzyme denoted protein kinase M ζ (PKMζ) is thought essential for maintaining LTP. Only synapses that have been “tagged” by a stimulus, such as stimuli needed for LTP and learning, can “capture” PKMζ. We developed a model simulating dynamics of key molecules required for LTP and its opposite, long-term depression (LTD). The model concisely represents relationships between tagging, capture, LTD, and LTP maintenance. It makes testable predictions concerning the dynamics of PKMζ. The maintenance of LTP and memory is predicted to require positive feedback in which PKMζ enhances its own synthesis at potentiated synapses. Without synaptic capture of PKMζ, no positive feedback would occur. LTD induction is also predicted to increase PKMζ synthesis. The model also makes predictions about regulation of PKMζ synthesis. Experiments testing the above predictions would advance the understanding of memory maintenance.

Coupling of metabolic, second messenger pathways and insulin granule dynamics in pancreatic beta-cells: a computational analysis

Insulin secretory responses to nutrient stimuli and hormonal modulators in pancreatic beta-cells are controlled by a variety of secondary messengers. We have analyzed numerous mechanisms responsible for regulated exocytosis in these cells and present an integrated mathematical model of cytosolic Ca²⁺, cAMP and granule dynamics. The insulin-containing granules in the beta-cell were divided into four classes: a large "reserve" granule pool, a smaller pool of the morphologically docked granules that is chemically 'primed' for release or the "readily releasable pool", and a pool of "restless newcomer granules" that undergoes preferential exocytosis. The model incorporates glucose and other aspects of metabolism, the cAMP amplifying pathway, insulin granule dynamics and the exocyst concept for granule binding. The values of most of the model parameters were inferred from available experimental data. The model can generate both the fast first phase and slow biphasic insulin secretion found experimentally in response to a step increase of membrane potential or of glucose. The numerical simulations have also reproduced a variety of experimental conditions, such as periodic stimulation by high K⁺ and the potentiation induced in islets by pre-incubation with cAMP pathway activators. The explicit incorporation of Ca²⁺ channels, Ca²⁺ and cAMP dynamics allows the model to be further connected to current models for calcium and metabolic dynamics and provides an interpretation of the roles of the triggering and amplifying pathways of glucose-stimulated insulin secretion. The model may be important in the identification of pharmacological targets for improving insulin secretion in type 2 diabetes.

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.

STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python

We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and becoming increasingly complex as new features and new simulation algorithms were added. We solved all of these problems by tightly integrating STEPS with Python, using SWIG to expose our existing simulation code.

Translational switch for long-term maintenance of synaptic plasticity

Memory can last a lifetime, yet synaptic contacts that contribute to the storage of memory are composed of proteins that have much shorter lifetimes. A physiological model of memory formation, long-term potentiation (LTP), has a late protein-synthesis-dependent phase (L-LTP) that can last for many hours in slices or even for days in vivo. Could the activity-dependent synthesis of new proteins account for the persistence of L-LTP and memory? Here, we examine the proposal that a self-sustaining regulation of translation can form a bistable switch that can persistently regulate the on-site synthesis of plasticity-related proteins. We show that an αCaMKII–CPEB1 molecular pair can operate as a bistable switch. Our results imply that L-LTP should produce an increase in the total amount of αCaMKII at potentiated synapses. This study also proposes an explanation for why the application of protein synthesis and αCaMKII inhibitors at the induction and maintenance phases of L-LTP result in very different outcomes.

The effects of cascade length, kinetics and feedback loops on biological signal transduction dynamics in a simplified cascade model

How intracellular signals are propagated with appropriate strength, duration and fidelity over time is poorly understood. To address these issues, intracellular signal transduction was studied both analytically and numerically using a simplified cascade model. The main observations can be summarized as follows: when the response kinetics is of the Michaelis-Menten type, the signal strength will always reach the same magnitude as the cascade length increases, regardless of the type of stimulus applied (i.e. either continuous or unitary pulse). However, when the response kinetics is of the Hill type (Hill coefficient >1), there exists a stimulation threshold. If the stimulus is below the threshold, the signal decays toward zero; in contrast, if the stimulus is above the threshold, the signal amplitude reaches a nonzero steady state. The time taken for the signal to proceed through the cascade increases as the half-maximum point, or Hill coefficient, increases, whereas the duration of the output signal at the end of the cascade decreases as the half-maximum point increases. In the presence of positive feedback, the stimulation threshold increases; under these conditions, the feedback strength necessary for bistability changes (with power-law characteristics) inversely related to the length of the cascade. In the presence of negative feedback, oscillations are induced when the Hill coefficient is greater than 1 and the cascade has more than two steps. Likewise, the feedback strength required to generate oscillations changes (again with power-law characteristics) inversely with the length of the cascade.

Tag-trigger-consolidation: a model of early and late long-term-potentiation and depression

Changes in synaptic efficacies need to be long-lasting in order to serve as a substrate for memory. Experimentally, synaptic plasticity exhibits phases covering the induction of long-term potentiation and depression (LTP/LTD) during the early phase of synaptic plasticity, the setting of synaptic tags, a trigger process for protein synthesis, and a slow transition leading to synaptic consolidation during the late phase of synaptic plasticity. We present a mathematical model that describes these different phases of synaptic plasticity. The model explains a large body of experimental data on synaptic tagging and capture, cross-tagging, and the late phases of LTP and LTD. Moreover, the model accounts for the dependence of LTP and LTD induction on voltage and presynaptic stimulation frequency. The stabilization of potentiated synapses during the transition from early to late LTP occurs by protein synthesis dynamics that are shared by groups of synapses. The functional consequence of this shared process is that previously stabilized patterns of strong or weak synapses onto the same postsynaptic neuron are well protected against later changes induced by LTP/LTD protocols at individual synapses.

Calmodulin-kinases: modulators of neuronal development and plasticity

In the nervous system, many intracellular responses to elevated calcium are mediated by CaM kinases (CaMKs), a family of protein kinases whose activities are initially modulated by binding Ca(2+)/calmodulin and subsequently by protein phosphorylation. One member of this family, CaMKII, is well-established for its effects on modulating synaptic plasticity and learning and memory. However, recent studies indicate that some actions on neuronal development and function attributed to CaMKII may instead or in addition be mediated by other members of the CaMK cascade, such as CaMKK, CaMKI, and CaMKIV. This review summarizes key neuronal functions of the CaMK cascade in signal transduction, gene transcription, synaptic development and plasticity, and behavior. The technical challenges of mapping cellular protein kinase signaling pathways are also discussed.

Calmodulin-kinases: modulators of neuronal development and plasticity

In the nervous system, many intracellular responses to elevated calcium are mediated by CaM kinases (CaMKs), a family of protein kinases whose activities are initially modulated by binding Ca(2+)/calmodulin and subsequently by protein phosphorylation. One member of this family, CaMKII, is well-established for its effects on modulating synaptic plasticity and learning and memory. However, recent studies indicate that some actions on neuronal development and function attributed to CaMKII may instead or in addition be mediated by other members of the CaMK cascade, such as CaMKK, CaMKI, and CaMKIV. This review summarizes key neuronal functions of the CaMK cascade in signal transduction, gene transcription, synaptic development and plasticity, and behavior. The technical challenges of mapping cellular protein kinase signaling pathways are also discussed.

Initiation and propagation of a neuronal intracellular calcium wave

The ability to image calcium movement within individual neurons inspires questions of functionality including whether calcium entry into the nucleus is related to genetic regulation for phenomena such as long term potentiation. Calcium waves have been initiated in hippocampal pyramidal cells with glutmatergic signals both in the presence and absence of back propagating action potentials (BPAPs). The dendritic sites of initiation of these calcium waves within about 100 microm of the soma are thought to be localized near oblique junctions. Stimulation of synapses on oblique dendrites leads to production of inositol 1,4,5-trisphosphate (IP(3)) which diffuses to the apical dendrite igniting awaiting IP(3) receptors (IP(3)Rs) and initiating and propagating catalytic calcium release from the endoplasmic reticulum. We construct a reduced mathematical system which accounts for calcium wave initiation and propagation due to elevated IP(3). Inhomogeneity in IP(3) distribution is responsible for calcium wave initiation versus subthreshold or spatially uniform suprathreshold activation. However, the likelihood that a calcium wave is initiated does not necessarily increase with more calcium entering from BPAPs. For low transient synaptic stimuli, timing between IP(3) generation and BPAPs is critical for calcium wave initiation. We also show that inhomogeneity in IP(3)R density can account for calcium wave directionality. Simulating somatic muscarinic receptor production of IP(3), we can account for the critical difference between calcium wave entry into the soma and failure to do so.

Bistable MAP kinase activity: a plausible mechanism contributing to maintenance of late long-term potentiation

Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (Markevich NI, Hoek JB, Kholodenko BN. J Cell Biol 164: 353–359, 2004) predicts bistability due to interactions of the kinases and phosphatases in the MAPK pathway, without feedback from MAPK to earlier reactions. Using this model and enzyme concentrations appropriate for neurons, we simulated bistable MAPK activity, but bistability was present only within a relatively narrow range of activity of Raf, the first pathway kinase. Stochastic fluctuations in molecule numbers eliminated bistability for small molecule numbers, such as are expected in the volume of a dendritic spine. However, positive-feedback loops have been posited from MAPK up to Raf activation. One proposed loop in which MAPK directly activates Raf was incorporated into the model. We found that such feedback greatly enhanced the robustness of both stable states of MAPK activity to stochastic fluctuations and to parameter variations. Bistability was robust for molecule numbers plausible for a dendritic spine volume. The upper state of MAPK activity was resistant to inhibition of MEK activation for >1 h, which suggests that inhibitor experiments have not sufficed to rule out a role for persistent MAPK activity in the maintenance of long-term potentiation (LTP). These simulations suggest that persistent MAPK activity and consequent upregulation of translation may contribute to LTP maintenance and to long-term memory. Experiments using a fluorescent MAPK substrate may further test this hypothesis.

Gene expression in human hippocampus from cocaine abusers identifies genes which regulate extracellular matrix remodeling

The chronic effects of cocaine abuse on brain structure and function are blamed for the inability of most addicts to remain abstinent. Part of the difficulty in preventing relapse is the persisting memory of the intense euphoria or cocaine “rush”. Most abused drugs and alcohol induce neuroplastic changes in brain pathways subserving emotion and cognition. Such changes may account for the consolidation and structural reconfiguration of synaptic connections with exposure to cocaine. Adaptive hippocampal plasticity could be related to specific patterns of gene expression with chronic cocaine abuse. Here, we compare gene expression profiles in the human hippocampus from cocaine addicts and age-matched drug-free control subjects. Cocaine abusers had 151 gene transcripts upregulated, while 91 gene transcripts were downregulated. Topping the list of cocaine-regulated transcripts was RECK in the human hippocampus (FC = 2.0; p<0.05). RECK is a membrane-anchored MMP inhibitor that is implicated in the coordinated regulation of extracellular matrix integrity and angiogenesis. In keeping with elevated RECK expression, active MMP9 protein levels were decreased in the hippocampus from cocaine abusers. Pathway analysis identified other genes regulated by cocaine that code for proteins involved in the remodeling of the cytomatrix and synaptic connections and the inhibition of blood vessel proliferation (PCDH8, LAMB1, ITGB6, CTGF and EphB4). The observed microarray phenotype in the human hippocampus identified RECK and other region-specific genes that may promote long-lasting structural changes with repeated cocaine abuse. Extracellular matrix remodeling in the hippocampus may be a persisting effect of chronic abuse that contributes to the compulsive and relapsing nature of cocaine addiction.

A new principle for information storage in an enzymatic pathway model

Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activity-dependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans.

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 Ca²⁺. Ongoing activity was modeled as continual brief elevations of Ca²⁺. In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca²⁺ 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.