Voltage- and Calcium-Gated Membrane Currents Tune the Plateau Potential Properties of Multiple Neuron Types

Many neurons exhibit regular firing that is limited to the duration and intensity of depolarizing stimuli. However, some neurons exhibit all-or-nothing plateau potentials that, once elicited, can lead to prolonged activity that is independent of stimulus intensity or duration. To better understand this diversity of information processing, we compared the voltage-gated and Ca2+-gated currents of three identified neurons from hermaphroditic Aplysia californica Two of these neurons, B51 and B64, generated plateau potentials and a third neuron, B8, exhibited regular firing and was incapable of generating a plateau potential. With the exception of the Ca2+-gated potassium current (I KCa), all three neuron types expressed a similar array of outward and inward currents, but with distinct voltage-dependent properties for each neuron type. Inhibiting voltage-gated Ca2+ channels with Ni+ prolonged the plateau potential, indicating I KCa is important for plateau potential termination. In contrast, inhibiting persistent Na+ (I NaP) blocked plateau potentials, empirically and in simulations. Surprisingly, the properties and level of expression of I NaP were similar in all three neurons, indicating that the presence of I NaP does not distinguish between regular-firing neurons and neurons capable of generating plateau potentials. Rather, the key distinguishing factor is the relationship between I NaP and outward currents such as the delayed outward current (I D), and I KCa We then demonstrated a technique for predicting complex physiological properties such as plateau duration, plateau amplitude, and action potential duration as a function of parameter values, by fitting a curve in parameter space and projecting the curve beyond the tested values.SIGNIFICANCE STATEMENT Plateau potentials are intrinsic properties of neurons that are important for information processing in a wide variety of nervous systems. We examined three identified neurons in Aplysia californica with different propensities to generate a plateau potential. No single conductance was found to distinguish plateau generating neurons. Instead, plateau generation depended on the ratio between persistent Na+ current (I NaP), which favored plateaus, and outward currents such as I KCa, which facilitated plateau termination. Computational models revealed a relationship between the individual currents that predicted the features of simulated plateau potentials. These results provide a more solid understanding of the conductances that mediate plateau generation.

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.

Specific Plasticity Loci and Their Synergism Mediate Operant Conditioning

Despite numerous studies examining the mechanisms of operant conditioning (OC), the diversity of OC plasticity loci and their synergism have not been examined sufficiently. In the well-characterized feeding neural circuit of Aplysia, in vivo and in vitro appetitive OC increases neuronal excitability and electrical coupling among several neurons leading to an increase in expression of ingestive behavior. Here, we used the in vitro analog of OC to investigate whether OC reduces the excitability of a neuron, B4, whose inhibitory connections decrease expression of ingestive behavior. We found OC decreased the excitability of B4. This change appeared intrinsic to B4 because it could be replicated with an analog of OC in isolated cultures of B4 neurons. In addition to changes in B4 excitability, OC decreased the strength of B4's inhibitory connection to a key decision-making neuron, B51. The OC-induced changes were specific without affecting the excitability of another neuron critical for feeding behavior, B8, or the B4-to-B8 inhibitory connection. A conductance-based circuit model indicated that reducing the B4-to-B51 synapse, or increasing B51 excitability, mediated the OC phenotype more effectively than did decreasing B4 excitability. We combined these modifications to examine whether they could act synergistically. Combinations including B51 synergistically enhanced feeding. Taken together, these results suggest modifications of diverse loci work synergistically to mediate OC and that some neurons are well suited to work synergistically with plasticity in other loci.SIGNIFICANCE STATEMENT The ways in which synergism of diverse plasticity loci mediate the change in motor patterns in operant conditioning (OC) are poorly understood. Here, we found that OC was in part mediated by decreasing the intrinsic excitability of a critical neuron of Aplysia feeding behavior, and specifically reducing the strength of one of its inhibitory connections that targets a key decision-making neuron. A conductance-based computational model indicated that the known plasticity loci showed a surprising level of synergism to mediate the behavioral changes associated with OC. These results highlight the importance of understanding the diversity, specificity and synergy among different types of plasticity that encode memory. Also, because OC in Aplysia is mediated by dopamine (DA), the present study provides insights into specific and synergistic mechanisms of DA-mediated reinforcement of behaviors.

Neuronal population activity dynamics reveal a low-dimensional signature of operant learning in Aplysia

Learning engages a high-dimensional neuronal population space spanning multiple brain regions. However, it remains unknown whether it is possible to identify a low-dimensional signature associated with operant conditioning, a ubiquitous form of learning in which animals learn from the consequences of behavior. Using single-neuron resolution voltage imaging, here we identify two low-dimensional motor modules in the neuronal population underlying Aplysia feeding. Our findings point to a temporal shift in module recruitment as the primary signature of operant learning. Our findings can help guide characterization of learning signatures in systems in which only a smaller fraction of the relevant neuronal population can be monitored.

Costa et al. use single-neuron resolution voltage imaging to identify two low-dimensional motor modules in the neuronal population underlying Aplysia feeding. Their findings point to a temporal shift in module recruitment as the primary signature of operant learning.

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.

Computational model of the distributed representation of operant reward memory: combinatoric engagement of intrinsic and synaptic plasticity mechanisms

Operant reward learning of feeding behavior in Aplysia increases the frequency and regularity of biting, as well as biases buccal motor patterns (BMPs) toward ingestion-like BMPs (iBMPs). The engram underlying this memory comprises cells that are part of a central pattern generating (CPG) circuit and includes increases in the intrinsic excitability of identified cells B30, B51, B63, and B65, and increases in B63-B30 and B63-B65 electrical synaptic coupling. To examine the ways in which sites of plasticity (individually and in combination) contribute to memory expression, a model of the CPG was developed. The model included conductance-based descriptions of cells CBI-2, B4, B8, B20, B30, B31, B34, B40, B51, B52, B63, B64, and B65, and their synaptic connections. The model generated patterned activity that resembled physiological BMPs, and implementation of the engram reproduced increases in frequency, regularity, and bias. Combined enhancement of B30, B63, and B65 excitabilities increased BMP frequency and regularity, but not bias toward iBMPs. Individually, B30 increased regularity and bias, B51 increased bias, B63 increased frequency, and B65 decreased all three BMP features. Combined synaptic plasticity contributed primarily to regularity, but also to frequency and bias. B63-B30 coupling contributed to regularity and bias, and B63-B65 coupling contributed to all BMP features. Each site of plasticity altered multiple BMP features simultaneously. Moreover, plasticity loci exhibited mutual dependence and synergism. These results indicate that the memory for operant reward learning emerged from the combinatoric engagement of multiple sites of plasticity.

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.

Paradoxical LTP maintenance with inhibition of protein synthesis and the proteasome suggests a novel protein synthesis requirement for early LTP reversal

The transition from early long-term potentiation (E-LTP) to late long-term potentiation (L-LTP) is a multistep process that involves both protein synthesis and degradation. The ways in which these two opposing processes interact to establish L-LTP are not well understood, however. For example, L-LTP is attenuated by inhibiting either protein synthesis or proteasome-dependent degradation prior to and during a tetanic stimulus (e.g., Huang et al., 1996; Karpova et al., 2006), but paradoxically, L-LTP is not attenuated when synthesis and degradation are inhibited simultaneously (Fonseca et al., 2006). These paradoxical results suggest that counter-acting 'positive' and 'negative' proteins regulate L-LTP. To investigate the basis of this paradox, we developed a model of LTP at the Schaffer collateral to CA1 pyramidal cell synapse. The model consists of nine ordinary differential equations that describe the levels of both positive- and negative-regulator proteins (PP and NP, respectively) and the transitions among five discrete synaptic states, including a basal state (BAS), three states corresponding to E-LTP (EP1, EP2, and ED), and a L-LTP state (LP). An LTP-inducing stimulus: 1) initiates the transition from BAS to EP1 and from EP1 to EP2; 2) initiates the synthesis of PP and NP; and finally; 3) activates the ubiquitin-proteasome system (UPS), which in turn, mediates transitions of EP1 and EP2 to ED and the degradation of NP. The conversion of E-LTP to L-LTP is mediated by the PP-dependent transition from ED to LP, whereas NP mediates reversal of EP2 to BAS. We found that the inclusion of the five discrete synaptic states was necessary to simulate key empirical observations: 1) normal L-LTP, 2) block of L-LTP by either proteasome inhibitor or protein synthesis inhibitor alone, and 3) preservation of L-LTP when both inhibitors are applied together. Although our model is abstract, elements of the model can be correlated with specific molecular processes. Moreover, the model correctly captures the dynamics of protein synthesis- and degradation-dependent phases of LTP, and it makes testable predictions, such as a unique synaptic state (ED) that precedes the transition from E-LTP to L-LTP, and a well-defined time window for the action of the UPS (i.e., during the transitions from EP1 and EP2 to ED). Tests of these predictions will provide new insights into the processes and dynamics of long-term synaptic plasticity.

Unique Configurations of Compression and Truncation of Neuronal Activity Underlie l-DOPA-Induced Selection of Motor Patterns in Aplysia

A key issue in neuroscience is understanding the ways in which neuromodulators such as dopamine modify neuronal activity to mediate selection of distinct motor patterns. We addressed this issue by applying either low or high concentrations of l-DOPA (40 or 250 μM) and then monitoring activity of up to 130 neurons simultaneously in the feeding circuitry of Aplysia using a voltage-sensitive dye (RH-155). l-DOPA selected one of two distinct buccal motor patterns (BMPs): intermediate (low l-DOPA) or bite (high l-DOPA) patterns. The selection of intermediate BMPs was associated with shortening of the second phase of the BMP (retraction), whereas the selection of bite BMPs was associated with shortening of both phases of the BMP (protraction and retraction). Selection of intermediate BMPs was also associated with truncation of individual neuron spike activity (decreased burst duration but no change in spike frequency or burst latency) in neurons active during retraction. In contrast, selection of bite BMPs was associated with compression of spike activity (decreased burst latency and duration and increased spike frequency) in neurons projecting through specific nerves, as well as increased spike frequency of protraction neurons. Finally, large-scale voltage-sensitive dye recordings delineated the spatial distribution of neurons active during BMPs and the modification of that distribution by the two concentrations of l-DOPA.

Inferring neuronal network functional connectivity with directed information

A major challenge in neuroscience is to develop effective tools that infer the circuit connectivity from large-scale recordings of neuronal activity patterns. In this study, context tree maximizing (CTM) was used to estimate directed information (DI), which measures causal influences among neural spike trains in order to infer putative synaptic connections. In contrast to existing methods, the method presented here is data driven and can readily identify both linear and nonlinear relations between neurons. This CTM-DI method reliably identified circuit structures underlying simulations of realistic conductance-based networks. It also inferred circuit properties from voltage-sensitive dye recordings of the buccal ganglion of Aplysia. This method can be applied to other large-scale recordings as well. It offers a systematic tool to map network connectivity and to track changes in network structure such as synaptic strengths as well as the degrees of connectivity of individual neurons, which in turn could provide insights into how modifications produced by learning are distributed in a neural network.NEW & NOTEWORTHY This study brings together the techniques of voltage-sensitive dye recording and information theory to infer the functional connectome of the feeding central pattern generating network of Aplysia. In contrast to current statistical approaches, the inference method developed in this study is data driven and validated by conductance-based model circuits, can distinguish excitatory and inhibitory connections, is robust against synaptic plasticity, and is capable of detecting network structures that mediate motor patterns.

Computational model of a positive BDNF feedback loop in hippocampal neurons following inhibitory avoidance training

Inhibitory avoidance (IA) training in rodents initiates a molecular cascade within hippocampal neurons. This cascade contributes to the transition of short- to long-term memory (i.e., consolidation). Here, a differential equation-based model was developed to describe a positive feedback loop within this molecular cascade. The feedback loop begins with an IA-induced release of brain-derived neurotrophic factor (BDNF), which in turn leads to rapid phosphorylation of the cAMP response element-binding protein (pCREB), and a subsequent increase in the level of the β isoform of the CCAAT/enhancer binding protein (C/EBPβ). Increased levels of C/EBPβ lead to increased bdnf expression. Simulations predicted that an empirically observed delay in the BDNF-pCREB-C/EBPβ feedback loop has a profound effect on the dynamics of consolidation. The model also predicted that at least two independent self-sustaining signaling pathways downstream from the BDNF-pCREB-C/EBPβ feedback loop contribute to consolidation. Currently, the nature of these downstream pathways is unknown.

Contribution of PKC to the maintenance of 5-HT-induced short-term facilitation at sensorimotor synapses of Aplysia

Aplysia sensorimotor synapses provide a useful model system for analyzing molecular processes that contribute to heterosynaptic plasticity. For example, previous studies demonstrated that multiple kinase cascades contribute to serotonin (5-HT)-induced short-term synaptic facilitation (STF), including protein kinase A (PKA) and protein kinase C (PKC). Moreover, the contribution of each kinase is believed to depend on the state of the synapse (e.g., depressed or nondepressed) and the time after application of 5-HT. Here, a previously unappreciated role for PKC-dependent processes was revealed to underlie the maintenance of STF at relatively nondepressed synapses. This PKC dependence was revealed when the synapse was stimulated repeatedly after application of 5-HT. The contributions of the PKA and PKC pathways were examined by blocking adenylyl cyclase-coupled 5-HT receptors with methiothepin and by blocking PKC with chelerythrine. STF was assessed 20 s after 5-HT application. The effects of PKC were consistent with enhanced mobilization of transmitter, as assessed by application of hypertonic sucrose solutions to measure the readily releasable pool of vesicles and recovery of the readily releasable pool after depletion. A computational model of transmitter release demonstrated that a PKC-dependent mobilization process was sufficient to explain the maintenance of STF at nondepressed synapses and the facilitation of depressed synapses.

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.

Computational analyses of synergism in small molecular network motifs

Cellular functions and responses to stimuli are controlled by complex regulatory networks that comprise a large diversity of molecular components and their interactions. However, achieving an intuitive understanding of the dynamical properties and responses to stimuli of these networks is hampered by their large scale and complexity. To address this issue, analyses of regulatory networks often focus on reduced models that depict distinct, reoccurring connectivity patterns referred to as motifs. Previous modeling studies have begun to characterize the dynamics of small motifs, and to describe ways in which variations in parameters affect their responses to stimuli. The present study investigates how variations in pairs of parameters affect responses in a series of ten common network motifs, identifying concurrent variations that act synergistically (or antagonistically) to alter the responses of the motifs to stimuli. Synergism (or antagonism) was quantified using degrees of nonlinear blending and additive synergism. Simulations identified concurrent variations that maximized synergism, and examined the ways in which it was affected by stimulus protocols and the architecture of a motif. Only a subset of architectures exhibited synergism following paired changes in parameters. The approach was then applied to a model describing interlocked feedback loops governing the synthesis of the CREB1 and CREB2 transcription factors. The effects of motifs on synergism for this biologically realistic model were consistent with those for the abstract models of single motifs. These results have implications for the rational design of combination drug therapies with the potential for synergistic interactions.

Cellular responses to stimuli are controlled by complex regulatory networks that comprise many molecular components. Understanding such networks is critical for understanding normal cellular functions and pathological conditions. Because the complexity of these networks often precludes intuitive insights, a useful approach is to study mathematical models of small network motifs having reduced complexity yet consisting of key regulatory components of the more complex networks. Computational studies have analyzed the behavior of small motifs, and have begun to describe the ways in which variations in parameters affect their functional properties. Here, we investigated how variations in pairs of parameters act synergistically (or antagonistically) to alter responses of ten common network motifs. Simulations identified parameter variations that maximized synergism, and examined the ways in which synergism was affected by stimulus protocols and motif architecture. The results have implications for the rational design of combination drug therapies where a goal is to identify drugs that when administered together have a greater effect than would be predicted by simple addition of single-drug effects (i.e., super-additive effects), thereby allowing for lower drug doses, minimizing undesirable effects.

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.

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.

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

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

Molecular mechanisms underlying a cellular analog of operant reward learning

Operant conditioning is a ubiquitous but mechanistically poorly understood form of associative learning in which an animal learns the consequences of its behavior. Using a single-cell analog of operant conditioning in neuron B51 of Aplysia, we examined second-messenger pathways engaged by activity and reward and how they may provide a biochemical association underlying operant learning. Conditioning was blocked by Rp-cAMP, a peptide inhibitor of PKA, a PKC inhibitor, and by expressing a dominant-negative isoform of Ca2+-dependent PKC (apl-I). Thus, both PKA and PKC were necessary for operant conditioning. Injection of cAMP into B51 mimicked the effects of operant conditioning. Activation of PKC also mimicked conditioning but was dependent on both cAMP and PKA, suggesting that PKC acted at some point upstream of PKA activation. Our results demonstrate how these molecules can interact to mediate operant conditioning in an individual neuron important for the expression of the conditioned behavior.

Changes in neuronal excitability serve as a mechanism of long-term memory for operant conditioning

Learning can lead to changes in the intrinsic excitability of neurons. However, it is unclear to what extent these changes persist and what role they play in the expression of memory. Here, we report that in vitro analogues of operant conditioning produce a long-term (24 h) increase in the excitability of an identified neuron (B51) critical for the expression of feeding in Aplysia. This increase in excitability, which is cAMP dependent, contributes to the associative modification of the feeding circuitry, providing a mechanism for long-term memory storage.

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.

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

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

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Feeding behavior of Aplysia: a model system for comparing cellular mechanisms of classical and operant conditioning

Feeding behavior of Aplysia provides an excellent model system for analyzing and comparing mechanisms underlying appetitive classical conditioning and reward operant conditioning. Behavioral protocols have been developed for both forms of associative learning, both of which increase the occurrence of biting following training. Because the neural circuitry that mediates the behavior is well characterized and amenable to detailed cellular analyses, substantial progress has been made toward a comparative analysis of the cellular mechanisms underlying these two forms of associative learning. Both forms of associative learning use the same reinforcement pathway (the esophageal nerve, En) and the same reinforcement transmitter (dopamine, DA). In addition, at least one cellular locus of plasticity (cell B51) is modified by both forms of associative learning. However, the two forms of associative learning have opposite effects on B51. Classical conditioning decreases the excitability of B51, whereas operant conditioning increases the excitability of B51. Thus, the approach of using two forms of associative learning to modify a single behavior, which is mediated by an analytically tractable neural circuit, is revealing similarities and differences in the mechanisms that underlie classical and operant conditioning.

Simulator for neural networks and action potentials

A key challenge for neuroinformatics is to devise methods for representing, accessing, and integrating vast amounts of diverse and complex data. A useful approach to represent and integrate complex data sets is to develop mathematical models [Arbib (The Handbook of Brain Theory and Neural Networks, pp. 741-745, 2003); Arbib and Grethe (Computing the Brain: A Guide to Neuroinformatics, 2001); Ascoli (Computational Neuroanatomy: Principles and Methods, 2002); Bower and Bolouri (Computational Modeling of Genetic and Biochemical Networks, 2001); Hines et al. (J. Comput. Neurosci. 17, 7-11, 2004); Shepherd et al. (Trends Neurosci. 21, 460-468, 1998); Sivakumaran et al. (Bioinformatics 19, 408-415, 2003); Smolen et al. (Neuron 26, 567-580, 2000); Vadigepalli et al. (OMICS 7, 235-252, 2003)]. Models of neural systems provide quantitative and modifiable frameworks for representing data and analyzing neural function. These models can be developed and solved using neurosimulators. One such neurosimulator is simulator for neural networks and action potentials (SNNAP) [Ziv (J. Neurophysiol. 71, 294-308, 1994)]. SNNAP is a versatile and user-friendly tool for developing and simulating models of neurons and neural networks. SNNAP simulates many features of neuronal function, including ionic currents and their modulation by intracellular ions and/or second messengers, and synaptic transmission and synaptic plasticity. SNNAP is written in Java and runs on most computers. Moreover, SNNAP provides a graphical user interface (GUI) and does not require programming skills. This chapter describes several capabilities of SNNAP and illustrates methods for simulating neurons and neural networks. SNNAP is available at http://snnap.uth.tmc.edu .

Teaching basic principles of neuroscience with computer simulations

It is generally believed that students learn best through activities that require their direct participation. By using simulations as a tool for learning neuroscience, students are directly engaged in the activity and obtain immediate feedback and reinforcement. This paper describes a series of biophysical models and computer simulations that can be used by educators and students to explore a variety of basic principles in neuroscience. The paper also suggests 'virtual laboratory' exercises that students may conduct to further examine biophysical processes underlying neural function. First, the Hodgkin and Huxley (HH) model is presented. The HH model is used to illustrate the action potential, threshold phenomena, and nonlinear dynamical properties of neurons (e.g., oscillations, postinhibitory rebound excitation). Second, the Morris-Lecar (ML) model is presented. The ML model is used to develop a model of a bursting neuron and to illustrate modulation of neuronal activity by intracellular ions. Lastly, principles of synaptic transmission are presented in small neural networks, which illustrate oscillatory behavior, excitatory and inhibitory postsynaptic potentials, and temporal summation.

Role of A-type K+ channels in spike broadening observed in soma and axon of Hermissenda type-B photoreceptors: a simulation study

In Hermissenda type-B photoreceptors, the spike is generated in the axon and back-propagated to the soma, resulting in smaller somatic spikes. Experimentally, blocking the A-type K+ current (IK,A) results in broadening of somatic spikes. Similarly, in a compartmental model of the photoreceptor, reducing the maximum A-type K+ conductance (gK,Amax) results in broadening of somatic spikes. However, simulations predict that little or no broadening of axonal spikes occurs when gK,Amax is reduced. The results can be explained by the voltage-dependent properties of IK,A and the different potential ranges that the somatic and axonal spike traverse. Because of the steeper I-V curve and faster activation of the K+ channels at higher potentials, the recruitment of additional K+ channels in the axon is able to compensate for the decrease in K+ conductance, yielding less spike broadening. These results also support the idea that spike duration in the axon may not be reliably inferred based upon recordings collected from the soma.

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

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

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

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

Classical and operant conditioning differentially modify the intrinsic properties of an identified neuron

A long-standing debate in neuroscience is whether classical and operant conditioning are mechanistically similar or distinct. The feeding behavior of Aplysia provides a model system suitable for addressing this question. Here we report that classical and operant conditioning of feeding behavior differentially modify the intrinsic excitability of neuron B51, a critical element for the expression of the feeding response, thus revealing that these two forms of associative learning differ at the cellular level.

Reinforcement in an in vitro analog of appetitive classical conditioning of feeding behavior in Aplysia: blockade by a dopamine antagonist

In a recently developed in vitro analog of appetitive classical conditioning of feeding in Aplysia, the unconditioned stimulus (US) was electrical stimulation of the esophageal nerve (En). This nerve is rich in dopamine (DA)-containing processes, which suggests that DA mediates reinforcement during appetitive conditioning. To test this possibility, methylergonovine was used to antagonize DA receptors. Methylergonovine (1 nM) blocked the pairing-specific increase in fictive feeding that is usually induced by in vitro classical conditioning. The present results and previous observation that methylergonovine also blocks the effects of contingent reinforcement in an in vitro analog of appetitive operant conditioning suggest that DA mediates reinforcement for appetitive associative conditioning of feeding in Aplysia.

Dynamic properties of regulatory motifs associated with induction of three temporal domains of memory in aplysia

A model was developed to examine dynamical properties of regulatory motifs correlated with different temporal domains of memory. The model represents short-, intermediate-, and long-term phases of protein kinase A (PKA) activation, which appear related to corresponding phases of facilitation of the Aplysia sensorimotor synapse. The model also represents phosphorylation of the transcription factor CREB1 by PKA and consequent induction of the immediate-early gene Aplysia ubiquitin hydrolase (Ap-uch), which is essential for long-term synaptic facilitation (LTF). Simulations suggest mechanisms responsible for differing profiles of synaptic facilitation following massed vs. spaced exposures to 5-HT, and suggest a novel regulatory motif (gated positive feedback) is important for LTF. Simulations suggest zero-order ultrasensitivity may underlie a requirement of a threshold number of exposures to 5-HT for LTF induction. The model makes predictions for the dynamics of PKA activation and Ap-uch induction when MAP kinase is activated, or when repression of Ap-uch is relieved by inhibiting the transcription factor CREB2. This model may therefore be useful for understanding processes underlying memory formation in Aplysia and other systems.

Voltage-clamp analysis and computational model of dopaminergic neurons from mouse retina

Isolated dopaminergic amacrine (DA) cells in mouse retina fire rhythmic, spontaneous action potentials and respond to depolarizing current with trains of low-frequency action potentials. To investigate the roles of voltage-gated ion channels in these processes, the transient A-type K+ current (IK,A) and Ca2+ current (ICa) in isolated mouse DA cells were analyzed by voltage clamp. The IK,A activated at −60 mV and inactivated rapidly. ICa activated at around −30 mV and reached a peak at 10 mV without apparent inactivation. We also extended our previous computational model of the mouse DA cell to include the new electrophysiological data. The model consisted of a membrane capacitance in parallel with eight currents: Na+ transient (INa,T), Na+ persistent (INa,P), delayed rectifier potassium (IKdr), IK,A, calcium-dependent potassium (IK,Ca), L-type Ca2+ ICa, hyperpolarization-activated cation current (Ih), and a leak current (IL). Hodgkin-Huxley type equations were used to define the voltage- and time-dependent activation and inactivation. The simulations were implemented using the neurosimulator SNNAP. The model DA cell was spontaneously active from a wide range of initial membrane potentials. The spontaneous action potentials reached 35 mV at the peak and hyperpolarized to −76 mV between spikes. The spontaneous firing frequency in the model was 6 Hz. The model DA cell responded to prolonged depolarizing current injection by increasing its spiking frequency and eventually reaching a depolarization block at membrane potentials greater than −10 mV. The most important current for determining the firing rate was IK,A. When the amplitude of IK,A was decreased, the firing rate increased. ICa and IK,Ca also affected the width of action potentials but had only minor effects on the firing rate. Ih affected the firing rate slightly but did not change the waveform of the action potentials.

Computational Model of Touch Sensory Cells (T Cells) of the Leech: Role of the Afterhyperpolarization (AHP) in Activity-Dependent Conduction Failure

Bursts of spikes in T cells produce an AHP, which results from activation of a Na+/K+ pump and a Ca2+-dependent K+ current. Activity-dependent increases in the AHP are believed to induce conduction block of spikes in several regions of the neuron, which in turn, may decrease presynaptic invasion of spikes and thereby decrease transmitter release. To explore this possibility, we used the neurosimulator SNNAP to develop a multi-compartmental model of the T cell. The model incorporated empirical data that describe the geometry of the cell and activity-dependent changes of the AHP. Simulations indicated that at some branching points, activity-dependent increases of the AHP reduced the number of spikes transmitted from the minor receptive fields to the soma and beyond. More importantly, simulations also suggest that the AHP could modulate, under some circumstances, transmission from the soma to the synaptic terminals, suggesting that the AHP can regulate spike conduction within the presynaptic arborizations of the cell and could in principle contribute to the synaptic depression that is correlated with increases in the AHP.

Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest that two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. However, eliminating positive feedback by fixing vri expression altered the oscillation period. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations, of per overexpression, and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. Temperature compensation of oscillation period could be simulated if temperature elevation slowed PER nuclear entry or PER phosphorylation. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.

Current- and Voltage-Clamp Recordings and Computer Simulations of Kenyon Cells in the Honeybee

The mushroom body of the insect brain is an important locus for olfactory information processing and associative learning. The present study investigated the biophysical properties of Kenyon cells, which form the mushroom body. Current- and voltage-clamp analyses were performed on cultured Kenyon cells from honeybees. Current-clamp analyses indicated that Kenyon cells did not spike spontaneously in vitro. However, spikes could be elicited by current injection in approximately 85% of the cells. Of the cells that produced spikes during a 1-s depolarizing current pulse, approximately 60% exhibited repetitive spiking, whereas the remaining approximately 40% fired a single spike. Cells that spiked repetitively showed little frequency adaptation. However, spikes consistently became broader and smaller during repetitive activity. Voltage-clamp analyses characterized a fast transient Na+current ( INa), a delayed rectifier K+current ( IK,V), and a fast transient K+current ( IK,A). Using the neurosimulator SNNAP, a Hodgkin–Huxley-type model was developed and used to investigate the roles of the different currents during spiking. The model led to the prediction of a slow transient outward current ( IK,ST) that was subsequently identified by reevaluating the voltage-clamp data. Simulations indicated that the primary currents that underlie spiking are INaand IK,V, whereas IK,Aand IK,STprimarily determined the responsiveness of the model to stimuli such as constant or oscillatory injections of current.

Extending in vitro conditioning in Aplysia to analyze operant and classical processes in the same preparation

Operant and classical conditioning are major processes shaping behavioral responses in all animals. Although the understanding of the mechanisms of classical conditioning has expanded significantly, the understanding of the mechanisms of operant conditioning is more limited. Recent developments in Aplysia are helping to narrow the gap in the level of understanding between operant and classical conditioning, and have raised the possibility of studying the neuronal processes underlying the interaction of operant and classical components in a relatively complex learning task. In the present study, we describe a first step toward realizing this goal, by developing a single in vitro preparation in which both operant and classical conditioning can be studied concurrently. The new paradigm reproduced previously published results, even under more conservative and homogenous selection criteria and tonic stimulation regime. Moreover, the observed learning was resistant to delay, shortening, and signaling of reinforcement.

Spontaneous activity of dopaminergic retinal neurons

Dopaminergic local circuit neurons in the retina (DA cells) show robust, spontaneous, tetrodotoxin-sensitive pacemaking. To investigate the mechanism underlying this behavior, we characterized the sodium current and a subset of the potassium currents in the cells in voltage-clamp experiments. We found that there is a persistent component of the sodium current in DA cells which activates at more depolarized potentials than the transient component of the current. The transient component was completely inactivated at -50 mV, but DA cells remained able to fire spontaneous action potentials when potassium channels were partially blocked and the membrane potential remained above -40 mV. Based on these electrophysiological data, we developed a reduced computer model that reproduced the major features of DA cells. In simulations at the physiological resting potential, the persistent component of the sodium current was both necessary and sufficient to account for spontaneous activity, and the major contribution of the transient component of the sodium current was to initiate the depolarization of the model cell during the interspike interval. When tonic inhibition was simulated by lowering the input impedance of the model cell, the transient component played a larger role.

Multimodal behavior in a four neuron ring circuit: mode switching

We study a four-neuron ring circuit comprised of oscillating burst-type neurons unidirectionally coupled via inhibitory synapses. Simple circuits of this type have been used previously to study gait patterns. The ring circuit itself is a variant of the basic reciprocal inhibition network, and it exhibits the property of multistability (multiple stable modes of behavior). That is, different gait modes can be achieved via appropriate initialization of and parameterization of this self-excited oscillatory network. We demonstrate three common gait modes with this circuit: the walk, the bound, and a slightly rotated trot mode. Attention is focused mainly on the mechanisms of rapidly and effectively switching between these modes. Our simulations suggest that neuron membrane dynamics, as well as synaptic junctional properties, strongly influence phase sensitivity in the network; each synapse is a combination of both and can be characterized by a transient phase response curve (PRC). We use the same bursting neuron model to characterize all network neurons, and shape different transient PRCs by using different synaptic properties. The characteristics of these PRCs determine the gait modes sustained in any network configuration, as well as, the ability to switch between modes. The mechanisms explored in this simple circuit, may find application in the switching of more complicated gait pattern networks, as well as, in the design of neuromorphic gait pattern circuits.

In vitro analog of classical conditioning of feeding behavior in aplysia

The feeding behavior of Aplysia californica can be classically conditioned using tactile stimulation of the lips as a conditioned stimulus (CS) and food as an unconditioned stimulus (US). Moreover, several neural correlates of classical conditioning have been identified. The present study extended previous work by developing an in vitro analog of classical conditioning and by investigating pairing-specific changes in neuronal and synaptic properties. The preparation consisted of the isolated cerebral and buccal ganglia. Electrical stimulation of a lip nerve (AT4) and a branch of the esophageal nerve (En2) served as the CS and US, respectively. Three protocols were used: paired, unpaired, and US alone. Only the paired protocol produced a significant increase in CS-evoked fictive feeding. At the cellular level, classical conditioning enhanced the magnitude of the CS-evoked synaptic input to pattern-initiating neuron B31/32. In addition, paired training enhanced both the magnitude of the CS-evoked synaptic input and the CS-evoked spike activity in command-like neuron CBI-2. The in vitro analog of classical conditioning reproduced all of the cellular changes that previously were identified following behavioral conditioning and has led to the identification of several new learning-related neural changes. In addition, the pairing-specific enhancement of the CS response in CBI-2 indicates that some aspects of associative plasticity may occur at the level of the cerebral sensory neurons.

Modeling interactions between electrical activity and second-messenger cascades in Aplysia neuron R15

The biophysical properties of neuron R15 in Aplysia endow it with the ability to express multiple modes of oscillatory electrical activity, such as beating and bursting. Previous modeling studies examined the ways in which membrane conductances contribute to the electrical activity of R15 and the ways in which extrinsic modulatory inputs alter the membrane conductances by biochemical cascades and influence the electrical activity. The goals of the present study were to examine the ways in which electrical activity influences the biochemical cascades and what dynamical properties emerge from the ongoing interactions between electrical activity and these cascades. The model proposed by Butera et al. in 1995 was extended to include equations for the binding of Ca(2+) to calmodulin (CaM) and the actions of Ca(2+)/CaM on both adenylyl cyclase and phosphodiesterase. Simulations indicated that levels of cAMP oscillated during bursting and that these oscillations were approximately antiphasic to the oscillations of Ca(2+). In the presence of cAMP oscillations, brief perturbations could switch the electrical activity between bursting and beating (bistability). Compared with a constant-cAMP model, oscillations of cAMP substantially expanded the range of bistability. Moreover, the integrated electrical/biochemical model simulated some early experimental results such as activity-dependent inactivation of the anomalous rectifier. The results of the present study suggest that the endogenous activity of R15 depends, in part, on interactions between electrical activity and biochemical cascades.

Desensitization of postsynaptic glutamate receptors contributes to high-frequency homosynaptic depression of aplysia sensorimotor connections

Withdrawal reflexes of Aplysia are mediated in part by a monosynaptic circuit of sensory (SN) and motor (MN) neurons. A brief high-frequency burst of spikes in the SN produces excitatory postsynaptic potentials (EPSPs) that rapidly decrease in amplitude during the burst of activity. It is generally believed that this and other (i.e., low-frequency) forms of homosynaptic depression are entirely caused by presynaptic mechanisms (e.g., depletion of releasable transmitter). The present study examines the contribution that desensitization of postsynaptic glutamate receptors makes to homosynaptic depression. Bath application of cyclothiazide, an agent that reduces desensitization of non-NMDA glutamate receptors, reduced high-, but not low-frequency synaptic depression. Thus, a postsynaptic mechanism, desensitization of glutamate receptors, can also contribute to homosynaptic depression of sensorimotor synapses.

Reduced Models of the Circadian Oscillators in Neurospora crassa and Drosophila melanogaster Illustrate Mechanistic Similarities

We have developed a reduced model representing feedback loops of transcriptional regulation underlying circadian rhythms in Neurospora crassa. The model contains two delay differential equations that describe the dynamics of two core gene products, FRQ and WCC. In a negative feedback loop, FRQ protein represses frq transcription by binding the white-collar complex (WCC), which consists of the WC-1 and WC-2 proteins. In a positive feedback loop, WCC indirectly enhances its own formation. The model simulates circadian oscillations, light entrainment, and a phase-response curve (PRC) similar to experimental PRCs. The Neurospora model is virtually identical to a model describing Drosophila circadian rhythm generation, illustrating that rhythm generation in these divergent organisms shares important mechanistic elements. Significant dynamic differences were found when the parameter spaces of both models were explored to analyze changes in oscillations and bifurcations to steady states. Stochastic fluctuations in molecule numbers were simulated with the Gillespie algorithm. Circadian oscillations and entrainment to light were simulated with <80 molecules of FRQ and WCC present on average. Simulations suggest that in both Neurospora and Drosophila, only the negative feedback loop is essential for circadian oscillations. Similar models may aid understanding of circadian mechanisms in mammals and other organisms.

Burst-induced synaptic depression and its modulation contribute to information transfer at Aplysia sensorimotor synapses: empirical and computational analyses

The Aplysia sensorimotor synapse is a key site of plasticity for several simple forms of learning. Plasticity of this synapse has been extensively studied, albeit primarily with individual action potentials elicited at low frequencies. Yet, the mechanosensory neurons fire high-frequency bursts in response to even moderate tactile stimuli delivered to the skin. In the present study, we extend this analysis to show that sensory neurons also fire bursts in the range of 1-60 Hz in response to electrical stimuli similar to those used in behavioral studies of sensitization. Intracellular stimulation of sensory neurons to fire a burst of action potentials at 10 Hz for 1 sec led to significant homosynaptic depression of postsynaptic responses. The depression was transient and fully recovered within 10 min. During the burst, the steady-state depressed phase of the postsynaptic response, which was only 20% of the initial EPSP of the burst, still contributed to firing the motor neuron. To explore the functional contribution of transient homosynaptic depression to the response of the motor neuron, computer simulations of the sensorimotor synapse with and without depression were compared. Depression allowed the motor neuron to produce graded responses over a wide range of presynaptic input strength. In addition, enhancement of synaptic transmission throughout a burst increased motor neuron output substantially more than did preferential enhancement of the initial phase of a burst. Thus, synaptic depression increased the dynamic range of the sensorimotor synapse and can, in principle, have a profound effect on information processing.

A computational study of the role of spike broadening in synaptic facilitation of Hermissenda

Pavlovian conditioning in Hermissenda produces a decrease in voltage-dependent (I(K,A) and I(Ca)) and Ca2+-dependent (I(K,Ca)) currents, and an increase in the action potential (AP) duration in type B-photoreceptors. In addition, synaptic connections between B and A photoreceptors and B photoreceptor and type I interneurons are facilitated. The increase in AP duration, produced by decreasing one or more K+ currents, may account for synaptic facilitation. The present study examined this issue by using a mathematical model of the B-photoreceptor and the neurosimulator SNNAP. In the model, decreasing g(K,A) by 70% increased the duration of the AP in the terminal by 41% and Ca2+ influx by 30%. However, if the decrease in g(K,A) was combined with a decrease in g(Ca), similar to what has been reported experimentally, the Ca2+ influx decreased by 54%. Therefore, the concomitant change in I(Ca) counter-acted the broadening-induced increase in Ca2+ influx in the synaptic terminal. This result suggests that a spike-duration independent process must contribute to the synaptic facilitation observed following Pavlovian conditioning.

Computational study of enhanced excitability in Hermissenda: membrane conductances modulated by 5-HT

Serotonin (5-HT) applied to the exposed but otherwise intact nervous system results in enhanced excitability of Hermissenda type-B photoreceptors. Several ion currents in the type-B photoreceptors are modulated by 5-HT, including the A-type K+ current (I(K,A)), sustained Ca2+ current (I(Ca,S)), Ca-dependent K+ current (I(K,Ca)), and a hyperpolarization-activated inward rectifier current (I(h)). In this study, we developed a computational model that reproduces physiological characteristics of type B photoreceptors, e.g. resting membrane potential, dark-adapted spike activity, spike width, and the amplitude difference between somatic and axonal spikes. We then used the model to investigate the contribution of different ion currents modulated by 5-HT to the magnitudes of enhanced excitability produced by 5-HT. Ion currents were systematically varied within limits observed experimentally, both individually and in combinations. A reduction of I(K,A) or I(K,Ca), or an increase in I(h) enhanced excitability by 20-50%. Decreasing I(Ca,S) produced a dramatic decrease in excitability. Reductions of I(K,V) produced only minimal increases in excitability, suggesting that I(K,V) probably plays a minor role in 5-HT induced enhanced excitability. Combinations of changes in I(K,A), I(K,Ca), I(h) and I(Ca,S) produced increases in excitability comparable to experimental observations. After 5-HT application, the cell's depolarization force is shifted from the I(h)-I(Ca,S) combination to predominantly I(h).