The human brain has 100 billion neurons that are constantly humming with electrical and chemical activity. These individual neurons are networked into complex local and inter-region circuits that are thought to implement functions that support life. One such circuit that is critical for survival is the fear circuit, the key elements of which are thought to include the amygdala, prefrontal cortex, and the hippocampus. Amygdala is an important site of plasticity in auditory fear conditioning and plays a key role in both the acquisition and storage of fear and extinction memories (Blair et al., 2001; LeDoux, 2000; Malkani and Rosen, 2000; Maren, 2001). The role of the amygdala in fear has been studied using fear conditioning, a training paradigm in which an organism learns to predict aversive events. Typically, a relatively neutral stimulus (conditioning stimulus, CS), such as a tone, light or an odor, is paired with an aversive one (unconditioned stimulus, US), such as a footshock. After only a few pairings, the previously neutral stimulus becomes aversive and can itself evoke an emotional reaction typically resulting in a freezing behavior. The learning processes underlying conditioning develop rapidly and the memory of this association persists for long periods of time, reflecting the biological significance of the learning experience for the organism. Even though there is consensus that the amygdala is a critical component of the mammalian fear circuit, the relevant interconnections among the amygdalar nuclei and their contributions to the acquisition and storage of fear and extinction memories are not well understood presently.
Disruption of the fear circuit is thought to underlie the pathology of post-traumatic stress and of other anxiety disorders (Corcoran and Quirk, 2007). Such disruptions are also manifested as changes in excitability of individual neurons, as well as changes in synaptic strengths between neurons in specific sub-circuits, within these areas. Increasing understanding of brain functioning due to advances in basic neuroscience techniques and imaging modalities has led to the emergence of computational modeling as an important tool for studying such changes. Progress in the areas of cellular neurophysiology and synaptic plasticity permit the development of biologically realistic computational models that more closely approximate learning, both at the membrane and network levels.
Computational modeling is a tool that has been effectively used in a variety of disciplines to integrate information related to different aspects of a problem, and to provide testable predictions. For instance, computational modeling is presently an indispensable part of the design of airplanes, e.g., Boeing 777 was claimed as being the ‘first entirely computer-designed commercial aircraft’ (Boeing 777, 2012). For an airplane, such a model would integrate the complex mathematical equations for air flow, engine dynamics, frame vibrations, and responses of the control surfaces, and then predict their effect on outputs such as ride quality. Computational models have now become indispensable for the airplane designer because they enable rapid and inexpensive evaluation of a variety of ‘what if’ scenarios, including the effect of design changes. It is argued that increased understanding of the functional organization of the brain requires integration of similar mathematical/statistical equations from molecular, cellular and network levels, something that can be facilitated by computational models (Koch and Segev, 2011). For instance, recent technical advances have resulted in a rapid accumulation of information on intracellular signaling pathways and their relationships to long-term neuronal changes (Byrne and Roberts, 2004). Computational techniques and tools are being developed to model such mechanisms with increasing accuracy and are found to be essential to generate an understanding of the underlying functions in such cases (Koch and Segev, 2001; Mauk, 2000). The term ‘computational neuropharmacology’ has recently been proposed for the application of computational modeling to drug development, drug discovery, and the modeling of the mechanisms of action of psychiatric drugs (Aradi and Erdi, 2006).
In this chapter, we review the preliminary insights related to the amygdalar fear circuit provided by biologically realistic computational models. Specifically, we investigate how sensory information might be associated within the amygdala, and how the various amygdalar nuclei interact to
2. Auditory fear and the amygdala
Fear is one of the few emotions that can be observed in non-primate mammalian organisms (LeDoux, 2000). After fear conditioning, a number of physiological manifestations can be observed upon re-exposure to the conditioning stimulus, including increased autonomic arousal, increased stress hormone release, reflex potentiation, and defensive behaviors (LeDoux, 2000). Extensive studies indicate that freezing is a defensive behavior and serves as a reliable index of fear in rodents (Blanchard and Blanchard, 1972).
The mammalian circuit related to auditory fear and extinction has been studied by several researchers and, although not fully understood, consensus is emerging about the specific roles of the amygdalar nuclei in this circuit. In rodents, such studies typically use fear conditioning, which is a form of Pavlovian learning where the stimulus parameters can be regulated by the experimenter. Fear conditioning is a highly conserved form of behavior that is exhibited in both laboratory situations and in normal environments (LeDoux, 1994). Animals do not need to be food- or water-deprived to demonstrate fear conditioning.
The components of the amygdala that are critical for fear conditioning are the lateral nucleus (LA), the basal nucleus (BA), intercalated cells (ITC) and the central nucleus (Ce) (Maren, 2001). Thalamic inputs conveying information about the auditory tone (conditioned stimulus, CS) and foot shock (unconditioned stimulus, US) arrive first at the lateral nucleus. LA is widely accepted to be a key site of synaptic events that contribute to fear learning (LeDoux, 1995; Paré et al., 2004; Sigurdsson et al., 2007). There are two main types of neurons within the LA and the BA: pyramidal glutamatergic projection neurons and local circuit γ-aminobutyric acid (GABA) releasing interneurons. The amygdalar nuclei LA, BA, Ce and the ITC clusters act in concert to store auditory fear and extinction memories, and these nuclei are in turn modulated by external structures such as the prefrontal cortex and hippocampus. In auditory fear conditioning, convergence of tone (conditioned stimulus, CS) and foot-shock (unconditioned stimulus, US) inputs in LA leads to potentiation of CS inputs, resulting in subsequent LA tone responses being larger (Quirk et al., 1995; Blair et al., 2001). These increased LA responses are relayed to the Ce via BA (Amano et al., 2011), and the intercalated (ITC) cell masses (Paré et al., 2004), eliciting fear responses via successive projections to brain stem and hypothalamic sites (LeDoux, 2000). As a result, rats learn to freeze to tones CS that predict foot shock US.
In the rodent brain, estimates of the numbers of cells (unilateral) in the amygdalar nuclei are as follows: LA – 60,000; BA – 47,000; ITC – 19,000; and Ce – 37,000 (Tuunanen and Pitkanen, 2000). The principal cell to GABAergic interneuron ratio in BLA is 80:20. The amygdalar nuclei are themselves not homogeneous. LA has distinct dorsal and ventral regions which seem to store fear memories in different ways (Repa et al., 2001). Herry et al. (2008) reported three subpopulations of neurons in BA whose CS responsiveness varied with fear training and they termed these as ‘fear,’ ‘extinction’ and ‘extinction-resistant’ cells. Fear cells acquire CS responses as a result of fear conditioning, but lose them following extinction training; extinction cells become CS responsive only following extinction training, and extinction- resistant cells acquire CS responses during conditioning and remain CS responsive even after extinction training. Also, Amano et al. (2011) have shown that the two sub-regions within BA, the lateral part (BL), and the medial part (BM), act in concert to express fear but possess a certain amount of redundancy between themselves. Similarly, there are two different ITC cell clusters and they are thought to contribute differentially to the expression of fear and extinction memories (Royer et al., 2000; Pape and Paré, 2010). The output nucleus Ce also has distinct sub-circuits with different functions in fear learning (Coicci et al., 2010; Haubensak et al., 2010). Even with these advances in understanding, a clear portrait of how the various amygdalar nuclei interact to acquire and store fear is still lacking.
Once acquired, conditioned fear associations are not always expressed. Repeated presentation of the tone CS in the absence of the US causes conditioned fear responses to diminish rapidly, a phenomenon termed as fear extinction (Myers and Davis, 2007). The neural mechanisms of fear extinction are not well understood, and a neural analysis of extinction and inhibition is still in its infancy (Delamater, 2004; Quirk and Mueller, 2008). Some psychological theories describe extinction as an “unlearning” process due to a violation of the CS-US association established during acquisition of fear (Rescorla and Wagner, 1972). This unlearning view has been challenged by the observation that fear recovers spontaneously after extinction. An alternative theory proposes that extinction does not erase the CS-US association but instead forms a new memory that inhibits conditioned responding (Bouton and King, 1983; Quirk, 2002).
What are the structures that might modulate the memory of auditory fear extinction? Again, several studies by Quirk and others reveal that the infralimbic (IL) region of mPFC modulates the amygdala during recall of extinction memory: activity in IL, which is adjacent to PL, was found to facilitate recall of extinction (Quirk et al., 2006; Quirk and Mueller, 2008), and deficient IL activity results in failure to recall extinction (e.g., Milad and Quirk, 2002). Burgos-Robles et al. (2009) also noted that a higher percentage of PL neurons responded to tones in rats showing poor recall of extinction, suggesting that these rats had excessive consolidation of fear memory. This led the authors to suggest that extinction failure might be caused by excessive activity in PL, combined with deficient activity in the IL, and that recall of fear and extinction memories may depend on the optimal balance of activity between PL and IL.
What is the role of context in auditory fear? Since fear conditioning takes place in a chamber (Fig. 1b; with its own flooring, color, odor, lighting, etc. – the ‘context’), the rat subsequently learns to fear not only the tone but also the context. That is, after fear conditioning, it will express fear by freezing in the trained context, even in the absence of tone. Acquisition of contextual fear may involve configural or spatial learning and many lines of evidence support hippocampal involvement in contextual fear conditioning (Anagnostaras et al., 1999). It is well established that contextual information gates behavioral response to conditioned stimuli, especially following extinction (e.g., Bouton, 2004). Contextual information is processed in the hippocampal formation (HPC), which plays a critical role in gating the response of rats to extinguished tone stimuli (Corcoran et al., 2005). The route by which the HPC exerts its effects is thought to be through the mPFC (Hobin et al., 2003; Maren and Quirk, 2004). The HPC (especially the ventral HPC) projects strongly to both PL and IL (e.g., Hoover and Vertes, 2007). This pathway has been hypothesized to serve a ‘teaching’ role for IL neurons, by generating Ca-dependent bursting in IL neurons. Also, it has been shown that contextual fear memories formed in the absence of the baso-lateral amygdala (BLA which includes BA and LA; Poulos et al., 2009) or the dorsal hippocampus (DH; Zelikowsky et al., 2012) do not persist across time, suggesting that both the DH and BLA are essential components of the circuitry required for a contextual fear memory to become permanent (Zelikowsky et al., 2012).
3. Modeling fear memories - A simple computational model
Computational models have been used in the field of emotional learning and memory to explain behavioral responses (e.g., Grossberg and Schmajuk, 1987). Single unit recording data were used by Armony et al. (1995) to develop an anatomically constrained thalamo-cortico-amygdala connectionist model of fear conditioning which associated tone inputs with a specific frequency (CS) with foot shock (US). The model was trained using a modified Hebbian-type learning rule and was able to reproduce data related to frequency-specific changes of the receptive fields known to exist in the auditory thalamus and amygdala. However, extinction and other related phenomena were not simulated. Balkenius and Morén (2001) proposed a neural network model for emotional conditioning focusing on the amygdala and the orbitofrontal cortex and their interaction. Amygdala was the locus of acquisition and the orbitofrontal cortex was the site for extinction learning. The model simulated basic phenomena related to emotional conditioning including acquisition, extinction, blocking, and habituation. Vlachos et al. (2011) reported a neural network model that reproduced the differential recruitment of two distinct subpopulations of basal amygdala neurons as seen in experiments. The model revealed how the two populations might encode contextual specificity of fear and extinction memories. Krasne et al. (2011) report a model of the amygdala and hippocampus where fear conditioning and extinction memories are the result of neuromodulation-controlled LTP at synapses of thalamic, cortical, and hippocampal afferents on principal cells and inhibitory interneurons of lateral and basal amygdala. The model was developed using a firing rate framework and was able to reproduce several known features of fear learning and make testable predictions. Although connectionist and reduced order models provide very useful information from a top-down systems perspective, they do not fully incorporate the neurobiological information related to individual current channels and their effect on intrinsic excitability, or related to synaptic plasticity mechanisms, and so may be not be able to shed light on the underlying mechanisms to any significant level of detail.
This chapter focuses on a class of computational models that incorporate biological realism (i.e., they include membrane channels, synapses and receptors) to more effectively model the learning brain. Such models integrate information from intracellular and cellular levels of neuroscience with the network/systems level to provide a coherent picture of the higher level functions in health and disease (e.g., behavior, symptom). Software exists presently to model systems in neuroscience at typically only one of the levels, either molecular, cellular, or network/systems level. One reason for this is the large difference in both temporal and spatial complexities between the levels. We focus largely on cellular and network level modeling in this chapter.
Computational modeling platforms at the cellular and network levels include public domain software such as NEURON (Carnevale and Hines, 2006) and GENESIS (Bower and Beeman, 2003) which are being designed for biologists, and require minimal understanding of the underlying mathematics. Figure 3 shows the hierarchical structure used for modeling. Such packages can perform simulations of models ranging from single neurons to complex networks representing brain circuits. Sources for biological information to develop such models include research articles, and databases such as CellPropDB, NeuronDB and ModelDB (http://neuron.duke.edu/). For example, Leblois et al. (2006) used a mathematical model to explain the pathology in the basal ganglia circuit with Parkinson’s disease.
schematically in Fig. 5b. This unit of two cells illustrates how conditioning and extinction are learned in this network, i.e., conditioning is essentially the strengthening of the tone-pyramidal synapse which increases pyramidal cell activity, and extinction is the strengthening of tone-interneuron, interneuron-pyramidal cell and pyramidal cell-interneuron synapses, all of which decrease pyramidal cell activity. The concepts and insights illustrated by this simple two-cell network, such as potential storage sites for memory, translate directly to larger networks, as we discuss in the following.
4. Reverse engineering auditory fear circuits in the amygdala
The overall goal of the reverse engineering effort is to integrate diverse morphological and neurophysiological data into biologically realistic models of the various amygdalar nuclei (lateral nucleus, basal nucleus, intercalated cells, and the central nucleus) and then use the model to investigate how the different nuclei participate in the acquisition and extinction of auditory fear memories, and how they are modulated by cortical structures. We initiated the model development of the overall fear circuit using a bottom-up approach starting with the core unit: the lateral amygdala nucleus, LA. As the next step, we modeled the amygdala intercalated cell clusters, ITC. The LA and ITC models provided unique insights that are presently not possible to obtain via experiments.
A. Modeling the lateral amygdala (Li et al., 2009)
Principal neurons in the LA exhibit a range of firing properties in response to prolonged current injection (Faber et al., 2001). Accordingly three types of pyramidal cells were modeled, types A, B, and C, where type A had strong, B had medium, and C had minimal frequency adaptation. The interneuron was modeled as a basket-type, fast-spiking, aspiny cell with each compartment containing a fast Na+ current and a delayed rectifier K+ current with different kinetics from those of pyramidal cells to reproduce its much shorter spike duration (Durstweitz et al., 2000). Similar to pyramidal cells, interneurons can also receive excitatory glutamatergic inputs from the thalamus and/or the cortex, and inhibitory inputs from other local interneurons. For each cell, the AMPA and the N-methyl D-aspartate (NMDA) channels were placed in the dendrite compartment, and the inhibitory GABAA channels were placed on the soma. Fig.4 provides details of typical pyramidal cell and interneuron models with the various ionic and synaptic channels.
Excitatory glutamatergic AMPA synapses capable of strengthening (long term potentiation, LTP) or weakening (long term depression, LTD) with training were placed on the following synapses of each cell: (i) thalamic/cortical auditory tone synapses to pyramidal cells or interneurons, (ii) synapses between the pyramidal cells themselves, and (iii) pyramidal cell to interneuron synapses. In addition, plasticity was also modeled in GABAergic inhibitory synapses from interneurons to pyramidal cells. The occurrence of synaptic potentiation versus depression was determined by intracellular calcium levels, according to the calcium control hypothesis. Details related to the equations can be found in Li et al. (2009). Learning of conditioned fear leads to changes in synaptic strength in the neural circuitry and the magnitude and sign of these variations are unique insights that a computational model can provide.
To achieve the low average spontaneous firing rate of ~1 Hz in the experiments modeled (Quirk et al., 1995), independent, Poisson distributed, random excitatory background inputs were delivered to all the pyramidal cells. These inputs represent unmodeled synaptic connections from other brain areas such as prefrontal cortex and hippocampus. Similar background inputs were provided to the interneurons to generate the reported spontaneous firing rates of ~8 Hz (Paré and Gaudreau, 1996). Simulations were performed on a personal computer using the software package GENESIS with the Crank-Nicholson integration method, and a time step of 10 μs.
Model validation. In addition to matching unit responses in the model to unit experimental data, the model of the ‘network’ should also reproduce experimentally observed behavior. Unit tone responses from the lateral amygdala of behaving animals have been reported by Quirk et al. (1995). Their main finding was that conditioning significantly increased the number of tone-elicited spikes with the greatest effects at the shortest latency following tone onset. These conditioned responses were reversed by extinction training. With tuning of the plasticity parameters in the model, the LA network model unit tone responses successfully reproduced experimental data in Quirk et al. (1995). All pyramidal neurons in the model
showed clear frequency adaptation with the tone responses concentrated in the first 100 ms, indicating a good match with the experimental recordings. Figure 7
The Li et al. (2009) network model represents the first attempt to incorporate cellular neurophysiology and synaptic plasticity mechanisms into a biophysical model to investigate the underlying mechanisms of fear learning. The model was used to determine how the intrinsic and synaptic mechanisms interact in a network to shape unit tone responses. Computational models are unique in their ability to contribute to such insights.
The model also suggested that the different types of principal neurons have different functional roles due to their distinct frequency adaptation characteristics (Faber et al., 2001). The cells with stronger adaptation are slower to learn fear but are able to maintain fear memory for a long time, whereas the cells with weaker adaptation learn fear faster, but also extinguish faster (Fig. 5,
Considering extinction memory, the model suggests three possible sites of plasticity: the tone synapse at the interneuron, the inhibitory synapse from interneuron to pyramidal cell, and the excitatory synapse from pyramidal cell to interneuron. Model runs showed different decay rates of these three synapses suggesting that the first two, with large and uniform decay rates during the gap, may mediate short-term extinction memory, while the last, with smaller decay rate, could store long-term extinction memory (e.g., P1-I1 in Fig. 5C in Li et al., 2009). However, the tone-interneuron and inter-pyramidal cell synapses potentiated much larger during both extinction sessions, compared to the pyramidal-interneuron synapses.
The LA model can be used as a test bed to investigate several other ‘what if’ scenarios that may be of interest but are difficult to test in experiments. Our study showed how such models are poised to complement experimental investigations by providing insights into how cellular and synaptic mechanisms contribute to implementing functions in brains. This is illustrated further by the model of intercalated cells discussed next.
B. Modeling the network of amygdala intercalated cells (Li et al., 2011)
It is currently believed (Paré et al., 2004; Quirk and Mueller, 2008) that extinguished conditioned stimuli activate infralimbic (IL) neurons that have glutamatergic projections to ITC cells and ITC cells in turn reduce conditioned fear responses by generating feedforward inhibition in fear output Ce neurons (Paré et al., 2004). Consistent with this, IL stimulation was found to dramatically reduce the responsiveness of Ce neurons to BLA inputs (Quirk et al., 2003). IL axons are known to target ITC cells clusters located medially (McDonald et al., 1996), and there are inhibitory connections between (Royer et al., 2000) as well as within ITC cell clusters (Geracitano et al., 2007). Additionally, three different types of short-term synaptic plasticity have been observed in inter-ITC connections (Geracitano et al., 2007), but the role of such synaptic heterogeneity is not clear. How then might IL inputs overcome the inter-ITC inhibition and reduce the responsiveness of Ce? Again, it is currently difficult to address this question experimentally, because we lack criteria to identify ITC cells on the basis of their extracellularly recorded activity. So, in order to study how inter-ITC inhibitory connections affect their responses to IL inputs, we developed a biologically realistic model of the ITC network (Fig. 8). Another objective of the Li et al. (2011) study was to examine how the peculiar electroresponsive properties of ITC cells shape their responsiveness to BLA/IL inputs. ITC cells express an unusual voltage-dependent K+ conductance whose slow-deinactivation kinetics allow them to produce a prolonged depolarizing plateau after a transient suprathreshold depolarization (Royer et al., 2000). This enables ITC neurons to transform transient excitatory inputs into a prolonged state of increased excitability with possibly important consequences for the regulation of conditioned fear.
During prolonged auditory CSs, BLA principal neurons show rapidly adapting responses (Quirk et al., 1995, 1997; Repa et al., 2001; Herry et al., 2008), but it is not clear how such transient responses are converted into sustained behavioral output, since rats freeze throughout the duration of the tone. Also, pairing CSs with brief (300 msec) electrical IL stimulation reduces conditioned freezing in a temporally specific manner (Milad and Quirk, 2002; Milad et al., 2004), again sustaining this transient input. We used the model to test whether bistable electroresponsive properties of ITC cells allow them to transform transient BLA/IL signals into a more sustained output.
membrane potential and current dynamics were modeled using the standard Hodgkin-Huxley formulation (Li et al., 2011).
We modeled three different types of Ce neurons differing by their spike patterns, regular spiking, late firing, and low-threshold bursting. Each cell model had two compartments: a soma (diameter of 15 μm; length of 15 μm) and a dendrite (diameter of 5 μm; length of 300 μm), and the following currents: a leakage current IL, a sodium current INa, a delayed rectifier IDR, a muscarinic current IM, a hyperpolarization-activated current IH, a high-voltage-activated Ca2+ current ICaL, and a slow Ca2+-dependent after-hyperpolarization current IsAHP. The late firing cell contained an additional inactivating transient K+ current IA known to delay the onset of the action potential (Storm 1986), while the low-threshold bursting cell included an additional low-threshold inactivating calcium current ICaT.The passive membrane properties were as follows: Rm = 30 KΩ-cm2, Cm = 1.0 μF/cm2, and Ra =150 Ω-cm.
ITC neurons exhibit NMDA-dependent bidirectional synaptic plasticity (Royer and Paré, 2002) and in a recent experimental study, the BA inputs to ITC cells were reported to show a three-fold potentiation during extinction training (Fig. 4 in Amano et al., 2010). Given the fact that the firing rate of LA neurons is significantly increased after conditioning (Quirk et al., 1995), it is reasonable to assume that the LA–ITCD connection is potentiated by conditioning. Hence, we used a threefold synaptic weight (compared with the habituation state) for the LA–ITCD synapses in the fear state and a threefold synaptic weight for the BA–ITC synapses in the extinction state. For the LA–ITCD connection, the potentiated synapses were assumed to be partially depotentiated in the extinction state (strength reduced from 3 to 2 for AMPA synapses only, Amano et al., 2010) based on results from a previous LA network model (Li et al., 2009). The BA–Ce, ITC–ITC, and ITC–Ce synaptic weights were assumed to be fixed. However, based on experimental findings (Geracitano et al., 2007), the presynaptic release probability of the ITC–ITC and ITC–Ce synapses was modifiable, and were split equally into facilitating, depressing, and constant types. The equations and specifics related to the plasticity mechanisms can be found in Li et al. (2011).
Model runs were performed on a personal computer using the software package GENESIS with the Crank-Nicholson integration method, and a time step of 20 msec. A simulation of 5 sec of network activity took 15 min of CPU time.
We developed the model to investigate how the electroresponsive properties of ITC cells shape their responsiveness to BLA/IL inputs, and how IL inputs might overcome the inter-ITC inhibition after extinction training and reduce the responsiveness of Ce. The model showed that ITC neurons could transform the transient CS-related signals arising in the BLA into a persistent pattern of activity. It also showed that over a wide range of stimulation strengths, brief IL activation can overwhelm inter-ITC inhibition and reduce the activity of fear output Ce neurons. Importantly, both intrinsic properties (i.e., bistability) and variations in the short-term synaptic dynamics of ITC neurons contributed to the effectiveness of IL stimulation. Similar to the LA model case discussed earlier, the ITC model provided several insights into the functioning of this cluster of cells and how they might modulate the expression of fear and extinction memories.
C. Modeling the other amygdalar nuclei, and modulation by cortical structures
The primary structures of the fear circuit, as presently understood, include the amygdala, the prefrontal cortex, and the hippocampus. These structures, in turn, are themselves composed of different sub-circuits, with different roles in auditory fear learning. The amygdala, as cited, consists of several nuclei LA, BA, Ce and the ITC clusters, all acting in concert to store auditory fear and extinction memories, and express them later via the fear output station Ce. Interestingly, these individual nuclei themselves are not homogeneous. For instance, the dorsal and ventral regions of LA participate in fear learning in different ways (Repa et al., 2001); BA has different nuclei, BL and BM, which have recently been shown to relay fear differently to Ce (Amano et al., 2011); the two different ITC cell clusters associated with the fear circuit again contribute in different ways to the expression of fear and extinction memories (Royer et al., 2000); and the output nucleus Ce has also been shown recently to have very distinct sub-circuits whose specific roles as far as influencing fear await further investigation (Coicci et al., 2010; Haubensak et al., 2010).
Amygdalar fear, in turn, is known to be modulated by mPFC (both PL and IL) and by the hippocampus, and so the expression of fear and extinction memories is also under control of these ‘higher’ level structures. At present, modulation of amygdalar fear by mPFC (see Burgos-Robles et al., 2009) is better understood in comparison to modulation by the hippocampus. As discussed earlier, studies related to contextual fear conditioning (Fanselow, 2010), which involve the hippocampus, have been complicated by this lack of understanding. Hence computational models of the hippocampus and its linkages to the amygdala and mPFC in auditory fear may have to await progress in our understanding of anatomical linkages between these regions and experimental data on their interactions during the different phases of fear learning.
These are important challenges that have to be addressed in order to gain an understanding of the functioning of the mammalian fear circuit. As demonstrated in the discussion above, biologically realistic models can potentially supplement experimental modalities such as patch clamp recordings, single unit recordings, pharmacological manipulations and transgenic approaches, and assist with reverse engineering the functioning of this critical circuit. They also provide tremendous opportunities for research in interdisciplinary settings with participation of neuroscientists, electrophysiologists and computational experts. For instance, similar to the insights obtained for LA and ITC clusters, such interdisciplinary research would also aid in elucidating the roles of the various sub-circuits within the other nuclei, BA and Ce. After development of the individual models of these nuclei, they can be integrated into an overall model of the amygdalar fear circuit. The level of robustness and redundancy that the circuit components and the circuit as a whole possesses (e.g., in BA as reported by Amano et al., 2011) can then be addressed effectively by such models. As cited, the role of context in fear learning is not well understood at the present time. Thus, improved neurobiological understanding of information processing within the hippocampus and of the anatomical connectivity (hippocampus to mPFC and to the amydgala) will have to precede modeling efforts related to contextual auditory fear circuits.
5. Summary and potential applications
There has been a surge in interest related to the role of intra-amygdaloid structures in Pavlovian fear learning. Research papers have risen from an average of 25/year in the 1980s to 200/year in the 2000s (Paré et al., 2004). Although this has resulted in an improved understanding of the underlying mechanisms, it has also highlighted the complexity of the circuit, including possible distributed storage of fear and extinction memories in the various nuclei/structures, distinct mechanism of LTP/LTD at different synapses, and recruitment of alternative pathways providing redundancy that is probably an important trait of such a critical circuit. This complexity renders the understanding of the amygdalar involvement in fear learning a bigger challenge than previously envisaged. Furthermore, modulation of the amygdala by the prefrontal cortex, hippocampus and other related regions is only beginning to be understood. Computational modeling has the potential to play an important role in our efforts to unravel this complex fear circuit.
Insights into the functioning of the sub-circuits using computational models would also be useful for studying disruptions associated with the fear circuit, leading to PTSD and anxiety disorders. For instance, studies have shown that humans with PTSD exhibit a delay in acquisition of extinction as compared to controls (Rothbaum and Davis, 2003). With the model, one can modify parameters to predict changes in the fear circuit that could be correlated with a delay in acquisition of extinction. These parameters would then point to the changes in the circuit with PTSD and provide insights into the pathology of the illness. The model could also shed light on how therapeutic approaches such as cognitive restructuring provide a new emotional significance to a negative cognition and reduce physiological arousal (Debiec et al., 2006).
The author is grateful to his former PhD student Guoshi Li, and to Gregory Quirk and Denis Paré for their contributions, in many ways, to the collaborative research that this review significantly draws upon. This work was supported by NIMH grant MH087755 to SSN.