Skip to main content

Synaptic competition in the lateral amygdala and the stimulus specificity of conditioned fear: a biophysical modeling study

Abstract

Competitive synaptic interactions between principal neurons (PNs) with differing intrinsic excitability were recently shown to determine which dorsal lateral amygdala (LAd) neurons are recruited into a fear memory trace. Here, we explored the contribution of these competitive interactions in determining the stimulus specificity of conditioned fear associations. To this end, we used a realistic biophysical computational model of LAd that included multi-compartment conductance-based models of 800 PNs and 200 interneurons. To reproduce the continuum of spike frequency adaptation displayed by PNs, the model included three subtypes of PNs with high, intermediate, and low spike frequency adaptation. In addition, the model network integrated spatially differentiated patterns of excitatory and inhibitory connections within LA, dopaminergic and noradrenergic inputs, extrinsic thalamic and cortical tone afferents to simulate conditioned stimuli as well as shock inputs for the unconditioned stimulus. Last, glutamatergic synapses in the model could undergo activity-dependent plasticity. Our results suggest that plasticity at both excitatory (PN–PN) and di-synaptic inhibitory (PN–ITN and, particularly, ITN–PN) connections are major determinants of the synaptic competition governing the assignment of PNs to the memory trace. The model also revealed that training-induced potentiation of PN–PN synapses promotes, whereas that of ITN–PN synapses opposes, stimulus generalization. Indeed, suppressing plasticity of PN–PN synapses increased, whereas preventing plasticity of interneuronal synapses decreased the CS specificity of PN recruitment. Overall, our results indicate that the plasticity configuration imprinted in the network by synaptic competition ensures memory specificity. Given that anxiety disorders are characterized by tendency to generalize learned fear to safe stimuli or situations, understanding how plasticity of intrinsic LAd synapses regulates the specificity of learned fear is an important challenge for future experimental studies.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Armony JL, Servan-Schreiber D, Romanski LM, Cohen JD, LeDoux JE (1997) Stimulus generalization of fear responses: effects of auditory cortex lesions in a computational model and in rats. Cereb Cortex 7:157–165

    CAS  Article  PubMed  Google Scholar 

  2. Balkenius C, Moren J (2001) Emotional learning: a computational model of the amygdala. Cybernet Syst 32:611–636

    Article  Google Scholar 

  3. Ball JM, Hummos AM, Nair SS (2012) Role of sensory input distribution and intrinsic connectivity in lateral amygdala during auditory fear conditioning: a computational study. Neurosci 224:249–267

    CAS  Article  Google Scholar 

  4. Bauer EP, LeDoux JE (2004) Heterosynaptic long-term potentiation of inhibitory interneurons in the lateral amygdala. J Neurosci 24:9507–9512

    CAS  Article  PubMed  Google Scholar 

  5. Benito E, Barco A (2010) CREB’s control of intrinsic and synaptic plasticity: implications for CREB-dependent memory models. Trends Neurosci 33:230–240

    CAS  Article  PubMed  Google Scholar 

  6. Bissiere S, Humeau Y, Luthi A (2003) Dopamine gates LTP induction in lateral amygdala by suppressing feedforward inhibition. Nat Neurosci 6:587–592

    CAS  Article  PubMed  Google Scholar 

  7. Bordi F, LeDoux JE (1994) Response properties of single units in areas of rat auditory thalamus that project to the amygdala. II. Cells receiving convergent auditory and somatosensory inputs and cells antidromically activated by amygdala stimulation. Exp Brain Res 98:275–286

    CAS  Article  PubMed  Google Scholar 

  8. Byrne JH, Roberts JL (ed) (2004) From molecules to networks—an introduction to cellular and molecular neuroscience. Elsevier, San Diego

    Google Scholar 

  9. Carnevale NT, Hines ML (2006) The NEURON book. Cambridge University Press, Cambridge

    Book  Google Scholar 

  10. Collins DR, Paré D (2000) Differential fear conditioning induces reciprocal changes in the sensory responses of lateral amygdala neurons to the CS(+) and CS(−). Learn Mem 7:97–103

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  11. Domjan M (2006) The principles of learning and behavior: active learning edition, 5th edn. Thomson, Wadsworth, Belmont

    Google Scholar 

  12. Durstewitz D, Seamans JK, Sejnowski TJ (2000) Dopamine-mediated stabilization of delay-period activity in a network model of prefrontal cortex. J Neurophysiol 83:1733–1750

    CAS  PubMed  Google Scholar 

  13. Duvarci S, Bauer EP, Pare D (2009) The bed nucleus of the stria terminalis mediates inter-individual variations in anxiety and fear. J Neurosci 29:10357–10361

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  14. Faber ES, Sah P (2003) Ca2+-activated K+ (BK) channel inactivation contributes to spike broadening during repetitive firing in the rat lateral amygdala. J Physiol 552:483–497

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  15. Faber ES, Callister RJ, Sah P (2001) Morphological and electrophysiological properties of principal neurons in the rat lateral amygdala in vitro. J Neurophysiol 85:714–723

    CAS  PubMed  Google Scholar 

  16. Farb C, Chang W, LeDoux JE (2010) Ultrastructural characterization of noradrenergic axons and beta-adrenergic receptors in the lateral nucleus of the amygdale. Front Behav Neurosci 4:162

    Article  PubMed  PubMed Central  Google Scholar 

  17. Gaiarsa JL, Caillard O, Ben-Ari Y (2002) Long-term plasticity at GABAergic and glycinergic synapses: mechanisms and functional significance. Trends Neurosci 25:564–570

    CAS  Article  PubMed  Google Scholar 

  18. Gaudreau H, Paré D (1996) Projection neurons of the lateral amygdaloid nucleus are virtually silent throughout the sleep-walking cycle. J Neurophysiol 75:1301–1305

    CAS  PubMed  Google Scholar 

  19. Goosens KA, Hobin JA, Maren S (2003) Auditory-evoked spike firing in the lateral amygdala and Pavlovian fear conditioning: mnemonic code or fear bias? Neuron 40:1013–1022

    CAS  Article  PubMed  Google Scholar 

  20. Han JH, Kushner SA, Yiu AP, Cole CJ, Matynia A, Brown RA, Neve RL, Guzowshi JF, Silva AJ, Josselyn SA (2007) Neuronal competition and selection during memory formation. Science 316:457–460

    CAS  Article  PubMed  Google Scholar 

  21. Han JH, Kushner SA, Yiu AP, Hsiang HL, Buch T, Waisman A, Bontempi B, Neve RL, Frankland PW, Josselyn SA (2009) Selective erasure of a fear memory. Science 323:1492–1496

    CAS  Article  PubMed  Google Scholar 

  22. Headley DB, Weinberger NM (2014) Relational associative learning induces cross-modal plasticity in earl visual cortex. Cereb Cortex. doi:10.1093/cercor/bht325

    Google Scholar 

  23. Herry C, Ciocchi S, Senn V, Demmou L, Muller C, Luthi A (2008) Switching on and off fear by distinct neuronal circuits. Nature 454:600–606

    CAS  Article  PubMed  Google Scholar 

  24. Honig WK, Urcuioli PJ (1981) The legacy of Guttman and Kalish (1956): 25 years of research on stimulus generalization. J Exp Anal Behav 36:405–445

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  25. Hu H, Real E, Takamiya K, Kang M, LeDoux J, Huganir R, Malinow R (2007) Emotion enhances learning via norepinephrine regulation of AMPA receptor trafficking. Cell 131:160–173

    CAS  Article  PubMed  Google Scholar 

  26. Hummos A, Franklin CC, Nair SS (2014) Intrinsic mechanisms stabilize encoding and retrieval circuits differentially in a hippocampal network model. Hippocampus 24:1430–1448

    Article  PubMed  Google Scholar 

  27. Johnson LR, Hou M, Prager EM, LeDoux JE (2011) Regulation of the fear network by mediators of stress: norepinephrine alters the balance between cortical and subcortical afferent excitation of the lateral amygdala. Front Behav Neurosci 5:23

    Article  PubMed  PubMed Central  Google Scholar 

  28. Kim D, Pare D, Nair SS (2013a) Mechanisms contributing to the induction and storage of Pavlovian fear memories in the lateral amygdala. Learn Mem 20:421–430

    Article  PubMed  PubMed Central  Google Scholar 

  29. Kim D, Pare D, Nair SS (2013b) Assignment of lateral amygdala neurons to the fear memory trace depends on competitive synaptic interactions. J Neurosci 33(36):14354–14358

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  30. Kitajima T, Hara K (1997) An integrated model for activity-dependent synaptic modifications. Neural Networks 10:413–421

    Article  Google Scholar 

  31. Komatsu Y (1996) GABAB receptors, monoamine receptors, and postsynaptic inositol trisphosphate-induced Ca2+ release are involved in the induction of long-term potentiation at visual cortical inhibitory synapses. J Neurosci 16:6342–6352

    CAS  PubMed  Google Scholar 

  32. Krasne FB, Fanselow MS, Zelikowsky M (2011) Design of a neurally plausible model of fear learning. Front Behav Neurosci 5:41

    Article  PubMed  PubMed Central  Google Scholar 

  33. Kroner S, Rosenkranz JA, Grace AA, Barrionuevo G (2004) Dopamine modulates excitability of basolateral amygdala neurons in vitro. J Neurophysiol 93:1598–1610

    Article  PubMed  Google Scholar 

  34. LeDoux JE (2000) Emotional circuits in the brain. Annu Rev Neurosci 23:155–184

    CAS  Article  PubMed  Google Scholar 

  35. Letzkus JJ, Wolff SB, Meyer EM, Tovote P, Courtin J, Herry C, Lüthi A (2011) A disinhibitory microcircuit for associative fear learning in the auditory cortex. Nature 480:331–335

    CAS  Article  PubMed  Google Scholar 

  36. Li G, Nair S, Quirk GJ (2009) A biologically realistic network model of acquisition and extinction of conditioned fear associations in lateral amygdala neurons. J Neurophysiol 101:1629–1646

    Article  PubMed  PubMed Central  Google Scholar 

  37. Lissek S, Biggs AL, Rabin SJ, Cornwell BR, Alvarez RP, Pine DS, Grillon C (2008) Generalization of conditioned fear-potentiated startle in humans: experimental validation and clinical relevance. Behav Res Ther 46:678–687

    Article  PubMed  PubMed Central  Google Scholar 

  38. Lissek S, Rabin S, Heller RE, Lukenbaugh D, Geraci M, Pine DS, Grillon C (2010) Over generalization of conditioned fear as a pathogenic marker of panic disorder. Am J Psychiatry 167:47–55

    Article  PubMed  PubMed Central  Google Scholar 

  39. Loretan K, Bissiere S, Luthi A (2004) Dopaminergic modulation of spontaneous inhibitory network activity in the lateral amygdale. Neuropharmacology 47:631–639

    CAS  Article  PubMed  Google Scholar 

  40. Mahanty NK, Sah P (1998) Calcium-permeable AMPA receptors mediate long-term potentiation in interneurons in the amygdala. Nature 394:683–687

    CAS  Article  PubMed  Google Scholar 

  41. Maren S, Yap SA, Goosens KA (2001) The amygdala is essential for the development of neuronal plasticity in the medial geniculate nucleus during auditory fear conditioning in rats. J Neurosci 21:RC135

    CAS  PubMed  Google Scholar 

  42. Martina M, Bergeron R (2008) D1 and D4 dopaminergic receptor interplay mediates coincident G protein-independent and dependent regulation of glutamate NMDA receptors in the lateral amygdala. J Neurochem 106:2421–2435

    CAS  Article  PubMed  Google Scholar 

  43. Moustafa AA, Gilbertson MW, Orr SP, Herzallah MM, Servatius RJ, Myers CE (2013) A model of amygdala-hippocampal-prefrontal interaction in fear conditioning and extinction in animals. Brain Cogn 81(1):29–43

    Article  PubMed  Google Scholar 

  44. Muller JF, Mascagni F, McDonald AJ (2009) Dopaminergic innervation of pyramidal cells in the rat basolateral amygdala. Brain Struct Funct 213:275–288

    Article  PubMed  Google Scholar 

  45. Pape HC, Paré D (2010) Plastic synaptic networks of the amygdala for the acquisition, expression, and extinction of conditioned fear. Physiol Rev 90:419–463

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  46. Polepalli JS, Sullivan RK, Yanagawa Y, Sah P (2010) A specific class of interneuron mediates inhibitory plasticity in the lateral amygdala. J Neurosci 30:14619–14629

    CAS  Article  PubMed  Google Scholar 

  47. Power JM, Bocklisch C, Curby P, Sah P (2011) Location and function of the slow after hyperpolarization channels in the basolateral amygdala. J Neurosci 31:526–537

    CAS  Article  PubMed  Google Scholar 

  48. Quirk GJ, Repa JC, LeDoux JE (1995) Fear conditioning enhances short latency auditory responses of lateral amygdala neurons: parallel recordings in the freely behaving rat. Neuron 15:1029–1039

    CAS  Article  PubMed  Google Scholar 

  49. Repa JC, Muller J, Apergis J, Desrochers TM, Zhou Y, LeDoux JE (2001) Two different lateral amygdala cell populations contribute to the initiation and storage of memory. Nat Neurosci 4:724–731

    CAS  Article  PubMed  Google Scholar 

  50. Resnik J, Sobel N, Paz R (2011) Auditory aversive learning increases discrimination thresholds. Nat Neurosci 14(6):791–796

    CAS  Article  PubMed  Google Scholar 

  51. Sah P, Faber ES, Lopez de Armentia M, Power J (2003) The amygdaloid complex: anatomy and physiology. Physiol Rev 83:803–834

    CAS  Article  PubMed  Google Scholar 

  52. Samson RD, Paré D (2006) A spatially structured network of inhibitory and excitatory connections directs impulse traffic within the lateral amygdala. Neuroscience 141:1599–1609

    CAS  Article  PubMed  Google Scholar 

  53. Sara SJ (2009) The Locus coeruleus and noradrenergic modulation of cognition. Nat Neurosci Rev 10:211–223

    CAS  Article  Google Scholar 

  54. Schechtman E, Laufer O, Paz R (2010) Reinforcement affects stimulus generalization. J Neurosci 30(31):10460–10464

    CAS  Article  PubMed  Google Scholar 

  55. Shouval HZ, Bear MF, Cooper LN (2002a) A unified model of NMDA receptor-dependent bidirectional synaptic plasticity. Proc Natl Aca Sci USA 99:10831–10836

    CAS  Article  Google Scholar 

  56. Shouval HZ, Castellani GC, Blais BS, Yeung LC, Cooper LN (2002b) Converging evidence for a simplified biophysical model of synaptic plasticity. Biol Cybern 87:383–391

    Article  PubMed  Google Scholar 

  57. Sigurdsson T, Doyere V, Cain CK, Ledoux JE (2007) Long-term potentiation in the amygdala: a cellular mechanism of fear learning and memory. Neuropharmacology 52:215–227

    CAS  Article  PubMed  Google Scholar 

  58. Spampanato J, Polepalli J, Sah P (2011) Interneurons in the basolateral amygdala. Neuropharmacol 60:765–773

    CAS  Article  Google Scholar 

  59. Szinyei C, Heinbockel T, Montagne J, Pape HC (2000) Putative cortical and thalamic inputs elicit convergent excitation in a population of GABAergic interneurons of the lateral amygdala. J Neurosci 20:8909–8915

    CAS  PubMed  Google Scholar 

  60. Tully K, Bolshakov VY (2010) Emotional enhancement of memory: how norepinephrine enables synaptic plasticity. Mol Brain 3:15

    Article  PubMed  PubMed Central  Google Scholar 

  61. Tuunanen J, Pitkanen A (2000) Do seizures cause neuronal damage in rat amygdala kindling? Epilepsy Res 39:171–176

    CAS  Article  PubMed  Google Scholar 

  62. Varela J, Sen K, Gibson J, Fost J, Abbott L, Nelson S (1997) A quantitative description of short-term plasticity at excitatory synapses in layer 2/3 of rat primary visual cortex. J Neurosci 17:7926–7940

    CAS  PubMed  Google Scholar 

  63. Viosca J, Lopez de Armentia M, Jancic D, Barco A (2009) Enhanced CREB-dependent gene expression increases the excitability of neurons in the basal amygdala and primes the consolidation of contextual and cued fear memory. Learn Mem 16:193–197

    Article  PubMed  Google Scholar 

  64. Vlachos I, Herry C, Luthi A, Aertsen A, Kumar A (2011) Context-dependent encoding of fear and extinction memories in a large-scale network model of the basal amygdala. PLoS Comput Biol 7:e1001104

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  65. Warman EN, Durand DM, Yuen GLF (1994) Reconstruction of hippocampal CA1 pyramidal cell electrophysiology by computer simulation. J Neurophysiol 71:2033–2045

    CAS  PubMed  Google Scholar 

  66. Washburn MS, Moises HC (1992) Electrophysiological and morphological properties of rat basolateral amygdaloid neurons in vitro. J Neurosci 12:4066–4079

    CAS  PubMed  Google Scholar 

  67. Weinberger NM (2011) The medial geniculate, not the amygdala, as the root of auditory fear conditioning. Hear Res 274:61–74

    Article  PubMed  PubMed Central  Google Scholar 

  68. Zador A, Koch C, Brown TH (1990) Biophysical model of a Hebbian synapse. Proc Natl Acad Sci 87:6718–6722

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  69. Zhou Y, Won J, Karlsson MG, Zhou M, Rogerson T, Balaji J, Neve R, Poirazi R, Silva AJ (2009) CREB regulates excitability and the allocation of memory to subsets of neurons in the amygdala. Nat Neurosci 12:1438–1443

    CAS  Article  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgments

This research was supported in part by grants from the National Institute of Mental Health (MH083710 to DP and MH087755 to SSN).

Conflict of interest

The authors declare no competing financial interests.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Satish S. Nair.

Appendices

Appendix

Here, we list additional information related to methods, including the mathematical equations, implementation of the effects of neuromodulators, and the iterative procedures. All model runs were performed using parallel NEURON (Carnevale and Hines 2006) running on a Beowulf supercluster with a time step of 50 μs. Simulation output was analyzed using MATLAB.

Mathematical equations for voltage-dependent ionic currents

The equation for each compartment (soma or dendrite) followed the Hodgkin–Huxley formulations (Byrne and Roberts 2004) in Eq. (1),

$$C_{\text{m}} {\text{d}}V_{\text{s}} /{\text{d}}t = - g_{\text{L}} (V_{\text{s}} - E_{\text{L}} ) - g_{\text{c}} (V_{\text{s}} - V_{\text{d}} ) - \mathop \sum \nolimits I_{\text{cur,s}}^{\text{int}} - \mathop \sum \nolimits I_{{{\text{cur,}}\;{\text{s}}}}^{\text{syn}} + I_{\text{inj}}$$
(1)

where \(V_{\text{s}} /V_{\text{d}}\) are the somatic/dendritic membrane potential (mV), \(I_{\text{cur,s}}^{\text{int}}\) and \(I_{\text{cur,s}}^{\text{syn}}\) are the intrinsic and synaptic currents in the soma, \(I_{\text{inj}}\) is the electrode current applied to the soma, \(C_{\text{m}}\) is the membrane capacitance, \(g_{\text{L}}\) is the conductance of leak channel, \(g_{\text{c}} = 1/{\text{Ra}}\) is the coupling conductance between the soma and the dendrite (similar term added for other dendrites connected to the soma), and E L is the leak reversal potential. Eq. (1) represents a current balance, with the sum of all currents being equal to the injected current. The term on the left represents the capacitance current. The intrinsic current \(I_{\text{cur,s}}^{\text{syn}}\), was modeled as \(I_{\text{cur,s}}^{\text{int}} = g_{\text{cur}} m^{p} h^{q} (V_{\text{s}} - E_{\text{cur}} )\), where \(g_{\text{cur}}\) is its maximal conductance, m its activation variable (with exponent p), h its inactivation variable (with exponent q), and \(E_{\text{cur}}\) its reversal potential (a similar equation is used for the synaptic current \(I_{\text{cur,s}}^{\text{syn}}\) but without m and h). The kinetic equation for each of the gating variables x (m or h) takes the form

$$\frac{{{\text{d}}x}}{{{\text{d}}t}} = \frac{{x_{\infty } \;\left( {V,\left[ {{\text{Ca}}^{2 + } } \right]_{i} } \right) - x}}{{\tau_{x} \;\left( {V,\left[ {{\text{Ca}}^{2 + } } \right]_{i} } \right)}}$$
(2)

where \(x_{\infty }\) is the steady state gating voltage- and/or Ca2+-dependent gating variable and \(\tau_{x}\) is the voltage- and/or Ca2+ -dependent time constant. The equation for the dendrite follows the same format with ‘s’ and ‘d’ switching positions in Eq. (1). Details related to the model, including types of channels and parameter values are provided in Tables 2 and 3.

Table 2 Gating variables for ion channels used in the single cell models
Table 3 Maximal conductance densities of ion channels

Mathematical equations for synaptic currents

Excitatory transmission was mediated by AMPA/NMDA receptors, and inhibitory transmission by GABAA receptors. The corresponding synaptic currents were modeled by dual exponential functions (Durstewitz et al. 2000), as shown in Eqs. (3)–(5),

$$I_{\text{AMPA}} = w\left( t \right)\;{ \times }\;G_{\text{AMPA}} \;{ \times }\;(V - E_{\text{AMPA}} )$$
(3)
$$I_{\text{NMDA}} \; = \;w\;{ \times }\;G_{\text{NMDA}} \;{ \times }\;(V - E_{\text{NMDA}} )$$
(4)
$$I_{\text{GABA}} \; = \;w\left( t \right)\;{ \times }\;G_{\text{GABA}} \;{ \times }\;(V - E_{\text{GABA}} )$$
(5)

where V is the membrane potential (mV) of the compartment (dendrite or soma) where the synapse is located and w is the adjustable synaptic weight for the synapse (w was variable for AMPA and GABA synapses, but fixed for NMDA synapses), and G X is the conductance of the particular synapse (see Sect. “Calcium dynamics and Hebbian learning” for expressions for G X ). The synaptic reversal potentials were E AMPA = E NMDA = 0 mV and E GABAA = −75 mV (Durstewitz et al. 2000).

Calcium dynamics and Hebbian learning

Intracellular calcium concentration, \(\left[ {{\text{Ca}}^{2 + } } \right]_{\text{pool}}\), was regulated by a simple first-order differential equation shown in Eq. (6) (Warman et al. 1994),

$$\frac{{d\left[ {{\text{Ca}}^{2 + } } \right]_{\text{pool}} }}{{{\text{d}}t}} = - f\frac{{I_{\text{Ca}}^{X} }}{zFV} + \frac{{\left[ {{\text{Ca}}^{2 + } } \right]_{\text{rest}} - \left[ {{\text{Ca}}^{2 + } } \right]_{\text{pool}} }}{{\tau_{\text{Ca}} }}$$
(6)

where \(I_{\text{Ca}}^{X}\) is the relevant current (NMDA, AMPA, or GABA) contributing to the pool (refer to Eqs. 810); f if the fraction of the Ca2+ component of the relevant current (f = 0.024); volume V = (4/3 × π × r_pool3) with r_pool = 0.9086 mm, z = 2 is the valence of the Ca2+ ion; F is the Faraday constant; and is τ Ca the time constant associated with Ca2+ removal. The resting Ca2+ concentration was \(\left[ {{\text{Ca}}^{2 + } } \right]_{\text{rest}}\) = 50 nmol/l (Durstewitz et al. 2000).

The biophysical Hebbian rule was implemented by adjusting the synaptic weight w(t) in synaptic conductances (Eqs. 3, 5) using Eq. (7),

$$\Delta w_{j} = \eta \left( {\left[ {{\text{Ca}}^{2 + } } \right]_{j} } \right)\Delta t\left( {\lambda_{1} \Omega \left( {\left[ {{\text{Ca}}^{2 + } } \right]_{j} } \right) - \lambda_{2} \omega_{j} } \right)$$
(7)

where η is the Ca2+-dependent learning rate and Ω is a Ca2+-dependent function with two thresholds (θ d and θ p; θ d ≤ θ p) (for details, see Li et al. 2009); λ 1 and λ 2 represent scaling and decay factors, respectively; the local calcium level at synapse j is denoted by \(\left[ {{\text{Ca}}^{2 + } } \right]_{j}\) and Δt is the simulation time step. With this learning rule, the synaptic weight decreases when θ d < \(\left[ {{\text{Ca}}^{2 + } } \right]_{j}\) < θ p, and increases when \(\left[ {Ca^{2 + } } \right]_{j}\) > θ p, with modulation by the decay term λ 2 w j.

Concentration of calcium pools

The concentration of the calcium pool at synapse j followed the dynamics in Eq. (6), with f j  = 0.024 (Warman et al. 1994), τ j  = 50 ms (Shouval et al. 2002b), V is the volume of a spine head with a diameter of 2 μm (Kitajima and Hara 1997). All the synaptic weights were constrained by upper (W max) and lower (W min) limits (Li et al. 2009). Maximum (f max) and minimum (f min) folds were specified for each modifiable synapse so that W max = f max × w(0) and W min = f min × w(0).

Excitatory synapses onto principal cells

For tone-PN, and PN–PN connections, the calcium influx \(I_{\text{Ca}}^{N}\) which determines learning was estimated as in Li et al. (2009), using Eq. (8),\(I_{\text{Ca}}^{N} = P_{0} G_{\text{NMDA}} (V - E_{\text{Ca}} ),\) where

$$\begin{aligned} G_{\text{NMDA}} = g_{\text{NMDA,max}} \;{ \times }\;{\text{STP}}_{\text{NMDA}} { \times }s\left( V \right)\;{ \times }\;r_{\text{NMDA}} \hfill \\ r_{\text{NMDA}} = \alpha T{ \hbox{max} }_{\text{NMDA}} { \times }{\text{ON}}_{\text{NMDA}} { \times }\left( {1 - r_{\text{NMDA}} } \right) - \beta_{\text{NMDA}} { \times }r_{\text{NMDA}} \hfill \\ \end{aligned}$$
(8)

where P 0 = 0.015, the reversal potential of calcium E Ca = 120 mV; the maximal conductance for NMDA current \(g_{\text{NMDA,max}}\) = 0.5 nS; STPNMDA is the short-term plasticity factor (see Sect. “Short-term presynaptic plasticity”); the voltage-dependent variable s(V) which implements the Mg2+ block was defined as: s(V) = [1 + 0.33 exp(−0.06 V)]−1 (Zador et al. 1990); \(r_{\text{NMDA}}\) is the fraction of bound receptors; \(\alpha T{ \hbox{max} }_{\text{NMDA}}\) = 0.2659/ms and \(\beta_{\text{NMDA}}\) = 0.0008/ms are specific synaptic current parameters; and ONNMDA = 1 if the NMDA receptor is open, else 0.

Excitatory synapses onto interneurons

For tone-interneuron, and principal cell–interneuron connections, the calcium influx (used for learning) at the excitatory synapses on interneurons occurs through both NMDA and AMPA receptors Eqs. (8) and (9) (details in Li et al. 2009) with P 0 = 0.001 in Eq. (9).

\(I_{\text{Ca}}^{A} = P_{0} wG_{\text{AMPA}} (V - E_{\text{Ca}} )/w(0)\), where

$$\begin{aligned}G_{\text{AMPA}} &= g_{\text{AMPA,max}} \;{ \times }\;{\text{STP}}_{\text{AMPA}} \;{ \times }\;r_{\text{AMPA}} \\ r_{\text{AMPA}} &= \alpha T_{\text{AMPA}} \;{ \times }\;{\text{ON}}_{\text{AMPA}} \;{ \times }\;\left( {1 - r_{\text{AMPA}} } \right) - \beta_{\text{AMPA}} \;{ \times }\;r_{\text{AMPA}} \end{aligned}$$
(9)

where the parameters are as defined in Eq. (8), with P 0 = 0.001; the maximal conductance for AMPA current \(g_{\text{AMPA,max}}\) = 1 nS; \(r_{\text{AMPA}}\) is the fraction of bound receptors; \(\alpha T{ \hbox{max} }_{\text{AMPA}}\) = 3.8142/ms and \(\beta_{\text{AMPA}}\) = 0.1429/ms, and w(0) is the initial weight of the synapse. The Ca2+ current through the AMPA/NMDA receptors was separated from the total AMPA/NMDA current in this manner and used for implementation of the learning rule (Kitajima and Hara 1997; Shouval et al. 2002a; Li et al. 2009).

Inhibitory synapses onto principal cells

Several different mechanisms have been reported for potentiation at GABAergic synapses in other brain regions (e.g., Gaiarsa et al. 2002). A rise in postsynaptic intracellular Ca2+ concentration seems to be required in most mechanisms to trigger long-term plasticity. In the neonatal rat hippocampus, potentiation could be induced by Ca2+ influx through the voltage-dependent Ca2+ channels (VDCCs), whereas in the cortex and cerebellum, this process requires Ca2+ release from postsynaptic internal stores that is dependent on stimulation of GABA receptors (Gaiarsa et al. 2002). Thus, both presynaptic activity (GABA receptor stimulation or interneuron firing) and postsynaptic activity (activation of VDCCs by membrane depolarization) contribute to the potentiation of GABA synapses. The process from GABA receptor stimulation to internal Ca2+ release involves activating a cascade of complex intracellular reactions (Komatsu 1996). Such a complex process can be simplified by assuming that the Ca2+ release is proportional to the stimulation frequency or GABAA conductance (Li et al. 2009). Hence, we modeled this simplified process by considering Ca2+ release from the internal stores into a separate Ca2+ pool, using an equation similar to that for the AMPA/NMDA case cited above, as shown in Eq. (10), \(I_{\text{Ca}}^{G} = P_{0} G_{\text{GABA}} (V - E_{\text{Ca}} )\), where

$$\begin{aligned} G_{\text{GABA}} = g_{\text{GABAmax}} \;{ \times }\;{\text{STP}}_{\text{GABA}} \;{ \times }\;r_{\text{GABA}} \hfill \\ r_{\text{GABA}} = \alpha T{ \hbox{max} }_{\text{GABA}} \;{ \times }\;{\text{ON}}_{\text{GABA}} \;{ \times }\;\left( {1 - r_{\text{GABA}} } \right) - \beta_{\text{GABA}} \;{ \times }\;r_{\text{GABA}} \hfill \\ \end{aligned}$$
(10)

with the parameters again as defined in Eq. (8), with P 0 = 0.01; the maximal conductance for GABA current \(g_{\text{GABA,max}}\) = 0.6 nS; \(r_{\text{GABA}}\) is the fraction of bound receptors; \(\alpha T{ \hbox{max} }_{\text{GABA}}\) = 7.2609/ms and \(\beta_{\text{GABA}}\) = 0.2667/ms.

The current \(I_{\text{Ca}}^{G}\) models the dependence of Ca2+ release on GABAA stimulation frequency but not Ca2+ influx through the GABAA channel. \(I_{\text{Ca}}^{G}\), together with portion of postsynaptic voltage-dependent calcium current (I Ca), contributed towards plasticity. The total calcium influx into the pool for learning was \(I_{\text{Ca}}^{G} + 0.01I_{\text{Ca}}\) for such synapses (Li et al. 2009).

Intrinsic connectivity in LAd

By comparing the responses of LAd cells to local applications of glutamate at various positions with respect to recorded neurons, Samson and Paré (2006) inferred general principles of connectivity among principal cells, as well as between local-circuit and principal neurons. In particular, Samson and Paré (2006) determined that excitatory connections between principal cells prevalently run ventrally and medially with significant rostrocaudal divergence. In contrast, inhibitory connections prevalently run mediolaterally in the horizontal plane and have no preferential directionality in the coronal plane. Samson and Paré (2006) also recognized that principal LAd neurons located along the external capsule (in the “shell” region of LA) form different connections than those found more medially (in the “core” region of LA; shell thickness of 100 µm). In the shell region, inhibitory neurons only affect nearby principal neurons, whereas excitatory connections between principal cells are spatially less limited. While not providing precise connectivity data, this information could be used to infer critical estimates about directionality and ratio of excitation to inhibition. The directionality information from the Samson and Paré (2006) study, described in the two paragraphs that follow, were implemented in the model, using a third of the connectivity numbers. Such an implementation for one model run showed that a model principal cell had, on average, 21.4 mono- and 40.6 di-synaptic excitatory inputs, and 20.4 mono-synaptic inhibitory inputs.

Coronal plane

Within a 100-µm coronal slice, principal shell neurons excite shell cells located 300–400 µm more ventrally with 10 % probability (mono-synaptic connectivity). Core to shell connections occur with a much lower probability (2 %). In addition, principal shell neurons are inhibited by more dorsally located interneurons (23 % connectivity for cells within 300 μm). In the core region, excitatory connections between principal cells have a greater extent in the lateromedial direction (50–800 μm, 2–6 %, connectivity) than in the mediolateral direction (50–200 μm, 5 % connectivity), whereas inhibitory connections have similar strengths in all directions (interneurons formed inhibitory inputs with 10–24 % of principal cells at a distance of 50–600 μm).

Horizontal plane

Within a 100-µm horizontal slice, connections were set in the following manner. Connection probability increased with distance for lateromedial connections, and the opposite for mediolateral connections. As to inhibitory connections, they prevalently run in the mediolateral direction with 8–20 % connectivity in the range 50–600 μm and 5–20 % connectivity in the lateromedial direction within a distance of 50–600 μm. Principal cells project to all interneurons within a spherical radius of 100 μm. Figures related to these connectivity configurations can be found in Kim et al. (2013a; Fig. 2).

Short-term presynaptic plasticity

Short-term plasticity was implemented as follows (Varela et al. 1997; Hummos et al. 2014): For facilitation, the factor F was calculated using Eq. (11).

$$\tau_{F} { \times }\frac{{{\text{d}}F}}{{{\text{d}}t}} = 1 - F;F\left( 0 \right) = 1, \;{\text{and it is constrained to be}} \ge 1$$
(11)

After each stimulus, F was multiplied by a constant f (≥1) representing the amount of facilitation per presynaptic action potential, and updated as \(F \to F{ \times }f\). Between stimuli, F recovered exponentially back toward 1. A similar scheme was used to calculate the factor D for depression,

$$\tau_{Di} { \times }\frac{{{\text{d}}Di}}{{{\text{d}}t}} = 1 - D_{i} ;D_{i} \left( 0 \right) = 1,\;{\text{and it is constrained to be}} \le 1$$
(12)

where i varied from 1 to the number of depression factors, permitting use of different time constants. After each stimulus, D i was multiplied by a constant d i (≤1) representing the amount of depression per presynaptic action potential, and updated as \(D_{i} \to D_{i} { \times }d_{i}\). Between stimuli, D i recovered exponentially back toward 1. We modeled depression using two factors d 1 and d 2 with d 1 being fast and d 2 being slow subtypes. The parameters for the short-term plasticity models, the initial weights and other learning parameters for the synapses are listed in Table 4.

Table 4 Model synaptic strengths and learning parameters

Modeling neuromodulator effects

Blockade of DA and NE has been shown to impair the acquisition of fear memory in LA. These have been modeled by adjusting both intrinsic and synaptic parameters based on experimental reports (see Kim et al. 2013a for details) as shown in Table 5.

Table 5 Variations in maximal conductances to model neuromodulator effects

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kim, D., Samarth, P., Feng, F. et al. Synaptic competition in the lateral amygdala and the stimulus specificity of conditioned fear: a biophysical modeling study. Brain Struct Funct 221, 2163–2182 (2016). https://doi.org/10.1007/s00429-015-1037-4

Download citation

Keywords

  • Hebbian learning
  • Amygdala
  • Competition
  • Specificity
  • Memory