A robust in vivo-like persistent firing supported by a hybrid of intracellular and synaptic mechanisms

Abstract

Persistent firing is believed to support short-term information retention in the brain. Established hypotheses make use of the recurrent synaptic connectivity to support persistent firing. However, this mechanism is known to suffer from a lack of robustness. On the other hand, persistent firing can be supported by an intrinsic cellular mechanism in multiple brain areas. However, the consequences of having both the intrinsic and the synaptic mechanisms (a hybrid model) on persistent firing remain largely unknown. The goal of this study is to investigate whether a hybrid neural network model with these two mechanisms has advantages over a conventional recurrent network based model. Our computer simulations were based on in vitro recordings obtained from hippocampal CA3 pyramidal cells under cholinergic receptor activation. Calcium activated non-specific cationic (CAN) current supported persistent firing in the Hodgkin-Huxley style cellular models. Our results suggest that the hybrid model supports persistent firing within a physiological frequency range over a wide range of different parameters, eliminating parameter sensitivity issues generally recognized in network based persistent firing. In addition, persistent firing in the hybrid model is substantially more robust against distracting inputs, can coexist with theta frequency oscillations, and supports pattern completion.

Fig 1. The CAN current supports persistent firing in the single cell model.

(A) Response of an in vitro hippocampal CA3 pyramidal cell in the normal ACSF. The brief current injection did not induce persistent firing. Ionotropic synaptic blockers, 20 μM CNQX, 50 μM D,L-APV and 100 μM PTX, were present in all in vitro recordings to block AMPA/kainite receptors, NMDA receptors and GABA_A receptors, respectively. (B) Response of the same cell in carbachol (10 μM). Long-lasting (≥ 30 s) persistent firing is observed after the same brief stimulation. (C) Self-terminating persistent firing (< 30 s) was observed in the same condition as in B in some cells. (D) Response of the single pyramidal cell model to a brief current injection without the CAN current. No persistent firing was seen. (E) Long-lasting persistent firing observed in the single pyramidal cell model with 100% CAN current. (F) Self-terminating persistent firing observed in the single pyramidal cell model with 90% CAN current. (G-I) Further reduction of the CAN current caused self-terminating persistent firing with shorter durations (G and H) and an after-depolarization without spikes (I). In all figures, (i) Membrane potential, (ii) Frequency of firing, (iii) Intracellular calcium concentration, (iv) CAN current conductance, and (v) Current injection.

Fig 2. The hybrid model supports persistent firing within a physiological frequency range across a wide range of synaptic conductances.

(A1-3) Responses of the pure network model to a brief stimulation. Conductance of recurrent synaptic connections (Wpp) was 0.005, 0.011, and 0.017 nS, respectively. Activity of only one of the pyramidal cell models is shown. Bottom trace indicates current injection. (B1-3) Responses of the hybrid model with Wpp = 0.005, 0.011 and 0.017 nS, respectively. Frequency of persistent firing increased gradually with the increase in Wpp. (C) Model network structure. Three pyramidal cells were connected in an all-to-all fashion. (D) Frequency of persistent firing as a function of the synaptic conductance (Wpp). While pure network model (solid line with square symbols, I_CAN off) shows an abrupt frequency jump at around Wpp = 0.016 nS, the hybrid model (dotted lines with circle symbols, I_CAN on) shows a gradual increase of the frequency as a function of Wpp covering frequency range observed in vivo (3–50 Hz). Letters in the figure correspond to Figs. A1-3 and B1-3. I_CAN: CAN current.

Fig 3. Persistent firing with smaller CAN current conductances.

(A1 and 2) Responses of the model with 90% CAN current conductance. Conductance of recurrent synaptic connections (Wpp) was 0.005 and 0.008 nS, respectively. (B) Frequency of persistent firing as a function of Wpp. Relatively small CAN current conductances, which supported only self-terminating persistent firing in the single cell model, supported long-lasting persistent firing in the network model. A gradual increase of firing frequency was observed with these smaller CAN current conductances as well. I_CAN: CAN current.

Fig 4. Persistent firing in the hybrid model is more robust against distracting stimuli.

(A1-3) Responses of the pure network model to a negative current injection with different durations: 20 ms, 1 s, and 7.6 s, respectively. (B1-3) Responses of the hybrid network model to a negative current injection with different durations: 20 ms, 1 s, and 7.6 s, respectively. (C) Frequency of persistent firing as a function of the duration of the negative current injection. Persistent firing in the pure network model was easily terminated by a short (≥ 20 ms) current injection. (D) Frequency of persistent firing in the pure network model as a function of the duration and the amplitude of the negative current injection. (E) Same as in D from the hybrid network model. Persistent firing is more robust in the hybrid model. (F) Same as in E but with a reduced Wpp (0.01 μS). Note different frequency scale. In all figures, (i) Membrane potential, (ii) Intracellular calcium concentration, (iii) CAN current conductance, and (iv) Current injection. I_CAN: CAN current.

Fig 5. Persistent firing in the hybrid model can co-exist with theta rhythm.

(A1 and 2) Responses of the pure network model to a 7 Hz sinusoidal current injection. The amplitude of the current injection was 0.12 nA in A1, and 0.13 nA in A2. (B1 and 2) Responses of the hybrid network model to the same current injection with an amplitude of 0.12 nA in B1, and 0.13 nA in B2. Theta entrainment was observed only in the hybrid model. (C) Frequency of persistent firing as a function of the amplitude of the sinusoidal current injection. In all figures, (i) Membrane potential, (ii) Intracellular calcium concentration, (iii) CAN current conductance, (iv) Current injection. I_CAN: CAN current.

Fig 6. The effect of the CAN current in a network model with a feedback inhibition.

(A1 and 2) Responses of the pure network model with different inhibitory synaptic conductances: 0.007 and 0.03 nS, respectively. (B1 and 2) Responses of the hybrid network model with different inhibitory synaptic conductances: 0.007 and 0.03 nS, respectively. (C) The model network structure. White circles represent pyramidal cells and shaded circles represent inhibitory cells. (D—F) Frequency of persistent firing as a function of the inhibitory synaptic conductance (Wip), with different time constants for IPSC: 5 ms, 50 ms and 250 ms, respectively. Frequency of persistent firing is modulated gradually by the increased inhibitory conductance in the hybrid model with the CAN current but not in the pure network model.

Fig 7. An ability for pattern completion is intact in the hybrid model.

(A and B) Responses of all three cells in the hybrid model with different excitatory synaptic conductances: 0.005 nS and 0.015 nS, respectively. Note that the stimulation (retrieval cue) is given only to the cell 1. (C) Average frequency of persistent firing of the non-stimulated cells (cell 2 and cell 3) as a function of the synaptic conductance for different levels of CAN current conductance. (D) Frequency of persistent firing of the non-stimulated cells (cell 3) when stimulation was given to the cell 1 and cell 2 for different levels of CAN current conductance. The ability for pattern completion was present in the hybrid model within a physiologically observed frequency range, even when CAN current conductances were used that support only self-terminating persistent firing in individual cells.