A computational study on altered theta-gamma coupling during learning and phase coding

Abstract

There is considerable interest in the role of coupling between theta and gamma oscillations in the brain in the context of learning and memory. Here we have used a neural network model which is capable of producing coupling of theta phase to gamma amplitude firstly to explore its ability to reproduce reported learning changes and secondly to memory-span and phase coding effects. The spiking neural network incorporates two kinetically different GABA(A) receptor-mediated currents to generate both theta and gamma rhythms and we have found that by selective alteration of both NMDA receptors and GABA(A,slow) receptors it can reproduce learning-related changes in the strength of coupling between theta and gamma either with or without coincident changes in theta amplitude. When the model was used to explore the relationship between theta and gamma oscillations, working memory capacity and phase coding it showed that the potential storage capacity of short term memories, in terms of nested gamma-subcycles, coincides with the maximal theta power. Increasing theta power is also related to the precision of theta phase which functions as a potential timing clock for neuronal firing in the cortex or hippocampus.

Figure 1. Stimulus-enhanced theta wave as well as CFC.

(A) A network of 100 excitatory (EX), 50 fast inhibitory (INf) and 50 slow inhibitory neurons (INs). The outputs of EX neurons are projected to a downstream neuron. (B) The firing behaviors of single INs, INf and EX neurons. The bottom trace is the firing pattern of 50 EX neurons. (C) Input stimulus (Iapp), the LFP which is the average of membrane potentials of all EX neurons, the time-dependent power spectrum of the LFP of mean powers in the theta (red curve) and in the gamma band (blue curve). (D) Coherence of CFC between the theta phase and the gamma amplitude for the pre and during stimulus epochs.

Figure 2. Coordinated regulation of GABA_A,fast and GABA_A,slow currents is the key for generating theta-nested gamma oscillations.

(A) Three different response behaviors of the network to a stimulus: (A1) Only gamma rhythm (by blocking INs→EX connection); (A2) only theta rhythm (by blocking INf→EX connections); (A3) theta-nested gamma rhythm (in the presence of both INs→EX and INf→EX connection). The three traces from the upper to the bottom are the time-frequency power spectrum, the firing behaviors of EX cells and the firing behavior of a downstream neuron, respectively. (B-C) Effects of increasing g and on the theta and gamma amplitudes, the coherence of cross-frequency coupling, the tightness of theta phase.

Figure 3. Effects of modulating GABA conductances between and within inhibitory cells.

The amplitudes of theta and gamma oscillations, the coherence of CFC, theta phase variation and the firing of excitatory neurons as a function of changes in the strength of (A) g_{GAss ’} (B) g_Gff (C) g_GAsf are shown.

Figure 4. Effects of modulating NMDA conductances from excitatory to inhibitory neurons.

The amplitudes of theta and gamma oscillations, the coherence of CFC, the phase variation vs. and are depicted, respectively. (A) shows the effect of increasing , (B) shows the effect of increasing , (C) shows the effect of increasing .

Figure 5. Effect of coordinately regulating synaptic gains of NMDA and GABA_A,slow to simulate learning effects.

(A1–A3) Theta amplitude. (B1–B3) The coherence of CFC. (C1–C3) The temporal dynamics of theta phase. The stimulus is applied during 0–500 ms. To mimic different learning stages, we set NMDA receptor mediated conductances , and the GABA_A,slow mediated conductance as: 0.0001, 0.001, 0.05 (1st), 0.00025, 0.0025,0.06 (2nd), 0.00035 and 0.004, 0.07 (3rd), 0.00045, 0.005, 0.08(4th). The values of and in the three panels in A1–C1 are corresponding to the three marked points (1^st, 2^nd and 3^rd) in A2–C3. The values of other parameters are stated in Table 1. (A4–C4) Variations of theta and gamma amplitudes, the coherence of cross-frequency coupling and the phase variation with the increase of . (D) The firing rates of a downstream neuron vs.. (E) Comparison of the membrane potentials of single EX neurons before and after learning. In (C) the blue curve where represents before learning, while the red one where represents after learning.

Figure 6. Relationship of maximal theta amplitude, the number of nested spikes per theta cycle and theta-phase concentration.

(A-B) From the upper trace to the bottom trace:Theta amplitudes vs. the stimulus strength , the corresponding number of nested spikes per theta cycle vs., theta phase variation vs. , and the time-frequency spectra at of one curve. In (A), the three curves correspond to . In (B), , the three curves correspond to . (C) The number of nested spikes per theta cycle calculated at vs. the frequency of the corresponding maximal gamma power. The marked points are obtained from different curves of theta amplitude vs. . One can see that for low gamma power (20–50 Hz), around 5±2 spikes could be nested in each theta cycle, while for high gamma power (>50 Hz), around 7±2 spikes could be nested. (D) Theta phases of the EX cells for different stimulus strength. It was shown that for too weak and too strong stimulus, the theta phases of neurons are less synchronized than that of the intermediate stimulus strength.

Figure 7. Relationship of theta amplitude, shape of nested gamma wave and the phase precision.

(A). Variation of theta phase vs. theta amplitude. The increased theta amplitude is realized by increasing the conductance . (B) and (C). From the upper panel to the bottom panel are corresponding to three points chosen for low, intermediate and high theta powers in (A) for . It was shown in that with the increase of theta amplitude, gamma oscillation becomes more and more shallowly nested in the theta rhythm, and meanwhile, the theta-band phases among EX neurons become more and more concentrated.