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Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks.

Solanka L, van Rossum MC, Nolan MF - Elife (2015)

Bottom Line: Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity.This beneficial role for noise results from disruption of epileptic-like network states.Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

View Article: PubMed Central - PubMed

Affiliation: Centre for Integrative Physiology, University of Edinburgh, Edinburgh, United Kingdom.

ABSTRACT
Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

No MeSH data available.


Related in: MedlinePlus

Seizure-like states in networks that contain direct I → I synapses.(A–C) Raster plots show activity of all neurons in the excitatory (red) and inhibitory (blue) populations for the duration of two theta cycles (top), along with the average population firing rates for both populations (center and bottom; calculated with a sliding rectangular window with 2 ms duration and 0.5 ms time step), for networks where noise is absent (A; σ = 0), with noise set to σ = 150 pA (B), and with noise set to σ = 300 pA (C). Simulations were performed in the absence of animal movement and place cell input; gE = 1 nS and gI = 3 nS. (D) Maximal average population firing rate of E cells estimated from the whole simulation run (10 s; 500 ms at the beginning of the simulation excluded) for each simulated level of noise. Each point is an average of maxima from five simulation runs. (E) Probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz, that is, at least 60% of E cells firing synchronously within a time period of 2 ms, in the parameter space of gE and gI when σ = 0 pA. Black lines indicate the regions from Figure 7A–C where gridness score equals 0.5. (F) Scatter plots show the relationship between gridness score and the maximal firing rate during the simulation (left) and the probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz (right).DOI:http://dx.doi.org/10.7554/eLife.06444.030
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fig7s5: Seizure-like states in networks that contain direct I → I synapses.(A–C) Raster plots show activity of all neurons in the excitatory (red) and inhibitory (blue) populations for the duration of two theta cycles (top), along with the average population firing rates for both populations (center and bottom; calculated with a sliding rectangular window with 2 ms duration and 0.5 ms time step), for networks where noise is absent (A; σ = 0), with noise set to σ = 150 pA (B), and with noise set to σ = 300 pA (C). Simulations were performed in the absence of animal movement and place cell input; gE = 1 nS and gI = 3 nS. (D) Maximal average population firing rate of E cells estimated from the whole simulation run (10 s; 500 ms at the beginning of the simulation excluded) for each simulated level of noise. Each point is an average of maxima from five simulation runs. (E) Probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz, that is, at least 60% of E cells firing synchronously within a time period of 2 ms, in the parameter space of gE and gI when σ = 0 pA. Black lines indicate the regions from Figure 7A–C where gridness score equals 0.5. (F) Scatter plots show the relationship between gridness score and the maximal firing rate during the simulation (left) and the probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz (right).DOI:http://dx.doi.org/10.7554/eLife.06444.030

Mentions: Our analysis so far focuses on E-I attractor networks as simple models of grid firing that are compatible with the finding that synaptic interactions between stellate cells in layer 2 of the MEC are mediated via inhibitory interneurons (Dhillon and Jones, 2000; Couey et al., 2013; Pastoll et al., 2013). However, there is evidence that interneurons active during theta-nested gamma activity make connections to one another as well as to stellate cells (Pastoll et al., 2013). To establish whether this recurrent inhibition substantially modifies our conclusions from simpler E-I networks, we extended the E-I model to also include synapses between interneurons (see ‘Materials and methods’). In the resulting E-I-I networks, in the absence of noise, grid firing emerges across a much larger region of parameter space compared to E-I networks (Figure 7A, Figure 7—figure supplements 1–4). However, as in E-I networks occasional seizure like activity was present across a wide range of gE and gI (Figure 7—figure supplement 5), and gamma frequency activity was largely absent (Figure 7D,G). Following addition of noise with standard deviation of 150 pA to E-I-I networks, grid firing was maintained, seizure like activity was abolished, and gamma like activity emerged (Figure 7B,E,H and Figure 7—figure supplement 5). Increasing the noise amplitude to 300 pA reduced grid firing and interfered with the emergence of gamma oscillations (Figure 7C,F,I and Figure 7—figure supplements 1–5). Importantly, just as in E-I networks, the presence of moderate noise in E-I-I networks enables tuning of gamma activity by varying gE and gI while maintaining the ability of the networks to generate grid firing fields. Gamma activity had a higher frequency in E-I-I compared to E-I networks, with a greater proportion of the parameter space supporting gamma frequencies >80 Hz. This higher frequency gamma is similar to fast gamma observed experimentally in the MEC (cf. Chrobak and Buzsáki, 1998; Colgin et al., 2009; Pastoll et al., 2013). Thus, by including additional features of local circuits in layer 2 of the MEC, E-I-I models may more closely recapitulate experimental observations. Nevertheless, E-I-I networks maintain the ability, in the presence of moderate noise, for variation in gE and gI to tune gamma oscillations without interfering with grid firing.10.7554/eLife.06444.025Figure 7.Gridness scores and gamma activity in networks with recurrent inhibition.


Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks.

Solanka L, van Rossum MC, Nolan MF - Elife (2015)

Seizure-like states in networks that contain direct I → I synapses.(A–C) Raster plots show activity of all neurons in the excitatory (red) and inhibitory (blue) populations for the duration of two theta cycles (top), along with the average population firing rates for both populations (center and bottom; calculated with a sliding rectangular window with 2 ms duration and 0.5 ms time step), for networks where noise is absent (A; σ = 0), with noise set to σ = 150 pA (B), and with noise set to σ = 300 pA (C). Simulations were performed in the absence of animal movement and place cell input; gE = 1 nS and gI = 3 nS. (D) Maximal average population firing rate of E cells estimated from the whole simulation run (10 s; 500 ms at the beginning of the simulation excluded) for each simulated level of noise. Each point is an average of maxima from five simulation runs. (E) Probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz, that is, at least 60% of E cells firing synchronously within a time period of 2 ms, in the parameter space of gE and gI when σ = 0 pA. Black lines indicate the regions from Figure 7A–C where gridness score equals 0.5. (F) Scatter plots show the relationship between gridness score and the maximal firing rate during the simulation (left) and the probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz (right).DOI:http://dx.doi.org/10.7554/eLife.06444.030
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fig7s5: Seizure-like states in networks that contain direct I → I synapses.(A–C) Raster plots show activity of all neurons in the excitatory (red) and inhibitory (blue) populations for the duration of two theta cycles (top), along with the average population firing rates for both populations (center and bottom; calculated with a sliding rectangular window with 2 ms duration and 0.5 ms time step), for networks where noise is absent (A; σ = 0), with noise set to σ = 150 pA (B), and with noise set to σ = 300 pA (C). Simulations were performed in the absence of animal movement and place cell input; gE = 1 nS and gI = 3 nS. (D) Maximal average population firing rate of E cells estimated from the whole simulation run (10 s; 500 ms at the beginning of the simulation excluded) for each simulated level of noise. Each point is an average of maxima from five simulation runs. (E) Probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz, that is, at least 60% of E cells firing synchronously within a time period of 2 ms, in the parameter space of gE and gI when σ = 0 pA. Black lines indicate the regions from Figure 7A–C where gridness score equals 0.5. (F) Scatter plots show the relationship between gridness score and the maximal firing rate during the simulation (left) and the probability of the maximal population-average firing rate during each theta cycle exceeding 300 Hz (right).DOI:http://dx.doi.org/10.7554/eLife.06444.030
Mentions: Our analysis so far focuses on E-I attractor networks as simple models of grid firing that are compatible with the finding that synaptic interactions between stellate cells in layer 2 of the MEC are mediated via inhibitory interneurons (Dhillon and Jones, 2000; Couey et al., 2013; Pastoll et al., 2013). However, there is evidence that interneurons active during theta-nested gamma activity make connections to one another as well as to stellate cells (Pastoll et al., 2013). To establish whether this recurrent inhibition substantially modifies our conclusions from simpler E-I networks, we extended the E-I model to also include synapses between interneurons (see ‘Materials and methods’). In the resulting E-I-I networks, in the absence of noise, grid firing emerges across a much larger region of parameter space compared to E-I networks (Figure 7A, Figure 7—figure supplements 1–4). However, as in E-I networks occasional seizure like activity was present across a wide range of gE and gI (Figure 7—figure supplement 5), and gamma frequency activity was largely absent (Figure 7D,G). Following addition of noise with standard deviation of 150 pA to E-I-I networks, grid firing was maintained, seizure like activity was abolished, and gamma like activity emerged (Figure 7B,E,H and Figure 7—figure supplement 5). Increasing the noise amplitude to 300 pA reduced grid firing and interfered with the emergence of gamma oscillations (Figure 7C,F,I and Figure 7—figure supplements 1–5). Importantly, just as in E-I networks, the presence of moderate noise in E-I-I networks enables tuning of gamma activity by varying gE and gI while maintaining the ability of the networks to generate grid firing fields. Gamma activity had a higher frequency in E-I-I compared to E-I networks, with a greater proportion of the parameter space supporting gamma frequencies >80 Hz. This higher frequency gamma is similar to fast gamma observed experimentally in the MEC (cf. Chrobak and Buzsáki, 1998; Colgin et al., 2009; Pastoll et al., 2013). Thus, by including additional features of local circuits in layer 2 of the MEC, E-I-I models may more closely recapitulate experimental observations. Nevertheless, E-I-I networks maintain the ability, in the presence of moderate noise, for variation in gE and gI to tune gamma oscillations without interfering with grid firing.10.7554/eLife.06444.025Figure 7.Gridness scores and gamma activity in networks with recurrent inhibition.

Bottom Line: Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity.This beneficial role for noise results from disruption of epileptic-like network states.Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

View Article: PubMed Central - PubMed

Affiliation: Centre for Integrative Physiology, University of Edinburgh, Edinburgh, United Kingdom.

ABSTRACT
Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

No MeSH data available.


Related in: MedlinePlus