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Dynamic Control of Synchronous Activity in Networks of Spiking Neurons

View Article: PubMed Central - PubMed

ABSTRACT

Oscillatory brain activity is believed to play a central role in neural coding. Accumulating evidence shows that features of these oscillations are highly dynamic: power, frequency and phase fluctuate alongside changes in behavior and task demands. The role and mechanism supporting this variability is however poorly understood. We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics. Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations. We show that afferent noise, mimicking inputs to the neurons, causes smoothing of the system’s response function, displacing equilibria and altering the stability of oscillatory states. Our analysis further shows that these noise-induced changes cause a shift of the peak frequency of synchronous oscillations that scales with input intensity, leading the network towards critical states. We lastly discuss the extension of these principles to periodic stimulation, in which externally applied driving signals can trigger analogous phenomena. Our results reveal one possible mechanism involved in shaping oscillatory activity in the brain and associated control principles.

No MeSH data available.


Frequency tuning curve.Frequency of the network synchronous oscillations as a function of noise intensity. Noise causes the peak frequency of the network oscillations to shift from the baseline frequency ωo towards the critical frequency ωc. The peak frequency is plotted according to numerical simulations of the network dynamics (red dotted curve), the mean-field approximation (grey; as per Eq 10) and using the frequency tuning curve (black; as per Eq 17). Other parameters are taken from Fig 3.
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pone.0161488.g004: Frequency tuning curve.Frequency of the network synchronous oscillations as a function of noise intensity. Noise causes the peak frequency of the network oscillations to shift from the baseline frequency ωo towards the critical frequency ωc. The peak frequency is plotted according to numerical simulations of the network dynamics (red dotted curve), the mean-field approximation (grey; as per Eq 10) and using the frequency tuning curve (black; as per Eq 17). Other parameters are taken from Fig 3.

Mentions: Expanding to third order for weak noise, i.e. D ≈ 0ω≈π2τ−2πDw¯τ−132π3D3w¯3τ+O(D5/2)(18)leading to the frequency tuning curveω≈ωo⋅(1+Δ(D))(19)where Δ(D) is a noise-induced shift with Δ(D) > 0. Fig 4 shows the frequency with respect to the noise intensity. Together with the results above, while approximate, demonstrate that under the action of noise, the network oscillation frequency gradually shifts from a non-linear baseline frequency towards the critical frequency . Eqs (18) and (19) thus imply that as noise increases in the system, the network transits from slow non-linear rhythms to fast linear oscillations. This can also be understood by looking at the susceptibility, which gauges the relative influence of recurrent interactions in the network, plotted in Fig 3B. As susceptibility decreases under the action of noise, the system accelerates and shifts from a recurrent deeply synchronous state to an asynchronous input driven regime.


Dynamic Control of Synchronous Activity in Networks of Spiking Neurons
Frequency tuning curve.Frequency of the network synchronous oscillations as a function of noise intensity. Noise causes the peak frequency of the network oscillations to shift from the baseline frequency ωo towards the critical frequency ωc. The peak frequency is plotted according to numerical simulations of the network dynamics (red dotted curve), the mean-field approximation (grey; as per Eq 10) and using the frequency tuning curve (black; as per Eq 17). Other parameters are taken from Fig 3.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5036852&req=5

pone.0161488.g004: Frequency tuning curve.Frequency of the network synchronous oscillations as a function of noise intensity. Noise causes the peak frequency of the network oscillations to shift from the baseline frequency ωo towards the critical frequency ωc. The peak frequency is plotted according to numerical simulations of the network dynamics (red dotted curve), the mean-field approximation (grey; as per Eq 10) and using the frequency tuning curve (black; as per Eq 17). Other parameters are taken from Fig 3.
Mentions: Expanding to third order for weak noise, i.e. D ≈ 0ω≈π2τ−2πDw¯τ−132π3D3w¯3τ+O(D5/2)(18)leading to the frequency tuning curveω≈ωo⋅(1+Δ(D))(19)where Δ(D) is a noise-induced shift with Δ(D) > 0. Fig 4 shows the frequency with respect to the noise intensity. Together with the results above, while approximate, demonstrate that under the action of noise, the network oscillation frequency gradually shifts from a non-linear baseline frequency towards the critical frequency . Eqs (18) and (19) thus imply that as noise increases in the system, the network transits from slow non-linear rhythms to fast linear oscillations. This can also be understood by looking at the susceptibility, which gauges the relative influence of recurrent interactions in the network, plotted in Fig 3B. As susceptibility decreases under the action of noise, the system accelerates and shifts from a recurrent deeply synchronous state to an asynchronous input driven regime.

View Article: PubMed Central - PubMed

ABSTRACT

Oscillatory brain activity is believed to play a central role in neural coding. Accumulating evidence shows that features of these oscillations are highly dynamic: power, frequency and phase fluctuate alongside changes in behavior and task demands. The role and mechanism supporting this variability is however poorly understood. We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics. Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations. We show that afferent noise, mimicking inputs to the neurons, causes smoothing of the system’s response function, displacing equilibria and altering the stability of oscillatory states. Our analysis further shows that these noise-induced changes cause a shift of the peak frequency of synchronous oscillations that scales with input intensity, leading the network towards critical states. We lastly discuss the extension of these principles to periodic stimulation, in which externally applied driving signals can trigger analogous phenomena. Our results reveal one possible mechanism involved in shaping oscillatory activity in the brain and associated control principles.

No MeSH data available.