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Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses.

Kriener B, Enger H, Tetzlaff T, Plesser HE, Gewaltig MO, Einevoll GT - Front Comput Neurosci (2014)

Bottom Line: We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network.During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states.We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

View Article: PubMed Central - PubMed

Affiliation: Neural Coding and Dynamics, Center for Learning and Memory, University of Texas at Austin Austin, TX, USA ; Computational Neuroscience, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences Ås, Norway.

ABSTRACT
Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

No MeSH data available.


Related in: MedlinePlus

Lifetime (A) and firing rate (B) of SSAI. Dependence of the SSAI lifetime (A) and mean firing rate (B) [cf. Equation (7)] on the synaptic weight J and the relative strength g of inhibition. Lifetimes and mean firing rates were measured after the external input was turned off. Data represent averages over 10 network realizations. White curves in (A) mark saddle-node bifurcations obtained from the diffusion approximation of the LIF neuron [see Brunel, 2000 and Equation S1 in the Supplementary Material with input current mean and variance derived from Equation (17); dotted curve] and from the Abeles-type two-state model (19) (dashed; with rmax = 1/2τref, see Section 3.4.1). Other parameters as in Figure 1.
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Figure 3: Lifetime (A) and firing rate (B) of SSAI. Dependence of the SSAI lifetime (A) and mean firing rate (B) [cf. Equation (7)] on the synaptic weight J and the relative strength g of inhibition. Lifetimes and mean firing rates were measured after the external input was turned off. Data represent averages over 10 network realizations. White curves in (A) mark saddle-node bifurcations obtained from the diffusion approximation of the LIF neuron [see Brunel, 2000 and Equation S1 in the Supplementary Material with input current mean and variance derived from Equation (17); dotted curve] and from the Abeles-type two-state model (19) (dashed; with rmax = 1/2τref, see Section 3.4.1). Other parameters as in Figure 1.

Mentions: The lifetime of the SSAI increases rapidly from zero to more than 1000 s (i.e., networks stay active for the whole duration of the simulation) within a narrow band in the parameter space spanned by g and J, see Figure 3A. This transition band becomes wider, i.e., more gradual in terms of J, as g is increased, indicating a more shallow transition between transient and stable self-sustained activation. The rate of the persistent activity is typically between 20 and 50 s−1, increasing to 400 s−1 when excitation becomes dominant at g < 4, see Figure 3B.


Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses.

Kriener B, Enger H, Tetzlaff T, Plesser HE, Gewaltig MO, Einevoll GT - Front Comput Neurosci (2014)

Lifetime (A) and firing rate (B) of SSAI. Dependence of the SSAI lifetime (A) and mean firing rate (B) [cf. Equation (7)] on the synaptic weight J and the relative strength g of inhibition. Lifetimes and mean firing rates were measured after the external input was turned off. Data represent averages over 10 network realizations. White curves in (A) mark saddle-node bifurcations obtained from the diffusion approximation of the LIF neuron [see Brunel, 2000 and Equation S1 in the Supplementary Material with input current mean and variance derived from Equation (17); dotted curve] and from the Abeles-type two-state model (19) (dashed; with rmax = 1/2τref, see Section 3.4.1). Other parameters as in Figure 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4214205&req=5

Figure 3: Lifetime (A) and firing rate (B) of SSAI. Dependence of the SSAI lifetime (A) and mean firing rate (B) [cf. Equation (7)] on the synaptic weight J and the relative strength g of inhibition. Lifetimes and mean firing rates were measured after the external input was turned off. Data represent averages over 10 network realizations. White curves in (A) mark saddle-node bifurcations obtained from the diffusion approximation of the LIF neuron [see Brunel, 2000 and Equation S1 in the Supplementary Material with input current mean and variance derived from Equation (17); dotted curve] and from the Abeles-type two-state model (19) (dashed; with rmax = 1/2τref, see Section 3.4.1). Other parameters as in Figure 1.
Mentions: The lifetime of the SSAI increases rapidly from zero to more than 1000 s (i.e., networks stay active for the whole duration of the simulation) within a narrow band in the parameter space spanned by g and J, see Figure 3A. This transition band becomes wider, i.e., more gradual in terms of J, as g is increased, indicating a more shallow transition between transient and stable self-sustained activation. The rate of the persistent activity is typically between 20 and 50 s−1, increasing to 400 s−1 when excitation becomes dominant at g < 4, see Figure 3B.

Bottom Line: We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network.During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states.We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

View Article: PubMed Central - PubMed

Affiliation: Neural Coding and Dynamics, Center for Learning and Memory, University of Texas at Austin Austin, TX, USA ; Computational Neuroscience, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences Ås, Norway.

ABSTRACT
Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

No MeSH data available.


Related in: MedlinePlus