Reproducible Sequence Generation In Random Neural Ensembles

Little is known about the conditions that neural circuits have to satisfy to generate reproducible sequences. Evidently, the genetic code cannot control all the details of the complex circuits in the brain. In this Letter, we give the conditions on the connectivity degree that lead to reproducible and robust sequences in a neural population of randomly coupled excitatory and inhibitory neurons. In contrast to the traditional theoretical view we show that the sequences do not need to be learned. In the framework proposed here just the averaged characteristics of the random circuits have to be under genetic control. We found that rhythmic sequences can be generated if random networks are in the vicinity of an excitatory-inhibitory synaptic balance. Reproducible transient sequences, on the other hand, are found far from a synaptic balance.

Figure 1

Phase portrait of RS of three clusters using $p_{EE}=0.05,p_{EI}=0.3,p_{IE}=0.1,p_{II}=0.15$, and $g^E=2,g^I=0.2$ with $N_E=N_I=100$.

Figure 2

Comparison between the simulations (solid lines with error bars) and the theoretical estimation (dotted line) for the excitatory  (a) and inhibitory populations (b) obtained by using $p_{EE}=0.05,p_{EI}=0.3,p_{IE}=0.1$, and $g^E=2,g^I=0.2$ with $N_E=N_I=100$.

Figure 3

(a) Estimation of the curve of balanced synaptic input (solid line) and maximum probability of crossing the threshold. The parameter values of this figure are $p_{EI}=0.3$ and $g^E=2,g^I=0.2$ with $N_E=N_I=100$ for $p_{IE}=0.0$, 0.05, 0.1, 0.2, 0.3, 0.4. (b-d) Result of simulations of the limit cycle (solid lines) and fixed points (dashed lines) with parameter values for (b) $p_{EE}=0.04$, (c) $p_{EE}=0.05$, and (d) $p_{EE}=0.07$. We also compare them to the probability of crossing the threshold, $h$, which is the dotted line.

Figure 4

Entropy measure (solid line) of the reproducibility of the sequential activity for parameter values $p_{EE}=0.05$ as in Fig. 3. The dashed line represents the estimation of falling into different states, $1-r$.