Figure 1 shows an overview of the model used in this study. The model consists of multiple neuron groups, each of which has 800 excitatory and N_I inhibitory neurons. We used regular-spiking neurons and fast-spiking neurons from the Izhikevich model (Izhikevich, 2003, 2006; Izhikevich and Edelman, 2008) for the excitatory and inhibitory neurons, respectively. Here, the fast-spiking neuron corresponds to a parvalbumin-expressing interneuron of which the number and activity are smaller in the brains of individuals with psychiatric than in those of normal healthy persons (Fatemi and Folsom, 2009; Oblak et al., 2009, 2011; Blatt and Fatemi, 2011; Hashemi et al., 2018). Each excitatory neuron has 70 connections with randomly selected neurons within the same neuron group (intraconnection) and 30 connections with randomly chosen neurons in other neuron groups (interconnection). These parameters were determined based on the biological evidence that the ratio of local and global connections of pyramidal excitatory neurons is ~7:3 (Gruner et al., 1974). Intra- and interconnections have time delays for the propagation of potentials sampled from uniform distributions in the range of 2–4 and 4–10 ms, respectively. The synaptic weights of these excitatory connections change based on an STDP rule (Pfister and Gerstner, 2006), which is a biologically plausible plasticity mechanism. Each inhibitory neuron has 100 intraconnections but does not have interconnections. To control the strength of inhibition by parameters, we assume that inhibitory synapse does not have plasticity, i.e., two synaptic weight matrices, W_IE, from inhibitory neurons to excitatory neurons, and W_II, between inhibitory neurons, are fixed. The time delay for inhibitory connections is sampled from a uniform distribution in the range of 1–3 ms.

We performed simulations using two kinds of network models; one with two neuron groups and the other with ten neuron groups, to investigate the effects of the local E/I imbalance in a single neuron group on the entire network. The following parameters were used to control the E/I balance in a neuron group:

Hereafter, a neuron group with these control parameters is called an imbalanced neuron group, while other non-controlled (baseline) neuron groups are called balanced neuron groups. The imbalanced neuron group is shown as neuron group 1 in Figure 1. The parameters in the balanced neuron groups were set to N_I = 200, W_IE = 0.025, and W_{II = 0.013}. Initial excitatory synaptic weight W_E were sampled from uniform distributions in the range of 0.0–0.04. The number of inhibitory neurons were determined based on the existing study that showed the ratio of number of excitatory and inhibitory neurons in the mammalian cortex is ~4:1 (Nowak et al., 2007). The parameters for synaptic weights were determined to show resting-state-like neural activity in vivo (Softky and Koch, 1993; Wilson, 1994), where each neuron shows Poisson firing patterns with low frequency after the STDP process.

The total simulation time was 1,520 s, and one time step was 0.05 ms. The duration for changes of excitatory synaptic weights through STDP was set as 1,500 s from 5 s. Each neuron received excitatory input of homogeneous Poisson spike trains with 0.6 Hz throughout the simulation using the following equation:

where, λ is the firing rate, and n is the number of spikes during a time interval Δt. A synaptic weight of Poisson input was set to 0.6. After the changes of synaptic weights, the complexity was evaluated using neural activity from 1,510 s for 5 s, when neural activity reached a steady state. Neural activity in each neuron group is represented as a time series of the local average potential (LAP), which is the average membrane potential of excitatory neurons in a neuron group. Therefore, LAP reflects the synchronized neural activity of excitatory neurons. The simulation was conducted independently 20 times for each condition.

To investigate how well the organized network can transfer the external input to other neuron groups, we measured the MI between the external input and neural activity of each neuron group when the external input was given to excitatory neurons in one neuron group in the network from 1,515 s for 5 s. We also measured the TE to understand the information transmission from neural activity of a neuron group receiving external input to those of other neuron groups. In this study, we constructed the external input using an inhomogeneous Poisson process. The firing rate of the process λ was determined by λ(t) = 25sin²(2πt). A synaptic weight of external Poisson input was set to 0.05. The LAP signal in each neuron group and the summation of external Poisson input in each time step were used to calculate the MI and TE.

We used regular-spiking and fast-spiking neurons of the Izhikevich neuron model (Izhikevich, 2003, 2006; Izhikevich and Edelman, 2008). The equations are as follows:

where v and u represent membrane potential and recovery variable, respectively. Variables a and b denote the time scale and sensitivity of the recovery variable u, respectively. Variables c and d represent the reset values of the membrane potential and the recovery variable after the spike, respectively. These parameters are the same as in other studies (Izhikevich, 2003, 2006). Synaptic current I_syn is expressed as follows:

Each conductance g is given by:

where w is a synaptic weight. We used τ₁ = 0.5 ms and τ₂ = 2.4 ms for g_AMPA, τ₁ = 4.0 ms and τ₂ = 40.0 ms for g_NMDA, and τ₁ = 1.0 ms and τ₂ = 7.0 ms for g_GABA based on existing studies (Hill and Tononi, 2005; Gerstner et al., 2014). In our study, the fourth-order Runge-Kutta method was used to calculate the neuron model.

We used the triplet rule of STDP (Pfister and Gerstner, 2006) to update the synaptic weights of excitatory connections. The triplet rule of STDP changes synaptic weights based on the firing timing of two postsynaptic spikes and one presynaptic spike, considering their firing frequency. The amount of change in a weight, Δw, is determined using the following equations:

where t_pre and t_post denote the presynaptic spike arrival time and the postsynaptic spike time, respectively. Synaptic weights increase and decrease with t_pre [long-time potentiation (LTP)] and t_post [long-time depression (LTD)], respectively. Here, A2+ and A2- control the amplitudes of the weight change based on the two pair of spikes. The A3+ and A3- control the amplitudes of LTP and LTD for the triplet rule, respectively. We used A2+=5×10-11, A2-=7×10-4, A3+=6.2×10-4, and A3-=2.3×10-5. The time constants τ₊, τ₋, τ_x, and τ_y for controlling LTP and LTD decay were set as 16.8, 33.7, 101, and 125 ms, respectively. Accordingly, ϵ is a small positive constant that allows the weight to be updated prior to r₂ or o₂. Here, we used ϵ = 1 ms. These parameters were determined based on an existing study (Pfister and Gerstner, 2006). The weights of the inhibitory neurons (W_IE and W_II) were not updated, and the minimum and maximum values of the weight were 0 and 0.04, respectively.

Neural activity in each neuron group is represented as a time series of the LAP, which is the average membrane potential of excitatory neurons in a neuron group. Therefore, LAP reflects the synchronized neural activity of excitatory neurons. Here, we analyzed the MSE, MI, and TE of LAP signals to investigate the effect of local E/I imbalance in a neuron group on the complexity of neural activity and information transmission among neuron groups.

To investigate the effect of the local E/I imbalance within a single neuron group on the whole network, we constructed a network model using ten neuron groups. We used a simple ring topology in which all neuron groups were coupled in the same way to eliminate the influence of network topology as much as possible and to clarify the graph-theoretical distance between neuron groups. Each neuron had interconnections with randomly selected neurons from four neighboring neuron groups. The results of only three cases ([high (H)-E/I; N_I = 100 and W_IE = 0.0125], [low (L)-E/I; N_I = 300 and W_IE = 0.0375], and [baseline (B)-E/I; N_I = 200 and W_IE = 0.025]) were given provided below to make the outcomes under different conditions comprehensible. An imbalanced neuron group with H-E/I and L-E/I had weak and strong inhibitions, respectively, compared with neuron groups with B-E/I.

Figure 5 shows intra- and interconnections after the STDP process in the model with ten neuron groups. The simulation results show that intra- and interconnections were greater in all neuron groups in H-E/I than those in L-E/I and B-E/I. That is, over-connectivity in the network was caused by locally weak inhibitory activity in one neuron group. Particularly, the intra- and interconnections around the imbalanced neuron group were stronger than other intra- and interconnections. In the case of L-E/I, interconnections between the imbalanced neuron group and other neuron groups slightly decreased compared to B-E/I, but several interconnections between balanced neuron groups slightly increased compared to B-E/I, e.g., interconnections between neuron groups from 3 to 5.

Figure 6 shows the complexity of neural activity and interconnections after the STDP process. As shown in the figure, the complexity was low in all neuron groups in H-E/I. Notably, the neuron groups with low complexity corresponded to those with increased connectivity, as shown in Figure 5. Particularly, a neuron group with more incoming interconnections showed lower complexity than other groups (see Supplementary Figure S4). That is, the low complexity of neural activity in the network might result from excessive incoming connections that were strengthened by interactions with the imbalanced neuron group.

Figure 7 shows the MI between the neural activity of the neuron group and external input, and the TE from neural activity of a neuron group receiving external input to those of other neuron groups, when the external input was given to an imbalanced group 1. Figure 8 shows almost the same, but the external input was given to a balanced neuron group 3. As shown in Figure 7, the MI and TE decreased in all neuron groups in H-E/I compared to those in other conditions. In the L-E/I condition, the TE was slightly higher than in the other conditions. However, when the external input was given to the balanced neuron group (Figure 8), the MI between the external input and neural activity of the imbalanced neuron group in L-E/I was slightly lower than that in the B-E/I condition (Tukey's test, p = 0.017). These results indicate that the imbalanced E/I ratio, especially the high E/I ratio, disrupted the information transmission of the external input to other neuron groups.

Our results showed that an increased E/I ratio causes the decreased complexity of neural activity and increased intra- and interconnections. Based on these analyses, we consider a possible mechanism behind them as follows:

The STDP under synchronous neural activity in turn might strengthen the connections further by repeating the above procedures. Thus, structure-function interactions through STDP might magnify the effect of locally imbalanced E/I, leading to the global effect. This result is similar to our previous study (Park et al., 2019) that showed a decreased in the complexity of neural activity of neuron groups when many local connections were given. Therefore, our results showed that locally imbalanced E/I ratio induces local-over connectivity that reduces the complexity of neural activity.

Our results imply that the locally imbalanced E/I ratio might cause atypical brain structure and low complexity of brain activity, which are observed in neuropsychiatric disorders. As shown in Figures 2, 5, intra- and interconnections increased with an increased E/I ratio. These results are similar to those reported by ASD and schizophrenia studies, which showed increased neural density within certain local areas (Selemon et al., 1998; Casanova et al., 2006) and excessive interconnections (Li et al., 2014; Solso et al., 2016), respectively. Our MSE analysis showed the complexity of neural activity decreased with an increased E/I ratio (Figure 4), especially at high scales (Supplementary Figure S1). This result aligns with those of studies that showed lower complexity of functional near-infrared spectroscopy (Xu et al., 2020), EEG (Bosl et al., 2011), and MEG (Ghanbari et al., 2015; Hadoush et al., 2019) signals in children with ASD compared to that of TD children or children with mild ASD. Further, similar to our previous studies (Park et al., 2019), the current simulation results showed a decrease in the complexity of neural activity of neuron groups with many local connections, especially incoming interconnections (Figure 6; Supplementary Figure S5). Thus, our model could predict that a decrease in the complexity of brain activity in a brain region of ASD or schizophrenia might be induced by excessive synaptic input from other brain regions through incoming interconnections that were strengthened by interactions with the brain region with imbalanced E/I ratio.

However, in contrast to studies showing increased interconnections that are consistent with our results, weak interconnections with distant regions have also been reported in ASD (Rane et al., 2015). Ghanbari et al. (2015) showed that although the complexity of brain activity in children with ASD compared with children with TD was lower in some regions (frontal regions in the delta band and occipital-parietal regions in the alpha band), it was higher in other regions (parietal regions in delta, central and temporal regions in theta, and frontal-central boundary regions in gamma). Furthermore, even though our results showed that an increase in the E/I ratio increased the firing rate and connections, studies of ASD and Schizophrenia using fMRI or positron emissions tomography showed hyper- and hypoactivity during resting state appeared simultaneously depending on regions (e.g., hyperactivity in the right supplementary motor area and bilateral lingual gyrus, and hypoactivity in the right middle temporal gyrus and ventromedial prefrontal cortex) (Kuhn and Gallinat, 2013; Wang et al., 2018). We associate these differences to the effect of different structures in each region. In our study, we assumed that all neuron groups have the same types of neurons and connections (each neuron group is regularly connected with neighboring neuron groups), but the human brain has different types of neurons and long-range connections with other regions, depending on the region. Especially, existing computational studies showed the a neuron group with many interconnections decreases the complexity of the neural activity (Park et al., 2019), and small-world network structure suppresses the chaoticity in neural activity (Kawai et al., 2019). Future studies using a computational model with various network structures, e.g., small-world network, scale-free network, or network structure based on real human connectome data, and neuron types may clarify our speculation.

Many studies reported hypersensitivity or hyposensitivity to external input in ASD (Hazen et al., 2014; Schauder and Bennetto, 2016) and dysfunction of sensory processing in schizophrenia (Javitt and Sweet, 2015). We found that the locally increased E/I ratio decreased information transmission in the entire network (see Figures 7, 8). These results suggest a possibility that abnormal neural responses to external input in ASD and schizophrenia might originate from an imbalanced E/I ratio in not only in sensory area but also in other regions.

The current model had fixed control parameters with regard to inhibition, and it had plastic excitatory synapses that were updated according to STDP. However, several physiological studies have shown that inhibitory synapses also exhibit plasticity (Caporale and Dan, 2008). A neurophysiological study using rats (D'amour and Froemke, 2015) and computational studies (Vogels et al., 2011; Akil et al., 2021) showed that STDP of inhibitory synapses contributes to homeostasis of neural activity. Especially, Wang and Maffei (2014) showed that excitatory LTP decreases as inhibitory LTP increases in the visual cortex of rats. Intrinsic plasticity that changes the intrinsic electrical properties of neurons is another mechanism that directly contributes to homeostasis (Turrigiano, 2011). If we consider synaptic and intrinsic homeostatic plasticity, the actual effects of the E/I balance might be less than those in our study. In addition, the time window for LTP and LTD of excitatory plasticity or inhibitory plasticity differs depending on brain regions and layers (Caporale and Dan, 2008). In the future, the relationship between several types of plasticity, including homeostatic plasticity, and E/I balance should be investigated in detail. Further, we only used regular-spiking neurons and fast-spiking neurons for excitatory neurons and inhibitory neurons, respectively. Although these neurons occupy a large proportion of the cortex, other types of neurons, bursting type neurons or somatostatin-expressing neurons, also exist, and their importance in neural dynamics has been discussed (Tremblay et al., 2016; Zeldenrust et al., 2018). The contribution of different types of inhibitory neurons to the information transmission in the organized network is also a fascinating subject.

Although we evaluated the complexity and information transmission of neural activity, we did not assess how the transferred information and the complexity of neural activity contribute to cognitive functions and motor behavior. Moreover, in this study, organization of the network occurred with Poisson input. However, the brains of humans and animals receive structured sensory signals through the body and reflect them in behavior. The mechanism through which altered E/I balance affects the self-organization of the brain and behavior through interactions with the environment is a cutting-edge research topic in developmental science, especially in the field of developmental disorders.