To explore the answers to these questions, we construct models of feedforward networks with lateral inhibitory circuits and study how propagated correlation influences STDP learning, and what kind of learning algorithm such circuits achieve.

By analytically investigating the propagation of input correlations through feedback circuits, we revealed how lateral inhibition influenced plasticity at feedforward connections.

Our results also suggested that anti-Hebbian plasticity was helpful for learning from minor sources and implied that different STDP rules at lateral connections induced different algorithms at feedforward connections.

We analyzed the propagation of spike correlations through inhibitory circuits, and revealed how such secondary correlations influence STDP learning at both feedforward and feedback connections.

When the network is excited by inputs from external sources, excitatory postsynaptic potential (EPSP) sizes of feedforward connections WX change according to STDP rules.

In this approximation, by inserting Eq (32) into Eq (29), the mean synaptic weight changes of feedforward connections follow

We constructed a network model with three feedforward layers as shown in Fig 1A (see Neural dynamics in Methods for details).

Synaptic weight dynamics by STDP is written as ods for details), the weight change of the feedforward connection WX can be approximated as

Previous simulation studies showed lateral inhibition has critical effects on excitatory STDP learning [17—19]; however, it has not yet been well studied how a secondary correlation generated through the lateral circuits influences STDP at feedforward connections, and it is still largely unknown how lateral inhibition functions with various stimuli in different neural circuits.

This result suggests that in the STDP model, eXpected external states are naturally sampled through membrane dynamics that are generated through the interplay of feedforward and feedback inputs.

Therefore, STDP rules implemented in a feedforward neural network With lateral inhibition serve as a spike-based solution to the blind source separation or cocktail party effect problem.

The contribution of FSI inhibition (term 11) could be effectively positive or negative, depending on the ratio of feedforward (I11: and IZF) and recurrent ((IuL + I12) and (I22 + I20) inhibition.

In fact, in this scenario, AMSN reverses its sign with respect to XCTX even in the absence of feedforward inhibition.

However, for higher cortical driving rates, stronger feedforward inhibition to the D1 MSNs ensures that D2 MSNs exceed the firing rates of D1 MSNs, reversing the sign of AMSN (Fig 3D).

Importantly, DTT can be modulated by input correlations, local connectivity, feedforward inhibition and dopamine.

An increase in GPe activity (for instance due to an increase in STN activity) would effectively release D1 and D2 MSNs from the feedforward inhibition.

In the multiplicative input scenario, When FSI projections to the D1 and D2 MSN subpopulations are equally strong (IIF 2 I21: 2 IF), the Eqs 13 and 14 reduce to: where commeff is the common FSI feedforward inhibition to both types of MSNs.

Moreover, the striatal circuit also shows a highly specific connectivity in terms of the mutual inhibition between the MSN subpopulations [14, 15] and the feedforward inhibition from FSIs [16].

Being the primary source of feedforward inhibition, FSIs play an important role in both the existence and the actual value of the DTT.

Therefore, to understand the effect of the recurrent, mutual connectivity and feedforward inhibition [14—16] on the relative balance of the activities in the direct and indirect pathways we studied the dynamics of the striatal network.

The identification and quantitative description of relevant feedback, feedforward and crosstalk regulation of signaling pathways is an important step towards understanding cellular signaling networks and a key prerequisite for the development of successful drug targeting strategies [41—43]

However, if one considers all possible combinations of reported crosstalk, feedback and feedforward mechanisms, these possibilities result in an enormous number of candidate models.

However, signaling pathways involve extensive crosstalk and feedforward as well as feedback loops resulting in complex, nonlinear intracellular signaling networks, whose topologies are often context-specific and altered in diseases [1].

We started with an interaction graph master model containing previously reported crosstalk, feedback and feedforward mechanisms and selected then minimal model structures of the interaction graph master model that can explain the observed qualitative characteristics of the experimental data.

The candidate mechanisms within model 4_8_12 generate crosstalk as well as feedforward and feedback loops within the network structure leading to robust network behavior.