The cortex exhibits an intricate vertical and horizontal architecture, the latter often featuring spatially clustered projection patterns, so-called patches. Many network studies of cortical dynamics ignore such spatial structures and assume purely random wiring. Here, we focus on non-random network structures provided by long-range horizontal (patchy) connections that remain inside the gray matter. We investigate how the spatial arrangement of patchy projections influences global network topology and predict its impact on the activity dynamics of the network. Since neuroanatomical data on horizontal projections is rather sparse, we suggest and compare four candidate scenarios of how patchy connections may be established. To identify a set of characteristic network properties that enables us to pin down the differences between the resulting network models, we employ the framework of stochastic graph theory. We find that patchy projections provide an exceptionally efficient way of wiring, as the resulting networks tend to exhibit small-world properties with significantly reduced wiring costs. Furthermore, the eigenvalue spectra, as well as the structure of common in- and output of the networks suggest that different spatial connectivity patterns support distinct types of activity propagation.

Egg laying in the nematode worm Caenorhabditis elegans is a two-state behavior modulated by internal and external sensory input. We have previously shown that homeostatic feedback of embryo accumulation in the uterus regulates bursting activity of the serotonergic HSN command neurons that sustains the egg-laying active state. How sensory feedback of egg release signals to terminate the egg-laying active state is less understood. We find that Gαo, a conserved Pertussis Toxin-sensitive G protein, signals within HSN to inhibit egg-laying circuit activity and prevent entry into the active state. Gαo signaling hyperpolarizes HSN, reducing HSN Ca2+ activity and input onto the postsynaptic vulval muscles. Loss of inhibitory Gαo signaling uncouples presynaptic HSN activity from a postsynaptic, stretch-dependent homeostat, causing precocious entry into the egg-laying active state when only a few eggs are present in the uterus. Feedback of vulval opening and egg release activates the uv1 neuroendocrine cells which release NLP-7 neuropeptides which signal to inhibit egg laying through Gαo-independent mechanisms in the HSNs and Gαo-dependent mechanisms in cells other than the HSNs. Thus, neuropeptide and inhibitory Gαo signaling maintains a bi-stable state of electrical excitability that dynamically controls circuit activity in response to both external and internal sensory input to drive a two-state behavior output.

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27Caenorhabditis elegans egg laying is a two-state behavior modulated by sensory input. 28Feedback of egg accumulation in the uterus drives activity of the serotonergic HSN command 29 neurons to promote the active state, but how aversive sensory stimuli signal to inhibit egg laying 30 is not well understood. We find the Pertussis Toxin-sensitive G protein, Go, signals in HSN to 31 inhibit circuit activity and prolong the inactive behavior state. Go signaling hyperpolarizes HSN, 32reducing Ca 2+ activity and input into the postsynaptic vulval muscles. Loss of inhibitory Go 33 signaling uncouples presynaptic HSN activity from a postsynaptic, stretch-dependent homeostat, 34 causing precocious entry into the egg-laying active state. NLP-7 neuropeptides signal to reduce 35 egg laying both by inhibiting HSN and by activating Go in cells other than HSN. Thus, Go 36integrates diverse signals to maintain a bi-stable state of electrical excitability that dynamically 37 controls circuit activity and behavior output in response to a changing environment. 38 . 39 40 41 42 43 44 45 46 We have recently identified a stretch-dependent homeostat that scales egg-laying circuit 95 activity in response to feedback of egg accumulation. Juvenile and young adult animals lacking 96 eggs in the uterus have low circuit activity, and optogenetic stimulation of the HSNs is unable to 97 stimulate vulval muscle activity in these animals (Ravi et al., 2018a). Chemical or genetic 98 sterilization leads to a reduction in both HSN and vulval muscle Ca 2+ activity, locking animals in 99 the inactive state (Collins et al., 2016; Ravi et al., 2018a). Acute chemogenetic silencing of vulval 100 muscle electrical activity similarly blocks egg laying and presynaptic HSN Ca 2+ activity. Reversal 101 of this muscle silencing drives a homeostatic rebound in HSN 'burst' firing Ca 2+ activity where 102 'bursts' of HSN Ca 2+ transients promote ongoing circuit activity that drives release of the excess 103 accumulated eggs (Ravi et al., 2018a). Feedback of successful egg release also signals to inhibit 104 HSN activity. Four uv1 neuroendocrine cells which line the vulval canal are mechanically 105 activated by the passage of eggs. The uv1 cells are peptidergic and tyraminergic, and inhibition 106 of egg laying by tyramine requires the LGC-55 tyramine-gated Clchannel which is expressed 107 on the HSNs (Collins et al., 2016). uv1 also expresses the FLP-11 and NLP-7 neuropeptides 108 that signal to inhibit HSN activity and egg laying through receptors that remain unidentified 109 (Banerjee et al., 2017). Full NLP-7 inhibition of egg laying requires the EGL-47 receptor and the 110 G protein, Go, both of which are expressed in HSN (Moresco and Koelle, 2004; Banerjee et al., 111 2017). HSN Ca 2+ activity and egg laying are also inhibited by aversive signals from the external 112 environment. Elevated environmental CO2 activates BAG and other sensory neurons (Hallem et 113 al., 2011;Fenk and de Bono, 2015). BAG releases FLP-17, which binds to EGL-6 recepto...