We will focus on cross-correlations between the pre- and postsynaptic neurons for estimating neuronal connectivity (Perkel et al., 1967; Ts’o et al., 1986; Fujisawa et al., 2008; Berényi et al., 2014). With the introduction of multi-channel extracellular recordings those methods have been used to estimate short and long range connectivity (Berényi et al., 2014), feedforward connectivity from primary visual cortex to secondary visual cortex (Zandvakili and Kohn, 2015) and local connectivity (Isomura et al., 2009). Although general correlations in neuronal data can be tested for significance using powerful mathematical methods (Grun, 2009), we argue here that it is crucial to acquire data that is suitable for applying cross-correlation techniques. We will cover endogenous/spontaneous activity caused by the brain itself, and exogenous activity caused by the experimenter.

Cross-correlations have a limitation whereby detected relationships may not correspond to real anatomical connections. For example, a third brain area targeting the neuronal pair of interest could generate spurious connections (i.e., the common source problem). Importantly, the number of spurious connections is dictated by the brain state (Figure 1C). For slow wave sleep the activity of different neurons co-vary with zero-lag (first row in Figures 1C–E). Close to 100% of those apparent connections will be false positives because they are not anatomically connected. For a more decorrelated (or random) spontaneous activity, a more reasonable estimate of the connection probability of 0.3%–0.5% is obtained for spiking activity in vivo (Fujisawa et al., 2008; Zandvakili and Kohn, 2015). Using in vitro patching a larger connectivity probability of 2% is seen between pyramidal cells which may be explained by the more sensitive post synaptic potential (Nowak et al., 1999; Holmgren et al., 2003; Song et al., 2005; Fujisawa et al., 2008). Even during the more decorrelated state typically associated with sensory stimulation there are detectable correlations between neurons that are not necessarily connected in the anesthetized animal (Yu and Ferster, 2010), and in the awake animal (Fries et al., 2001; Ray and Maunsell, 2010; second row in Figure 1C). Therefore, although the brain automatically randomize/decorrelated activity by means of heterogenous populations of neurons and inhibitory neurons (Padmanabhan and Urban, 2010; Renart et al., 2010; Tetzlaff et al., 2012; Bernacchia and Wang, 2013), in some cases it may be advantageous to artificially decorrelate neurons (third row in Figure 1C). Decorrelation has previously been accomplished by optogenetically injecting a one-dimensional noise signal (Han and Boyden, 2007). In the future, the degree of decorrelation might be enhanced using various light-sculpting approaches (Rickgauer and Tank, 2009; Dal Maschio et al., 2010; Zahid et al., 2010; Katona et al., 2012; Quirin et al., 2013; Schrödel et al., 2013; Rickgauer et al., 2014). Even single neurons can be selectively activated by the experimenter (fourth row in Figure 1C; Rickgauer et al., 2014; Szabo et al., 2014; Packer et al., 2015).

For estimating connectivity, the background input to a neuron is both beneficial and problematic. The background input creates spurious connections and adds variability to the connectivity estimation. On the other hand, this input may be crucial for the generation of action potentials; thus, without this input it would be impossible to detect a connection using extracellular recordings or calcium imaging. One alternative is to provide this additional input via artificial stimulation. The firing threshold can be decreased using two-photon stimulation of a single postsynaptic neuron (Prakash et al., 2012). A small number of postsynaptic neurons can now be activated, and even decorrelated, in similar ways using light patterning methods (see references above). The sparse activation practically eliminates the problem of common source input. Also sparse activation of presynaptic neurons may be beneficial when studying weak long range connections. To this end, projection neurons may be selectively stimulated through retrograde labeling (Wickersham et al., 2007a,b; Reardon et al., 2016). Overall, it may be pragmatic to try to measure connectivity in terms of postsynaptic spikes, since spikes are reliably detected using two-photon imaging of calcium indicators or with dense extracellular recordings, something which is not yet established with voltage indicators in vivo.

Ultimately, connectivity should be estimated in terms of the postsynaptic potential (Figure 1E). Ongoing attempts combine whole-cell recordings with selective two-photon stimulation of potential presynaptic cells (Packer et al., 2012). The yield for these whole-cell recordings may be increased through the use of patching robots, which may allow for the simultaneous patching of multiple neurons (Kodandaramaiah et al., 2012). Furthermore, fluorescent voltage markers might allow for the recording of membrane potentials across multiple neurons via two-photon imaging (Akemann et al., 2012; Knopfel, 2012; Flytzanis et al., 2014; St-Pierre et al., 2014; Vogt, 2014; Yang and St-Pierre, 2016).

Neurons that project to a specific target area can be found by anatomical means. To this end a retrogradely transported virus expressing an excitatory opsin is injected in the target area (Zhang et al., 2013; Figure 1F), or a specific cell type is targeted using transgenic animals (Lima et al., 2009). A brief light pulse will then evoke a spike in expressing neurons (Lima et al., 2009). If a spontaneously evoked spike matches this light evoked spike waveform then it is assumed that it was generated by the expressing neuron. The problem is that multiple expressing neurons will fire simultaneously to the brief light pulse such that spike sorting becomes difficult. Even neurons far from the electrode may show up in the population spike, since the number of neurons increases with distance (Du et al., 2011). Therefore one should use a small optical fiber to illuminate as small a volume as possible (Stark et al., 2012, 2014; Pi et al., 2013; Wu et al., 2015). Indeed, the required emitting light power for evoking a spike can be reduced by several orders of magnitude if the emitter is decreased in size, indicating a large increase in selectivity (Buzsáki et al., 2015), and somatic stimulation (Wu et al., 2015). Indirectly activated neurons can be detected by means of the spike jitter since it will in general be larger for an indirect activation than for a direct activation (Zhang et al., 2013). Synaptic antagonists can be used to block indirect activation (Lima et al., 2009; Zhang et al., 2013). To avoid the population spike photo-tagging can be done with inhibition instead of excitation (Courtin et al., 2014). Here the latency until spike cancelation is indicative of an indirect or direct inhibition. In addition the Becquerel effect can be subtracted since it will not be time-locked to the spontaneous spikes.

Projection neurons can also be found by infecting the source area with an excitatory opsin and by evoking an anti-dromic spike in the projecting neurons by illuminating the axonal terminals (Sato et al., 2014; Li et al., 2015; Figure 1G). The fundaments for this technique were laid out several decades ago when researches started to use anti-dromic electric stimulation of axons (Miller, 1975; Cleland et al., 1976; Lipski, 1981; Ferster and Lindström, 1983). Although, electrical stimulation is simpler than optogenetic stimulation it may require comparable higher stimulation intensities since the electric field decays quicker over space than the photon distribution. Indeed, in a beautiful study of geniculo-cortical connectivity it was noted that the electrical stimulation had to be so strong that it sometimes leads to small lesions (Ferster and Lindström, 1983). Typical light intensities may at worst cause reversible changes in neuronal activity (Stujenske et al., 2015). In comparison to the retrograde approach in which a virus is taken up by the presynaptic terminals, the axonal stimulation approach may run the risk of stimulating en passant axons. Furthermore, it may be difficult to know where the emitter should be placed given the location of the recorded neuron (in the retrograde approach the emitter should be placed where the neuron/electrode is; Figure 1G). Instead it might be advantageous if the emitter is very large such that many axons are stimulated. Note that the population-spike is weaker for axonal stimulation since the relatively large heterogeneity of axonal conduction delays separates the evoked spikes in time. Axonal phototagging also has the advantage that the number of target structures is not constrained by the number of opsins with non-overlapping wavelengths (e.g., blue and red depolarizing opsins Yizhar et al., 2011; Lin et al., 2013; Klapoetke et al., 2014; Emiliani et al., 2015), as is the case for the retrogradely transported opsin approach. To assure the identity of the sorted unit one can do a collision test (Ciocchi et al., 2015; Li et al., 2015), and to control for collaterals one can assure a low spike jitter, and/or apply synaptic blockers (Sato et al., 2014). Although the choice between somatic or axonal phototagging depends on the question at hand, there is so far no study that has systematically studied the advantages and disadvantages of those two approaches.

It is possible to approximate neuronal connectivity based on axonal and dendritic reconstructions (Stepanyants and Chklovskii, 2005). Typically, the distance between neurites indicates whether there is a synapse. Similarly to the functional approaches discussed above, this anatomical approach may produce both false negatives and spurious connectivity (Stepanyants and Chklovskii, 2005). Dense extracellular recordings may allow the position of a recorded cell group to be estimated and matched to histology (Blanche et al., 2005; Scholvin et al., 2016). Various tissue-clearing approaches may increase the chance of finding a match between an extracellularly recorded cell and a histologically-identified cell, since the brain remains intact and therefore is minimally distorted (Chung et al., 2013; Ke et al., 2013; Miyawaki, 2015). Finally, in one intriguing study, electron microscopy was used to reveal reconstructed connections in a 350 μm × 450 μm × 52 μm block of tissue, combined with two-photon calcium imaging of the corresponding tissue (Bock et al., 2011). If done properly the electron microscopy reconstruction will generate a negligible number of spurious or false negative connections (Denk and Horstmann, 2004; Jurrus et al., 2009). Recent developments could facilitate reconstruction within a larger volume, if not the entire mouse brain (Hua et al., 2015; Mikula and Denk, 2015).