This paper indirectly explores some of the strings that hold the “cell grid” puppet up:
González-Burgos, G. et al. (2000) Horizontal synaptic connections in monkey prefrontal cortex: an in vitro
electrophysiological study. Cereb. Cortex 10, 82–92
The paper is a hard read if you are not into cell recording and is heavy on lab technique.
Some tantalizing tidbits from this paper:
Given that the stripes revealed by a given tracer injection in the PFC appear to be reciprocally connected (Pucak et al., 1996), it is reasonable to hypothesize that other pyramidal neurons in the superficial layers are the principal synaptic targets of these connections (Melchitzky et al., 1998).
They do confirm that the target is “300–500 μm away” The inhibitory circuit responses are evident in the results but it does not look like they choose to interpret them this way.
" initial experiments showed that the PSCs typically had mixed excitatory and inhibitory components (EPSCs and IPSCs, respectively …"
In fact - they considered these inhibitory signal a nuance and tried to separate them out. This is unfortunate as I see the inhibitory surround as a key part of the grid-forming behavior. They did not consider the possibility that it may take a trio of cells to start a strong response.
Conclusion offered: The Majority of Layer 3 Neurons Are Postsynaptic Targets of Long-distance Horizontal Monosynaptic Connections
A large proportion of the excitatory input to cortical pyramidal neurons is generally assumed to be provided by short-distance, local axon collaterals of neighboring pyramidal cells (Douglas et al. , 1995; Markram, 1997). However, in many of our experiments, monosynaptic EPSCs elicited from distal stimulation sites had a similar or larger amplitude than EPSCs elicited from more proximal sites
Therefore, this finding suggests that long-distance, horizontal, intrinsic projections are a relatively strong source of excitatory input to layer 3 pyramidal neurons.
What Proportion of Layer 3 Pyramidal Cells Receive Long-distance, Excitatory, Monosynaptic Inputs?
Our findings also suggest that most pyramidal neurons in layer 3 are targets of long-distance, horizontal projections. Specifically, low-intensity stimulation at long distances from the recorded layer 3 pyramidal cell evoked monosynaptic EPSCs in the majority (77%) of these neurons. However, this proportion is likely to be an underestimate since some long-distance axon collaterals were probably severed by slicing of the tissue blocks.
Here is a bit for @gmirey and the V1 studies:
" Interestingly, the range of horizontal distances (135–810 μm) between the stimulation sites that evoked peaks in EPSC amplitude was very similar to the range of distances (200–1200 μm) between centers of stripe-like clusters in anatomical studies of monkey PFC (Levittet al.,1993). In fact, previous studies in other cortical regions suggest that clustered connections are the basis of a peaked distribution in EPSC amplitudes. For example, using whole-cell recordings and multisite electrical stimulation in visual cortex slices, Weliky and colleagues (Weliky and Katz, 1994; Weliky et al.,1995) observed EPSC peaks when stimulation was applied at the locations of clusters of neurons that shared orientation selectivity with the recorded cell. These iso-orientation clusters of visual cortex neurons are known to be linked by intrinsic horizontal axons (Gilbert and Wiesel, 1989)"
So - griddy cells are possible useful when they are not forming grids.