First, we confirmed that the Hubel&Wiesel connectome is a viable circuit to generate orientation specificity in the afferent connectome. We then miniaturize the early visual afferent pathway, shrinking eye size, cranium and the cortical target area, but preserving the total number of hy-percolumns and therefore arguably the number of processing units to process natural scenes in the framework of the cortical miniaturization scenario. In the limit of a small brain, the synthetic visual system resembles a mouse visual pathway, or the layout of late cretaceous eutherians, like
Figure 5.12: The spatial organization of tuning is sparse. AElectrode recordings reveal no similarity in tuning between neighboring electrodes. BSpectral separation between stimulation and calcium light (see methods) allows simultaneous recording and stimulation. C Calcium imaging also reveals a small subset of spatially unorganized and orientation tuned cells; shown are two examples of tuned cells. Left is a polar map of tuned pixels. Shown right is a fluorescence image. DCalcium imaging also reveals groups of neurons with highly correlated calcium activity, shown in red and green. E The calcium fluorescence signals from the two groups of neurons in D. The calcium data was processed by Julian Vogel.
Asioryctes, closely related to the eutherian common ancestor. We found that shrinking the visual system leads to a massive loss of visual acuity, to a loss of the orientation specificity of the afferent connectome and to a larger point spread function. Surprisingly, we also found that a number of neurons exhibited orientation biased responses in the limit of homogeneous and unselective input, that are generated by the recurrent network alone. We find that these cells are mostly simple cells. In addition, we also find a small number of complex and direction tuned cells. This diversity of responses suggests that even in this most generic case, a recurrent circuit is sufficient to spontaneously generate a basic level of orientation selectivity. This phenomenon, already present in recurrent networks as disorganized as a primary culture, might provide a robust and generic scaffold for input classification and is potentially the first workpiece refined by the selective forces of natural selection to generates the functional organization of neuronal circuits across many species of mammals.
Orientation selectivity in this system might seem surprising, but is in fact consistent with
Figure 5.13: Contrast invariant tuning. AStimulating a patch of the surrogate cortex with tuned inputs. BFour tuning curves recorded from the culture in A with three different contrasts (see text). COrientation selectivity index for the three contrast levels. Confidence intervals are 95% statistical CIs for the fits.
several models that build on very different ideas. While many models are hard to test experimen-tally due to the precision connectome required68,323,445 or the interplay of intracortical dynamics and plasticity of the projections305,456, other models that use generic mechanisms should work in living recurrent networks, too. These models for orientation selectivity cannot be tested in a living animal, but in vitro they can. It was shown that sharp orientation tuning can emerge from only weakly tuned inputs in a random network in the balanced state. In this state, the untuned fractions of excitation and inhibition roughly cancel and allow the tuned components to render neurons strongly orientation selective. The result is a spatial structure of orientation preference similar to the interspersed layout which is observed in rodents173,377. Furthermore, a network with stochastic mexican hat interconnectivity can create layouts of orientation do-mains, similar to the layout in carnivores and primates131, basically realizing a ring network in two dimensions, that form bumps by spontaneous symmetry braking. Attractor models are used for a variety of purposes22,23,521. Several experiments might yield deeper insights into the un-derlying mechanisms of orientation selectivity in the cell culture. The application of a threshold to a contrast dependent tuning curve appears to broaden orientation tuning. This broadened orientation tuning with contrast is called iceberging or the Iceberg-effect411,529. Contrast in-variance can be generated intracortically, or by mechanisms of synaptic depression between thalamus and cortex388. For a long time, it has been considered a smoking gun of cortical processing. The discovery of the alternative explanation shifted the interested away from the field. However, for our system it is still an important property, as our holographic system, by construction, does not have depressing synapses and contrast invariance is a feature in a variety of models30,377,380. Also, considering that simple and complex cells might be generated with a similar circuit with various contributions of recurrent connections72, our synthetic hybrid system might contain neuronal circuits with functions, surprisingly similar to circuits in the living brain.
The scales of projections into the primary visual cortex seemed to imply a common organiz-ing scheme. Is there more evidence to it? Let us first look at cortical coverage in cat and mouse.
Coverage here is defined as the number of geniculate centers covering every point in the visual world. Area 17 in cats is typically around 400 to 500 mm2, and grows with age247,392. A cat has a field of view of around 200 deg, and 140 deg of binocular overlap (very similar to humans with 180 deg field of view with also 140 deg binocular overlap)300. In the cat, there are 90.000β-cells
in the retina203,209, from a total of about 200.000 RGCs and a similar number of fibers in the optic nerve203, so that across the entire cortex, ≈ 200 RGCs provide input into one hypercol-umn. Note that the scaling of receptive field sizes with eccentricities145 might keep the number of inputs in units of fibers into each column roughly constant. In cat, layer IV spiny stellate cells are roughly isotropic with a radius of≈200µm93. In the mouse, V1 is typically 4 mm2153, its binocular view of view is about 45 degrees. the total field of view exceeds 240 deg116. The mouse retina contains 48000 to 70000 RGCs, has a radius of about 2 mm with a typical density between 8000−2000 mm−2116,117,223, which scales with distance from the optic disc. The optic nerve of the mouse contains around 55000 axons (C57/B6), of which only a fraction targets the dLGN509. In a mouse, the brain receives input from factor two to four less retinal fibers than a cat, but projecting to a factor 225-fold smaller cortex443. Geniculocortical arbors in mice are small, typically around 0.5 mm in diameter and not as finely branched as in cat14. In rats and mice, the radius of a spiny stellate layer IV cell is about 100−150 µm31,124,169. There are also genuine differences in the excitatory/inhibitory loop between mice and cat49,313 and potentially even in cellular organization between cat, rat and mouse on one side and primates on the other452. One should note at this point that the neurons in our surrogate cortex certainly do not have apical and basal dendrites dendrites and thus the surrogate cortex forms a generic proxy for the input layer of sensory cortex. At this scale of approximation, the neocortices of mammals are remarkably similar regarding the typical size of cells and the cellular densities, and consistent with measurements in our surrogate cortex. Despite a difference of O(100) in size, we find that the scale of projections and cell densities are similar to O(1), and consistent within the experimental error margins. This highlights the possibility of a common organizing scheme.
The contributions from recurrent inputs change orientation selective responses and the ex-istence of inhibitory OFF regions in the receptive fields highlights that the tuning is a network effect. If anisotropic dendrites or fiber tracts mattered, the receptive fields would rather re-semble single elongated ON regions, reflecting the expression of ChR2 across the dendrite or across the fibers. An explicit test could be done using ChR2 expressed only in the axon initial segment167, but the light intensities required would make long experiments and the collection of large statistics challenging. We can not study the complete connectome of neurons in the culture, but there is a set of rules for the thalamocortical connectome, referred to as Peter’s rule, that might at least serve as a proxy. It states that the expected number of synapses between neurons is proportional to the occurrence of possible synaptic targets, i.e. to the product of their dendritic and axonal tree densities35. It would not be surprising to find such simple rules gov-erning neuronal circuits in a dish, too, and as this overlap has a stochastic component, so should the network. An additional source of feed-forward randomness are speckles in the holographic patterns. Taking the hypothesis seriously that stochasticity in the network contributes criti-cally to orientation bias, can we test this hypothesis? (1) We can pharmacologicriti-cally potentiate synapses using Phorbol esters189,338and thus increase stochasticity in the network by increasing synaptic strength. (2) Alternatively, cultures grown under Tetrodotoxin (TTX) blockade show no activity during development, but connections between neurons form78,143. After washout of the TTX, these cultures burst78 with larger synaptic currents, compared to untreated con-trols143. (3) The strength of synapses also depends very much on the density of a culture215, the denser a culture, the smaller the typical epsc and ipsc amplitude, and the more inputs. To test this hypothesis, we would need to study various cell densities. (4) Finally, we could test how removal of the contributions of single neurons pharmacologically impairs tuning, similar to the methods in448.
Despite the relatively controlled system, there is still substantial variability across individual
cultures. The most crucial step should therefore be reducing the variability of the living cell component. One method would be to further abstract the network, for instance by designing virtual networks using a single neuron as computing element162. The inter-sample variability might be related to variations in cellular content and differences in the tissue extraction. These points might be addressed using more homogeneous samples, for instance by FACS sorting of neurons. Alternatively, with the advent of iPSC-technologies326, we might circumvent the prob-lem by not using rodent tissue in the first place, but both methods do not come for free. FACS sorting reduces the number of neurons massively, and neurons differentiated from stem cells often come with peculiar gene expression patterns and protein composition.
We showed that recurrent networks as disorganized as in the surrogate cortex can generate feature selectivity. Theoretically, neural networks with connections organized by probabilistic rules are conceptually powerful model systems. Random neural networks have been shown to generically exhibit computationally favorable properties for stimulus representation and infor-mation processing, for instance by reservoir computing293, liquid state machines, a particular type of a reservoir computer which consists of randomly connected spiking neurons298 and more recently FORCE learning in random rate network461. Our experimental data highlights that feature selectivity generated by the disorganized connections in living recurrent networks might be a generic scaffold for input classification, and the first workpiece refined by the selective forces of natural selection.