Neuronal arithmetic – How retinal neurons integrate their inputs
Neurons typically receive multiple inputs, which they have to combine into an output of their own. Whether this signal integration occurs linearly or in some nonlinear way strongly determines what computational function the neuron may have. For ganglion cells in the retina, we have identified two classes of cells with different types of nonlinear signal integration, which render the cells particularly sensitive to either small or large objects.
HFSP Career Development Award holder Tim Gollisch and colleagues
Neurons throughout the nervous system receive multiple input signals in parallel and transform these into an output signal of their own. In the retina, for example, an individual ganglion cell typically pools the signals originating from many photoreceptor cells within a specified region, the so-called receptive field of the ganglion cell. How are these signals combined? Are they simply summed linearly, or do they undergo some more complex, nonlinear transformation in the pooling process? This is an important question with respect to the neuron’s computational function. In fact, several recent studies have indicated that in the retina, nonlinear pooling of input signals is essential for providing solutions to specific visual tasks, such as the detection of local motion signals or of approaching objects.
Figure: Circuit and function of nonlinear signal integration by retinal ganglion cells. Left: A retinal ganglion cell (G) integrates inputs from several bipolar cells (B), whose signals are thresholded and squared. For some ganglion cells, a gain control mechanism reduces the effectiveness of the local inputs as these become stronger. Right: Representation of an image by populations of ganglion cells with and without the gain control mechanism, according to the model on the left. Without gain control, small high-contrast objects are well represented; with gain control, large objects are enhanced.
Studying whether or not the pooling of input signals by a given neuron is linear or nonlinear, however, is complicated by the fact that the neuron’s output itself undergoes a nonlinear transformation through the conversion of its activation into spikes. As a solution, we have devised experiments in which we actively search for different combinations of inputs that yield the same neuronal output, for example, the same number of spikes. The obtained input combinations form iso-response curves in the space of all possible stimulus combinations. Along these curves, the effect of the spike generation nonlinearity is constant, and the shape of the curve can thus reveal how the neuron pools over its input. Experimentally, we identify such iso-response curves by using automated online analysis of the cells’ responses and feedback control of the applied stimuli, in order to tune the stimulus until the desired response is reached.
For ganglion cells in the salamander retina, we surprisingly found two fundamental types of iso-response curves. One type corresponds to a simple nonlinear transformation of the inputs, in particular a rectification, which cuts off negative inputs, together with a squaring operation, which boosts strong positive signals. The other type of iso-response curves was more intricate and revealed particular sensitivity to homogeneous activation of the receptive field. This sensitivity was brought about by particular inhibitory signals that acted locally in parallel with excitatory inputs and thereby functioned as a local gain control by attenuating strong local activation. The two principled types of signal pooling have obvious functional consequences for the retina. The simple rectification–squaring nonlinearity renders the cells most sensitive to those objects with the highest visual contrast within a scene. The gain control mechanism, on the other hand, makes the respective cells most sensitive to large objects, even when these occur at relatively low contrast.
Reference
Closed-Loop Measurements of Iso-Response Stimuli Reveal Dynamic Nonlinear Stimulus Integration in the Retina. Daniel Bölinger and Tim Gollisch (2012). Neuron 73: 333-346, doi: 10.1016/j.neuron.2011.10.039.
