When you think of codebreakers, you usually think of Alan Turing. But times have changed, and the hip new code everyone is trying to break these days is the Enigma of the neural code.
This week’s speaker is Dr. Alex Reyes. His work has established some fundamental properties about the relationships between neural spike trains and sensation and the implications these relationships have for neural codes. Much of his work has been focused on understanding how sensory information is represented in neural networks. Of particular interest to Dr. Reyes is the auditory cortex. Dr. Reyes’ work blends computational, theoretical, and experimental approaches to understand the general principles behind signal processing in cortical circuits.
A fundamental concept in signal processing is correlation. Measuring correlation is essentially asking, “how similar are these two signals?” If you’re not familiar with how one calculates correlation, a simple analogy is comparing drawings on sheets of paper: overlap the sheets of paper and look at them through the light. The darker the overlap, the more they match up. Similarly, to measure correlations between signals, one overlaps them and sums them up by taking a few integrals.
One question involving correlation that comes up frequently in neuroscience is,”How are correlations between neural signals relevant for coding information in spike trains?”
This is a huge question that is actively being debated and researched. One of the reasons the debate is so persistent is pointed out in Dr. Reyes’ recent paper (Graupner and Reyes 2013). It boils down to this: a wide range of correlation values between neural signals are measured in different parts of the brain, or even in the same part of the brain during different experiments. Theoretical arguments have been put forward claiming that correlations enhance population coding, or claiming that they are detrimental to population coding. Additionally, correlation patterns have been shown to change over time.
Clearly, understanding the mechanisms that effect neural correlations is a critical step in piecing together this apparently contradictory observations of neural correlations, and ultimately what the “neural code” is.
Given the wide range of correlations observed, a natural question to ask is whether these correlations simply come from correlations in the input to the neurons. In (Graupner and Reyes 2013), the events that lead to correlations between neurons sharing synaptic inputs were investigated.
One might expect that neurons receiving similar (correlated) inputs would show correlated outputs. Surprisingly, they found that neurons in the auditory cortex actively suppress input correlations to produce only weakly correlated outputs. How could this be?
Graupner and Reyes performed their experiments in slices taken from the auditory cortex of mice. Of interest were pairs of pyramidal cells in layer IV: the “input” layer. They did their recordings in media that had higher potassium concentrations to induce greater levels of spontaneous activity. They noted two kinds of activity in their membrane potential recordings: low amplitude epochs and high amplitude epochs. They used these categories to epoch their data for separate analysis.
First, they analyzed the low amplitude epochs. A major goal of the paper was to look at the sub-threshold computations taking place on the correlated inputs. To do this, they measured the correlations between isolated inhibitory post-synaptic potentials (IPSPs), isolated excitatory post-synaptic potentials (EPSPs), and the composite EPSP and IPSPs. To isolate the EPSPs and IPSPs, they did their recordings while holding the membrane potential at the reversal potentials for the inhibitory and excitatory inputs. Thus, they were able to measure the correlations of the different kinds of input between pairs of neurons. Strikingly, they found that while the excitatory and inhibitory inputs were correlated between the two neurons, the combination of the two (the sub-threshold membrane potential) was significantly less correlated than either of the kinds of inputs! A similar effect was observed during the high amplitude epochs, where correlations were generally higher across the board.
The following figure from their paper captures this effect:
You can see that the red and green lines, representing only EPSP-EPSP correlations and only IPSP-IPSP correlations, are much higher than the blue, representing the actual membrane potential.
Somehow, the neurons were actively canceling out correlations in their shared inputs!
One possible explanation for this is that if the excitatory and inhibitory inputs are tightly coupled in time, then since they are of opposite sign, their combination will lead to cancellation of the correlations. To test this hypothesis, Graupner and Reyes measured IPSCs and EPSCs to determine the correlations between the excitatory and inhibitory input currents and the relative timing of these inputs.
Similar to the results obtained from measuring post synaptic potentials, they found that excitatory-excitatory and inhibitory-inhibitory input currents were correlated between the neurons in each recording. As predicted by the hypothesis, the excitatory-inhibitory correlations were relatively strong and negative – indicating that the excitatory inputs are tracked by correspondingly opposite inhibitory inputs. Moreover, the time delay between excitation and inhibition was short and got shorter with increased activity. This indicates that inhibitory feedback happens on a very short time scale and so inhibition can effectively track excitation. This is consistent with the idea that cancellation of the correlations between these inputs leads to the decorrelation in sub-threshold membrane activity.
At this point, readers may notice that these conclusions are critically dependent on being able to isolate the excitatory inputs from the inhibitory inputs to each neuron. In a perfect world, each synapse of each kind of input would have the same reversal potential, and the potential to which the neuron was held at the electrode would be the same throughout the neuron. Graupner and Reyes very astutely point out that because these pyramidal cells are spatially extended, the assumption that the membrane potential is the same throughout the cells is probably false. Thus, it is unlikely that they are truly isolating the individual kinds of inputs. Therefore, the correlations they measured between the inputs are probably not the true correlations. How are they able to believe their conclusions? Two words: computational neuroscience.
The next section of their paper contains a beautiful example of the use of computational neuroscience techniques to address experimental questions. Graupner and Reyes constructed a model to estimate the impact of the spatial extent of the neurons on their measured correlations. They set up a recurrent neural network to drive two test neurons. These neurons were either point neurons, or spatially extended neuron models with different kinds of spatial input distributions. Essentially performing the same experiment on the model, they found was that the spatial extent of the neurons leads to an underestimate of the membrane correlations. However, the amount of this underestimate depends on which correlations they were measuring. When measuring excitatory input, the model indicated an underestimate by a factor of 8.2. When measuring inhibitory input, the model indicated an underestimate by a factor of 3.1. The exciting result was that the model indicated an underestimate by a factor of only 1.77 at the resting membrane potential, when both inputs were acting together.
This means that it is likely that even though they underestimated the correlations in the slice, the overall conclusions still stand. Since the correlations at resting membrane potential were less underestimated than the individual inputs, the inputs still have higher correlations individually than together in the neurons and their conclusion still holds. This is an excellent demonstration of how computational neuroscience offers tools to forge a reasoned path around experimental difficulties.
So, what implications does this study have? For one, it demonstrates that this cortical circuit seems to be wired to decorrelate its inputs. Thus, the observed correlations observed between neurons in previous studies can’t necessarily always be explained by correlations in their input. The correlations are coming from somewhere, though! This suggests something deeper is happening, and future work must find where these correlations are generated and what they mean in the context of network activity. Graupner and Reyes suggest that modulators of overall network activity could shape these correlations.
For now, the tug of war between excitation and inhibition in our brains continues as we keep trying to break the neural code.
To hear from Dr. Reyes himself, be sure to come to his talk this Tuesday at 4 p.m. in the Center for Neural Circuits and Behavior Farquhar Conference Room. His talk is titled, “Mathematical and eletrophysiological bases of maps between acoustic and cortical spaces.” Based on that title alone, the seamless integration of theory and experiment that permeates Dr. Reyes’ work is sure to be apparent!
Brad Theilman is a first-year Neurosciences student currently rotating with Dr. Eran Mukamel. When not processing signals from the brain, he is probably out searching for signals from satellites on his amateur radio.
Graupner, M. and Reyes, A. (2013). Synaptic input correlations leading to membrane potential decoration of spontaneous activity in cortex. J. Neurosci. 33(38): 15075-15085. doi: 10.1523/JNEUROSCI.0347-13.2013.