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If you are reading this sentence, it is quite likely that you have heard of “gain control” in a neuroscience context. You may notice that the picture provided above has very little to do with the context in which this blog post shall discuss “gain control”. You may also notice that this blog post has a dry, technical, and boring title, which promises a fair amount of eventually enlightening but difficult-to-wade-through mathematics. Given the limited time and intellect of yours truly, however, there will be no equations in this blog post. Instead, a summary/teaser will be provided.

First, a definition of “gain control” according to Dr. Adrienne Fairhall (University of Washington, Seattle) and others in their 2013 Journal of Neuroscience article1:

“…a neural system’s mapping between inputs and outputs adjusts to dynamically span the varying range of incoming stimuli. In this form of adaptive coding, the nonlinear function relating input to output has the property that the gain with respect to the input scales with the [standard deviation] of the input.”

In other words, it is known that neurons can become more or less sensitive (in terms of the absolute input amplitude required to generate the same response) depending on how variable the stimuli are, i.e. how noisy the inputs happen to be. This gain-control property ensures that neurons extract the relevant information (e.g. determine whether someone in a chattering crowd is calling your name) from constantly varying stimuli in a consistently context-dependent manner (e.g. one has to shout louder in order to be heard when everyone else is, oddly enough, shouting). From both behavioral and neural perspectives, gain control has been investigated in different sensory modalities (visual/auditory) 2, 3, and in different animal models3, 4. It is also known that mature single neurons are capable of gain control, based on electrophysiology3. But where does that capability come from?

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An example of mature neuron with excellent gain control. The legend contains details that may or may not be of interest to you. (Fig. 2, Mease et al.)

Dr. Fairhall and her colleagues chose to investigate this problem with both in vitro recording and biophysical models of single neurons. Recording from developing (E18-P1) and mature (P6-P8) mouse somatosensory cortex neurons revealed that mature neurons had better gain scaling than immature ones. In less ambiguous terms, the “symmetrized divergence” in spike-triggered average stimulus (STA, roughly describing the stimulus variability) distribution, which reflects how different the input–output function shapes (which loosely translates to “gain”) for a pair of STA series are, was smaller for mature neurons than immature neurons. The STA series pairs were generated by applying two stimuli with different standard deviations to the same neuron, as well as by applying the same stimulus to different neurons of the same maturity. Therefore, not only were mature neurons recorded in this study better at intrinsic gain control, they were also better by the same degree over the immature counterparts, suggesting that an intrinsic and consistent developmental programme underlies gain control improvement for this type of neurons.

Top left: histogram showing the propensity of immature neurons to have higher pairwise symmetrized divergence (read: more variable gain scaling). Bottom left: Voltage clamp for immature (P0) and mature (P7) neurons, showing an elevation of sodium currents during development. Right: Each dot represents a neuron with color-coded maturity, again showing an elevation of sodium currents during development. (Fig. 3C-E, Mease et al.)

Top left: histogram showing the propensity of immature neurons to have higher pairwise symmetrized divergence (read: more variable gain scaling). Bottom left: Voltage clamp for immature (P0) and mature (P7) neurons, showing an elevation of sodium currents during development. Right: Each dot represents a neuron with color-coded maturity, again showing an elevation of sodium currents during development. (Fig. 3C-E, Mease et al.)

How might this program work, if it exists? Glad that you asked. The short answer, of course, is “not sure.” But Fairhall and colleagues had a promising clue1:

“We have shown previously that INa increases in density much faster than IK during early postnatal development (Picken-Bahrey and Moody, 2003a).”

Indeed, using a biophysical model of single neurons (EIF, or exponential integrate-and-fire) where a single parameter describes how a fixed spike generating kinetics interact with ion channel expression.  By modifying this parameter (which is inversely proportional to the difference between spiking threshold and effective resting potential), a proportionate change in the ratio between sodium channel and potassium channel numbers was implied, and this parameter alone was sufficient to bring about the improvement of gain scaling observed during in vitro cortical neuron development. In confirmation, using sodium and potassium channel blockers, Fairhall and colleagues found in organotypical culture that partial blockage of potassium channels improved gain scaling (less variability/better distribution coverage), whereas partial blockage of sodium channels did the opposite.

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Two pharmacological manipulations of INa/IK change gain-scaling behavior in agreement with model results. Sample estimate of standard deviation (Fig. 5A-B, Mease et al.)

This series of encouraging results spurred Fairhall and colleagues to further apply the EIF model and test the model neurons for gain control abilities based on their sodium/potassium conductance ratios, as well as for conditions under which the model might fail. For the sake of brevity and clarity, however, this blog post will not go into further details.

Based on the results so far, Fairhall and colleagues proposed that the development of gain control in neurons of mouse somatosensory cortex (and, perhaps, beyond) may be a property intrinsic to the single neuron’s gradual self-mediated differential expression of ion channels. An alternative that remained undiscussed, however, is that the differential rate of ion channel production could be mediated in vivo by, say, astrocytic factors, or even dependent on nascent synaptic activities and subsequent calcium entry. Generally speaking, while manipulating only one parameter in a model with good fit seems to reproduce experimental results, it may also be a good idea to keep in mind that said parameter can be altered in different ways in vivo. Another important factor to consider, of course, is the relatively small sample size used in the experimental part of this study, which would in turn impact the model’s generalizability.

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Mease et al., Fig. 7

As part of the UCSD Neurosciences Graduate Program Seminar Series, at 4:00pm on Tuesday, April 22, 2014, in the CNCB Large Conference Room, Dr. Adrienne Fairhall will give a talk on the computational properties of single neurons, as well as how they interact with network-level functions. Come for what might be a refreshingly basic perspective in this age of “map everything”.

Xi Jiang is a first year student in the UCSD Neurosciences Graduate Program. He is now a rotation student under the guidance of Dr. Mark Tuszynski, studying neural stem cell fate determination.

References:

1. Mease R.A., Famulare M., Gjorgjieva J., Moody W.J. & Fairhall A.L. (2013). Emergence of Adaptive Computation by Single Neurons in the Developing Cortex, Journal of Neuroscience, 33 (30) 12154-12170. DOI:

2. Piëch V, Li W, Reeke GN, Gilbert CD. Network model of top-down influences on local gain and contextual interactions in visual cortex. Proc Natl Acad Sci U S A. 2013, 110(43):E4108-17.

3. Hildebrandt KJ, Benda J, Hennig RM. Multiple arithmetic operations in a single neuron: the recruitment of adaptation processes in the cricket auditory pathway depends on sensory context. J Neurosci. 2011, 31(40):14142-50.

4. Chen Y, Li H, Jin Z, Shou T, Yu H. Feedback of the amygdala globally modulates visual response of primary visual cortex in the cat. Neuroimage. 2014, 84:775-85.

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