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Edited by Charles F. Stevens, The Salk Institute for Biological Studies, La Jolla, CA, and approved January 13, 2015 (received for review September 19, 2014)
Significance
It is unknown what functional properties influence the number of cell types in the brain. Here we show how one can use a powerful framework from physics that describes the transitions between different phases of matter, such as between liquid and gas, to specify under what conditions it becomes optimal to split neural populations into new subtypes to maximize information transmission. These results outline a conceptual framework that spans both physical and biological systems and can be used to explain the emergence of different functional classes of neuronal types.
Abstract
Computation in the brain involves multiple types of neurons, yet the organizing principles for how these neurons work together remain unclear. Information theory has offered explanations for how different types of neurons can maximize the transmitted information by encoding different stimulus features. However, recent experiments indicate that separate neuronal types exist that encode the same filtered version of the stimulus, but then the different cell types signal the presence of that stimulus feature with different thresholds. Here we show that the emergence of these neuronal types can be quantitatively described by the theory of transitions between different phases of matter. The two key parameters that control the separation of neurons into subclasses are the mean and standard deviation (SD) of noise affecting neural responses. The average noise across the neural population plays the role of temperature in the classic theory of phase transitions, whereas the SD is equivalent to pressure or magnetic field, in the case of liquid–gas and magnetic transitions, respectively. Our results account for properties of two recently discovered types of salamander Off retinal ganglion cells, as well as the absence of multiple types of On cells. We further show that, across visual stimulus contrasts, retinal circuits continued to operate near the critical point whose quantitative characteristics matched those expected near a liquid–gas critical point and described by the nearest-neighbor Ising model in three dimensions. By operating near a critical point, neural circuits can maximize information transmission in a given environment while retaining the ability to quickly adapt to a new environment.
Footnotes
↵1Present address: Department of Psychiatry, University of California, San Francisco, CA 94143.
- ↵2To whom correspondence should be addressed. Email: sharpee{at}salk.edu.
Author contributions: D.B.K., S.A.B., and T.O.S. designed research; D.B.K. performed research; D.B.K. and T.O.S. analyzed data; and D.B.K., S.A.B., and T.O.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1418092112/-/DCSupplemental.
Freely available online through the PNAS open access option.
- aNeuroscience Program and
- cDepartment of Neurobiology, Stanford University School of Medicine, Stanford, CA 94305;
- bComputational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, CA 92037; and
- dCenter for Theoretical Biological Physics and Department of Physics, University of California, San Diego, La Jolla, CA 92093
Edited by Charles F. Stevens, The Salk Institute for Biological Studies, La Jolla, CA, and approved January 13, 2015 (received for review September 19, 2014)
Significance
It is unknown what functional properties influence the number of cell types in the brain. Here we show how one can use a powerful framework from physics that describes the transitions between different phases of matter, such as between liquid and gas, to specify under what conditions it becomes optimal to split neural populations into new subtypes to maximize information transmission. These results outline a conceptual framework that spans both physical and biological systems and can be used to explain the emergence of different functional classes of neuronal types.
Abstract
Computation in the brain involves multiple types of neurons, yet the organizing principles for how these neurons work together remain unclear. Information theory has offered explanations for how different types of neurons can maximize the transmitted information by encoding different stimulus features. However, recent experiments indicate that separate neuronal types exist that encode the same filtered version of the stimulus, but then the different cell types signal the presence of that stimulus feature with different thresholds. Here we show that the emergence of these neuronal types can be quantitatively described by the theory of transitions between different phases of matter. The two key parameters that control the separation of neurons into subclasses are the mean and standard deviation (SD) of noise affecting neural responses. The average noise across the neural population plays the role of temperature in the classic theory of phase transitions, whereas the SD is equivalent to pressure or magnetic field, in the case of liquid–gas and magnetic transitions, respectively. Our results account for properties of two recently discovered types of salamander Off retinal ganglion cells, as well as the absence of multiple types of On cells. We further show that, across visual stimulus contrasts, retinal circuits continued to operate near the critical point whose quantitative characteristics matched those expected near a liquid–gas critical point and described by the nearest-neighbor Ising model in three dimensions. By operating near a critical point, neural circuits can maximize information transmission in a given environment while retaining the ability to quickly adapt to a new environment.
- neural coding
- information theory
- phase transitions
- scaling
Footnotes
↵1Present address: Department of Psychiatry, University of California, San Francisco, CA 94143.
- ↵2To whom correspondence should be addressed. Email: sharpee{at}salk.edu.
Author contributions: D.B.K., S.A.B., and T.O.S. designed research; D.B.K. performed research; D.B.K. and T.O.S. analyzed data; and D.B.K., S.A.B., and T.O.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1418092112/-/DCSupplemental.
Freely available online through the PNAS open access option.
Phase transitions describe retinal cell types
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