Paper available: Neural Noise and Power-Law Nonlinearities

[Ken Miller]

The following paper is now available from 
ftp://ftp.keck.ucsf.edu/pub/ken/miller_troyer02.pdf
or from
http://www.keck.ucsf.edu/~ken (click on 'Publications', then on 
                               'Models of Neuronal Integration and Circuitry')
This is a final draft of a paper that appeared as Journal of
Neurophysiology 87, 653-659 (2002).


Neural Noise Can Explain Expansive, Power-Law Nonlinearities in Neural
Response Functions
	 Kenneth D. Miller and Todd W. Troyer

Abstract:

Many phenomenological models of the responses of simple cells in
primary visual cortex have concluded that a cell's firing rate should
be given by its input raised to a power greater than one.  This is
known as an expansive power-law nonlinearity.  However, intracellular
recordings have shown that a different nonlinearity, a
linear-threshold function, appears to give a good prediction of firing
rate from a cell's low-pass-filtered voltage response.  Using a model
based on a linear-threshold function, Anderson et al. (2000) showed
that voltage noise was critical to converting voltage responses with
contrast-invariant orientation tuning into spiking responses with
contrast-invariant tuning. We present two separate results clarifying
the connection between noise-smoothed linear-threshold functions and
power-law nonlinearities.  First, we prove analytically that a
power-law nonlinearity is the only input-output function that converts
contrast-invariant input tuning into contrast-invariant spike
tuning. Second, we examine simulations of a simple model that assumes
(i) instantaneous spike rate is given by a linear-threshold function
of voltage, and (ii) voltage responses include significant noise.  We
show that the resulting average spike rate is well described by an
expansive power law of the average voltage (averaged over multiple
trials), provided that average voltage remains less than about 1.5
standard deviations of the noise above threshold.  Finally, we use
this model to show that the noise levels recorded by Anderson et
al. (2000) are consistent with the degree to which the orientation
tuning of spiking responses is more sharply tuned than the orientation
tuning of voltage responses.  Thus, neuronal noise can robustly
generate power-law input-output functions of the form frequently
postulated for simple cells.


 
        Kenneth D. Miller               telephone: (415) 476-8217
	Associate Professor		fax: (415) 476-4929
        Dept. of Physiology, UCSF	internet: ken at phy.ucsf.edu
        513 Parnassus			www: http://www.keck.ucsf.edu/~ken
        San Francisco, CA 94143-0444