What is it? Where is it? How strong is it? Perceived quantity. Intensity Coding in Sensory Systems. What must sensory systems encode?

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1 Sensory Neurophysiology Neural response Intensity Coding in Sensory Systems Behavioral Neuroscience Psychophysics Percept What must sensory systems encode? What is it? Where is it? How strong is it? Perceived quantity Some Definitions magnitude (units of intensity, displacement, concentration, contrast, frequency, etc.) Response magnitude (units of millivolts, spikes/second, moles/sec, etc.) Threshold (minimum stimulus magnitude that produces a reliable response) Sensitivity (the reciprocal of threshold) 1

2 Response Subthreshold Suprathreshold Strength Absolute threshold Probability No stimulus (noise) Response Strength (stimulus+noise) Response to subthreshold stimulus Response to superthreshold stimulus Definitely absent Definitely present Response Uncertain Signal detection theory Green and Swets, 1966 Weber s Law Threshold a single point on the intensive dimension Our sensory systems are sensitive over an astounding range of stimulus intensities The is proportional to the baseline stimulus intensity ΔI = I Constant ΔI = I = baseline intensity Just Noticeable Difference a detectable change in stimulus magnitude difference limen increment threshold ΔI (just noticeable change in intensity) ΔI I = Constant ΔI () I (Background intensity) The perceptual effect of an added stimulus is proportional to the intensity of the background stimulus.

3 Let s test it Detectable Increment Fechner s Extension of Weber s Law Psychological Domain ΔΨ = C ΔΨ ΔΨ ΔΨ ΔΨ ΔΨ ΔI/I = C Physical Domain Baseline Intensity Fechner postulated the subjective equality of s 1 Weber s Law ΔI/I = Constant The Weber-Fechner Law ΔΨ = Constant = K ΔI/I In the limit δψ = K δi/i Integrating gives Ψ = K ln (I) + Q At threshold (I 0 ), Ψ = 0; solving for Q, Q = -K ln (I 0 ) So, Ψ = K ln (I) - K ln (I 0 ) = K ln (I/I 0 ) How good is the fit? Sometimes good, sometimes not so good. 3

4 What's a Logarithm?! Stevens power law: S.S. Stevens Ψ = (I I 0 ) K log(a n ) = n log(a) Logarithms (logs) are just exponents: x = b y can be rewritten as y = log b x Ψ = (I - I 0 ) K log Ψ = K log (I I 0 ) 100 = 10 can be rewritten as = log = 6 can be rewritten as 6 = log 64 log Ψ slope = k Logarithms are used to model many natural processes log (I - I 0 ) Exponents in Steven s Power Law Model Exponent Loudness (binaural) 0.6 Brightness 0.33 Temperature 1.6 Taste (salt) 1.3 Smell (coffee odor) 0.55 Electric shock (skin) 3.5 Electric shock (teeth) 7.0 Log Response Magnitude A Slope > 1 (expansive) Log Intensity Slope = 1 (linear) Slope < 1 (compressive) Psychological Magnitude (arbitrary units) Electric shock Expansive functions: potentially damaging stimuli Compressive functions: modalities in which a large range of intensities must be discriminated B Brightness Magnitude (arbitrary linear units) 4

5 How does the nervous system actually represent stimulus intensity? Processes 1. Modulation of firing rate (rate code). Recruitment of responding neurons Stimulation Ion Channels Open or Close Current Transduction Potential Transmitter Release or Action Potentials Encoding + mv - potential Current Current Transmitter release E = IR Action potential Figure Dependence of subjective intensity of taste sensations (open circles) and of the frequency of discharge in fibers of the chorda tympani nerve (filled circles) upon the concentration of citric acid (red) and sucrose (green) solutions. Log-log plot. The slopes of the lines correspond to the exponents, k, of power functions with k=0.85 and 1.1. (Borg G, Diamant H, Strom L et al: J Physiol (Lond) 19:13-0, 1967) 5

6 Discharge rate (% maximum) Rate of activity in peripheral somatosensory neurons as function of intensity R=9.4 (S) Log stimulus intensity intensity (% maximum) Log R Stimulation Ion Channels Open or Close Stimulate electrically to produce constant receptor potential here? Current Transduction Discharge rate (% maximum) Record spike discharge R=9.4 (S) Log stimulus intensity intensity (% maximum) Potential Compression occurring here Discharge rate (spikes/sec) Log R or here? Transmitter Release or Action Potentials Encoding potential (mv) The Operating Characteristic of a Adaptation Response Magnitude (R) 0 Dynamic Range Δ R gain = Δ Ι Saturation Baseline Previous conditions of stimulation alter responsiveness at a later time Change in gain of a receptor produced by background stimulation In the visual system, the absolute threshold can increase by a factor of 1 million when comparing dark adapted to light adapted state Absolute Threshold Log Intensity (I) 6

7 Adaptation Studying adaptation using the increment threshold Response (mv) Background = 1 Background = intensity Detectable Increment (ΔΙ) I Δ I time ΔI/I = C (Weber's Law) Note the logarithmic abscissa Background Intensity (I) Response of a Rod Photoreceptor to Flashes of Increasing Intensity 7

8 The Enzymatic Cascade of the Vertebrate Rod Light (quanta) Photoreceptor Outer Segment R* [1] T T* cgmp Na + Ca ++ [] PDE PDE* [3] [4] Na + Ca ++ Ca + GMP BCP 9.19 To Inner Segment Steps [1] and [3] are catalytic, resulting in multiple substrate molecule transformations for each activated enzyme molecule. Gain of the Vertebrate Rod Role of Intracellular Ca + Change light level (+quanta) Photoreceptor Outer Segment Δ Out = Δ In Δ cgmp Δ cgmp Quantum cgmp GMP In Light: Ca + 1. R* inactivates faster Calcium continously extruded from cell by an exchanger driven by sodium ion gradient 4 Na + Adaptation: a form of automatic gain control (AGC) To Inner Segment Calcium slows rhodopsin inactivation (Rhodopsin kinase, Recoverin) R* ) Ca + ( R inactive T T* PDE Ca + GTP PDE* ) ( Ca + GMP cgmp Calcium slows conversion of GTP to cgmp Calcium entry slowed by absorption of light Na + Ca + Na + Ca +. GTP cgmp faster As Ca+ decreases (in light), each quanta has less effect on cgmp 8