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

Intensity Coding in Sensory Systems

Stimulus Neural response Percept Psychophysics Sensory Neurophysiology Behavioral Neuroscience

Where is it?

What is it?

How strong is it ?

“Perceived quantity”

Some Definitions

Stimulus 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)

Res p o n se Absolute threshold Stimulus Strength Subthreshold Suprathreshold Response Response to superthreshold stimulus Response to subthreshold stimulus Uncertain Response Strength

No stimulus (noise) Stimulus (stimulus+noise)

Pro b ab il it y Definitely present Definitely absent

JND – Just Noticeable Difference

a detectable change in stimulus magnitude “difference limen”

“increment threshold”

Threshold a single point on the “intensive” dimension Our sensory systems are sensitive over an astounding range of stimulus intensities

DI (just noticeable change in intensity)

Weber‟s “Law”

The JND is proportional to the baseline stimulus intensity DI = JND

I = baseline intensity

The perceptual effect of an added stimulus is proportional to the intensity of the „background‟ stimulus.

D

I

I

= Constant DI = I Constant DI (JND)

I

(Background intensity)

Fechner‟s Extension of Weber‟s “Law”

DI/I = C

Fechner postulated the subjective equality of JND‟s Baseline Stimulus Intensity

JND JND JND JND JND 10 20 30 40 50 1 2 3 5 4 Det ec tab le Incre me nt Physical Domain DY= C DY DY DY DY DY Psychological Domain 1 2

Weber’s “Law” DI/I = Constant

The Weber-Fechner “Law”

DY= Constant = K DI/I

In the limit Y= K I/I

Integrating gives Y= K ln (I) + Q

At threshold (I0), Y= 0; solving for Q, Q = -K ln (I0)

So,

Y= K ln (I) - K ln (I0) = K ln (I/I0)

How good is the „fit‟? Sometimes good, sometimes not so good.

What's a Logarithm?!

• Logarithms (logs) are just exponents:

x = by _{can be rewritten as y = log}

bx

100 = 102 _{can be rewritten as 2 = log}

10100

64 = 26 _{can be rewritten as 6 = log}

264

• Logarithms are used to model many natural

processes

Y= (I - I₀)K

log Y

log (I - I₀)

S.S. Stevens

Stevens’ power law: Y= (I – I0)K

log Y= K log (I – I₀)

log(an_{) = n log(a)}

slope = k

Exponents in Steven‟s

Power Law Model

Stimulus 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 Stimulus Intensity

Lo g R es po ns e M a gn it u de .5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 Slope = 1 (linear) Slope < 1 (compressive) Slope > 1 (expansive) 2 4 6 8 10 2 4 6 8 10 Stimulus Magnitude (arbitrary linear units)

P syc ho log ica l M ag n it ud e ( ar b it rar y un it s) Electric shock Brightness A B

Expansive functions: potentially damaging stimuli Compressive functions: modalities in which a large range of intensities must be discriminated

How does the nervous system actually „represent‟ stimulus intensity?

2. Recruitment of responding neurons 1. Modulation of firing rate (rate code)

Receptor Processes

Stimulation Ion Channels Open or Close Receptor Current Receptor Potential Transmitter Release Action Potentials or Transduction Encoding Recepto r Current E = IR Recepto r Current mV + -Stimulus Stimulus Stimulus Receptor potential Transmitter release Action potential

Figure 10-6. 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) 192:13-20, 1967)

R=9.4 (S) 0.52 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.8 1.2 1.6 2.0 100 80 60 40 20 20 40 60 80 100

Stimulus intensity (% maximum) Log stimulus intensity

D is c h a rg e r a te (% m a x im u m ) L o g R

Rate of activity in peripheral somatosensory neurons as function of intensity

R=9.4 (S) 0.52 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.8 1.2 1.6 2.0 100 80 60 40 20 20 40 60 80 100 Stimulus intensity (% maximum)

Log stimulus intensity

D is c ha rg e ra te (% m ax im u m ) L o g R here? or here? Stimulate electrically to produce constant

receptor potential Record spike discharge Dis

c h a rg e r a te (s p ik e s /s e c )300 200 100 Compression occurring here Stimulation Ion Channels Open or Close Receptor Current Receptor Potential Transmitter Release Action Potentials or Transduction Encoding

The Operating Characteristic of a Receptor

Dynamic Range

Log Stimulus Intensity (I)

R es pons e Magnit ud e (R ) Absolute Threshold 0 Saturation D I D R gain = Baseline

Change in gain of a receptor produced by background stimulation

Adaptation

Previous conditions of stimulation alter responsiveness at a later time

In the visual system, the absolute threshold can increase by a factor of 1 million when comparing dark adapted to light adapted state

Stimulus intensity R e sp o n se (m V ) 0.1 1.0 0.01 10 100 1000 1 2 3 4 Ba ckg rou nd = 1 Ba ckg rou nd = 1 0

Note the logarithmic abscissa

Background Intensity (I)

Detecta

ble Inc

rement

Studying adaptation using the increment threshold

(DI) DI time (Weber's Law) DI/I = C I

Response of a Rod Photoreceptor to Flashes of Increasing Intensity

Ca2+ BCP 9.19 R* T T* PDE PDE* cGMP GMP Photoreceptor Outer Segment

Na+ Ca++ Na+ Ca++ To Inner Segment [1] [2] [3] [4]

The Enzymatic Cascade of the Vertebrate Rod

Steps [1] and [3] are catalytic, resulting in multiple substrate molecule transformations for each activated enzyme molecule. Light (quanta)

“Gain” of the Vertebrate Rod Change light level

(+quanta)

|cGMP| Photoreceptor Outer Segment

D Quantum |cGMP| D D In D Out = cGMP GMP

Adaptation: a form of automatic gain control

(AGC) cGMP GMP To Inner Segment Na + Ca2+ Na + Ca2+ Ca2+ GTP T T* PDE PDE* Ca2+ _{R inactive} R* Ca2+

Calcium slows rhodopsin inactivation

Calcium continously extruded from cell by an exchanger driven by sodium ion gradient

Calcium entry slowed by absorption of light

Calcium slows conversion of GTP to cGMP

Na+ 4

(Rhodopsin kinase, Recoverin)

) (

) (

Role of Intracellular |Ca2+_|

2. GTP → cGMP faster 1. R* inactivates faster

In Light: |Ca2+_{| ↓}