Stochastic Resonance and Receptor Function

Experimental Protocols

Basic Experiments

1. Start the simulation and observe its features. In particular, note the threshold at V_m = -60 mV. Using the default settings (Signal = 0, Noise = 0, Threshold = 10), do a run by clicking the “Go” button. The signal (thick blue line) and the signal + noise (thin red line) will appear as a single line constant at the membrane's resting V_m of -70 mV. (Because the latter two tracings are superimposed, they may appear as a single purple line, depending on your monitor's performance) Now, increase the Signal setting to 1 and click “Go”. The signal/noise tracings will appear as a single sine wave that varies between a minimum of -70.5 mV and a maximum of -69.5 mV. Observe the short horizontal blue lines in the upper (yellow) panel that indicate the 'peaks' of the signal. Next, increase the Noise setting to 1 and do another run. You will now see the signal is the same sine wave as before, but the addition of noise to the signal results in a discrete red line that fluctuates at values that are generally slightly closer to threshold than those of the signal alone.

2. Increase the Signal setting to 10 (leave Noise = 1) and observe the result. Are any action potentials generated by the receptor (check the yellow panel)? Increase the Noise setting 1 unit at a time and observe the effect on the appearance of the signal + noise tracing. Notice the general correspondence between the fluctuations in the red line and the peaks and valleys of the noise function displayed in the lowermost panel. What happens when you increase the Noise setting to a value of 6?

3. Do 10 runs at the setting used in Exercise #2 (Signal = 10, Noise = 6), clearing the display between each run, and record the numbers displayed in the Total and False Response text fields (in the upper right corner of the display). Are the values for Total and False responses constant from run to run? Can you explain your observation? (Hint: remember that the phenomenon you're observing is termed “stochastic resonance”.) Is there any pattern to the action potentials generated by the receptor during each run?

4. Repeat Exercise #3, but do not clear the display between runs. This would simulate a 'memory' in the part of the brain that's receiving the action potentials generated by the receptor. Does this make it easier to distinguish any pattern in the receptor's action potentials? What information could that pattern convey to the brain?

5. Input the following settings: Signal = 1, Noise = 2, Threshold = 2. Do a run and record your results. Was your receptor effective at detecting the weak signal? Now, increase the Noise just a little bit, say to 3. What effect does this have on the tracings and on the ability of the system to detect the weak signal? Speculate about possible benefits and drawbacks to having the threshold V_m very close to resting V_m.

Advanced Experiments

6. Generate the data that will allow you to construct graphs of action potential frequency versus signal amplitude for three or four noise levels. Do regression analyses of the data to determine if there any dependence of action potential frequency on signal amplitude. If you find significant regressions, do the slopes and/or intercepts of the regression lines change as you increase the noise level? What functional or adaptive significance can you attach to your findings?

7. Do a number of repeat runs at a low-signal-amplitude/high-noise-amplitude setting. Pay careful attention to the Total and False Response values. Did you observe anything surprising in the counts of Total and False responses? How can you account for what you observed? (Hint: read the discussion about how the False Response feature is implemented in this simulation.)

Questions and Suggested Projects

1. If you set the noise level high enough to cause generation action potentials even in the absence of any signal (i.e., with Signal amplitude = 0), can you detect any apparent periodicity or groupings in the pattern of action potential generation by the receptor? If so, what are the implications of your findings for function of the sensory system of which the receptor is a part?

2. Can you think of how information about the frequency of the signal might be important to an organism? (Hint: think about what the frequency of the signal might tell the crayfish about the size or swimming speed of the animal producing the signal.)

3. In terms of facilitating detection of a weak signal, which noise distribution – uniform or Gaussian – works better? What criteria did you use to determine “better” and “worse”? Is one distribution ‘better’ under all circumstances?

4. Can you think of any costs of having a receptor that generated action potentials in the absence of a true signal? Can you think of any benefits?

5. The original paper that describe the stochastic resonance phenomenon in crayfish vibration detectors assumed that the noise came from the crayfish's external environment. Can you think of a way that the receptor itself could be made 'noisy'? That is, how could the receptor's V_m change relative to resting in a random way? Which noise pattern, uniform or Gaussian, do you think your noise-producing mechanism would generate? Justify your answer.

6. Do noisy receptors sacrifice ability to discriminate frequency of the signal for the ability to detect very faint signals? Do you think this would be an important consideration in the evolutionary 'design' of receptors?

7. For the situation in which the signal is strong enough to just drive the receptor’s membrane just past threshold, which type of receptor works best: a receptor that doesn’t respond to noise at all; a receptor that responds to (or generates its own) Gaussian noise; or, a receptor the responds to (or generates its own) uniform noise? Justify your answer.

8. Can you think of other receptors that could employ the stochastic resonance phenomenon to enhance their function? Can you think of any receptors that could not employ stochastic resonance? (Hint: think in terms of the type of signal energy that's being transduced, and whether stochastic resonance, however generated, could facilitate the signal's detection at low intensities)

9. Assume that the receptor you've been working with is primarily used to detect a swimming predator. Using the parameters of Noise function, Signal amplitude, Noise amplitude, and Threshold, design an optimal receptor. To do this, you will first have to decide on your criteria for an optimal receptor, which will require thinking about ecological/evolutionary context in which the receptor functions. Once you've designed your optimal receptor, use the simulation to evaluate its performance under differing combinations of Signal amplitude, noise level, etc. How did you do? Did you have to modify your original design to achieve optimal performance (according to your pre-specified criteria for an optimal receptor)?

10. Are the characteristics of the “optimal receptor” that you designed in the previous exercise the same as those of other students? What significance can you associate with this result?

Suggestions For Further Reading

A highly readable and informative presentation of the stochastic resonance phenomenon is found in the following article:

Wiesenfeld, K., and F. Jaramillo. 1998. Minireview of stochastic resonance. Chaos 8:539-548.

An on-line version of the abstract of this article may be accessed at:

http://ojps.aip.org/link/?cha/8/539

On that page, you will find links to .pdf and .zip versions of the entire article that you may download and print You’ll have to have cookies enabled on your browser to access and download the article.

Should you wish to investigate the stochastic resonance phenomenon further, here are a few references that will help you get access to the rapidly accumulating literature on the subject. This listing is nowhere near complete with respect to the either the breadth or depth of its coverage, but it will get you into the literature of the diverse fields in which stochastic resonance is currently being employed as a research tool.

Benzi, R., Parisi, G, Sutera, A., and A. Vulpiani. 1982. Stochastic resonance in climatic-change. Tellus. 34:10-16.

Benzi, R., Sutera, A., and A. Vulpiani. 1981. The mechanism of stochastic resonance. J. Physics A. 14:L453-L457.

Blackwell, K.T. 1998. The effect of white and filtered noise on contrast detection thresholds. Vision Res. 38:267-280.

Blarer, A., and M. Doebeli. 1999. Resonance effects and outbreaks in ecological time series. Ecology Letters 2:167-177.

Douglass, J.K., Wilkens, L., Pantazelou, E., and F. Moss. 1993. Noise enhancement of information-transfer in crayfish mechanoreceptors by stochastic resonance. Nature, Lond. 365:337-340.

Ezrukov, S.M., and I. Vodyanoy. 1995. Noise-induced enhancement of signal-transduction across voltage-dependent ion channels. Nature, Lond. 378:362-364.

Fulinski, A., and P. F. Gora, 2000. Universal character of stochastic resonance and a constructive role of white noise. J. Stat. Physics. 101: 483-493.

Gammaitoni, L., Hanggi, P., Jung, P., and F. Marchesoni. 1998. Stochastic resonance. Rev. Modern Phys. 70(1):223-287.

Grifoni, M., Hartmann. L., Berchtold, S., and P. Hanggi. 1996. Quantum tunneling and stochastic resonance . Phys. Rev. E. 53:5890-5898 .

Huppert, A., and L. Stone. 1998. Chaos in the Pacific's coral reef bleaching cycle. Amer. Natur. 152:447-459.

Haughton, V., and B. Biswal. 1998. Clinical application of basal regional cerebral blood flow fluctuation measurements by FMRI. Adv. Exper. Med. Biol. 454:583-590.

Jung, P. and K. Wiesenfeld. 1997. Too quiet to hear a whisper. Nature, Lond. 385:291-291.

Kaplan, D. T., Clay, J. R., Manning, T., Glass, L., Guevara, M. R., and A. Shrier. 1996. Subthreshold dynamics in periodically stimulated squid giant axons. Phys. Rev. Letters. 76:4074-4077.

McNamara, B., Wiesenfeld, K., and R. Roy. 1988. Observation of stochastic resonance in a ring laser. Phys. Rev. Letters. 60:2626-2629.

Richardson, K,A., Imhoff, T. T., Grigg, P., and J. J. Collins. 1998. Using electrical noise to enhance the ability of humans to detect subthreshold mechanical cutaneous stimuli. Chaos 8:599-603.

Russell, D. F., Wilkens, L. A., and F. Moss. 1999. Use of behavioural stochastic resonance by paddle fish for feeding. Nature, Lond. 402:291-294.

Simonotto, E., Riani, M., Seife, C., Roberts, M., Twitty, J., and F. Moss. 1997. Visual perception of stochastic resonance. Phys. Rev. Letters. 78:1186-1189.

Stone, L., Saparin, P. I., Huppert, A., and C. Price. 1998. El Niño chaos: The role of noise and stochastic resonance on the ENSO cycle. Geophys. Res. Letters 25: 175-178.

Wiesenfeld, K., and F. Moss. 1995. Stochastic resonance and the benefits of noise: From ice ages to crayfish and squids. Nature, Lond. 373:33-36.

Zeng, F. G., Fu, Q. J., and R. Morse. 2000. Human hearing enhanced by noise. Brain Res. 869:251-255.

Zeyer, K.P., Munster, A.F. and F.W. Schneider. 1995. Quasi-periodic forcing of a chemical reaction: Experiments and Calculations. J. Phys. Chem. 99:13173-13180.

Data Sheet For Stochastic Resonance Simulation

				Responses
Run #	Threshold dVm	Signal Vm	Noise mV	Total	False	Notes