Colour Waves on Squids -
    Andrew's Squid Experiments

    Revision of May 2005 with some additional remarks

    by Gerd Heinz



    Abstract

      Orderly colour changes of cephalopods normally require an intact brain. When the brain has died, or the nerve supply to the skin has been removed, the colours become chaotic. Such autonomous behaviour highlights a general principle.

      Andrew Packard [APa95], [AP2001] has observed wave-like excitements flowing through the coloured spots (chromatophore organs) of squids some days after cutting the nerve to one side of the body. These muscle-operated organs develop supersensitivity and (non-nervous?) communication between them. The different properties can be inspected directly through the the animal's transparent skin.

      Andrews pictures and films show, that bio-systems are able to form discrete "waves", that means waves on wires. These idea was suggested in Neuronale Interferenzen in 1993 for the nerve system.

      In addition, it shows non-linear wave field properties (dynamic deletion: #11, #12) known by frogs scatic nerve experiments.

      Interesting physical "interference" properties, like a geometrical wave length, can be observed with our eyes.


      Squid with centimeter scale




    Observations

      Waves proceding in a layered 'neural' wave space show relations within a single layer and between different layers. Black, red and yellow chromatophores act relatively independently of each other, and with different conductivities in the separate layers.

      Besides straight-going waves proceding from boundaries with innervated skin, we find circular waves radiating from a centre of irritation and spiral waves rotating around a stable core.

      Water temperature influences the waves. Below 6°C they are abolished. Above 10°C, frequency, velocity and numbers of waves differentially increase.

      Deletion of two colliding waves shows, that 1) the conductivity mechanism acts multidirectionally; 2) disappearance of waves behind the points of interference means that the wave space is cleaned during a chromatophore's refractory period.




    Picture Series of a Running Colour Wave










    Movies

      Andrews records from May 31, 1995

      #1: A black colour wave moves along the denervated side of a squid

      Please click with the right mouse button on the field and select "Open" or "Save as".

      #2: Pressure induced waves moving from left (head) to right

      #3: Circular waves coming from center region



      Experiments from October 27, 1995

      #4: Straight going waves from left (head) to right

      #5: Circular waves coming from center region

      #6: Clockwise turning spiral waves

      #7: Anti-clockwise turning spiral waves

      #8: Slower wave movement induced by cold water (8°C)

      #9: Externally stimulated circular wave

      #10: Yellow and black colour waves moving independently with only weak influence on each other

      #11: Deleting waves produced by wave collision

      #12: Diverging waves produced by collision



    Observations and Discussion

    In physical terms Andrews experiments demonstrate the following effects:
    • Between chromatophore cells any excitement moves wave-like from cell to cell (#1...12)
    • Velocity, frequency and number of waves is influenced by temperature (#8)
    • Waves of different colour (yellow and black) seem to have independent information exchange systems, waves do not influence waves of different color (#10)
    • Between the chromatophores of one colour a bi-directional information exchanche to the neighbours in all directions (#1...12) can be observed, indicated by a wave movement in all directions.
    • Waves end normally at the end of the field by unknown inhibition or damping effects (#9)
    • Using a ferule, we find (#1) a geomentric wave length s of approx. 5 mm. With velocity v of approx. 5 cm/sec the excitement T per cell is T = s / v = 5 mm / (5 cm/sec) = 100 msec.
    • Wave velocity varries direction-dependend, indicated by spiral waves, (#6)
    • In difference to water waves, squid waves delete one another by (nonlinear) wave overlay (#11, #12) on the location and in the minute of touch. This effect is well-known from sciatic-nerve experiments at frogs, if one try to excite both sides parallel.
    • For waves any destination is reachable only, if NO 'counter wave' deletes the wave beforehand (#11, #12)

    Specific Relevance for Neuro Science

    Deleting waves show, that we observe a kind of inhibition (signal/wave deletion) in an excitatory network.

    From sciatica-nerve of frogs an one-dimensional analogy of this experiment is well known: Contra-directional stimuli delete themselves, because periods of refractoriness (dead zones) run behind every pulse excitement [Hz93], Chapter 06, p.145 and kill any counter wave.

    Dynamic inhibition by wave deletion was introduced theoretically as one consequence of the frog experiment in [Hz04], p.5, Fig. 7b.

    In addition to traditional knowledge, inhibition of signals can have different reasons:
    1) Inhibiting substances (weights), compare to neural network theory
    2) Mask problems (delay vectors do not match), also neighbourhood inhibition [Bionet96]
    3) Counter wave deletion (as discussed here)
    Note, that no. 2) and 3) do not need any inhibiting substance or synapse!

    Andrews Experiments offer a rule for the understanding of excitatory and inhibitory data flows. Waves from one source can only reach a destination, if it has a higher fire rate, as the counter wave source. If the counter waves are in the range of maximum fire rate, no possibility exists, to propagate any wave to a destination against the counter waves!

    Up to now it has been difficult to perceive the relevance of this effect for the understanding of nervous systems. If we suppose that the same effect (observed in this special system) happens between any kind of "normal" (bi-directional) nerve cell, one of many possible interpretations would be, that there can be no information flow on any pathway if it is blocked by other waves.

    If we implement the idea formaly to nerve system, we can establish some laws:
    a) A growing number of counter waves on a field reduces the communication possibilities, because most waves are destroyed by counter waves before they can reach a certain destination
    b) A total decreasing pulse rate on a neural field enhances the possibility for communication between sources and destinations from different directions.
    c) But: Less excitement on the field supposed, the probability to reach a destination encreases with the fire rate!

    The effect can be computed in relation between geometrical impulse length, refractoriness, firing rate and empty field size, if we compute local time functions for each cell [NI93].

    For computer-simulations, wave deletion encreases the time of calculations dramatically. To calculate the effect adequate, we have to calculate each cell for each time step, overlay methods for linear superimposition like Heinz Interference Transformation (HIT) can not be applied.

    To name the effect of wave deletion on 2-dimensional fields I suggest the terms wave-blocking or wave deletion.

      Andrews remark: "AT THIS POINT I STOP BECAUSE THE REST SEEMS EMPTY SPECULATION THAT DETRACTS FROM THE REST!"

      The following discussion is for internal use only.
      Dear reader: please stop reading here!
      The rest is only for my own understanding of possible directions of research, that I have to check for the future.

      Thinking this way, nerve network theory get a different direction. Although we have an excitement-only-network (without inhibition), we only have to avoid (inhibiting) wave-blocking mechanisms to get a free runway for any (multi-channel) signal between locations of source and destination. It might be possible that a certain type of special synchrony within a whole network is a possible solution, compare with [Singer].

      Interpretations of the effect of wave deletion reach from orthopaedics to acupuncture and kinesiology. In this fields amazing numbers of experiments are known where any sensitivity or excitement blocks a different sensitivity or excitement. The facit here: Silence is a good environment to be creative and powerful (no counter waves).

      But there are further outstanding possibilities. Eccles [Ecc00], p. 254, remembers an experiment of Adrian and Matthews [AM34]. Using electro-encephalography they found, that any alpha-rythm of the brain (high amplitudes) can be suppressed completely by the opening of eyes. If we suppose, the the frontal pulse wave input is higher with opened eyes, this higher rate suppresses probably the alpha-rythm of the brain by wave deletion effects.

      In pain research, S. Mense experimented with rats and pain. He found encreasing areas of medula spinalis involved in excitments. (Pain is combined with highest fire rates, suppressing the possibility of all counter waves - what else should (local) nerve cells learn, if they get over month no other information then cross-interferences of pain excitment sources? They learn and reproduce the locations. And cross interference locations have a further property, generated data are nearly equivalent to learned data in different directions. gh).

    Acknowledgements

    Thanks to Andrew Packard for the very interesting cooperation in the specific field.

    Sources

      [AM34] Adrian, E.D. and Matthews, B.H.C. Brain 57, p. 355, 1934

      [APa95] Packard, A.: Organization of cephalopod chromatophore systems: a neuromuscular image-generator. In: Abbott, N.J., Williamson, R., Maddock, L., Cephalopod Neurobiology, Oxford University Press, 1995, pp. 331-367

      [AP2001] Packard, A 'neural' net that can be seen with the naked eye In : Backhaus. W. (ed) 2001 International School of Biocybernetics (Ischia): Neuronal coding of perceptual systems: pp. 397-402. World Scientific, Singapore, New Jersey, London, Hong Kong.

      [Bionet96] Heinz, G., Höfs, S., Busch, C., Zöllner, M.: Time Pattern, Data Addressing, Coding, Projections and Topographic Maps between Multiple Connected Neural Fields - a Physical Approach to Neural Superimposition and Interference. Proceedings BioNet'96, GFaI-Berlin, 1997, pp. 45-57, ISBN 3-00-001107-2

      [Ecc00] Eccles, J.C.: Das Gehirn des Menschen. Seehamer Verlag 2000

      [Hz96] Heinz, G.: Physikalisch orientierte Modelle von Nervennetzen - Hypothetische Modelle und Beispiele. (web-site only, 1996)

      [Hz04] The rule played by refractoriness: Compare with http://www.gfai.de/~heinz/publications/papers/2004_BICS.pdf page 5, Fig.7b

      [NI93] Heinz, G.: Neuronale Interferenzen (Pulsinterferenzen in Netzwerken mit verteilten Parametern). Autor gleich Herausgeber. GFaI Berlin, 1992, 1993, 1994, 1996, Persönlicher Verteiler in ca. 30 Exemplaren. 150...300 S.

      [Singer] Singer, W.: Neuronal representations, assemlies and temporal coherence. In T.P.Hicks et all: Progress in Brain Research. vol.95, Elsevier, 1993, Chapter 37, pp. 461-474

    Mail to Gerd Heinz: heinz@gfai.de
    Mail to Andrew Packard: andrew@packards.de

    May, 2005: The homepage http://www.gfai.de/www_open/perspg/heinz.htm is not longer valid.
    Please use the new table of contents: http://www.gfai.de/~heinz/ or the Publications Directory

    © All copyrights at Andrew Packard / Gerd Heinz.
    Any replication needs the written permission by authors.

    File created Nov. 24, 1998 gh/ap; revision of May 2005.

    Access no. to Andrews squid page since aug. 17, 1999