In the previous post it was clearly established that attributing any “real world” observation to the Liesegang Phenomena is an arbitrary decision because there is no established scientific theory that comprehensively defines the Liesegang Phenomena.
Other investigators have since repeated the experiment using a number of salts and gels that produce rhythmic banding. Some of the reactions produce secondary logarithmic bands; others form bands that are periodic but not logarithmic.
Collectively the patterns display all the colors of the rainbow.
Similar patterns are found in nature, some in minerals such as limonite, variscite and chalcedony and others in animals, including the wings of certain colorful butterflies.
Not everyone agrees that any of these natural patterns are formed by the Liesegang reaction, nor has the reaction itself been explained to everyone’s satisfaction.
Salts React in a Gel to Make the Colorful Liesegang Bands – C. L. Stong – 1969
Accordingly, biologists have been arbitrarily associating and disassociating biological observations with the Liesegang Phenomena for over a hundred years.
This arbitrary behaviour is particularly provoked when biologists observe ringed or banded patterns.
Most Liesegang patterns appear as rings or bands, but some of them are symmetrical figures.
A straight line drawn through the axis of symmetry divides these patterns into mirror images that resemble the markings of certain living creatures.
This resemblance, coupled with the fact that living body cells contain gel, has suggested to some biologists that Liesegang phenomena might be of biological significance.
Salts React in a Gel to Make the Colorful Liesegang Bands – C. L. Stong – 1969
Charles Darwin assumed producing patterns on a moth’s wing was probably a “simple” process.
Charles Darwin described patterns of color in many organisms.
Darwin described a South African moth ‘in which a magnificent ocellus occupies nearly the whole surface of each hinder wing; it consists of a black center. . . surrounded by successive, ocher-yellow, black, ocher-yellow, pink, white, pink, brown and whitish zones. Although we do not know the steps by which these wonderfully beautiful and complex ornaments have been developed, the process has probably been a simple one.’
Salts React in a Gel to Make the Colorful Liesegang Bands – C. L. Stong – 1969
Raphael Liesegang was “tempted” to associate animal markings with the Liesegang Phenomena.
Liesegang was tempted to explain the patterns as examples of periodic precipitation.
‘As no ornaments are more beautiful,’ he said, ‘than the ocelli on the feathers of various birds, on the hairy coats of some mammals, on the scales of reptiles and fishes, on the skin of amphibians, on the wings of many Lepidoptera and other insects, they deserve to be specially noticed. An ocellus consists of a spot within a ring of another color, like the pupil within the iris, but the central spot is often surrounded by additional concentric zones.’
D’Arcy Wentworth Thompson “tentatively” proposed that something analogous to the Liesegang Phenomena was involved in producing some animal markings.
Since Liesegang bands were the closest D’Arcy Thompson came to finding a reaction-diffusion system, we can understand that he seemed determined to get as much mileage as he could out of this barely understood patterning process.
He proposed, albeit tentatively, that something analogous was at play not only in the formation of stripes and whorls on cats and birds but also in the wing patterns of moths and butterflies.
This was not his idea, in fact: the German zoologist W. Gebhardt suggested it in 1912.
In particular, the concentric circles of eyespots patterns on the wings of species such as the emperor moth offered themselves as highly suggestive analogues of Liesegang’s rings.
Shapes: Nature’s Patterns: A Tapestry in Three Parts – Philip Ball – 2009
On Growth and Form – D’Arcy Wentworth Thompson – 1917
However, in the second half of the twentieth century the scientific consensus on animal markings moved away form the Liesegang Phenomena and in 1998 Heinz Henisch concurred with the value judgement that “enthusiasm has been carried beyond the bounds of prudence”.
Of course, periodic ring and layer formations found in nature offer only the most limited opportunities for research into their origin.
Indeed, many are due to quite different mechanisms, e.g. changes of overall environment, even though they bear the superficial appearance of Liesegang Rings.
As one critical analyst has put it when faced with the suggestion that the stripes of tigers and zebras may be glorified Liesegang phenomena: ‘enthusiasm has been carried beyond the bounds of prudence’ (Hedges, 1931), a verdict with which the present writer is inclined to concur.
In the same spirit of caution, we may want to reject the notion that Liesegang phenomena are responsible for the stripes on butterfly wings (Gebhardt, 1912).
Crystals in Gels and Liesegang Rings – Heinz K. Henisch – 1988
This change in the scientific consensus reflected academia’s [post-normal] preference for the mathematics of Alan Turing and the general [post-war] abandonment of the Scientific Method.
Alan Mathison Turing, OBE, FRS 23 June 1912 – 7 June 1954, was a British mathematician, logician, cryptanalyst, and computer scientist.
He was highly influential in the development of computer science, giving a formalisation of the concepts of “algorithm” and “computation” with the Turing machine, which can be considered a model of a general purpose computer.
Turing is widely considered to be the father of computer science and artificial intelligence.
During World War II, Turing worked for the Government Code and Cypher School (GC&CS) at Bletchley Park, Britain’s codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.
After the war, he worked at the National Physical Laboratory, where he designed the ACE, one of the first designs for a stored-program computer.
In 1948 Turing joined Max Newman’s Computing Laboratory at Manchester University, where he assisted in the development of the Manchester computers and became interested in mathematical biology.
The pivotal moment [with 20-20 hindsight] was the publication, in 1952, of Alan Turing’s “The Chemical Basis of Morphogenesis” which considered in some detail “the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system”.
The Chemical Basis of Morphogenesis is an article written by the English mathematician Alan Turing in 1952 describing the way in which non-uniformity (stripes, spots, spirals, etc.) may arise naturally out of a homogeneous, uniform state.
The theory (which can be called a reaction–diffusion theory of morphogenesis), has served as a basic model in theoretical biology, and is seen by some as the very beginning of chaos theory.
Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. The above-mentioned patterns (fronts, spirals, targets, hexagons, stripes and dissipative solitons) can be found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms.
It has also been argued that reaction-diffusion processes are an essential basis for processes connected to animal coats and skin pigmentation.
Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear partial differential equation, there are often possibilities for an analytical treatment.
The Chemical Basis of Morphogenesis- A M Turing – 1952
Philosophical Transactions of the Royal Society of London 237 (641)
However, the western mainstream had to wait until 1968 to discover the Belousov–Zhabotinsky reaction which produces an oscillating chemical reaction as predicted by Alan Turing.
The discovery of the phenomenon is credited to Boris Belousov.
He noted, some time in the 1950s (various sources date ranges from 1951 to 1958), that in a mix of potassium bromate, cerium(IV) sulfate, malonic acid and citric acid in dilute sulfuric acid, the ratio of concentration of the cerium(IV) and cerium(III) ions oscillated, causing the colour of the solution to oscillate between a yellow solution and a colorless solution.
This is due to the cerium(IV) ions being reduced by malonic acid to cerium(III) ions, which are then oxidized back to cerium(IV) ions by bromate(V) ions.
Belousov made two attempts to publish his finding, but was rejected on the grounds that he could not explain his results to the satisfaction of the editors of the journals to which he submitted his results.
His work was finally published in a less respectable, non-reviewed journal.
Later, in 1961, a graduate student named Anatoly Zhabotinsky rediscovered this reaction sequence; however, the results of these men’s work were still not widely disseminated, and were not known in the West until a conference in Prague in 1968.
Computer simulation of the Belousov–Zhabotinsky reaction occurring in a Petri dish.
By the end of the twentieth century the mathematics of Alan Turing reigned supreme and the scientific consensus was assured that “the development of animal coat patterns, plant phyllotaxis and chicken feathers follows the Turing mechanism” [see Peter Hantz below].
Alan Turing, and later the mathematical biologist James Murray, described a mechanism that spontaneously creates spotted or striped patterns: a reaction-diffusion system.
The cells of a young organism have genes that can be switched on by a chemical signal, a morphogen, resulting in the growth of a certain type of structure, say a darkly pigmented patch of skin.
If the morphogen is present everywhere, the result is an even pigmentation, as in a black leopard. But if it is unevenly distributed, spots or stripes can result.
Turing suggested that there could be feedback control of the production of the morphogen itself. This could cause continuous fluctuations in the amount of morphogen as it diffused around the body.
A second mechanism is needed to create standing wave patterns (to result in spots or stripes): an inhibitor chemical that switches off production of the morphogen, and that itself diffuses through the body more quickly than the morphogen, resulting in an activator-inhibitor scheme.
The Belousov–Zhabotinsky reaction is a non-biological example of this kind of scheme, a chemical oscillator.
Later research has managed to create convincing models of patterns as diverse as zebra stripes, giraffe blotches, jaguar spots (medium-dark patches surrounded by dark broken rings) and ladybird shell patterns (different geometrical layouts of spots and stripes).
Richard Prum’s activation-inhibition models, developed from Turing’s work, use six variables to account for the observed range of nine basic within-feather pigmentation patterns, from the simplest, a central pigment patch, via concentric patches, bars, chevrons, eye spot, pair of central spots, rows of paired spots and an array of dots.
More elaborate models simulate complex feather patterns in the Guinea fowl, Numida meleagris, in which the individual feathers feature transitions from bars at the base to an array of dots at the far (distal) end. These require an oscillation created by two inhibiting signals, with interactions in both space and time.
Unfortunately, biologists have fabricated this settled science although “there is no experimental evidence that proves this hypothesis”.
In his famous paper from 1952, A. M. Turing suggested that the above mechanism can account for the formation of various processes in biological morphogenesis.
Later, the ideas of Turing were improved, and today it is believed that the development of animal coat patterns, plant phyllotaxis and chicken feathers follows the Turing mechanism.
However, up to this time (2004) there is no experimental evidence that proves this hypothesis.
Figure 2.3: Marine angelfish Pomacanthus semicirculatus (juvenile).
The patterns on the skin are supposed to be Turing patterns.
We should mention that there are several other mechanisms that yield periodic structures in space.
Moreover, according to some recent results, periodic patterns where the number of stripes is smaller than four, or where the pattern must be precisely defined, are assumed to be built up not by the Turing mechanism, but by a so-called hierarchical process.
Pattern Formation in a New Class of Precipitation Reactions
Peter Hantz de Cluj/Kolozsvar (Roumanie)
Although the Liesegang Phenomena has fallen out of favour with many biologists there is evidence to suggest that their judgement is premature because “a vast number of organic reactions might proceed in gel media” if researcher actually experimented with organic reactants.
Incidentally, colonies of certain micro organisms grow in structures that consist of spirals or concentric bands, and Liesegang bands of growth-inhibiting substances have been used to grow cultures of bacteria in the form of concentric rings.
Not many Liesegang patterns have been made with organic reactants, although several experimenters have induced the periodic precipitation of compounds by reacting inorganic substances with organic compounds.
These reactions go quickest if the slowly diffusing organic compound is placed in the gel.
I was able to grow bands by placing nickel nitrate solution over silica gel prepared with .5M acetic acid solution that contained a trace of dimethylglyoxime.
The possibility that a vast number of organic reactions might proceed in gel media and that they may have biochemical significance suggests that the search for new organic examples of the Liesegang phenomenon could be an exciting and challenging hobby.
This perspective is supported by the observation that it “may be may be possible to relate the chemically produced Liesegang rings to the analogous appearances in fungi”.
The fascinating and familiar concentric distribution of fungous fruiting structures and the alternate concentric zones of dense and less dense mycelial aggregates have been many times reported in the literature but the data concerning the elusive factors which control them are too fragmentary and inadequate for a general theoretic treatment.
It may be possible to relate the chemically produced Liesegang rings to the analogous appearances in fungi and other organic forms and to apply the explanations given for the Liesegang phenomena to the fungi.
Liesegang Phenomena in Fungi. – Illo Hein – 1930
American Journal of Botany, 17 (2) 143-151
In fact, some people still seem to perceive Liesegang Rings in biology.
This seems to be particularly true in the very practical realm of medicine.
Liesegang rings in inflammatory breast lesions
K Gavin, N Banville, D Gibbons, C M Quinn
J Clin Pathol 2005;58:1343-1344
Liesegang-Like Rings in Lactational Changes in the Breast
Mohd T. Islam, Joyce J. Ou, Katrine Hansen, Rochelle A. Simon, and M. Ruhul Quddus
Case Reports in Pathology – Volume 2012 (2012), Article ID 268903
Balo concentric sclerosis is one of the borderline forms of multiple sclerosis.
Balo concentric sclerosis is a demyelinating disease similar to standard multiple sclerosis, but with the particularity that the demyelinated tissues form concentric layers. Scientists used to believe that the prognosis was similar to Marburg multiple sclerosis, but now they know that patients can survive, or even have spontaneous remission and asymptomatic cases.
Recently, a mathematical model for concentric sclerosis has been proposed. Authors review the previous pathogenic theories, discuss the link between concentric sclerosis and Liesegang’s periodic precipitation phenomenon and propose a new mechanism based on self-organization.
Cells, Tissues, and Disease : Principles of General Pathology
Guido Majno, Isabelle Joris
Liesegang rings are concentric noncellular lamellar structures, rarely seen in vivo, occurring as a consequence of the accumulation of insoluble products in a colloidal matrix.
These characteristic structures are a rare phenomenon usually found in association with cystic or inflammatory lesions and may be mistaken for parasites.
The authors examined Liesegang rings from an inflammatory kidney lesion identified previously as a tumoral lesion on computerized tomography.
On microscopic evaluation, Liesegang rings can be mistaken for eggs and larvae of parasites, psammoma bodies and calcification.
Special stains like PAS, Grocott, von Kossa and Masson’s trichrome facilitate the diagnosis.
Liesegang rings in xanthogranulomatous pyelonephritis: a case report.
Pegas KL, Edelweiss MI, Cambruzzi E, Zettler CG.
Patholog Res Int. 2010 Jan 4;2010:602523.
Overall, it is difficult not to conclude that biologists need to get back to basics and apply the Scientific Method to the study of the Liesegang Phenomena and oscillating chemical reactions.
The next post in this series will examine the entertainment geologists have enjoyed exploiting this confusion [aka post-normal gravy train] regarding the Liesegang Phenomena.