We have recently established a listserver at USM for the exchange of information on nonlinear chemical dynamics. The goal of the list is to provide a

forum for the discussion of current topics in nonlinear chemical dynamics, including (but not restricted to) chemical oscillations, waves, fronts,

self-organization, fractals, chaos, etc.

You may use it to ask questions about experimental and numerical methods, to advertise conferences and job openings in the field. Experts,

neophytes and the generally interested are encouraged to subscribe.


To subscribe to the list, send a message to list@wave.st.usm.edu. In the first line of the body put


subscribe nonlin your_first_name your_last_name



subscribe john pojman


Once you subsribe, you send messages to nonlin@wave.st.usm.edu that everyone on the list will receive.


Or to



To unsubcribe, do the same procedure but with the unsubcribe command or message to john.pojman@usm.edu asking to be removed.


To request a list of participant in the list, send a message to list@wave.st.usm.edu


review nonlin


Here are the postings to nonlin, starting March 2, 1999


From: "John A. Pojman" <john.pojman@usm.edu>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: StarLogo


Dear Colleagues,

I came across a nice programming environment for doing simulations of

spatially distributed systems. Starlogo is similar to cellular automata

but "turtles" can be programmed to move around and interact on the grid.


It is free and works only on a Macintosh. It comes with examples including

forest fires and slime molds




best regards,



From: 6155GUASTELL@marquette.edu

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: Call/Papers '99 Soc Chaos Theory in Psychology & Life Sciences





Ninth Annual International Conference of

The Society For Chaos Theory in Psychology & Life Sciences

Berkeley, CA, July 22-27, 1999


An invitation is extended to all interested scholars to submit papers

and programs reporting work involving chaos theory, fractals, nonlinear

dynamics and related principles. Research, theory, and application in

any of the psychological and life sciences sub-disciplines. Areas

represented at recent conferences have included neuroscience, biology,

medical research, economics, sociology, anthropology, physics, political

science, organizations/management, education, art, philosophy, and

literature. Programs will include single papers, symposia, roundtable or

salon programs. Subject matter may be theoretical, empirical, or

methodology oriented.




Special Guest Speakers

Fred Abraham

Ralph Abraham


Brief Schedule

July 22, Thursday, Early arrival day.

July 23, Friday, Registration, Intermediate Dynamics Workshop, Opening


July 24, Saturday, Conference Day 1,

Banquet and Speakers

July 25, Sunday, Conference Day 2,

July 26, Monday, Business Meeting,

Clinical Workshop,

Organizational Workshop

July 27, Tuesday, Departure day


Important Dates to Remember:




(Accepted papers' authors will be contacted on or before

May 15)


Jun 30 Registration for all speakers is required. All lodging requests

must be received (It's hard to guarantee rooms after this date).


July 15 Deadline for cancellations. At-door registration rates take




Submissions should include the title of the presentation, the names and

affiliations of all authors, and a short abstract (100-200 words).

All abstracts MUST be submitted in publishable, electronic form, either

as ASCII email enclosures or as WORD or WORDPERFECT attachments.

Submissions of abstracts in this form greatly facilitates the

publication and distribution of abstracts to our print and internet

readers. Thank you for your cooperation.


Please facilitate review of your abstract by:


1. DO NOT include diagrams, graphics, or special fonts, as these cannot

be printed in the program. If figures or math text are needed for proper

evaluation of proposal, send abstract by FAX instead; see below.

2. If you are using WORD or WORDPERFECT, TRY TO AVOID submissions with

hard carriage returns at the end of lines. Use returns only at paragraph


3. DO INCLUDE your address, phone/fax number, and email address for

notification regarding the status of your submission.

4. PLEASE INCLUDE notation of any special audio or visual needs.

Standard overhead projectors will be available. Unusual equipment is

difficult and expensive to obtain, so review your needs carefully.

5. Use the sample, below, as a guide.


All abstracts MUST be submitted in publishable, electronic form, either

as ASCII email enclosures or as WORD or WORDPERFECT attachments.


SAMPLE ABSTRACT SUBMISSION (Note:Your abstract will appear in the form

you submit it. Abstracts over 200 words will be edited.)



Applications of "chaos theory" in the study of really interesting stuff.


A. Tractor, Department of Interesting Stuff University of Everything,

City, Country, Postal Code.

and L. Sighcle, Department of Related Stuff, Research Place, City,

Country, Postal Code.


We report results of a two-year study of the fluctuations in several

interesting variables. Of particular interest are the relation between

several of the variables and several of the others. Our analysis

suggests that the relation of variables may be understood as reflecting

the operation of a nonlinear, complex system. Several suggestions about

the dynamics of this system as well as implications for further study

will be discussed. (Research supported, in part, by the National

Institute of Interesting Stuff).


CONTACT INFORMATION: Lymet Sighcle, Ph.D., Department of Related Stuff,

Research Place City/State, Country, Postal Code. Voice phone:

999-999-9999, Ext. 99; email: lsighcle@researchplace.com







The deadline for submission of abstracts is: April 30,1999.



Robert J. Porter, Ph.D. at:




Abstracts may also be mailed in the form of 3.25 diskettes, PC format,


Robert J. Porter, Ph.D.,

118 W. Plymouth St., Tampa, FL, 33603.


FAX special graphic material to RJP at 813-225-5678

Responses regarding abstracts acceptance will be made thru May 15,


Paper Titles and Presenters - will be available June 1.

Full Schedule of time slots -- June 15.



This year's conference will be held at University of California,

Berkeley. Lodging at the conference site and at nearby dorms will be

available at a reduced rate. Information regarding lodging and

registration will be available at a later date.

Registration Fees: The [early] registration fee for this conference will

be US$150 for regular members, US$110 for students, and $205 for

non-members until July 12, 1999. After June 12, the door-registration

rates of $135/125/225 apply. Lunches for the two main days of the

conference, the Banquet dinner on Saturday, July 24, as well as

refreshments are included with your registration.


Special: This year you can bring a non-member spouse to the conference

at a special discount rate. To avoid confusion, the non-member spouse

must register at the same time as the member.


Information regarding lodging and registration will be available at a

later date.


With Membership: The principal papers of this conference will be

published in Nonlinear Dynamics, Psychology & Life Sciences conditional

on arrangements with authors. A subscription to NDPLS is one of the

benefits of membership in SCTPLS. To become a member, use the Conference

Registration Form (next Newsletter, June, 1999) or the membership form

that is currently located on this SCTPLS Web site. ASCII copies may also

be obtained from Mary Ann Metzger, secretary <metzger@umbc.edu>.


An Invitation to All SCTPLS '99 Speakers

On behalf of the Society I am inviting all SCTPLS '99 speakers to submit

their conference papers for review pursuant to publication its research

journal, Nonlinear Dynamics, Psychology and Life Sciences. NDPLS is a

forum for the publication of peer-reviewed original papers that augment

the fundamental ways in which we understand, describe, and predict

nonlinear dynamical phenomena in psychology, the life, and social

sciences. "Nonlinear Dynamics" for purposes of the journal purview

refers to a group of mathematical concepts that includes (but it not

limited to) attractors, bifurcations, chaos, catastrophes, fractals,

solitons, cellular automata, evolutionary computations, and processes of



Regarding format, the final versions of your papers will need to be in

standard manuscript form. We use American Psychological Association

(APA) style, if you are familiar with that. Format details and other

information about NDPLS can be found on the Society website.

In all cases, we can only publish manuscripts that have not been

published already, and are not under consideration by any other journal.

This is, of course, a familiar boundary condition.

I look forward to seeing you all in Berkeley.




Stephen J. Guastello, Ph.D.

Editor in Chief


Dept. Psychology, Marquette University

P. O. Box 1881 Milwaukee, WI 53201-1881 USA.



Date: Wed, 10 Mar 1999 13:45:29 -0600 (CST)

From: 6155GUASTELL@marquette.edu

To: Multiple recipients of <nonlin@wave.st.usm.edu>






Brief FAQ for...





About the Society


The Society is an international forum bringing together researchers,

theoreticians, and practitioners interested in applying dynamical

systems theory, far-from-equilibrium thermodynamics, self-organiza-

tion, neural nets, fractals cellular automata, and related forms

of chaos, catastrophes, bifurcations, nonlinear dynamics, and

complexity theories to psychology and the life sciences.


The Society was founded at its first meeting held in San Francisco,

1991. Our members hail from numerous specialties within psychology

and the social sciences as well as from biology, physiology, ecology,

neuroscience, mathematics, philosophy, physics, computer

science, economics, education, management, political science, engineering,

and the world of art. At the time this announcement was prepared,

the Society has approximately 300 members in 31 countries.


Society Activities


The Society publishes a newsletter, holds an annual international

conference including workshops on new nonlinear methods, co-hosts

regional conferences, publishes a research journal (NDPLS), and

maintains the CHAOPSYC@LIST.UVM.EDU e-mail discussion group.


To subscribe to the e-mail disucssion group, send a message to

<listproc@list.uvm.edu> saying (only) <subscribe chaopsyc [yourname]>.



research journal, and is published by the Human Sciences Press, Inc.

div. Plenum, Inc. The debut issue (Vol. 1, No. 1) appeared in

January, 1997. Information on the preparation of manuscripts,

scope of the journal, its editorial board, cumulative contents

are available from the Editorial Office or the Society's World Wide

Web Site.


The SCTPLS World Wide Web Site is:


This site links to a wide range resources for researchers in nonlinear

dynamics. For linking information contact Elliott Middleton, Webmaster




The Society has, to date, published three edited book collections:


Abraham, F., & Gilgen A. (Eds., 1995). Chaos Theory in Psychology.

Westport CT: Greenwood Publishing Group.

ISBN 0-313-28961-1.


Robertson, R., & Combs, A. (Eds., 1995). Chaos Theory in Psychology and

the Life Sciences. Mahwah, NJ: Lawrence Erlbaum Associates.

ISBN 0-8058-1736-0 [hardbound], ISBN 0-8058-1737-9 [paper].


Sulis, W., & Combs, A. (Eds.). (1996). Nonlinear Dynamics in Human

Behaviour. A volume in the series Studies on Nonlinear

Phenomena in the Life Sciences (B. West, Series editor).

Singapore: World Scientific.



Annual Conferences


Annual conferences often precede one of the major psychological

conferences in North America, as possible, depending on site availability

and cost and membership locations. The 1998 (Eighth) annual conference

took place on July 31 - Aug 3, 1998, at Boston University, Boston, MA.

Information concerning the 1999 and future conferences, will be posted

in the Newsletter, on the website, CHAOPSYC and elsewhere.


The program and set of available abstracts to the 1996 (Sixth),

1997 (Seventh), and 1998 (eighth) Annual SCTPLS Conferences is available

on the Society's web site. Papers from the Sixth and subsequent annual

conferences will be published (pending the usual editorial review) in




Physical Location


Effective 1 Sept., 1998 the Society address for Newsletter submissions,

and general inquiries is:


Robert J. Porter, Ph.D., President, 1998-99


c/o Lambda Consulting

118 W. Plymouth

Tampa, FL 33603



webpage: http://www.mindspring.com/~rjporter

(RJP is Professor Emeritus of Psychology, University of New Orleans.

He consults in applications of psychology and nonlinear science.)



Newsletter printing, distribution



Dept. Psychology, Marquette University

P.O. Box 1881

Milwaukee, WI 53201-1881 USA




Please complete the following form and remit with your payment to:


Mary Ann Metzger, Ph.D., Membership Secretary


Dept. Psychology,

University of Maryland, UMBC

Baltimore, MD 21250 USA.



FAX: 410-455-1055


Please make your check or money order payable in US Dollars to the

Society for Chaos Theory in Psychology & Life Sciences (or SCTPLS).

We now accept American Express, Discover, MasterCard, and Visa

credit cards. (We are not outrigged for debit cards at this time.)


For those joining us from outside the USA: The Society can accept

payment by wire transfer. For details on how to use wire transfer,

contact Mary Ann Metzger at the addresses above. Note: Always check

with your local bank for any wire, currency purchase, or related

charges that might apply; bank charges vary in this regard.


The membership year begins on Sept. 1 of each year, and extends

until August 31, of the following calendar year. Your new or renewed

membership will include a subscription to NONLINEAR DYNAMICS, PSYCHOLOGY,

AND LIFE SCIENCES (to be issued January, March, July, and October, 1999).

Membership fees are US$60, or $50 for students.


Registration Form


Name ________________________________________________________________


Organization _________________________________________________________


Address ______________________________________________________________


City, State/Province, Zip or mail code, country:




Tel: ____________________ FAX: _____________________


e-mail: ____________________________________________


This is a (check one) _________ Regular _________ Student registration.


What topic areas within Nonlinear Dynamics interest you the most?






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(required if sent by s-mail. Your e-mail imprint is sufficient for

electronic membership).


Please return this membership form by e-mail, fax, or s-mail, depending

on mode of payment to MARY ANN METZGER at the addresses listed above.

Please DO NOT send this form through the World Wide Web.


Thank you for your interest in the




March 10, 1999


From: "John A. Pojman" <john.pojman@usm.edu>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: Chemical Waves, Fronts, and Patterns


"Laissez les bons fronts rouler"



There will be a symposium on Chemical Waves, Fronts and Patterns at the Fall National Meeting of the American Chemical Society to be held in New Orleans, Louisiana , Aug. 22-26, 1999.


The three day symposium will consist of the following sessions:


o Pattern Formation

o Convection and chemical waves

o Chemical waves in Excitable Media

o Thermal Fronts and Flames

o Catalysis

o Industrial Applications of Frontal Processes



This site has information on the meeting (Information on registration and housing will not be available until the summer)



Abstracts will due by April 15, 1999 and should be submitted via the ACS web site.


To submit an abstract, go to


(be patient - nothing may happen for a few moments). Note that you are being assigned a unique ID and password.


Then select our symposium and scroll down to the bottom and click "Submit Topic Selection" and follow the directions.



If you have problems or questions, contact the ACS or me for assistance. Using the www site instead of the old paper versions will be mandatory after New Orleans but hard copy versions can still be accepted for this meeting. But please try the www version first.


John Pojman

Department of Chemistry

University of Southern Mississippi

Hattiesburg, MS 39406-5043.






For more information on confirmed speakers, the ACS and New Orleans:







John A. Pojman, Ph.D.

Professor and Director of Undergraduate Programs

Department of Chemistry and Biochemistry

The University of Southern Mississippi

Hattiesburg, MS 39406-5043


(601) 266-5035

(601) 266-6075 (FAX)


TEC 404







From: "John A. Pojman" <john.pojman@usm.edu>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: dynamics software for the Mac


Dear Colleagues,


I am teaching a class on nonlinear chemical dynamics and am seeking freeware/shareware to run on a Mac to demonstrate dynamical phenomena, such as attractors, period doubling and chaos. Suggestions?







John A. Pojman, Ph.D.

Professor and Director of Undergraduate Programs

Department of Chemistry and Biochemistry

The University of Southern Mississippi

Hattiesburg, MS 39406-5043


From: "John A. Pojman" <john.pojman@usm.edu>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: Mathcad module for NLD


Dear Colleagues,


At this site




you can find many modules for Mathcad, for either Mac or PC for pchem, including one I wrote on numerical experiments on oscillating reactions, including the Lotka-Volterra model, Brusselator and Oregonator.





Sender: nonlin@wave.st.usm.edu

Reply-To: "Franco A. Bignone" <abignone@cisi.unige.it>

MIME-Version: 1.0

Precedence: Bulk

Date: Tue, 04 May 1999 10:06:56 +0200

X-SQLPH: V5.0Sql@po1.usm.edu

From: "Franco A. Bignone" <abignone@cisi.unige.it>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: Re: Turing Patterns and Morphogenesis?


John E. Pearson ha scritto:


> Hi John,


> I don't have all the literature in front of me but I would say that the

> answer is almost certainly NO. One of the main candidates, Drosophilla,

> was presented in a paper written by Kaufmann, Shymko, and Trabert (KST)

> (Science, 199 (1978) 259.)who hypothesized that the 7

> stripes in Drosophilla were generated by a Turing mechanism. ....


> Garrett Odell (U. of Washington) came

> to Texas in the late 80's and gave a beautiful talk on this subject.

> He had a list of reasons why it was unlikely that a Turing type mechansism

> was responsible for segmentation in Drosophilla. Primary among them

> was the fact that there are different species of Drosophilla which

> vary widely in size yet they all have the same number of stripes, 7,

> so the "wavelength" necessarily varies from species to species.





> So the picture here is that you

> have a gradient of some chemical which selectively activates various

> genes. Odell modeled the gene regulation and was able to robustly

> generate the proper number of stripes. Later others

> got into the game and the results appear robust.





> If you go deeper yet it may still be possible that the Turing mechanism

> operates inside the cell, but at this is currently no more than

> interesting speculation. Because of buffering by immobile agents diffusion

> coefficients can be dramatically reduced from their value in water. This

> is known to occur in the case of calcium for example. Whether this permits

> pattern formation is another question. It seems reasonable to suppose that

> perhaps the control size problems are somewhat less important for very

> small patterns in which you perhaps only want to form a structure with

> polarity. I also think that the coat patterns (see Murray's book) are

> probably right. There the issue of control is unimportant. To the best of

> my knowledge no one yet knows what chemicals are acting in the coat

> pattern problem.


> John Pearson E-mail: pearson@lanl.gov

> XCM MS F645 Phone:(505)-667-7585

> Los Alamos National Laboratory FAX (505)-665-4479

> Los Alamos, NM 87545

> http://www-xdiv.lanl.gov/XCM/pearson/home_page.html


> On Mon, 3 May 1999, John A. Pojman wrote:


> > Dear Colleagues,

> >

> > In a course on Nonlinear Chemical Dynamics, we are studying Turing patterns. What is the current state of our understanding of embryo development and Turing patterns? Is there a Turing mechanism?

> >

> > thanks.

> >

> > john

> >

> >

> > John A. Pojman, Ph.D.

> > Professor and Director of Undergraduate Programs

> > Department of Chemistry and Biochemistry

> > The University of Southern Mississippi

> > Hattiesburg, MS 39406-5043

> >

> > (601) 266-5035

> > (601) 266-6075 (FAX)

> >

> > TEC 404

> >

> > john.pojman@usm.edu

> >


I agree fully with the statement of Pearson. At the moment there are no experimental proofs

whatsoever that a Turing mechanism may act in setting structure in embryos or coat patterns,

and I would add Shell patterns. In this case in particular a search of the literature can show

that at least three different mechanisms have been proposed, one based on a neural network

scheme, and the others variations on the chemical pattern formation ideas. But there are no studies

done on the subject experimentally. From the literature it seems that the dynamics in

this case has a time step in the order of magnitude of days, this is how much far as you can go.


As far as Turing goes there are other possibilities, as Pearson was referring to, but what is

the role of these possibilities in setting games in biological systems is still unknown. You can

think about the problem in two different ways. In the first one, you can try to find mechanisms

for pattern formation using Turing mechanisms, and again referring to Pearson, you can split

the problem dimentionally. The structure of the cell - expecially in the

case of higher phyla - is still quite unknown in terms of possible mechanisms setting structure

and regulation.

We know for example that chromatin clusters - chromosomes - do not have a random

distribution inside cells, but the meaning of this is still lacking. And then you have the higher

dimentional systems, like the coat of a Zebra. But again no hints from experimentalists.


The second way to think about pattern formation is to look at the findings from Genetics.

In a lot of systems it has recently been shown that regulation of structures is done by clusters

of genes, from 50 to 200 depending on the system. So the question can thus become: is this

machinery set in order to control chemical instabilities, to achieve constantly a certain outcome (?),

or the system has set this way of proceeding in order to avoid those mechanisms because

are not stable enought? As you well know in some cases chemical instabilities are used:

Dictyostelium discoideum aggregation, and rective media in general, are good examples. But in other

cases dosen't seems to be so, like for Turing instability, and in general for development. It is obvious

that the rules of the game must be somehow rooted in the chemistry of the system, but it

is perhaps necessary to think of it in different terms. While in the case of D.discoideum what

is important is to set a certain proportion of cells becoming fruiting body or stalk cells, in

other cases cells are subdivided precisely. In Anellids, Gastropods and Nematodes you can

predict precisely what every cell will do. In C. elegans eggs, about 150,000 cubic microns, 558 cells

are formed before hatching by subdivision, in a repeatable way. You can thus map precisely the

inital volume into the final embryo. So, even if chemical instabilities must be obviously there, it is

still necessary to have a strict control to achieve such precision, how this is done, and

expecially why is done in this way, is still largely unknown.



Franco A. Bignone

Dpt. of Experimental Oncology, I.S.T., National Cancer Institute,

Lrgo Rosanna Benzi, 10, I-16132, Genova, Italy

Ph. Home +39-010-(247)3070 (secr)

Job: +39-010-(5600)641; +39-010-355839; +39-010-(5600)213 (secr)

FAX: +39-010-(5600)210;

e-mail: abignone@cisi.unige.it http://gendyn.ist.unige.it




X-Sender: mmenzing@alchemy.chem.utoronto.ca

Date: Mon, 03 May 1999 21:34:43 -0400

X-SQLPH: V5.0Sql@po1.usm.edu

To: "John A. Pojman" <john.pojman@usm.edu>

From: Michael Menzinger <mmenzing@alchemy.chem.utoronto.ca>

Subject: Re: Turiing Patterns and Morphogenesis?

Mime-Version: 1.0


Dear John,


shure enough there is no mention in the drosophila-related literature of

Turing's idea (e.g. the book 'the makng of a fly' - I forget its author -

does not even list Turing), and the 'mother gradient' theory seems to be

more or less accepted. With regards to animal coat patterns, butterfly

wings, seashells etc., the verdict is less clear, although long standing

efforts to identify a morphogen (i.e. an activator species) have not had

much success. And until the 'morphogen' eludes biochemists, biologists feel

justified in their reserve towards Turing. However: most of the Turing

models so far, including Turing's own, deal with 2-species

activator-inhibitor systems (except the 1969 paper by Othmer & Scriven; and

a more recent paper by KAJ White and CA Gilligan in

Phil.Trans.Roy.Soc.(1998) and our work to which I come now).

The paper by Rovinsky & Menzinger (Phys.Rev.Let.69, 1193 (1994)) on

Turing- and DIFI instabilities in 3-variable systems showed that the

unstable subsystem ('activator') can be two-dimensional, with no single

species being 'the activator'. Satnoianu & Menzinger recently generalized

this to n-dimensions where a cascade of distinct Turing bifurcations with

(n-1), (n-2), ... 2, 1-dimensional, unstable subsystems may occur (the

morphology of the corresponding patterns is also subtly different). One

thing that biochemistry teaches one is that nature takes little heed of the

minimal textbook mechanisms, and that it often adorns them with 'bells and

whistles'. The search for the 'morphogen' will have to become more

sophisticated, and

be extended to 'unstable matrices' from 'activators, or species with a

positive matrix element in the stability matrix'.


Best regards,





Michael Menzinger

Department of Chemistry

University of Toronto

Toronto ON M5S 3H6


tel & fax 416-978.6158


Date: Mon, 10 May 1999 12:01:59 -0700 (PDT)

X-SQLPH: V5.0Sql@po1.usm.edu

From: Harrison <lionel@pepe.chem.ubc.ca>

Subject: Turing patterns and morphogenesis

To: keshet@math.ubc.ca

cc: john.pojman@usm.edu, pearson@lanl.gov, david@pepe.chem.ubc.ca

MIME-Version: 1.0


Hi Leah!

This is my response to your invitation of 3 May to contribute to

this email discussion arising from John Pojman's question and John

Pearson's reply. The question was "Is there a Turing mechanism?" This

doesn't have a unique meaning: proving that a type of chemical mechanism

exists is a different thing from identifying the substances involved in

it. (Think, for instance of the gap of 60 or more years between clear

identification of the presence of powerful catalysts, enzymes, and the

first identification of an enzyme as a protein.) The question can be taken

to mean either of those. On the question of proof of a Turing mechanism,

without substance identification, I think the work of S. Kondo and R.

Asai, Nature, vol. 376, no. 6543, pp. 765-768, 31 August 1995, is

definitively positive. It was headlined on the cover of that issue "Turing

patterns come to life".

I should leave readers to make up their own minds on the degree of

definitiveness of the work in my own group, since I am likely to show a

biased attitude. I believe that my experimental work on the giant

single-celled alga Acetabularia is close to definitive for the existence

of a reaction-diffusion mechanism, Turing-type and probably in the

Brusselator category: Harrison et al. Protoplasma (1981) 106, 211-221; J.

Theor. Biol. (1985) 114, 177-192; Development (1988) 104, 255-262;

Protoplasma (1997) 196, 190-196. The last-mentioned summarizes all my

physicochemical evidence for a reaction-diffusion mechanism in which

extracellular calcium probably activates a membrane-bound protein to become

a morphogen precursor. Theoretical work in my group which takes strong

account of detailed biological evidence has been done for axolotl heart

formation (Holloway, Harrison and Armstrong (1994) Developmental Dynamics

200, 242-256) and for another large single-celled alga, Micrasterias,

Phil. Trans. R. Soc. Lond. (1999), series B, vol. 354, no. 1382, 417-433,

28 February 1999. (For my general attitude to chemical-kinetic mechanisms

for biological pattern, see also my book, L. G. Harrison, Kinetic Theory

of Living Pattern, Canbridge University Press (1993).

As to the definitive identification of the chemical identities of a

Turing activator-inhibitor morphogen pair, I beleive that Pearson's answer

"NO" remains correct, but is unlikely to remain correct much longer,

because there are many promising leads. To my mind the closest to a

definitive identification is the pair DIF-1 and ammonia, proposed for

Dictyostelium by Julian Gross et al. (1988) Differentiation 38, 91-98. In

the work of my own group, we have suggested that membrane-bound proteins,

with extracellular receptor activities and intracellular intermolecular

autophosphorylating kinase activity are very promising candidates for

Turing activators both in the large single-celled algae and in vertebrate

organogenesis (the axolotl heart problem, specifically).

Pearson mentions Hans Meinhardt as likely to provide a counter view

to his. I would indeed expect this. Hans has done a large amount of work

in which he has kept close to the detailed biological evidence for many

different phenomena. Pearson suggest that Hans has "strayed a long way

from the beauty and elegance of the Turing mechanism". Frankly, I find

this comment ignorant. Ignorant of what? There is a great tendency to

regard Turing mechanisms as belonging to "mathematical biology" or

"mathematical modelling". The latter term, particularly, has been

beginning to disturb me. Models in the natural sciences do not belong to

mathematics. They belong to physics and chemistry, which must ultimately

explain the material and mechanistic basis of everything around us. I

think the beauty and elegance to which Pearson refers are in the basic

Turing mathematics. But physical chemists, like me, find another beauty

and elegance in the interactions of not just two substances but many

substances in a complex mechanism in which various parts of the mechanism

control various aspects of a phenomenon.

For instance, in his book The Algorithmic Beauty of Sea Shells,

Springer (1995), Hans Meinhardt at one point uses rate equations for six

substances in a Turing-type mechanism with many additional features (p.

111). I find this quite beautiful and elegant, and very convincing as

expounding the necessary minimum dynamic requirements for generating cone

shell patterns. I see here an application of Ockham's razor, not a

departure from it. Physicochemical colleagues of mine to whom I have

mentioned these six equations tend to reply: "That isn't very many for a

phenomenon of that complexity".

And now I come to the edge of the Great Abyss itself for all of us

who have been trying to encourage biologists to make a start at last on

trying to establish the chemical-dynamic nature of patterning: Drosophila

segmentation, starting with the pair-rule stripes. In the middle 1980's,

Michael Akam was quite anxious to talk to me about Turing mechanisms, and

put some favourable words about them in a review (Akam (1987) Development

101, 1-22). And then the control of eve stripe 2 by itself was discovered,

and the fruit fly people rejected Turing mechanisms totally (Akam (1989),

making stripes inelegantly, Nature 341, 282-283). There are two views on

this rejection. Some, believe, as Pearson writes, that "In the case of

Drosophila I think the jury is in and that Turing has nothing to do with

segmentation". Others of us believe that the eve stripe 2 evidence proved

nothing of the kind. And at last there are beginning to be indications

from people much closer to the biological work that the segmentation

problem is unsolved: Leslie Pick (1998) Developmental Genetics 23, 1-10,

most especially the second column of page 3, containing the sentence

"However, despite intensive investigation in a number of laboratories, it

is not yet possible to provide a mechanistic explanation of a complete

striped pattern for any single pair-rule gene. Clearly, much remains to be

learned about how periodicity is generated, even in Drosophila."

No, I don't think the jury is in. I think the cops are still out

there collecting evidence, and that the charges are going to be laid and

the trial conducted in the next millennium - and not the first year of it


So what is my perspective? Read chapter 8 of my book. I have tried

there to begin a classification of developmental theories, starting with

the braod divisions: kinetic, equilibrium and structural. Within kinetic,

I have reaction-diffusion, mechanochemical, self-electrophoretic, and

complex intercellular signalling. I believe one has to keep all of these

in mind for any developmental phenomenon, and that it is very dangerous,

for example, to exclude reaction-diffusion from consideration for crucial

pattern-forming events early in embryogenesis.

At the 1998 annual meeting of the Society for Developmental Biology,

at Stanford University, Cheng-Ming Chuong (Pathology, U. of Southern

California) discussed new evidence on the hexagonal pattern of feather

follicles and ended up concluding that there was probably a Turing

mechanism acting, and suggesting: activators, sonic hedgehog (SHH), BMP

activators, cAMP and TGFbeta; inhibitor, BMP4.

I hope these comments add to the beauty and elegance of the debate.




Sender: nonlin@wave.st.usm.edu

Reply-To: Dwight Barkley <barkley@maths.warwick.ac.uk>

Precedence: Bulk

Date: Fri, 24 Sep 1999 14:20:12 +0100 (BST)

From: Dwight Barkley <barkley@maths.warwick.ac.uk>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: EZ-Scroll



Sorry to be a pain to those who have already received this.

EZ-Scroll is now publicly available and can be down loaded from my

web site: www.maths.warwick.ac.uk/~barkley






From: Mads Kaern <mkaern@alchemy.chem.utoronto.ca>

To: Multiple recipients of <nonlin@wave.st.usm.edu>

Subject: Novel mechansim for stationary waves


Dear All,


this message is to advertise the experimental verification of a novel

pattern generating mechanism published in this months issue of

Phys. Rev. E.


More info is available at http://www.chem.utoronto.ca/~mkaern



To: nonlin@pojman.com

From: "John A. Pojman" <john@pojman.com>

Subject: Errata for Intro. to Nonlinear Chem Dynamics


Dear Colleagues,


We have prepared an "Errata" site for an "Introduction to Nonlinear Chemical Dynamics."





We are sure we have only begun to find our errors. If you should happen to come across others, we would be much obliged if you would bring them to our attention.


Irv and John