[1] [1] {\huge --Rhythms in organisms--} \\ An introduction for observing, experimenting, recording and analysing

-Rhythms in organisms-
An introduction for observing, experimenting, recording and analysing

Wolfgang Engelmann

Institut für Botanik
Physiologische Ökologie der Pflanzen
Universität Tübingen
Auf der Morgenstelle 1
D72076 Tübingen (FRG)

In memoriam Jürgen Aschoff, Erwin Bünning and Colin S. Pittendrigh

Tübingen, September 1999 1


I    Methods and instrumentation
1  Scientific work
    1.1  How research work is done
        1.1.1  Introduction
        1.1.2  Method of multiple hypotheses and strong inference
        1.1.3  Testing hypotheses, analysing and interpreting data
    Formulation of hypotheses: Drinking duck
    Analysis and interpretation of data: Movement of the lateral leaflet of Desmodium motorium
    Planning, execution and analysis of an experiment
    Example for the solution of a problem: Does the period length of the lateral leaflet movement rhythm of Desmodium motorium depend on the temperature of the surrounding?
        1.1.4  Experimental protocol
    1.2  Communication in science
        1.2.1  Introduction
        1.2.2  How scientists report their results
        1.2.3  Scientific publication: An example
        1.2.4  Writing your own scientific article
        1.2.5  Literature search
    1.3  Controversies in science
    1.4  Unsolved problems
2  Recording methods
    2.1  Video recording and ana -lysis of rhythms
        2.1.1  Introduction
        2.1.2  Recording principle
        2.1.3  Recording
    2.2  Recording of locomotor activity of animals using light beams
        2.2.1  Introduction
        2.2.2  Recording principle
3  Display and analysis of time series
    3.1  Introduction
    3.2  Elementary terms
    3.3  Grafic display of timeseries
    3.4  Smoothing
    3.5  Trend removal:
    3.6  Time series analysis procedures
        3.6.1  RUN-test
        3.6.2  Frequency folding
        3.6.3  Digital filter
        3.6.4  Maximum-entropy-spectral analysis
        3.6.5  Signal average
        3.6.6  Actogram display
        3.6.7  TIMESDIA
4  Working with models
    4.1  Introduction
    4.2  Model construction and simulation with MODUS
    4.3  Model construction and simulation with other programs
    4.4  Model examples for rhythms
        4.4.1  Feedback model for biological rhythms
        4.4.2  Predator-prey model
        4.4.3  Model building and simulation with a model of Diez-Noguera
    4.5  Examples for construction of models


List of Figures

    1.1  Clover in day- and night-position
    1.2  Fragrence of Exacum affine as function of day time
    1.3  Golden hamsters at night and at day
    1.4  The drinking duck
    1.5  Desmodium rhythm: illustration
    1.6  Desmodium-rhythm: curve
    1.7  Desmodium-rhythm: recording
    1.8  Desmodium-rhythmicity: temperature effect
    1.9  Example from a laboratory book: content
    1.10  Example from a laboratory book: entrances
    1.11  Example from `Science Citation Index'
    1.12  Chronobiological journals
    1.13  Current Contents

    2.1  Imaging with video camera, framegrabber and computer

    3.1  Parameters of an oscillation
    3.3  Stomatal movement rhythm of Vicia
    3.2  Phase diagram of Desmodium
    3.5  Period determination with a fitting line
    3.4  Frequency folding
    3.6  Signal average method

    4.1  Predator-prey model
    4.2  Feedback model
    4.3  Phase diagram of oscillations of a predator-prey system


List of Tables

    1.2  Time of maxima, minima and points of deflection of the Desmo -dium lateral leaflet movement
    1.3  Time and standard deviation (SD) of maxima, minima and points of inflection (PI) of the Desmo -dium lateral leaflet movement.
    1.4  Table for recorded values of Desmodium motorium lateral leaflet movement.



Many processes in organisms are rhythmic. Rhythms with periods of about 24 hours are found already in the lowest organisms such as cyanobacteria. In unicellulars, fungi, plants and animals including humans they are widespread. Our knowledge of such rhythmic processes is increasing constantly by new observations and experimental results. But the underlying mechanisms are not yet clarified in a single case and are therefore a challenge for scientists.

This new area of `Chronobiology' is not only of interest to scientists. Even laymen, pupils and students find it intriguing. Furthermore, these rhythms in organisms can be observed and experiments performed by them, because simple procedures are often sufficient.

In the natural sciences it is important to learn scientific methods and to practice them. We believe, that this fascinating research area of chronobiology is useful for it. In order to get familiar with the field and the methods used in it we have published a few years ago a workbook [39]. It was written to facilitate the observation of and experimenting with rhythms in biological systems. For many of the proposed experiments special equipment was necessary. This can nowadays be replaced by computers. They are much more versatile and also usable for analysing the data. Often they are cheaper than the special equipment used before. We have therefore written this book. It was used as an instruction for biology students of the university of Tübingen attending courses in chronobiology. It might, however, be of interest also to students of other universities and to teachers at high schools, pupils and other people.

We hope that this book rises interest for this fascinating new area of life sciences. It should help to study rhythms more closely. If it furthermore mediates a little bit of the excitement and enthusiasm which results from solving problem s in science, its aim is fullfilled. Another book will be published here soon which serves as an introduction into the field of chronobiology.

To satisfy the curiosity of young people is unfortunately nowadays not much promoted, because schools stick often too tightly to the curiculum and offer too much matter of teaching. This leads easily to only secondarily motivated students for whom the scores are the main aim of going to school. It was the great pedagogue Pestalozzi who once stated:

All unsere Erziehung ist nicht einen Heller wert,
wenn Mut und Freude dabei verloren gingen2


Alle Schöpfung schwingt im Reigen,
Freude heisst ihr hohes Lied.
Nur der Mensch will sich nicht beugen,
jagt nach fremdem Glück sich müd.
Freunde, sucht den Sinn der Dinge,
dass auch Freude euch durchdringe

J.W. v. Goethe

All complicated systems tend to oscillate. Machines, bridges, electronic equipment are examples. The time it takes for one cycle (`period lengths'3) is the result of the properties of the system. It usually does not correspond to the period length of a rhythmic event in the physical environment.

Organisms as another example of complicated systems are also prone to oscillate. This ability is found at all levels of organisation. Plants and animals have adapted themself during the course of evolution to the time structure of their environment. This is periodic: The 24 hour day-night rhythm (daily rhythms), the 24.8, 12.4 and monthly rhythm (tidal and lunar rhythms) brought about by th orbit of the moon, or 12 months rhythms (annual rhythms, photoperiodism) caused by the orbit of the earth around the sun. Corresponding rhythms are found in numerous organisms.

This book consists of three parts. In the first part we describe methods and equipment. They are the basis for planning, execution and analysis of experiments. Many of the proposed experiments can be done by using a computer in connection with a video camera and a frame grabber (also called digitizer)4. In this way the experimental data can be recorded and analyzed. The system and the programs are mentioned briefly . They are described more detailed in a handbook [36] and in a book [37]. A system to record the locomotor activity of animals with infrared light beams is also described. In a special chapter we mention the importance of modelling, which allows the simulation of biological rhythms. We will also get a glimpse of the different methods to analyze rhythms (`time series analysis').

In the second part experiments are proposed. Some short term oscillations which are not adjustments to external periodicities (`ultradian rhythms') will be described: a chemical oscillator, the gravitropic pendulum, a transpiration rhythm and the lateral leaflet movement of the Indian telegraph plant. We will than take a few of the numerous biological rhythms which evolved as adaptations to the 24 hour time structure of the earth and which are especially suited for experimentation. For instance the leaf- and petal movement and rhythmic fragrance in plants, the rhythmic change in shape of a marine amoeba, rhythmic events in animals and man. The importance of the 24 hour periodicity has in the last years been studied intensively in respect to shift work, flights crossing time zones, and in certain deseases . The influences are meanwhile well known in the public. Less well known is the participation of the 24 hour rhythmicity in the measurement of the daylength . In this way many organisms, especially from temperate and higher latitudes, are able to determine the time of the year reliably. This has been pointed out already in the thirties of the ninetheens century by Bünning. The field of photoperiodism has in the meantime grown considerably and is of much practical importance. There are also numerous interesting studies on tidal and lunar rhythms as adaptations of many marine organisms to the coastal conditions of the oceans. However, we will not propose experiments for this field in this book. For information, a few movies can be used at school (see page pageref).

The third part of this book is devoted to different ways of teaching the field of rhythms in organisms. Simple experiments without expensive equipment are suited for schools and the interested layman (see page pageref). Teaching aids, teaching proposals, and didactic considerations are found from page pageref onward. You will find also hints for getting, rearing and keeping experimental organisms, sources for obtaining equipment and laboratory material (page pageref).

As is usual in life, the best way to learn something is by doing.

Verba docent
exempla trahunt5

A few technical remarks: This book was for some years in the process of evolving. It was used by students who participated in a course covering the area of chronobiology. This year (1999) it was polished up. Especially most of the figures were improofed. For diagrams I used `Scandata´ in order to obtain data from curves in figures from publications. They were produced with `Techplot´. Both programs are from Dittrich, Braunschweig. Vector graphics are made with `Killustrator´ under the operation system `Linux´. Text was applied to bitmap figures with the same program. The book text was written with `Lyx´. It uses Latex in the background. This program was also used under `Linux´. The figures are inserted as eps- or ps-files and the book stored under ps- or pdf-format.

Part 1
Methods and instrumentation

Chapter 1
Scientific work

The formulation of a problem is often
more important then its solution
A. Einstein

In scientific work certain rules are used which have proofen to be useful. The method of multiple working hypotheses will be explained. We will learn how to put forward and test critically hypotheses and how to plan, execute and analyse experiments by using as an example the telegraph plant Desmodium motorium. The significance of communication in science will be treated. Controversies and their function in science will be mentioned briefly. Finally we will point to some unsolved problems in the area of chronobiology to motivate you for own studies.

1.1  How research work is done

1.1.1  Introduction

Textbooks give often the wrong impression, that nature is well understood by man. They stress the collected body of knowledge and the problems solved, whereas the unknown is often not even mentioned. As soon as one starts to study more closely a special area of natural science it becomes, however, very obvious that many things are unknown, not studied or not understood.

In the area of chronobiology this is especially obvious. It is a relative young branch of biology and therefore not much knowledge has been accumulated. For the student this has the advantage, that he can do research work with simple methods and without intensive literature studies.


Figure 1.1: [
Clover in day- and night-position]Clover in day (left) and night position (right). Top view

In this part we will get to know some general methods of scientific work. They can easily be transferred later to similar situations. Scientific work consists to a substantial part of answering questions. Questions arise, for instance, by observing. If we walk in the evening through a meadow, the threeparted leaves of clover are differently positioned as compared to the day time. They are folded together in a vertical position, whereas during the day they are spread more horizontal (figure 1.1). How does this leaf movement work? We try to find answers (so called hypotheses) and to test them experimentally.


Figure 1.2: [
Fragrence of Exacum affine as function of day time]Fragrance intensity of flowers of Exacum affine as a function of day time, estimated by three different persons. Strongest odour in the early afternoon. Mean values with standard error.

Or we observe in the Gentianaceae Exaccum affine an intensive fragrancy in early afternoon. In the morning and evening the odour is less intense (figure 1.2).

Figure 1.3: Golden hamsters are night active (left) and rest during the day

Golden hamsters are night active and rest during the day (figure 1.3). Is this a direct consequence of the light-dark-cycle? Or would the animals show a rhythmic change between activity and rest also under constant light conditions (e.g. under very weak light)?

Such observations lead often to questions, which can be answered tentatively by hypotheses and be tested by experiments:

phenomenon Þ problem Þ hypothesis Þ experimental test

1.1.2  Method of multiple hypotheses and strong inference

According to [23] and [105] scientific work is favoured by the consequent use of the `method of multiple hypotheses' and `strong inference'. The method consists of the following steps:

  1. Stating alternative hypotheses
  2. Planning of crucial experiment(s) to disproof hypotheses
  3. Execution of the experiment(s), in order to obtain a clear result
  4. Repeat 1 to 3, if necessary with new hypotheses

The method of multiple working hypotheses was put forward in 1890 by Chamberlain, a geologist, in a lecture of a meeting of the Society of Western Naturalists. It avoids the danger of the method of simple working hypothesis, were one clinges with motherly affection to one owns hypothesis. This method is therefore especially suited for areas, in which much knowledge has accumulated, but much more is unknown.

Proposal: Read the reprint of the original article of Chamberlain `The method of multiple working hypotheses' [23]. Platt in 1964 has taken up this method and recommended it as especially useful for scientific work. He calls this strategy strong inference. The different steps have been mentioned already and we would advice strongly to read this article [105].

Using the way of scientific work in the `Laboratory of Molecular Biology' in Cambridge as an example, Platt demonstrates, how this method, if used systematically, leads rapidly to progress in solving problems. This is a problem oriented instead of a method oriented procedure. Each day the newest results are written on the blackboard, what went wrong, how errors can be avoided, and how the hypotheses can be tested critically by experiments. New experiments and controls to test the hypotheses are proposed. It is always advisable to use the simplest system, which does still show the characteristics one is interested in. It is more important to ask which experiment disproofs a hypothesis than to ask how to proof it:

'Verwende das einfachste System, das noch die Eigenschaften zeigt, die Du untersuchen willst'.

Scientific work is comparable with the work of a detective in solving a crime. By observation or by oral or written information he is confronted with a problem. He tries to solve the `case' by finding all kinds of possible explanations (`hypotheses'). Neither an able detective nor a good scientist would follow up just one single hypothesis.

If you play the game `mastermind', where you have to find out the sequence of differently coloured pins, it would be unwise to begin with a fixed idea of the correct solution, before you have collected enough informations. This game shows incidently, what is also true for science, that `negative results', i. e.  our guess was wrong, lead normally more rapidly to a solution as compared to a partly correct result. If, for instance, in our game out of four differently coloured pins none is correct, we know that only one or two of the remaining colours had been set.

To disproof hypotheses is a better strategy as compared to proofing it. In a strict sense, to proof something means only `with high probability correct' .

`Each conclusion, which is not an exclusion, is uncertain and must be tested again (Lederberg)'.

'A theory, which can not be vitally hit, can not live (Bacon)'.

'Hypotheses, which cannot be disproofed, are meaningless (Bacon)'.

Proposal: If you dont know the game `mastermind', play it with somebody.

Of course testing just one hypothesis does also help to advance our knowledge, however this method is less economic. The alternative hypotheses are than usually put forward by other researchers (see section `Controversies in science', page pageref). In this case, crucial experiments are also needed to decide between the different hypotheses, to disproof some and leave some as candidates for further testing.

Proposal: Read the article by Popper `Von den Quellen unseres Wissens und unserer Unwissenheit' [106] and a detective story (DuMont's Criminal-Rätsel [133]). In this detective story the solution of the `case' is reserved in closed pages. Use the method of multiple hypotheses in trying to solve the case.

1.1.3  Testing hypotheses, analysing and interpreting data

Besides putting forward hypotheses, important steps of scientific work are:

We will exercise these steps in different examples.  Formulation of hypotheses: Drinking duck

Using the drinking duck6 (figure 1.4), we will see how questions arise from observations and how they will lead to hypotheses.

Figure 1.4: [
The drinking duck]The drinking duck continuously dips its beak into the water beaker.

Instruction: Fill the beaker with tap water up to the rim and dip the beak of the drinking duck into the water, until the felt of the head is wet. Bring duck back in its original position and observe it. Note down your observations. What are the questions arising? Which hypotheses could answer your questions? How could you experimentally test your hypotheses? If the problem is too complicated, it usually helps to subdivide it into smaller problems. They are more easily solvable and might finally lead to the solution of the main problem.  Analysis and interpretation of data: Movement of the lateral leaflet of Desmodium motorium

The analysis and interpretation of data shall be demonstrated by using the rhythmic movement of the lateral leaflets of Desmodium motorium, the indian telegraph plant. This plant exhibits vertical movements of the small lateral leaflets (`telegraph plant'). Look at the movie `Desmodium motorium (Fabaceae) - Gyration' [127] and observe the movement on the plant directly (figure 1.5).


Figure 1.5: [
Desmodium rhythm: illustration]Example illustrations for lateral leaflet movements of Desmodium motorium. 20 second intervals between pictures.

The oscillation is quite regular. We want to determine the duration of one cycle of the up- and down movement (figure 1.6). Sequential periods are not exactly the same. We have to measure therefore several cycles and to calculate a mean value of the period. We should also find a measure of the variability of the period. For recording the time we use a stop watch. What is the best way to determine period length?

Figure 1.6: [
Desmodium-rhythm: curve]Time course of the Desmodium motorium lateral leaflet movement.

Period length is the time between identical phases of the oscillation: for instance the time between a maximum and the following one, or between minima, or between the point of inflections (figure 3.1). Which phase (=fixed time in a cycle) would you use and why? We will become familiar in a special chapter (page pageref) with methods in which period length is determined by using all the recorded data.

Here we will for the time being restrict ourself to a very simple method. Determine the period length of the lateral leaflet movement according to your considerations. Measure as exactly as possible the times of the phase points of the cycles which you decided to use. Use the stopwatch, and note down the times. Determine the periods from the differences of the phase points you have chosen. Calculate a mean value according to the following equation:

= å


the mean value, xi the individual values, and n the number of oscillations.

is the sum of the individual values (table 1.2, table 1.3).


Nr. max. min. deflect. \searrow deflect. \nearrow















Table 1.1: Time of maxima, minima and points of deflection of the Desmodium lateral leaflet movement

Why did we not determine the time between the first maximum, and the last maximum and divided it by the number of oscillations? The reason is, that we want to determine the variability of the period. In order to calculate the variability, we need the individual period lengths. Variability is caused by biological and methodological reasons. As a measure of the variability we will use the standard deviation (there are other measures of variability).

The standard deviation SD is
SD =   æ



the mean value, xi the individual values, and n the number of periods. The differences of the individual period lengths from the average period length


is determined. This value is squared. Then the sum of all squared differences is formed. Finally this value is divided by n-1 and the square root taken.

With the help of the standard deviation we can find out which phase is the most suitable one to determine the period length. It should have the lowest variability, i. e.  the smallest standard deviation. Find out whether the maximum, the minimum or the point of inflection to the minimum or to the maximum is the most suitable one (table 1.3).

timeresultstandard deviationresult
xmax = SDmax =
xmin = SDmMin =
xPI\nearrow = SDPI\nearrow =
xPI\searrow = SDPI\searrow =

Table 1.2: Time and standard deviation (SD) of maxima, minima and points of inflection (PI) of the Desmodium lateral leaflet movement.

The standard deviation can also be used to test whether the mean is significantly different from another mean (if, for instance, the period length was determined at another temperature, see page pageref).

For this purpose the standard error SE is calculated from the standard deviation SD using the following formula:
SE = SD/Ön
If the means are by 2 or more standard errors apart from each other, the difference is highly significant.

How accurate is the calculated period length? The largest possible error is half of the smallest unit of measurement. If, for instance, we have determined the time to one tenth of a second, it would not be significant to give more than 2 digits behind the decimal point. The last significant digit can be underlined, e.g. 3.75 minutes.

How do we interpret our evaluations? We have found, that under our conditions the mean period length of the lateral leaflet movement was 3.75 minutes. The standard deviation is 0.35 minutes. The variability is therefore about 10% of the mean. The standard error is 0.1 . We should remember this value for the experiments, where we will measure period length at different temperatures (see page pageref). We will then be able to determine whether the means of the periods are significantly different.  Planning, execution and analysis of an experiment

Planning of an experiment is one of the main tasks of a natural scientist. Here phantasy and creativity are needed as well as carefullness, exactness, wariness and critical proceeding. If we want to explain a problem or a phenomenon, we try to explain the occurrance or functioning: We put up one or more hypotheses. With an experiment we critically tests these hypotheses. In the following a few basic principles are listed [135].  Example for the solution of a problem: Does the period length of the lateral leaflet movement rhythm of Desmodium motorium depend on the temperature of the surrounding?

How would you build a recording device to record the lateral leaflet movement rhythm of Desmodium motorium? A temperature controlled box is used, in which temperature can be kept constant at a certain value (see page pageref `Building an air conditioned box'). An electronic thermometer serves to measure the temperature.

Plan an experiment in which the dependency of period length of the leaflet movement rhythm from the temperature is studied. Execute the experiment and use the analysis method explained in the foregoing section to determine mean values, standard deviation and standard error. Plot the period length as a function of the temperature. Add the standard errors as vertical bars to the means. Interprete the results and write a report of your experiments (see page pageref). What is the Q10 -value?7 It is calculated from
Q10 = (t1*t2)10/(t2-t1)
where t1 is the period length at temperature t1 and t2 the period length at temperature t2 . Is, for instance, t1 10 minutes at a temperature of t1 = 300C and t2 20 minutes at a temperature of t2 = 200C , the Q10 = (20/10)10/10 = 2 .

Some hints and helps: For growing the plants see the section on the telegraph plant Desmodium motorium in the chapter `ultradian rhythms' on page pageref. For recording the movement you can use the setup shown in figure 1.7[82]. It is easily constructed. Or you use the digitizing method described on page pageref. Cut off with a razor blade a leaf with lateral leaflets which are moving well. Put it immediately in a small hole in a polyurethan disc floating on distilled water in a small vial. Transfer to the air conditioned box. If you use the Koukkari method, stick (with a tiny amount of water soluble glue) a delicate thread or a human hair to the tip of the leaflet and to the end of the delicate wire balance. Cut off the second lateral leaflet and the terminal leaflet. Add a small droplet of vaseline to the cut surface.

Figure 1.7: [
Desmodium-rhythm: recording]Recording of the lateral leaflet movement of Desmodium motorium according to Koukkari et al.. At the tip of the lateral leaflet a delicate thread or a hair is fastened with a tiny amount of water soluble glue. The other end of the thread (hair) is connected to a delicate balance. The pointer of the balance shows the angle of the leaflet.

The measurement is better done by two persons: One calls the times at which the phase is reached which serves as the reference phase. The other person reads the time from a running stop watch and notes it down. Use the table 1.4 to enter the angles of a Desmodium motorium lateral leaflet every 15 seconds. It is the basis for a graphical display of the values as a function of time (figure 1.8).

Table 1.3: Table for recorded values of Desmodium motorium lateral leaflet movement.

timetemperature( 0 C)timetemperature( 0 C)
sec 150 250 350 sec 150 250 350


Figure 1.8: [
Desmodium-rhythmicity: temperature effect]Dependence of period length of the lateral leaflet movement of Desmodium motorium from the temperatur

1.1.4  Experimental protocol

A written protocoll is an undispensible part of scientific reasearch work and certain rules have been found to be of much help (see e. g. [135], page 130ff.):


Figure 1.9: [
Example from a laboratory book: content]Example from a laboratory book: page of content.


Figure 1.10: [
Example from a laboratory book: entrances]Example from a laboratory book: page with entrances.

1.2  Communication in science

1.2.1  Introduction

This section is mainly for students, for whom it is an important part of scientific work.

1.2.2  How scientists report their results

A scientist who has finished a research work usually reports the results. He would first explain it to his colleagues, who will constructively criticize methods and execution and propose alternatives to interprete the results. He would then give a talk to a larger group of scientists. This could be a colloquium of the department or a meeting (see the following invitation).

Kolloquium des Sonderforschungsbereichs

Vortragender: Prof. Dr. C.S.Pittendrigh

              Stanford University, USA 
Thema: Circadian rhythmicity: 
An evolutionist's view 
Ort: Zoologisches Institut Frankfurt 
Kleiner Hörsaal 
Zeit: Donnerstag, den 17. Dezember 1987

18 Uhr 30 
Gäste sind herzlich willkommen 
gez. Prof. Dr. G. Fleissner 
Frankfurt, den 1. Dezember 1987

The proposals and critique will be taken into account when writing the publication. The manuscript will be sent or given to colleagues and their oppinion and comments on content and style appreciated, before it is submitted to a journal. Usually the editor of the journal sends the manuscript to one or two referees. They use certain rules for their judgement. If the opinion of the two referees is too diverse, the editor has to send it to a third one or decide himself. In most cases the manuscript is send back to the author with proposals for improvements of style and content. The author will revise the manuscript.

It might take a long time from finishing the manuscript until acceptance by a journal. Therefore often short communications are published before the final publication, which have less stringend demands. Interesting new developments and results are reported and commented on in special journals such as `Science News' and others.

1.2.3  Scientific publication: An example

How does such a publication look like, how is it structured and how does one read it?

Proposal: Read the publication of Sulzman et al.: `Neurospora rhythm in space: a reexamination of the endogenous-exogenous question' from the journal `Science' [125] from 1984.

Read afterward the paper of Mergenhagen in the journal `Die Naturwissenschaften' [92]. Mark the different sections according to the scheme in the preceding paper. If you want a quick information about the content of the paper, the following procedure is proposed:

Title interesting? Þ Abstract Þ Figures Þ Introduction Þ Discussion Þ Result

First decide by reading the title, whether it is worthwhile for you to look at the publication more closely. Then read the abstract or summary. If it is of interest to you, look at the figures and tables and their legends, perhaps also introduction and discussion. Important papers must of course be read carefully also in the part containing the results. Sometimes one might be interested in a method or a special point of the discussion only. In this case you would start right away on the particular place.

1.2.4  Writing your own scientific article

The best method to find a good style in publishing a paper is to read scientific articles. In doing so you can learn from good and bad examples. There are also books on it such as Ebel et al. [81,33,121].

Task: Write a paper on the execution and evaluation of your experiments concerning the temperature dependency of the Desmodium-leaflet rhythm. Use the usual structure of an article. Make a sketch of the experimental setup, a table for the data and a graph showing the dependency of period length on temperature. Do not forget to include a list of references at the end of the article (see also literature search).

1.2.5  Literature search

Before we plan a scientific research project we would like to know whether the solution of the problem has perhaps already been found and published. Or, if not, we would at least like to know, whether other people have thought of the problem and what they found out about the background of my studies. Six hours work in the library might save you 6 month work in the laboratory.

Encyclopedias are the most general and useful sources of information if you want to become familiar with a research field. There exist furthermore literature guides for certain fields with basic references, reviews, and journals with abstracts such as [124]. Handbooks are also useful to become familiar with a new field  [8,].

With textbooks you can familiarize yourself with the background, with monographies you can become acquainted with details of certain fields. Subject catalogues of libraries, catalogues of books in bookstores [30] are helpful in this respect. To decide whether a certain book is interesting for you, you can consult reviews on books (`Reviews')[45,]. An abstract- und index-journal is `Biological Abstracts'[14]. Instructions are included in the halfmonthly editions.

Quite useful is also the `Science Citation Index'  [115](figure 1.11): We know an important, but older paper of the subject we are interested in, and we want to find more recent literature. This publication indicates all authors citing this particular article as a reference in their publication. It is likely that such a paper is also concerned with the same or a similar topic. With the help of the `Science Citation Index' it is therefore possible to find more recent publications to a topic.

Figure 1.11: [
Example from `Science Citation Index']Example from `Science Citation Index'. The publication of J. Aschoff in `Zeitschrift für Tierpsychologie 49, page 225 of 1979 was cited by M. Ferrer in Comp. Bioc. A. 107, page 81 (1994) and of R.V. Peters, Brain Res. 639, page 217 (1994).

The most recent papers can be found in the latest issues of scientific journals. The following journals are specialized in the field of chronobiology (figure 1.12):

Most papers in the field of chronobiology are, however, published in numerous journals of quite diverse areas: Plant physiology, animal physiology, microbiology, genetics, behavioural sciences, medicine. To avoid browsing through all those journals in the attempt to find relevant articles it is recommendable to use `Current Contents' which occur weakly (figure 1.13).

Figure 1.13: [
Current Contents]Cover page of `Current Contents' (left), a page of the key index (top right) and an example of the page of contents of a journal (bottom right). Under `circadian rhythms' top right one finds 127 41. On page 127 (bottom right) the page with the contents of `Journal of Interdisciplinary Cycle Research' is found. On page 41 is an article on circadian rhythms by Queiroz-Claret and Queiroz.

In the `Current Contents' the pages of contents of journals of the biosciences are reproduced and they contain an index of subjects and authors. In it one can find the wanted information quickly. Under circadian rhythms, for example, you find on page 229, 4th column in number 14, volume 34 (April 8, 1991):


The first number is the page in the particular issue of `Current Contents', the second number is the page of the corresponding article in the particular journal (in the case shown a paper by Queiroz-Claret and Queiroz). The `Current Contents' are also available on diskettes and can be used with a comfortable program allowing to search the literature for key words, authors, journals, and to produce files and printouts of the relevant literature.

It is often helpful if one knows names of scientists working in the particular field (see Science Citation Index). You can write to those people or ask them. But you should have gotten first a founded theoretical and general background in the field. Sometimes it is also advisable to browse through areas which are not directly connected with your field of interest. In this way you might, for instance, find solutions for methodological problems.

'Wise selection rather than all-inclusive coverage is the key to library work'.

If you are planning to start your own literature file, you could make use of modern data bases and data base systems. They are available through the university libraries and in the internet, but also from publishers. 9With their help it is easy to use reprint collections and to find papers of certain authors, according to certain key words, or according to e.g. the year of publication. Printed literature can be read with a scanner into a computer and made maschine readable with an optical character recognition program (OCR).

Proposal: Use the different methods mentioned above to find the more important publications of the last two years for a chronobiological topic of your choice. Make a literature list.

1.3  Controversies in science

The method of multiple hypotheses and 'strong inference' is not always used by a particular research worker, perhaps because he does not know it or because in a special case (where the problem is too complex to allow meaningful alternatives) the method is not useful. In these cases alternative hypotheses are put up at another level. Other scientists might disagree with the proposals and inferences and it comes to scientific controversies. One such controversy from the field of rhythm research is given in the following:

Proposal: Read the book of J.D.Palmer (1970): The biological clock: Two views. [101]. In this book two controversial views are discussed, how circadian rhythms arise. Brown denies, that they are the result of internal clocks of the organisms and claims, they are the direct result of external factors which are changing in a 24 hour pace. To exclude the light-dark-cycle or a temperature cycle, as is commonly done in research work on circadian rhythms, is according to Brown not sufficient. Instead, the rhythmic alternation of other factors should be prevented, which is, however, often impossible (magnetic fields, high altitude radiation etc.). Hastings, on the other hand, claims, that circadian rhythms are the expression of an internal clock inside the organism. It continues to run even under stringent constant conditions of the environment. This view is supported nowadays by most scientists working in the field. Describe the two views in your own words. How do the two authors explain freerun? Collect the arguments for the two hypotheses and note down the weak points of each. Try to find crucial experiments which can be used to test the hypotheses critically. Read in this context the following papers, which have been published after the book had appeared.[57,,,]

1.4  Unsolved problems

We have stressed already in the introduction, that many problems in the natural sciences are unsolved and that we are far from understanding the nature around us. One of the main goals of science is, to reduce ignorance and superstition of mankind.

Unsolved problems are numerous in the field of chronobiology. The highest priority in the list of unsolved problems is the search for the mechanism of biological rhythms. In no case this question has been answered satisfactorily at the physiological safe at the molecular level. A number of models exist [38,] which are, however, partly unsatisfactory or even wrong. New methods to clarify the mechanisms involved come from the field of molecular biology and systems analysis. Important in this respect are not only the methods, but also the systems studied. It is recommendable to use a minimal system, which shows the property to be studied, but exhibits only few phenomena which might disturb the studies.

In trying to unravel the mechanism of circadian rhythms a prokaryote would be more suitable as compared to a eukaryote: The former is much more primitive in respect to structure and function. The genetical structures are extremely simple, consisting of a ring-shaped chromosome without nucleus. Organelles and compartments are absent. New molecular genetic methods can be used [107].

Another minimal system are specialized eucaryotic cells such as the red blood cells of mammals. They are specialized to transfer O 2 . They do not possess a nucleic acid metabolism, have no mitochondria, no respiration, no protein synthesis. Finding a circadian rhythm in such a system would be an important step to understand the underlying mechanisms. A number of proposed models would be rejected if a circadian rhythm exists in red blood cells. And indeed a circadian rhythm of activities of different enzymes in red blood cells has been described [10]. However, attempts to repeat these results were unsuccessful in a number of laboratories [87,]. See also the preceeding subsection controversies in science (page pageref).

Finally, a circadian rhythm of dry seeds of beans was described [19]. This is another minimal system, since besides a very low respiration no other metabolic processes are found. This result has not been confirmed, although the experiments are simple and the results of paramount importance.

We have studied the lateral leaflet movement of Desmodium motorium and it would be interesting to understand the underlying mechanism. This is, however, a difficult problem and not solvable in the course of a laboratory exercise. In such a case it is advisable to divide the problem in smaller ones and try to clarify these. In the particular case of the lateral leaflet movement it would be recommendable to devide the problem into two questions: The question, what mechanism is responsible for the movement, and secondly, how the movement is controlled rhythmically. For the first question, the pulvinus and the turgor mechanism as the basis of the movement is of importance. For the second question of the timing, however, the kinetics of the movement, the temperature dependence of the rhythm, and the influence of inhibitors of various processes such as glycolysis or protein synthesis are of significance.

Proposal: Try to find a limited problem which can be solved during a laboratory course. Further unsolved problems can be found from the examples for rhythms in the second part of the book. For instance: which extraretinal photoreceptors are responsible for the synchronization of the locomotor activity of flies (see `Activity rhythms in animals', page pageref).

Chapter 2
Recording methods

Out of numerous recording methods we present two, which are quite versatile and which have stand the praxis. One method serves to record movements and uses a video camera connected to a computer via a frame grabber. With special programs the pictures are analyzed. Furthermore an infrared light beam method is explained, with which the locomotor activity of animals is recorded.

2.1  Video recording and analysis of rhythms

2.1.1  Introduction

Many rhythmic events in plants, animals and also in unicellulars express themself as movements. They are easily observable. With a video camera coupled via a framegrabber to a computer and imaging methods such movements are recorded, displayed and analyzed.

2.1.2  Recording principle

The recording principle is shown in fig 2.1. The rhythmic leaf movement of a plant is used as an example. Images of the object are taken in predetermined sequences and via a framegrabber transferred to and stored by a computer. The position of a leaf is determined by a program which automatically recognizes the tip of the leaf. It saves the values of the position of the tip as x and y values. They can than be graphically displayed as a function of time. The period length of the oscillation can be determined by time series analysis programs.

Figure 2.1: [
Imaging with video camera, framegrabber and computer]Recording of leaf movement with imaging method. The moving object is recorded by a video camera, digitized by a frame grabber of a computer and the images stored and displayed on the monitor screen. Data are stored and used for further analysis.

2.1.3  Recording

Since a handbook [37] exists for imaging, we will limit ourself here to the essentials. The video camera is connected via a cable to a framegrabber of a PC. (see also figure 2.1).

The imaging program needs Linux as the operation system. The programs are available on the internet and explained [37]. After starting the program, the object has to be put in focus (with the lense of the video camera) and the right size must be chosen (by adjusting the distance camera-object). A suitable illumination is important. To record in weak safelight or darkness infrared light is used. It can be produced with infrared light emitting diodes (LED). The object to be recorded should be clearly visible and not blocked partly by other structures. It is unimportant, whether the object is brighter or darker than the background. However, the lighting conditions should stay constant in time and space. Then the sampling rate of the digitizing and the recording interval have to be set.

Different kinds of data can be used for the analysis of the movement: The x- and/or y-coordinates of e. g.  the center or the tip of the leaf, the number of pixels (as a measure for the size of the object). The parameter setting and a commentary can be stored in files. After a file name has been entered, the recording can be started.

During recording the data can be displayed on screen as a function of time.

2.2  Recording of locomotor activity of animals using light beams

2.2.1  Introduction

The locomotor activity of many animals and mobile unicellulars is controlled by an endogenous clock. These movements can be recorded also by the imaging system just described. Examples are given in [36]. However, in the case of fast moving objects this system is not recommendable. We mention therefore an infrared lightbeam system which is described in a handbook [40] in detail.

2.2.2  Recording principle

  Individual animals are kept in translucent dishes and supplied with water and food. An infrared light beam watches a part of the dish and transmits a signal, if the animal interrupts the light beam.

The system allows to record activity of up to 288 individual animals. It is fast (each animal will be monitored every 25 msec) and quite sensitive (it was originally developed for activity recording of Drosophila flies). It functions reliably also at varying light conditions and temperatures of the surrounding.

The activity of the animals can be displayed in form of an actogram: It is determined, whether in a certain time span (e. g.  4 minutes) the animal has interrupted the light beam for a certain number (selectable). Or, alternatively, it is recorded, how often the light beams are interrupted in a predetermined time span (e. g.  one hour).

With the system the environmental conditions such as light intensity and temperature can be monitored. It is also possible to control temperature, light and other events with the system.

The data are stored in a peripheric processor unit (kind of minicomputer) via multiplexer (kind of inquiry mill, by which the data of different recording places pass the same data line) and are stored in a buffer connected to it. They are transferred hourly to the diskette of a host computer. A radio transmitter based clock serves as a time reference. The processor unit is buffered by a battery. In this way no data are lost in case of a power failure.

The data are available in a certain format, for which a plotting program exists. Furthermore the data can be transformed with a program (HELLRODA) into other formats. With special programs (see next chapter) the data can be analysed.

This system was constructed and the programs written by Winfried Hellrung10. The HELLRODA data transfer program was written by Joachim Schuster.

Chapter 3
Display and analysis of time series

If measurements of time variable parameters are performed and the data stored, we obtain socalled time series. An overview on timeseries analysis procedures and -programs is given. Using two examples from the field of biological rhythms some of these procedures will be demonstrated.

3.1  Introduction

If we want to study rhythms, we need not only to obtain data by using recording methods. We need also procedures to display and analyse the data. First elementary terms will be explained. Than the following questions will be dealt with:

  1. How are periodicities displayed and found? (Section `elementary terms' and `graphic display of timeseries', page pageref)
  2. How do we remove noise from the recorded data and how do we take care of trends in the curves? (Section `smoothing', page pageref and `trend removal', page pageref)
  3. What is the period length of the oscillation, which procedures are used to determine them? (section `timeseries analysis methods', page pageref).

This chapter is for students only, who need the informations for analysing experimental results.

3.2  Elementary terms

Signals with a rhythmic component are characterized by at least three items:

With these parameters an oscillation can be characterized (see figure 3.1). Furthermore, the form of the oscillation is important: It can be sinus like or like a rectangle, a sawtooth or all kinds of intermediates. An oscillation might possess a trend (upward or downward) and can be noisy (figure 3.1). A timeseries could also consist of several oscillations which might superimpose each other.


Figure 3.1: Left: Explanation of amplitude, period length and phase of an oscillation. Right: Superposition of an oscillation by trend and noise.

3.3  Grafic display of timeseries

Almost always the first step in analysing a timeseries is the graphical display of the experimental results. In this way one can find out whether trends (oscillation does not deviate from a mean value, but tends to higher or to lower values) or noise superimposes the oscillation. The graphical display shows furthermore, whether one or more periodicities exist at all, which form the oscillation has, whether it is damped and whether the period is constant. The graphical display allows to decide, whether a timeseries analysis of the data is worthwhile. If the period length of the oscillation can be determined already from the graphical display, the following procedures are not always necessary, especially since they are time consuming. This is especially true for data which are not machine readable and have to be entered into the computer by hand, and if they are not available in regular time intervals (socalled nonequidistant sampling).

An example for the graphical display of a timeseries is shown in figure 1.6. The lateral leaflet movement of the indian telegraph plant Desmodium motorium was plotted as a function of time (see page pageref and legend for details). The period length is in the minute range. The oscillations are quite regular and the amplitudes large. The noise of the recorded data is small. Therefore the period length can be estimated directly without using special timeseries analysis procedures.

If several outputs are measured simultaneously as in figure 3.2, the mutual phase relationship can be determined in a graphical way: The timeseries is not plotted in the usual way as a function of time, but one output as the function of the other output. The time information is still present, if for each pair of data a dot is plotted in the coordinate system and if the dots are subsequently entered as a function of time. With equidistant sampling the distance of sequential dots correspond to a certain time intervall. If amplitude and phase position of the two recorded outputs are stationary (i. e.  do not change with time), the later oscillations will lay on top of each other. If they damp out, the curve turns into the center. If the periods are varying, complicated figures will be seen.

An example for the interpretation of such a phase diagram is given in figure 3.2. The curves show results of measurements on lateral leaflets of Desmodium motorium [4]. The leaflet position was recorded simultaneously with the electrical potential in the pulvinus of the leaflet. The potential varies between -10 and -110 mV. The phaseplot leaflet position against potential shows first of all, that both outputs oscillate with the same period. Furthermore the amplitude is stable. A strong change of the potential to negative values occurs in the upper leaflet position. During this so called hyperpolarization the leaflet stays in its upper position. It is not before the repolarization occurs that the downward movement begins. This shows, that the hyperpolarization of the potential leads the downward movement. The upward movement begins not before the potential has reached small negative values. During the upward movement the potential stays rather constant. From the varying distance of sequential dots one can furthermore conclude: The hyperpolarization in the upper leaflet position and the following repolarization during the downward movement are fast events: Between two sequential dots large distances in the x direction are covered. The distance of the dots in the y direction informs about the time the leaflet movement takes.


Figure 3.2: [
Phase diagram of Desmodium]From the lateral leaflet ofDesmodium motoriumthe position and the electric potential in the pulvinus were recorded simultaneously and the former plotted against the latter.

With the help of this kind of display the causal relation between recorded values can be checked. In the example given it can be deduced, that the sum potential of the pulvinus of the leaflet is closer to the oscillator as is the leaflet movement, because the sudden hyperpolarization leads the downward leaflet movement. It could furthermore be, that there is a causal relation between the two items (which can, however, not be deduced from the plot).

An other example is shown in figure 3.3. It is from a publication of Gorton et al. [53]. The width of the stomata of isolated guard cells from the epidermis of Vicia faba was determined every hour under the microscope. The values were plotted as a function of time (for the basis of stomatal movement see page pageref). It is difficult to recognize directly an oscillation from the curve. It is therefore adequate to use certain procedures which will be demonstrated in the following.


Figure 3.3: [
Stomatal movement rhythm of Vicia]Mean values of stomatal width of 5 isolated guard cell systems of Vicia faba. Upper curve: original values. Center curve: After smoothing average was applied. Bottom curve: After trend removal.

3.4  Smoothing

A close look at the upper curve in figure 3.3 reveils a steplike course. However, noise is quite pronounced. Therefore the values were first smoothened. For this purpose a smoothing average was performed with the values. Of five sequential values the average is formed and this value is stored instead of the third original value. The `smoothing window', consisting of five data, is now moved to a later record and the procedure repeated. In this way we get a mean value for the original fourth value. After all values have thus been averaged, the new timeseries is shortened by the two first and last values, but the deviations of the curve are reduced (center curve in figure  3.3). The smoothing improves with the length of the smoothing window (but at the same time more data are lost at the begin and end)12.

We see now the steplike course of the curve of the stomata data better (figure 3.3, center curve), but there is a strong upward trend.

3.5  Trend removal:

A trend is usually disturbing for the analysis of an existing rhythm and should be removed by trend removal. After removal of the trend it can usually be better decided, whether a rhythm is pertinent.

A simple methode of trend removal is to fit the data with a so called polynomal curve. This fitted curve shows a minimal sum of the quadratic deviations from the smoothed individual values (a characteristic of a good fit). The deviations are shown in the lower curve of figure 3.3 and a rhythmic course is now clearly visible. Trend and noise are removed. The new data can now be analyzed for periodicities. How this is done will be described in the following.

3.6  Time series analysis procedures

3.6.1  RUN-test

The RUN-test is a simple and quick procedure to recognize periodicities. It is a distribution-free test, i. e.  no special requirements are made in respect to the distribution of the data. After an eventually needed trend removal the mean value of all data of the timeseries is determined. Afterward the values which are larger then the mean are replaced by a + and the values which are smaller with - . In the next step the length of socalled `runs' is determined. A `run' is the sequence of + or - signs. If the timeseries is characterized by noise only, the lengths of the runs will be randomly distributed. If however a rhythm is present, the runs will fluctuate around the length of half the period.

For further analysis we use three procedures. They serve to determine the period length of a rhythm which has been shown to exist by using the RUN-test or by simple observation.

3.6.2  Frequency folding

In this procedure the time series is cut into pieces which correspond roughly to the length of the period. The pieces are plotted underneath each other (see figure 3.4).


Figure 3.4: [
Frequency folding]Methode of frequency folding: The activity stripes which were originally cut into 24 hour pieces (left) are in the right figure cut into pieces in such a way that activity between the 7th and 24th period lies now below each other. The x-axis corresponds now to the period length in this time span (about 24.5 hours) and not 24 hours anymore.

Usually one can now easily recognize whether corresponding phase points of the individual periods lie below each other: In this case the period length was correctly estimated. Otherwise the period was too short or too long. In this case the period can be estimated anew or a line is layed through the maximum of each period (see figure 3.5): Its slope reflects the period length. This procedure allows also to recognize changes in period length. In this case the periods can be determined for the different sections separately. This procedure is especially well suited for the determination of period lengths in actograms (see page pageref).


Figure 3.5: [
Period determination with a fitting line]Period determination with the help of the slope of a fitting line. The period length is 24.6 hours.

3.6.3  Digital filter

In the case of digital filtering (page pageref) the timeseries is transformed by a digital algorithm. In this way period lengths can be determined from rhythms which would be due to noise, otherwise less well analyzable (see figure 1.6).

3.6.4  Maximum-entropy-spectral analysis

The relatively new procedure of maximum-entropy-spectral-analysis (MESA) is especially well suited to determine even short timeseries reliably.

3.6.5  Signal average

If the period length was determined, one might like to obtain an average curve of a period (see figure 3.6). For this purpose the signal-average-method of Cornelissen and DePrince [29] is useful. It superimposes the individual pieces corresponding to a period and determines the mean values with standard deviation. This method can also be used to analyse `residues'. If a periodicity was determined, other oscillations might still lurck in the data set which one obtains after the analysed oscillation was removed (`residues'). They can now be more easily analysed as compared to the situation where they were hidden by the main oscillation. This procedure is also useful for separating signals from noise.


Figure 3.6: [
Signal average method]Signal average method: The activity from day 7 to 24 of the right figure was summed up and a mean circadian day (24.6 hour period) was obtained. The smalles activity bin was 4 minutes.3.4

3.6.6  Actogram display

By measuring the locomotor activity of animals the distribution of events in time is obtained. It is usually displayed in the form of an actogram. The data are often reduced to yes/no events, i. e.  the animal is active or inactive. To obtain an actogram, the timeseries is cut into 24 hour pieces und lined up underneath each other (see page pageref and figure 3.5). Similar to the frequency folding method these time spans can be chosen also in such a length, that they correspond to the period length (see figure 3.6 right part). If the corresponding values of the individual (subjective) days are vertically summed up, an `average day' is obtained. This average day can be compared with the corresponding average day of another time span which might have received another treatment (see figure 3.6 and the preceeding section).

With this method superimposed oscillations with close frequencies can be differentiated. With other methods this is difficult to do. For this purpose a frequency folding is performed with one period. The superimposed oscillation is now usually more easily recognizable from the figure.


A program package for the analysis and simulation of timeseries was developed by W. Martin in Bonn. It is available on large computers (e. g.  VAX, IBM) and (sofar only) on a HP-computer. A detailed documentation is available [89]. The data must be equidistant.

The program allows in dialogues to enter and graphically display data sets (up to 9 timeseries at the same time). Two timeseries can be analysed simultaneously. The data can be manipulated (copied, deleted, supplemented, concattenated, selected, listed), characterized (maxima, minima, mean value, variance, standard deviation, standard error, variability, third moment, skewness) and analysed.

The analysis methods offered include complex demodulation (a band pass technique). Other analysis methods can be used such as periodogram analysis, spectral analysis, autocorrelation, Fourrier analysis, different filter techniques. Details are found in the description of the TIMESDIA program.

For literature concerning timeseries analysis see [89,,]. Programs for timeseries analysis are given on page pageref. Unfortunately for biologists there is still no useful book available for timeseries analysis. A collection of programs on disk for personal computers would be desirable.

Chapter 4
Working with models

Models play an important role in the study of biological rhythms. They allow to simulate the behaviour in time. The results of simulations are tested with experiments and the model improved, if differences are found. We refer here to some model programs and bring examples for rhythmic events.

4.1  Introduction

If man wants to understand his surrounding, be it the physical, social or economic one, he uses models. This is, because the real systems are much too complex for analysis. Only by simplification we have the chance to understand it better. This holds also for rhythmic processes. Dynamical models are especially suited in this case. They consist of state variables (indicators of the state of the system), of combinations of state variables and of parameters of the environment which affect the system. If these parts of the system are known, the behaviour can be simulated  [16].

To generate complex dynamical systems is quite elaborate. Fortunately procedure have been developed and programs are on the market which allow even the layman to construct dynamical models and to work with them. We will describe some of these programs and bring model examples from the field of biological rhythms with which oscillations can be simulated.

4.2  Model construction and simulation with MODUS

The `Deutsches Institut für Fernstudien (DIFF)' in Tübingen has developed the program `MODUS' for PC's13 [130]. With this program dynamical models can be constructed and used for simulations. Dynamical systems react time dependend. If their characteristic parameters are plotted against time, it is easy to recognize the behaviour of the system. In figure 4.1 an oscillating system is shown.


Figure 4.1: [
Predator-prey model]Oscillations in a predator-prey-system simulated as a model. Prey: red, predator: green curve.

With Modus certain symbols can be connected with each other and used to represent dynamical systems as a graph on the computer-screen. The structur diagrams thus formed are then converted to corresponding equations by the program. Different methods exist. MODUS uses a notation originally going back to Hering et al. [63]. It is based on the system-dynamics method introduced by Forrester [50] and allows to describe interacting dynamical systems.

The following symbols are used by MODUS: State- and changing variables, functions, constants and connections (in the form of arrows). One can also construct model components which can be connected with each other. If you want to work with the model you should obtain the program and the detailed description from the publisher. In eight steps you are introduced into the handling of the program. On the program disks are also a number of examples, among others the predator-prey model describing oscillations between populations of predator and prey.

4.3  Model construction and simulation with other programs

The DSP-program was developed by an audio-technician, M. Schick, and runs on the ATARI computer. Supply source see page pageref.

It allows simulations of digital audio-technique, control technique and non-learning neuronal networks. It can, however, also be used to build dynamical systems in biology, which oscillate. We add some examples in the appendix (page pageref).

You should get acquainted with the program by reading the instructions which come with the disk. In the creation mode, processes are created which are connected with each other as signal flows. Processes might have inputs and outputs. There are signal sources, signal transforming units and signal sinks (stores). Subsystems allow a hierarchical abstraction (block structure).

Matlab is a powerful program allowing also to simulate models.

4.4  Model examples for rhythms

We will get to know in the following some examples of models for biological rhythms. These examples are realizable with MODUS or with other programs.

4.4.1  Feedback model for biological rhythms

Johnsson and Karlsson developed a feedback model which simulates for instance the gravitropic pendulum movement (see page pageref) [3], but also circadian phenomena [74]. It was used by Lewis [83] to simulate the circadian rhythm of locomotor activity of night active insects. The model consists of functional units which are shown together with their connections in figure 4.2. One can study with this model the influence of a changed environmental temperature, light-dark-cycle or different light intensities. In this way the reaction of the model to these environmental conditions can be checked and compared with the data obtained experimentally.

Figure 4.2: [
Feedback model]Functional diagram of the feedback model to simulate the locomotor activity rhythm of a night active insects, after Lewis. The ct value oscillates in a circadian way if synthesis function, loss function and time delay are chosen adequately. Light influences by destroying the synthesis product of the system.

You might try the following situations:

Compare your results with those from the literature, which were found by Lewis using weta, a cricket from New Zealand [24,].

A slightly different feedback model simulates the lateral leaflet movement of Desmodium motorium. In contrast to the model explained before it shows a strong temperature dependency of the period. It is therefore useful to simulate rhythms as found in the lateral leaflet movement of Desmodium motorium. Try to determine the different period lengths at different environmental temperatures and calculate the Q10 value.

Further proposals:

4.4.2  Predator-prey model

Population rhythms occur, if a predator decimates the prey population. However, at a lower prey population density the predator has a reduced propagation rate. In the model of Lotka-Volterra these relations are described mathematically. It is assumed, that the death rate of the prey depends on the number of predators. The larger the predator population, the more prey animals will fall a victim. On the other hand, the predators are better off if many prey animals are available.

In the time diagram (figure 4.1) the number of predators and prey are plotted on the y axis. The x axis is a time scale with divisions in time units (generations).

The Lotka-Volterra-model is also a feedback model: The prey population has a positive effect on the size of the predator population, whereas the latter has a negative (inhibiting) effect on the size of the prey population. Oscillations shown in figure 4.1 result. The predator population which so to speak growth on the prey population as a substrate, lags the prey population by 900 . This is shown in a phase diagram in which the number of predators is plotted on the y axis and the number of prey animals on the x axis. If the parameters are adequately chosen, both populations move on a closed path around the equilibrium point.


Figure 4.3: [
Phase diagram of oscillations of a predator-prey system]Phase diagram of a predator-prey system. In the right lower part the predator population and the prey population increase (R+, B+), in the right upper part the predator population increases and the prey population decreases (R+, B-), in the left upper part the predator- and prey population decrease (R-,B-), and in the left lower part the predator population decreases and the prey population increases (R-, B+).

In nature such cycles were observed in snowhare and lynx in Canada. But things are more complicated than the model suggests, since it was found that the population of snowhare oscillates even in areas were the lynx has died out long ago.

4.4.3  Model building and simulation with a model of Diez-Noguera

A special model to simulate rhythms in animals was developed by Diez-Noguera for the PC14. With its help examples of rhythmic locomotor activity patterns were simulated in rats [31] and flies [61]. It uses coupled oscillators the properties of which are slightly different from each other. This situation is common in organisms.

4.5  Examples for construction of models

We learned how to simulate different biological rhythms with different programs. The disk added to the book contains examples of models for oscillations which can be viewed at and changed with the different programs.

Index (showing section)

abdomen, 9-3
abstract journal, 1-2
acid metabolism, 6-0
activity, 8-3
     conditions, 8-1
     data, 8-3
         collection of, 8-1
     locomotor, 2-2, 4-4, 8-3, 11-2
     locomotory, 8-1
     minimum, 8-3
     rhythm, 4-4, 8-0, 8-1, 11-2
actogram, 2-2, 3-6, 8-1
agar, 8-1
age, 8-3
agriculture, 9-1
aids, 12-0, 13-1
air conditioned
     box, 1-1, 8-1
     room, 13-1
air travel, 10-1
alcohol, 8-3
alertness, 8-3
algae, 10-1, 12-0
     naked, 7-1
Amphiprora, 7-1
amplitude, 3-2
amyloplast, 5-3
analysis, 1-1, 3-6, 5-4, 6-2, 8-1
     of experiment, 8-3
     program, 8-3
anatomy, 6-2
     day active, 8-1
     night active, 8-1
annual rhythm, 12-0
apex, 9-2
apparatus, 1-1
aquarium pump, 5-4
Arrhenius-plot, 5-2
arthropods, 10-1
attraction, 10-1
autocorrelation, 3-6
     day, 3-6
     smoothing, 3-4

baby, 11-2
banding formation, 11-2
bandpass, 3-6
bean, 5-5, 6-2, 11-2
Belousov-Zhabotinsky-reaction, 5-2, 11-2
binary data, 8-3
Biological Abstracts, 1-2
body temperature, 8-3
     temperature controlled, 13-1
bractea, 9-2
brome malonic acid, 5-2
bunker, 8-3
butterfly, 10-1

caffeine, 8-3
CAM-metabolism, 6-1
carbohydrate production, 10-1
     subject, 1-2
cave, 8-3
cell vacuole, 6-1
Cestrum, 6-1
chemical activities
     pattern formation of , 5-2
chemicals, 1-1
     coat, 10-1
     fibers, 10-1
Chlorella, 7-1
chronobiological phase type, 8-3, 11-2
chronobiology, 1-2, 11-2, 12-0
Cinemoid, 6-3
circadian, 0-0, 8-1
     rhythm, 7-0
circumnutation, 5-3
     circadian, 6-1
     endogenous, 1-3, 2-2, 8-1
     radio controlled, 2-2
clover, 5-5, 6-2
     leaf movement, 1-1
Clunio, 11-2
CO2, 5-4
cockroaches, 10-1, 11-2
coleoptile, 5-4
colloquium, 12-0
colour foil, 6-3
commentary, 2-1
communication, scientific, 1-2
computer, 2-1, 2-2, 5-3, 6-2, 6-3, 8-1
     model, 7-1
     program, 11-2, 13-1
     system, 8-1
content, 1-2
control, 1-1
     in time, 1-4
     scientific, 1-3
coordinates, x, y, 2-1
correlation, 8-3
cotton, 6-1
course, 12-0
     advanced, 11-2
Crassulaceae, 6-3
Crassulacean acid metabolism, 6-1
crickets, 10-1
     synchronous, 7-1
Current Contents, 1-2
     polynomial, 3-5
cuticula, 5-4
cuvette, 5-4
cyanobacteria, 7-0, 10-1

damping, 3-3
dark period, critical, 9-2
     physiological, 8-2
     logging, 5-4
     recorded, 8-3
daylength, 9-1, 9-2, 11-2
     critical, 9-3
     measurement, 0-0
     complex, 3-6
Desmodium, 1-1, 1-4, 3-3, 4-4, 5-5, 11-2
     movie, 1-1
     quadratic, 3-5
     standard, 1-1
     structural, 4-2
diapause, 9-1, 9-3
didactic aspects, 13-0
dielectricity constant, 5-4
dielectricum, 5-4
digitizer, 2-1, 6-2, 8-1, 8-2
diskette, 1-2, 2-2, 4-4, 5-4
     cell-, 12-0
drink nipple, 8-1
Drosophila, 1-1, 2-2, 8-0, 8-1, 8-2
     food, 8-1
     litoralis, 9-3
     per-mutant, 8-1
DSP-program, 4-3, 4-4
Dunaliella, 7-1

eclosion, 10-1
     rhythm, 8-0, 8-2
egg deposition, 10-1
encyclopedia, 1-2
endoplasmatic reticulum, 5-3
     free, 5-2
epidermis, 6-2, 6-3
Epstein methode, 12-0
Euglena, 10-1
eukaryote, 1-4
evening type, 8-3, 11-2
evolution, 5-4
Exaccum, 6-1, 10-1
exhaustor, 9-3
experiment, 1-1
     crucial, 1-1
     plan, 1-1
     planing and execution, 1-1
     crucial, 1-3

Fairy rings, 10-1
feedback, 11-2
     loop, 5-4
     model, 4-4, 13-1
ferroin, 5-2
fertilization, 10-1
figures, 1-1
     digital, 3-6, 5-3, 6-2
     program, 5-3
firefly, 10-1
flow meter, 5-4
flower, 6-1, 10-1
     induction, 12-0
     water lilly, 10-1
     light, 13-1
     tube, 6-3
fly, 9-3
     cage, 8-1
forceps, 8-2
     change in, 7-1
Fourrier analysis, 3-6
fragrance, 0-0, 1-1, 10-1
     production, 10-1
     rhythm, 6-0, 6-1, 6-3
freerun, 1-3, 6-2, 8-3, 11-2
     folding, 3-6
frq-mutation, 11-2
fructification, 10-1
fruitfly, 8-0
fur coloration, 9-1

generation, 4-4
Grafik, 6-3
graphic, 2-1, 3-3, 4-2, 5-3, 8-2, 8-3, 9-3
grasshopper, 10-1
     reaction, 5-3
gravity, 5-3
grey filter, 5-4
grey value, 2-1
growth, 10-1
Grunion, 11-2
guard cell, 3-3, 5-4

     cage, 8-1
     food, 8-1
     golden, 1-1
     pellet, 8-1
     sibirian, 9-1
     syrian, 8-0, 8-1
handbook, 1-2
heating, 13-1
     foil, 13-1
Hellrung-system, 8-1
horticulture, 9-1
housefly, 8-0
human, 8-0
     rhythm, 8-3, 11-2, 12-0
humidity sensor, 5-4
hyperpolarization, 3-3
hypocotyl, 5-3
     length, 5-3
hypothesis, 1-1
     alternative, 1-3

illumination, 2-1, 6-2
imaging, 2-2, 7-1, 8-1
     program, 2-1, 6-2
     system, 5-5, 6-3, 8-1, 8-2
index journal, 1-2
indifference type, 8-3
indolyl acetic acid, 5-3
     point of , 1-1
     light, 2-1
     light beam, 2-2, 8-1
inhibitor, 1-4
insect, 4-4, 6-3, 9-1, 10-1
     clocks, 12-0
instructions, 13-1
interface, 8-3
inverted, 11-2
Isabgol, 8-1

jetlag, 10-1
journal, 1-2
     chronobiology, 1-2

Kalanchoe, 6-0, 6-1, 6-3, 9-1, 10-1
kitchen cloth, 8-1
Koukkari method, 1-1

laboratory book, 1-1
Larvae, 8-1
larval shedding, 10-1
latency time, 5-3
layer deposition, 10-1
leaf movement, 2-1, 10-1
     Desmodium, 1-1
     lateral, 11-2
learning, 13-0
lecture, 12-0
     catalogue of, 12-0
Leguminosae, 5-5, 6-1, 10-1
light, 8-3
     additional, 9-1
     beam, 8-1
     intensity, 5-4, 6-3, 8-1
     polarized, 10-1
     red, 8-1
     change in, 8-1
     cycle, 7-1, 8-3, 11-2
light-dark cycle, 11-2
     guide, 1-2
     search, 1-2
lithium ion, 5-5, 6-3
localisation, 11-2
long day, 9-1
     plant, 11-2, 12-0
Lottka-Volterra model, 4-4
lunar rhythms, 0-0, 11-2
lynx, 4-4, 11-2

mammals, 9-1
manuscript, 1-2
Maranthaceae, 6-1, 6-2, 10-1
marriage, 8-3
mastermind, 1-1
maximum, 1-1
maximum entropy spectral analysis, 3-6
mean value, 1-1, 3-4
mechanism, 1-4
     of biological rhythm, 1-4
menstruation, 8-3
mesophyll, 6-3
     molecular genetical, 1-4
     of multiple hypotheses, 1-1, 1-3
     of strong inference, 1-1, 1-3
     recording, 2-0
     scientific research, 1-1
     time series analysis, 0-0
Mimosa, 5-5
minimal system, 1-4
minimum, 1-1
model, 1-4, 4-0
     dynamical, 4-1
     examples, 4-4
     program, 4-0
Modus-program, 4-2, 4-4
monography, 1-2
moonlight, 6-1
morning glory, 5-3, 10-1
morning type, 8-3, 11-2
motor cell, 5-5, 6-3
motor tissue, 6-2
moulds, 10-1
     bending, 5-3
movie, 0-0, 5-2, 7-1, 10-1, 11-2, 13-1
moving state, 7-1
multimedia show, 11-1
multiplexer, 2-2
Musca domestica, 8-1
mutant, 8-1
mycelium, 10-1

Neurospora, 11-2
night shift, 8-3
nipagin, 8-1, 9-3
nitrogen fixation, 6-1, 10-1
noise, 3-1, 3-3, 3-4, 3-6

oat seedling, 5-4
objectiv, 8-1
Oenothera, 10-1
organ, 7-0
organisation, 13-0
     chemical, 5-2, 11-2
     form, 3-2, 3-3
     in space, 5-2
ovaries, 9-3
Oxalidaceae, 6-1, 10-1
Oxalis, 6-2

Paloloworm, 11-2
Paramecium, 7-0
parameter, 2-1
pea, 5-5
     gravitropic, 4-4, 5-3, 11-2
performance, 8-3, 10-1
period, 1-1, 3-2, 3-6, 4-4, 5-3, 6-2, 6-3, 7-1, 8-1, 8-3
periodicity, 3-1, 3-5
     daily, significance, 0-0
periodogram analysis, 3-6
Petri dish, 8-1
pH rhythm, 6-1
Pharbitis, 5-3, 9-2, 10-1, 11-2
phase, 1-1, 3-2
     diagramm, 4-4
     position, 7-1
pheromone, 10-1
phosphoinositol cycle, 6-3
photo, 1-1
photoelectric methods, 8-1
     spectral, 8-1
photoperiod, 9-3
     induction, 6-1
     reaction, 6-1, 9-1
photoperiodism, 0-0, 6-1, 11-2, 12-0
photosynthesis, 5-4, 10-1
picture analyser, 2-1, 5-3
pigment migration, 10-1
pipette, 7-1
pixel, 2-1
     experimental, 1-1
     higher, 12-0
plasticine, 8-1
plate with holes, 8-2
polarisation foil, 10-1
pollination, 6-3
polyurethan disk, 6-2
population, 8-0
     rhythm, 4-4, 8-2, 12-0
potential, 3-3
     model, 4-2, 4-4, 11-2
primary leaf, 5-4
problem, 1-1, 13-0
     solving, 1-1
process, 4-3
processor, 2-2
program, 1-2, 3-0, 4-3, 5-3
project, 12-0, 13-0
prokaryote, 1-4, 7-0, 10-1
protocol, 1-1, 6-3
     notebook, 8-3
publication, 1-2
pulvinus, 1-4, 6-1
puparium, 8-2
pupation, 8-1, 10-1
pupils, 8-3

Q10 value, 1-1, 4-4, 5-2, 11-2
questionaire, 8-3, 11-2

     radical, 5-2
rearing, 8-1, 9-3
recording, 1-1, 8-1
     method, 1-1
     cuvette, 5-4
     device, 1-1
     method, 2-0, 12-0
     time, 2-1
red blood cell, 1-4
     length of, 11-2
repolarization, 3-3
report, 1-1, 5-2, 6-3, 7-1, 8-3
reproductive, 11-2
residue, 3-6
result, 1-2
     presenting, analysing, interpreting, 1-1
review, 1-2
rhizome bulbs, 6-2
     circadian, 7-1, 8-3
     man, 10-1, 12-0
     plants, 12-0
     several, 3-3
     ultradian, 5-4, 7-1
     unicellulars, 12-0
Robinia, 5-5
ROM-port, 8-1
run-test, 3-6
running wheel, 8-1
rutting season, 9-1

safelight, 2-1, 5-3, 8-2
salade, 9-1
sample, 1-1
     nonequidistant, 3-3
school, 8-3
Science Citation Index, 1-2
seed, 1-4, 5-3, 9-2
semilunar rhythm, 11-2
seminar, 12-0
     introductory, 12-0
shift work, 8-3, 10-1
short day, 9-1
     plant, 11-2, 12-0
     average, 3-6, 8-3
simulation, 7-1
singlet, 5-2
     movement, 6-3, 11-2
     sleep-wake cycle, 8-3
slide projector, 5-4
smoking, 8-3
smoothing, 3-4
     window, 3-4
snowhare, 4-4, 11-2
Solanaceae, 6-1
soot recording, 8-2
space experiments, 11-2
     analysis, 3-6
spore, 10-1
     deviation, 1-1
     error, 1-1, 5-2
stoma, 3-3, 5-4
subsidiary cell, 5-4
suction force, 6-3
     lump of, 8-1
sulfuric acid, 5-2, 5-3, 9-2
sun compass, 12-0
sunflower, 5-3
synchronisation, 7-0, 8-1, 11-2
system-dynamics method, 4-2

Tamarindus, 6-1
     adult education courses, 13-0
     aids, 12-0
     aims, 13-0
     at schools, 13-0
     universities, 13-0
telegraph plant, 1-1, 5-5
temperature, 1-1, 4-4, 5-2, 7-0, 7-1, 9-2
     body, 8-3
     compensation, 9-2
     dependency, 11-2
     minimum, 8-3
     recorder, 8-3
     rectal, 8-3
     rhythm, 11-2
testis, 9-3
     sampling rate, 8-1
tetraethylammoniumchloride, 6-3
textbook, 1-2
Thalassomyxa, 7-0, 7-1
theophylline, 8-3
thermodynamics, 5-2
     electronic, 1-1
Tibia, 10-1
tidal rhythms, 0-0, 11-2
tilting cages, 8-1
     diagram, 4-4
timelaps , 7-1
Timesdia, 3-6
timeseries, 3-3, 6-2
     analysis, 3-0, 6-3, 8-3
tissue, 7-0
traffic accidents, 8-3
transpiration, 5-4
     rhythm, 5-4
trend, 3-1, 3-3
     removal, 3-5
turgor, 6-3, 10-1
     mechanism, 1-4

ultradian, 5-1
unicellular, 2-2, 12-0
urin, 8-3

     cell-, 6-3
variability, 1-1
variable, 1-1
     independent, 1-1
vegetative, 11-2
ventilator, 13-1
vertical migration, 10-1
     diurnal, 10-1
Vicia, 3-3
     camera, 2-1, 5-3, 5-4, 6-2, 8-1, 8-2
     system, 11-2
voltage recorder, 5-4

wood sorrel, 6-2

     dry, 8-1

zeitgeber, 7-0, 7-1, 8-3
zero point adjustment, 5-4


Remark: in italics latin names and references to other entrances in the glossary

[agar]or agar-agar, gelatine like product (polysaccharide) of red seaweeds. Used as solidifying component for culture medium. Absorbs as much as 20 times its weight water.
[actogram]graphic presentation of locomotor activity of animals
[amyloplast]Organell (leukoplast) of plant cell, in which sugar is converted into starch
[apex]tip of shoot of higher plants from which all the tissue of the stem arises
[Arrhenius-equation]desribes effect of temperature on velocity of a chemical reaction. Basis for calculating reaction rate constants
[arthropod]member of the largest phylum of animal kingdom. Largest group of this phylum are insects. Furthermore chelicerata (spiders, scorpions, ticks, mites), crustaceae (shrimps, crabs, lobsters, crayfish, sand fleas) and trilobita. Bilaterally symmetrical, segmentated body with exoskeleton
[autocorrelation]measure of how strong a momentarious value correlates with a later one
[Avena sativa,]oat, cereal with edible, starchy grains, widely cultivated in temperated regions of the earth. Family Poaceae
[background noice]statistical deviations of recorded data
[bandpass filter]filter which passes frequencies between two border frequencies only
[Belousov-Zhabotinsky-reaction]an oscillating chemical reaction described by B. Belousov in 1958 and studied especially by A.M. Zhabotinskii
[binary]numerals used in the binary system are two distinct symbols only, 0 und 1. Used in computer devices
[bract(s)]modified leaves intermediate between the calyx (the outermost of the floral envelopes) and the normal leaves
[caffein]nitrogenous organic compound of the alcaloide group. Purin derivate trimethylxanthin. White powder. In tea, coffee, cacao and other plants
[CAM]see crassulacean acid metabolism
[carbohydrate]member of organic substances that include sugars, starch and cellulose. General formula Cx(H2O)x
[Cestrum]night jasmin, nightshade family Solanaceae, Cestroideae. Shrub with few seeded berries
[chitin]white horny substance which forms the outer skeleton of insects, crustaceans, and the cell wall of fungi. Formula (C8H13NO5)n , a complex carbohydrate with molecular weight of 400 000 that is derived from N-acetyl-D-glucosamine. Similar to the cellulose molecule.
[Chlorella]genus Chlorococcales of green algae, in fresh or salty water or soil. Spherical cubshaped chloroplast.
[chloroplast]cell organell for photosynthesis
[chronobiology]describes and studies the time structure of organisms
[circadian]cycles of about 24 hours in organisms
[circumnutation]climbing, circular or pendulum like movements of plants or plant organs. Based on unequal growth of different flanks
[Clunio]marine midge (chironomid), insect
[cockroach]or roach. Primitive, often large sized winged insect of the order Blattaria. Blattoidea. Usually found in tropical or other mild climates.
[coleoptile]protective sheet which covers embryonic leaves of grasses during germination
[colloquium]scientific talk, meeting of scientists and students
[complex demodulation]time series analysis method to determine the period length and phase position of data. Also usable for data sets with non-stationary periods.
[correlation]measure of association between two or more variables and its mathematical description. Correlation coefficient between -1 and +1 (0: no correlation)
[cotyledon]first leaves to appear after germination
[Crassulaceae]stonecrop or orpine family of perennial herbs or low shrubs. Native to warm and dry regions of the earth. Thick leaves. Order Rosales
[Crassulacean acid metabolism]or diurnal acid metabolism. Special mechanism in many succulent plants to fixate carbon dioxide (`CAM'-plants)
[cuticula]membrane lamella covering the outer walls of epidermis cells
[cuvette]small container out of glass or plastic material
[cyanobacteria]bacteria with bluegreen pigment which photosynthesize
[daylength ,critical]length of the light period in a 24 hour day at which 50% of a photoperiodic reaction has occurred. Example: at a critical daylength of 11.5 hours of a particular shortday plant half of the experimental plants would flower, at shorter light periods more, at longer less. At the critical daylength of a particular longday plant half of the experimental plants would flower, at shorter light periods less, at longer more.
[daily periodicity]Periodic process with period length of 24 hours. See also circadian.
[daily rhythm]rhythm found in organisms the period length of which is synchronized to 24 hours by 24 hour time cues (Zeitgeber)
[Desmodium]tick trefoil, Fabaceae, Indian telegraph plant
[diapause]spontaneous interruption of development of certain animals (especially insects) for a certain time span. Marked by reduction of metabolic activity. Serves to survive unfavorable conditions of the environment. May occur during any life stage
[dielectricum]Non-conductor with high specific resistance. Isolator in condensors
[dielectricity constant]indicates how much the capacity of a condensor is increased if a material with dielectric properties is brought betwee the condensor plates
[digitizer]see frame grabber
[digitizing]transformation of analog data in binary information needed as input for the computer
[Discette, disk]magnetic data storage for disk drive of computer
[Drosophila]vinegar fly or fruitfly, genus Drosophilidae, Diptera, Insect
[Dunaliella]Dunaliellaceae, Volvocales, unicellular flagellated green alga
[endogenous]caused by internal reasons
[endoplasmatic reticulum]`ER', intracellular, heavily branched membrane system of all eukaryotes
[enthalpy]sum of the internal energy and product of pressure and volume of a thermodynamic system. There is free and bound enthalpy
[epidermis]outermost layer of cells covering the different plant parts. With its waxy cuticle it provides a protective barrier against mechanical injury, water loss and infection.
[erythrocyte]red blood cell, component of blood which give it the characteristic colour. Circulates in the blood and its hemoglobin transports oxygen from lung to tissue. Without nucleus in humans
[Euglena]alga, single-cell protozoa, one or two flagella, spindle shaped, usually green, commonly found in stagnant water
[eukaryote]cell or organisms that possesses a clearly defined nucleus. Eukaryotes have nuclear membrane, well defined chromosomes and other organelles. All other organisms belong to prokaryotes
[evolution], theory of, postulates that the various types of organisms have their origin in other preexisting types and that the differences are due to modifications in successive generations
[Exaccum affine]xxblaues Lieschen, Gentianaceae
[exhaustor]gadget used here to suck up Drosophila flies made of a glass tube, net and rubber tube. Facilitates transfer of single flies
[fairy ring]circular appearance of fruiting bodies of fungi, caused by radial growth of the mycelium
[feedback]in biology: a response within a system that influences the continued activity or productivity of that system. Control of a biological reaction by the end product of that reaction
[ferroin]1,10 phenanthrolin-ferrisulfate-complex, redox indicator
[filter, digital]mathematical procedure to filter time series
[flow meter]for recording and controlling the flow of fluids and gasses
[forcept]elastic plier to grabb small objects
[Fourrier analysis]determination of the harmonic components of a time series
[frame grabber]printed circuit of a computer for digitizing analog recorded values
[freerun]course of biological rhythms without synchronising Zeitgeber.
[frequency folding]partitioning of a time series in parts which correspond to the period length of the recorded event. In this way sequential cycles are positioned underneath each other. Simple and sensitive procedure for determining the period length
[frq-mutants]mutants of Neurospora with changed circadian period length
[fructification]fruit formation. Here: formation of fruiting bodies in club fungi. See also fairy ring
[fruitfly]see Drosophila
[gravitropic pendulum](same as geotropic pendulum), unequal growth of flanks of plant tips and tendrills which is induced by gravity and leads to pendulum like movements
[grunion]Leuresthes tenuis, Atherinidae, fish. Eggs are fertilized and deposited on the beach at certain times of the lunar and tidal phases
[guard cell]special, often beanlike epidermis cell. Two guard cells surround a stoma
[hamster, Sibirian]Podopus sungorosus, dsungarian hamster. Order Rodentia of Family Critecidae. Short tailed with cheek pouches for carrying food.
[hamster, Syrian]Mesocricetus auratus, golden hamster. Order Rodentia of Family Critecidae. Short tailed with cheek pouches for carrying food.
[hamster pellet]hamster food pressed into small pieces
[Hellrung-system]infrared-lightbeam system for recording the locomotoric behaviour of animals
[humidity sensor]electric sensor to record humidity
[hyperpolarisation]increase of the negative membrane potential of cells
[hypocotyl]part between cotyledons and root of plants
[hypothesis]statement without contradiction, which could be true
[indolyl acetic acid](IAA), plant hormone for e.g. elongation
[infrared-lightbeam]infrared emitter (infrared light emitting diode) and -receiver (phototransistor). An interruption by e. g.  an animal leads to an electrical signal
[inhibitor]substance which inhibits a chemical reaction or a physiological process
[interface]printed circuit used to convert signals
[inverted light-dark-cycle]in an inverted 12:12 hour light-dark-cycle the normal light period is replaced by darkness, the dark period replaced by light
[isabgol]cheap agar substitue from the seedpods of an indian plantain
[jetlag]disturbance of the circadian system after jet plane travelling through time zones (to the west or east). It takes several days until the human circadian system is adapted to the new conditions
[Kalanchoe]panda plant, genus of succulent plants of the stone crop family Crassulaceae
[larva]juvenile stage of certain animals that undergoes changes in form and size to mature into the adult
[larval molding]shedding of the old cuticula when changing from one larval stage to the next
[latency time]time from the stimulus until the reaction is first seen
[lateral leaflet]lateral leaflets of pinnate leaves
[legumes]see Leguminosae
[Leguminosae]plant family Fabales, subfamily Fabaceae (Papilionaceae), largest group of legumes
[lens]piece of glass or other transparent substance to form an image of an object by focusing on it. Compound lenses are used in cameras, microscopes, telescopes. Lense system of an optical apparatus facing the object
[light beam]see infrared-lightbeam
[light, polarising]the waves of this light vibrate in a specific direction rather than randomly in all directions as in ordinary light
[longday]day with long light period and short dark period (e. g. 13 hours light, 11 hours darkness)
[longday plant]flowers in longdays only. See also daylength, critical
[Lotka-Volterra model]mathematical desciption of a predator-prey system by Lotka (1925) and Volterra (1926)
[lunar rhythm]Rhythms with periods in the range of a lunar cycle (28 days). See semilunar rhythm
[mammals]member of the Mammalia, class of vertebrates. Young are nourished with milk of the mother. Hairy, warm blooded, four limbed.
[manuscript]document submitted for publication
[Marantaceae]prayer plant, family of monocotyledonous plants of the order of ginger (Zingiberales) native to moist or swampy tropical forrests particularly in the Americas
[matrix]rectangular scheme of elements, here: division in horizontal and vertical fields
[maximum entropy spectral analysis]time series analysis method for determining the period length of data sets which can be rather short
[mean value]designation of a value overlinex , to which n given values are appointed to according to certain rules. It lies between the largest and the smalles value. Arithmetic, geometric, harmonic and quadratic mean value
[mean value, gliding]formation of average values of a series of values which are shifted by one value after each averaging
[menstruation]periodic discharge from vagine of blood, secretion, and disintegrated tissue that had lined the uterus of women
[mesophyll]parenchymatous tissue of leaves (pallisade- and spongeous parenchyme)
[Mimosa]sensitive plant, member of a genus in the Mimosaceae family, native to tropical and subtropical areas at the northern and southern hemisphere.
[Modus-program]special program for model simulation
[mold]mass of mycelium (masses of vegetative filaments) produced by various fungi
[molecular genetics]Subarea of genetics, in which the structure and fuction of genetic information is studied on the level of molecules (nucleic acids, proteins).
[monograph]a written account to a single subject
[morning glory]Pharbitis nil, twining plant in genus Ipomoea, Convolvulaceae
[motor cells]cells of the motor tissue of the pulvinus
[motor tissue]conglomerate of special motor cells which allow the pulvinus of plant leaves and -stalks to move
[multimedia presentation]Presentation which uses different technical media
[multiplexer]way of signal transduction in which each channel is used several times (there are time- and frequency-multiplexer)
[Musca domestica]common housefly (Diptera, Muscidae family)
[mutant]an individual strain or trait resulting from mutation of the wild type
[mutation]a relatively permanent change in hereditary material
[mycelium]mass of branched, tubular filaments (hyphae) of fungi
[Neurospora]red bread mold. Fungus of the Ascomycetes class, Xylariales order. Often found on wet bread
[nipagin]4-hydoxibenzoic acid-methylester, fungicid (kills fungi)
[nitrogen fixation]process of binding nitrogen of the athmosphere and converting it into protein
[OCR]optical character recognition: Program for the recognition of characters and its conversion into computer readable signs
[Oenothera]evening prime rose, Onagraceae family, Myrtales order
[organ]a group of tissues in an organism wich performs a specific function. Consists of certain kinds of tissue and is arranged in a certain way
[ovary]germ gland of females. Harbours, nurtures, and guides the development of the egg. Furthermore important endocrine functions.
[Oxalis]wood sorrel, Oxalidaceae
[palolo worm]Eunice viridis, annelide in corall reefs of polynesia
[paramecium]Pantoffeltierchen, free living protozoon of Holotricha (order) of Hymenostomatida. Covered with fine hairlike filaments (cilia) that beat rhythmically to propell them
[parameter]a variable for which the range of possible values identifies a collection of distinct cases in a problem
[per-mutants of Drosophila melanogaster]without circadian rhythm of locomotor activity or eclosion (per 0 ) or with changed period length per l (shorter), per s (longer)
[period]period length, time after which a certain phase of an oscillation occurs again
[periodicity]in regular distances reoccuring events
[periodogram analysis]mathematical procedure to determine the period length of an oscillation
[Petri dish]dish with nutrient medium for cultures of microorganisms after R.J. Pétri (1852-1921), bacteriologist
[Pharbitis]morning glory, twining plant in genus Ipomoea, Convolvulaceae
[phase]see phase position
[phase diagram]or phase plot: graphic display of two variables plotted on x- and y- axis respectively
[phase position]particular state in a cycle of changes. See also Period
[pheromone]substance for the chemical communication between organisms of a species. It is effective in extremely low concentrations
[phosphoinositol cycle]special cycle in cells for calcium release
[photoelectric method]recording method with electric light beam. See Infrared-lightbeam
[photoperiod](1) length of the light period of a day (2) ratio between the duration of the light and the dark period of a day
[photoperiodic induction]induction of a physiological reaction by the day length
[photoperiodic reaction]physiological answer of an organism to a photoperiodic treatment
[photoperiodism]Behaviour of an organism in respect to daylength. See shortday, longday
[photosynthesis]synthesis of organic compounds with the aid of light, especially formation of carbohydrates from CO2 and H sources (as water) under the catalysis of chlorophyll in chloroplast containing tissue of plants
[pH value]potentia hydrogenium (latin), hydrogen ion content of a solution, characterizes the acid, neutral oder basic character. pH 7 means 10-7 g H-Ions in a solution
[physiological darkness]light which has in the particular physiological process no effect. In this way the process can be observed without influencing it. see also safety light
[pigment]colouring matter in organisms
[pipette]calibrated thin glass tube for measuring volums
[pixel]any of the small discrete elements that together constitute an image (as on a monitor screen)
[plasticin]moulding made out of caolin, zinc, chalk, pigments, waxesand oils
[point of inflection]point of a curve in which the bending changes its sign
[polarisation of light]see light, polarizing
[polynome curve]mathematical expression in which the single memers are connected with each other by + or - only
[polyurethan]light polymeric material consisting of alcohols and isocyanates
[population]sum of individuals of a species in a certain area, They are genetically connected with each other over several generations
[potential]measure for the energy at a certain point in a field (e. g. an electric field)
[practical course]teaching unit for providing practical skills
[predator-prey-modell]describes the mutual interaction between the populations of predators and prey
[primary leaf]the first leaf following the cotyledons
[procaryote]all organisms (bacteria, bluegreen algae) with nucleus equivalent or nucleoide instead of a true nucleus as found in eukaryotes
[processor]the part of a computer that operates on data (central processing unit)
[propionic acid]stinging fluid with antimicrobial effect
[protocol]detailed description of a scientific experiment, treatment or procedure
[pulvinus]cushion, a mass of large thin walled cells surrounding a vascular strand at the base of a petiole or petiolule and fuctioning in turgor movements of leaves or leaflets. Found especially in Fabaceae, Oxalidaceae, Maranthaceae.
[puparium]a rigid outer shell formed during metamorphosis of insects from the larval skin that covers and protects a pupa
[pupation]to become a pupa. In the pupal stage the larva metamorphoses (changes) into the adult insect
[ Q10 -value]measure of the temperature dependence of a process. Calculated from
Q10 = (t1/t2)10/(t2-t1)
where t1 period length at temperature t1 and t2 period length at temperature t2
[reaction, radical]reaction involving radicals i.e. group of atoms bonded together to an entity
[recording]continuous measurement of physical entities
[rectal temperature]temperatur in the anus
[repolarisation]to restore the hyperpolarised condition
[rhizome bulb]more or less thickened rhizome, which are clearly different from roots
[rhythm]a regularly recurrent quantitative change in a variable biological process. See also oscillation
[Robinia pseudacacia,]locusts. Fabales, Leguminosae family
[ROM-port]input into a computer for read only memory (`ROM') storage containing special purpose programs which can not be altered.
[run-test]mathematical procedure to test whether the values of a time series are randomly distributed or not
[safety light]physiological darkness, light without effect in a special physiological process. It allows to observe a process without interfering with it
[sample]a representative part of a larger whole or population especially when presented for inspection
[scanner]device to scan point- or linewise objects such as images or text and store it in binary form. These informations can be transferred and worked at with a computer
[seed]propagative plant structure: fertilized ripened ovule of a flowering plant containing embryo, seed shell and usually also nurishing tissue. Capable of germinating to produce a new plant
[semilunar rhythm]rhythm with periods of 14 days, corresponding to half the lunar cycle. Lunar rhythm
[seminar]Teaching method at universities. Introduces in autonomous (independent) scientific work
[shift work]working hours are divided in two or three shifts (early, late and night shift)
[shortday]day with short light period and long dark period (e. g. 11 hours light, 13 hours darkness). See also photoperiodism
[shortday plant]plant which flowers under short day conditions only. See also daylength, critical
[signal-average]method for time series analysis, see in chapter `display and analysis of time series', `display of actograms'.
[simulation]technique that reproduces systems, actual events and processes by using models, often involving highly complex mathematical procedures.
[singlet]certain ground state of a molecule
[sleep movement]periodic vertical movement of leaves. See also pulvinus
[smoothing]mathematical procedure to reduce the deviations of recorded data. The smoothing window determines the kind of smoothing. See gliding average
[snowhare]Lepus timidus, mammal in forests of the northern hemisphere and the alps
[Solanaceae]night shade or potato family. Order Solanales, 95 genera with at least 2400 species, many of considerable economic impact such as the tomato, potato, tobacco
[spacelab]ESA (European Space Agency) build space station providing room and facilities for research in space.
[spectral analysis]method to measure the spectrum of a substance with spectral photometer
[spectral photometer]see spectral analysis
[spore]asexual germination- and propagation cell, often of considerable resistance against unfavourable conditions
[standard deviation]statistical measure of variability (dispersion or spread) of any set of numerical values about their arithmetic mean
[standard error]standard deviation devided by the the root of n of the single cases
[stoma]plural stomata, microscopic openings or pores in the epidermis of plant leaves and young stem. They provide for the exchange of gases between the outside air and the branched system of interconnecting air canals within the leaves. Surrounded by two guard cells
[structur diagram]Presentation of the structure of a dynamical process in form of a modell
[subsidiary cell]cell neighbouring the guard cell of stomata, which are different from the normal epidermal cells
[suction force]positiv value of the negative water potential ( S = -Y).
[sulfuric acid] H2SO4 , strongly hygroscopic and agressive fluid
[suncompass orientation]ability of organisms to navigate by using the sun direction (directly or by the polarization pattern of the sky). The daily and annual change of the sun is thereby taken into account.
[synchronisation]condition of two or more rhythms which have the same period length due to interactions
[synchronous culture]cell culture which divides at the same time
[Syrian hamster]see hamster Syrian, Mesocricetus auratus
[system-dynamics]complex network with one or more feedback loops in which the effects of a process return to cause changes in the source of the process
[Tamarindus]Tamarind, Caesalpiniaceae, tropical tree in Asia
[telegraph plant]see Desmodium gyrans
[temperature compensation]the period length of circadian rhythms is not or only slightly dependent on the temperature of the environment
[testis]or testicle. Male gonads. Contain germ cells that differentiate into mature spermatozoa, supporting cells (Sertoli cells) and testosterone producing cells (Leydig cells)
[tetraethylammoniumchloride] [(C2H5)4N]+Cl- , inhibitor of potassium channels
[Thalassomyxa]marine naked amoeba
[theophyllin]purin-alcaloidal (methylxanthine) from leaves of tea plant and other plants. Chemically related to caffeine and theobromine
[thermodynamics]fundamental science of energy and its transfer from one place to another
[tibia]part of insect leg. This consists of coxa (proximal to body), the small trochanter, femur, tibia and tarsus (with several segments and claws)
[tidal rhythm]periodic biological fluctuation in an organism that corresponds to and is in response to tidal environmental changes (regular ebb and flow of oceans). Two high tides and two low tides occur each day 24.8 hours apart. Thus the period of the tidal rhythm is around 12.4 hours.
[time-diagram]graphic display of a variable (y-axis) as a function of time (x-axis)
[Timesdia]program for the analysis of timeseries, written by W. Martin
[time series]serie of data (usually equidistant) of a variable during a certain time span
[time series-analysis]statistical analysis of time series, in order to determine for instance trend, influences of random events and periodicities
[transpiration]loss of water mainly through the stomates of plant leaves
[trend]here: tendency of a time series in a certain section
[trend removal]mathematical removal of a trend. In this way a periodicity can be better recognized if originally superimposed by a trend
[Trifolium repens,]clover, Fabaceae
[turgor]hydrostatic pressure caused by water in the vacuole of plant cells. Turgor is the cause of rigitity in living plant tissue
[ultradian rhythm]oscillation with period shorter than circadian oscillations, i.e. in the range of minutes to about 8 hours
[vacuole]cytoplasmic organelle performing functions such as storage, ingestion, digestion, excretion and expulsion of excess water. In plant cells large central space that is empty of cytoplasm, lined with membrane and filled with fluid
[variability]fluctuation, deviation from the norm
[variable]factor which can take different values during the course of observation. The independent variable is plotted on the x-axis, the dependent variable on the y-axis
[vegetative]asexual reproduction. No union of sperm and egg occurs
[vertical migration]up and down movement of small organisms in rivers, lakes and seas
[Vicia faba]broad bean, Fabales, Fabaceae
[voltage recorder]device to continuously record voltages or other values which can be converted into a voltage
[World Wide Web]part of the internet, an electronic information system
[tilting cage]cage which is balanced in such a way as to change its position if the animal is moveing. Contacts at the floor of the cage sens the movements
[time-lapse]recording with movie- or videocameras in a lower frequency as normal. The film runs therefore faster as in reality
[Zeitgeber](german) time giver, time cue. It synchronizes a biological rhythm


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1 Thanks to D. Engelmann (help with computer work), J. Dittami and P. Reinhard (proofreading), Schneider-Uhle (figures) and students (feedback). This book was typeset by LYX (http://www.lyx.org), a powerful document processor using the LATEX typesetting system.

2All our education is not worth a penny if courage and joy are lost.

3how oscillations are characterized is described on page pageref and illustrated in figure 3.1

4if you do not understand terms, check in the glossary at the end of the book

5words teach, examples bring you forward

6sometimes available in drug stores and gas stations

7The Q 10 value is a measure of the temperature dependency of a process

8if necessary cut out a page of the book to compensate for thickness

9Medline (http://www.biomednet.com), Biological Abstracts, Swets and Zeitlinger with the contents of more then 14000 journals (http://www.swetsnet.nl/direct)

10address: Buchenweg 27, D72820 Sonnenbühl(Germany)

11For this purpose the oscillation is normalized to an evident measure, e.g. to 3600 or 2p circumference of the unit circle or to 24 hours circadiane time. 1800 , p or 12 CT as phase references would all mean, that half of the oscillation has passed.

12there are further procedures for smoothing, in which the values of a smoothing window are weighted; the center value could for instance obtain a high weight, the neighbouring values a smaller weight, and the peripheral values a small weight. Digital filters weight with functions (page pageref)

13supplied by the `CoMet Verlag für Unterrichtssoftware, Duisburg'

14Dr. Diez-Noguera, Group de Cronobiologia, Laboratori de Fisiologia, Facultad de Farmacia, Av. Diagonal 643, SP 08028 BARCELONA (SPANIEN)

15available from the Marutane Trading Co. in Kyoto, Japan

16green fluorescence tubes Philips TL40W/17 covered with green foil nr. 39 Cinemoid

17e.g. plasticine

18If the offset of the recorder is not sufficient, use counter-voltage, to reduce the signal from the amplifier. This allows to switch to a smaller voltage range

19Fa. Stereo Optik, Mainstr. 13, D63128 DIETZENBACH, Tel. 06074 27222

20see study 4.

21substitute of agar from indian plantain-seed pots

22red fluorescence tube with red Cinemoid foil nr. 6, primary red

23e. g.  Altromin company

24soot with a candle. Cheap candles make more soot and are in this case to be preferred.

25Philips TL20W/15 with three layers of red Cinemoid foil nr. 6 and one layer of yellow foil nr. 5a.

File translated from TEX by TTH, version 2.60.
On 25 Mar 2000, 22:03.

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