A Physicochemical Theory of Tip Growth

By Pierre Pelce

A Physicochemical Theory of Tip Growth presents the latest information on experimental observations on living organisms, including unicellular algae, hyphae and neurons. These theories are analogous to the ones developed for the growth of nonliving matter, as already exposed by the author in the book.

• Presents the theory of growth and form of nonliving matter
• Provides discussions on simple, unstable flat or spherical shapes which restabilize in more robust pointed shapes
• Includes characteristics that are typical of the morphogenesis of living matter

• Language: English
• Publisher: Elsevier Science
• Release date: Nov 26, 2019
• ISBN: 9780128218112

Pierre Pelce

Pierre Pelce´ was born in Poitiers (France) on 4 June 1959. He was teached in the Paris region, before to become a student in Physics at Ecole Normale Supe´rieure of Paris in the beginning of 1980. He begun his scientific career as a CNRS researcher in Marseille (France), working on out of equilibrium systems like flame fronts, more generally chemical fronts and cristalline dendrite morphologies. He then spent one year in the James Franck institute of Chicago in 1986, where he begun to think to possible applications of the dynamics of non living matter to morphogenesis of unicellular algae, fungal cells and neurons. Then he became director of research in CNRS in the Institut de Recherches sur les Phe´nome`nes Hors Equilibre (IRPHE) in Marseille in 1991, where he realized many scientific works on morphogenesis, in teaching collaboration with Ecole Normale Supe´rieure of Lyon and fruitful research collaboration with the Neurocybernetic laboratory of Marseille. He is author of Theory of growth and form (2000), which appears as a prelude to a Physicochemical theory of Tip Growth presented in this book.

Book preview

A Physicochemical Theory of Tip Growth

From Louis Pasteur to Jules Hoffmann

Pierre Pelcé

Series Editor

Marie-Christine Maurel

Table of Contents

Cover image

Title page

Copyright

Preface

Introduction

I.1 Epigenetic growth

I.2 Similar physical growths

I.3 The pioneers

1: Constituents

Abstract

1.1 Lipid bilayers

1.2 Filaments

1.3 Cell walls

1.4 The need for ion channels

1.5 Stochastic nature of the ion channel current

1.6 Channels sensitive to the membrane potential

1.7 Ion channel diversity

1.8 Ion pumps

1.9 Symporters

1.10 ATP and energy coupling

2: Simple Laws

Abstract

2.1 Cell wall elongation law

2.2 The Lockhart equation

2.3 Filament growth

2.4 Electrodiffusion

2.5 Passive channel flux

2.6 The Goldman–Hodgkin–Katz equation

2.7 The Fucus membrane potential

2.8 Pump flow rate

2.9 The H+-ATPase of plant cells

2.10 Hyphae membrane potential

2.11 Diffusion slowed down by ligands

2.12 Cell diffusion layers

3: Instabilities

Abstract

3.1 Turing instability

3.2 Jaffe–Larter–Ortoleva instability

3.3 The Toko–Chosa–Yamafuji instability

3.4 Vesicle and proton instability

3.5 Energy competition between active transport and vesicle fusion

3.6 The Goodwin, Trainor and Hentschel–Fine instabilities

3.7 The Bohin–Pelcé instability

4: Geometrie Models

Abstract

4.1 Growth and elongation

4.2 Crystal geometric model

4.3 Geometric model of algae

5: Tip Growth

Abstract

5.1 The hyphoid curve

5.2 Hyphal growth rate

5.3 Determining N

6: The Neural Tree

Abstract

6.1 The instability that grows on the sides

6.2 Secondary hyphal branches

6.3 The effect of temperature on the tip growth

6.4 Actin polymerization limited by the membrane

6.5 Stochastic activation model

6.6 The effect of adhesion

7: Epilogue

Abstract

7.1 How the parameters of a living organism adjust their values in order for cells to always remain sensitive to thermal fluctuations

References

Index of Names

Index

Copyright

First published 2019 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd

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Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

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© ISTE Press Ltd 2019

The rights of Pierre Pelcé to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

Library of Congress Cataloging in Publication Data

A catalog record for this book is available from the Library of Congress

ISBN 978-1-78548-316-5

Printed and bound in the UK and US

Preface

Pierre Pelcé July 2019

The theory presented in this book is developed by analogy with the theory of inanimate matter growth forms. Simple unstable shapes that re-establish themselves into sharp, sturdier shapes can themselves form secondary branches through the same primary instability. In order to develop this theory, Pierre Pelcé, a theoretical physicist, has carried out many works on flame dynamics and dendritic crystal growth, before starting the adventure of the growth and form of living organisms. This was made possible after a postdoctoral sojourn at the James Franck Institute in Chicago, where access to a very rich literature enabled him to find a similar subject in the field of living organisms: tip growth. It was therefore also possible to develop this subject in Marseille, at the St Jérôme and Château-Gombert research centers, with works carried out in the 1980s which can be described as groundbreaking, such as those by L.F. Jaffe, F.M. Harold, P. Ortoleva, K. Toko and B. Goodwin, on unicellular algae, filamentous fungi and neurons. The study of the latter has progressed through sustained collaboration with the cellular neurocybernetics laboratory of Marseille. For 30 years, it has therefore been possible to establish a physicochemical theory for tip growth which we present in this book and which constitutes a coherent whole that should favor new research that can lead to the discovery of new morphogenetic mechanisms and increase knowledge in this field.

I would like to thank all the people who have been with me on this adventure towards the living: G. Albinet, J. Bohin, B. Denet, T. Frisch, A. Karma, M. Léonetti, A. Libchaber, L. Limozin, O. Parodi, A. Pocheau, L. Savtchenko, J. Sun, J. P. Ternaux and S. Tyc-Dumont.

Introduction

I.1 Epigenetic growth

Morphogenesis is programmed by genes. However, their mode of action on form is still relatively unknown and two extreme hypotheses can be considered. The first one is that of a permanent control exercised by genes on the form. The second one only considers genes in the first stage, during the synthesis of the different cell constituents which would in turn be structured according to the common laws of physics and chemistry.

It seems that nature offers a collection of living organisms which enables the second hypothesis to be accurately tested. Those are organisms that grow apically such as unicellular algae, filamentous fungi and neurons (Heath, 1991). These forms cause a variety of gradients in intra- and extracellular media, diffuse substance gradients and electric fields. They are also sensitive to these externally applied gradients, phenomena known as chemotropism, galvanotropism, phototropism, and group and flow effects (Jaffe et al., 1974). These phenomena gave rise to the idea that the electric field could play an active part in morphogenesis (Lund, 1923). Similarly, these forms are sensitive to different substances with a variety of concentrations in the culture medium, such as the Ca² + ion, pH, amino acids, acetylcholine (ACh) and acetylcholinesterase (AChE) for neurons. The latter are also sensitive to substrate adhesion during cell culture (Prochiantz, 1995) as well as to the temperature of the culture medium (Pelcé, 2000). These forms, which are easily affected by external conditions, can only be indirectly associated with genetic inheritance. They can therefore be described as epigenetic growths.

Let us now introduce three phenomena that illustrate this type of growth, starting with the ionic current loop that appears shortly after the fertilization of a Fucus zygote. Initially, the Fucus egg is spherically symmetric and potentially flattened by adhesion onto a glass coverslip when placed in the culture medium. One hour after fertilization, a cytoplasmic jelly secretion appears beyond the cell wall and simultaneously an ionic current loop extends into both the intra- and extracellular media. This current is composed of several ions, but the Ca² + component appears to be important in the subsequent evolution of the morphogenetic process. The loop renders the cell polar with the current entering through one pole and leaving through the other. The axis thus formed is initially labile since its direction changes from time to time but settles a few hours after the appearance of the loop and the cell begins to deform, becoming pear-shaped, with the tip growing towards the end where the current enters the cell. A significant increase in the Ca² + concentration in the active part of the cell (the growing end) is associated with this morphogenesis initiation. This phenomenon is a real symmetry breaker, physically speaking, as the initial egg is relatively homogeneous.

These ionic current loops can also be observed during the tip growth of filamentous fungi such as Achlya bisexualis or Neurospora crassa. As shown in Figure I.1c, these hyphae develop long tubes that grow at a roughly constant rate, depending particularly on the amino acid concentrations in the culture medium. In addition to the growth, there is a proton ionic current loop that enters at the tip and leaves through the sides. The current intensity of this loop increases with the amino acid concentration, suggesting that it results from a specific distribution of H+ pumps and H+/aa symporters in the plasma membrane, with aa being methionine in the case of Achlya and sugars for Neurospora crassa. In general, the growth rate increases with the current loop intensity, but a direct relationship does not always exist between the current and the growth rate. The secondary branching of the hyphae is accompanied by a modification of the current structure. An incoming current appears at the tip of the growing secondary branch causing a global reversal of the current loop, with the current now leaving through the primary tip. However, the hypha continues to grow normally at the same rate. The stretching out of the tips can occur in the virtual absence of any electric current in Achlya bisexualis hyphae growing in a medium with urea and thioglycollate, but without amino acids, in the stems of Acetabularia mediterranea growing in the dark and in the rhizoids of Griffithsia pacifica.

Figure I.1 Four growth forms: a) crystalline dendrite, b) cellular flame, c) hypha, d) neuron in culture. For a color version of this figure, see www.iste.co.uk/pelce/growth.zip

Neurons are also cells where epigenetic growth is particularly evident, perhaps as a result of their high sensitivity to external stimuli that can be memorized. As shown in Figure I.1d, the cultured neuron is first of all a cellular body or soma, with the appearance of a large vesicle flattened on a substrate by the phenomenon of adhesion. The neuron grows through small projections called neurites, which appear in arbitrary