Supramolecular Structure and Function

369 Pages·1983·11.463 MB·English

by  Shneior Lifson (auth.), Greta Pifat, Janko N. Herak (eds.)

Supramolecular
Structure and
Function
Supramolecular
Structure and
Function
Edited by
Greta Pifat
Rudjer BoJkovitlnstitute
Zagreb, Yugoslavia
and
Janko N. Herak
University of Zagreb
Zagreb, Yugoslavia
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
International Summer School in Biophysics (1981: Dubrovnik, Yugoslavia)
Supramolecular structure and function.
"Lectures given at the International Summer School in Biophysics, held September
16-25, 1981, in Dubrovnik, Yugoslavia"-T.p. verso.
Includes bibliographical references and index.
1. Molecular biology-Addresses, essays, lectures. 2. Macromolecules-Addresses,
essays, lectures. I. Pifat, Greta. II. Herak, Janko N. III. Title.
QH506.149 1983 574.8'8 82-24604
ISBN-13:978-1-4684-4480-3 e-ISBN-13:978-1-4684-4478-0
DOl: 10.1007/978-1-4684-4478-0
Lectures given at the International Summer School in Biophysics,
held September 16-25, 1981, in Dubrovnik, Yugoslavia
© 1983 Plenum Press, New York
Softcover reprint of the hardcover lst edition 1983
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
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recording, or otherwise, without written permission from the Publisher
PREFACE
The molecular basis of life has been a rapidly growing field
of science. There is perhaps no other field where such diverse
profiles of scientists, ranging from applied mathematicians and
theoretical physicists to experimental biologists and medical
doctors (physicians), are compelled to communicate and even to col
laborate. This diversity makes the exchange of information richer
but at the same time more cumbersome. One way to facilitate the
exchange of information and to overcome the barriers between the
different languages used by physicists, chemists and biologists
is to organize a meeting on a subject of common interest. A par
ticularly suitable form of such a meeting for younger scientists is
a school at an undergraduate or postgraduate level.
This volume contains a collection of lectures presented
at the International Summer School in Biophysics, held under
the title "Supramolecular Structure and Function" in Dubrovnik,
Yugoslavia, in September 1981. The topics discussed at the school
were inter- and intramolecular interactions in biological systems,
and structure, organization and function of biological macromole
cules and supramolecular structures. Although not all the lectures
could be prepared in a written form on time for publication, we
hope that the present volume contains valuable up-to-date infor
mation on various aspects of the molecular basis of life. We wish
to express our gratitude to the eminent authors and to state that,
having received so much valuable assistance from them, we as
editors can only attach our names to apologies for any erro~s
that may remain.
The School was sponsored by the International Union for Pure
and Applied Biophysics (IUPAB), the Yugoslav Biophysical Society
and the Croatian Biophysical Society as well as by the Scientific
Councils of Croatia and Yugoslavia. Financial aid granted by the
v
vi PREFACE
Councils has also been used in part for the preparation of this
volume.
Greta Pifat
Janko N. Herak
Zagreb, June 1982
CONTENTS
Potential Energy Functions for Structural
Molecular Biology . . . . . . . . . 1
S. Lifson
Theoretical and Experimental Aspects of
Protein Folding . . . . . . . . . 45
H.A. Scheraga
Some Aspects of the Macromolecular Chemistry
of Carbohydrate Polymers . . . . . . . 59
V. Crescenzi
Hydration and Interactions in Aqueous Solutions
of Ions and Molecules . 95
F. Franks
Biomembranes 127
D. Marsh
X-Ray and Neutron Small-Angle Scattering on
Plasma Lipoproteins 179
P. Laggner
Structure and Dynamics of Human Plasma Lipoproteins . 205
L.C. Smith, J.B. Massey, J.T. Sparrow, A.M. Gotto, Jr.,
and H.J. Pownall
Crystallographic Studies of the Protein
Biosynthesis System . . . 245
A. Liljas and M. Leijonmarck
vii
viii CONTENTS
Hemoglobin Oxygen Binding, Erythrocyte Shape
Transformations, and Modeling of Cell
Differentiation as Examples of Theoretical
Approaches in Studying the Structure-Function
Relationship in Biological Systems . . . . . 275
S. Svetina
Evolution of Polynucleotides 309
P. Schuster
List of Contributions 357
Subject index . . . . 359
POTENTIAL ENERGY FUNCTIONS FOR STRUCTURAL MOLECULAR BIOLOGY*
Shneior Lifson
Department of Chemical Physics
Weizmann Institute of Science
Rehovot, Israel
INTRODUCTION
Structural molecular biology is first and foremost an experi
mental science. This is quite understandable. As long as we did not
know what is the structure of enzymes how could we ask questions on
how do they obtain their structure or how is their structure deter
mining their catalytic function? However, as our knowledge of facts
about biological structures grows now at a tremendous rate, there
is an ever-growing need to apply theory, and calculations based on
theory, to supplement the experimental study of structural molecu
lar biology.
In the following chapters we shall discuss the empirical
methods of choosing the analytic forms of energy functions and of
determining their constant coefficients (the so-called energy para
meters). We shall enquire how the empirical methods and the quantum
mechanical methods are related to each other, and shall find it
*
The three lectures given here constitute a revised and enlarged
version of lectures given in the NATO Advanced Study Institute/
FEBS Advanced Course No. 78, Maratea, S. Italy, May 3-16, 1981,
published as Structural Molecular Biology. Methods and Applica
tions, D.B. Davies, ed., Plenum Press, 1982.
2 S. LlFSON
similar to the ways by which inductive and deductive methods are
related to each other in all branches of the exact sciences.
The potential energy of intra- and inter-molecular interac
tions is one of the central concepts in a theoretical approach to
problems of structure and function in biology. What do we know about
the molecular potential energy in biomolecules and related organic
compounds? Where does this knowledge come from? How reliable or ap
proximate is it? This is the subject of the first part of the pre
sentation.
In the second part we will ask what are the potentialities and
limitations of the applications of energy functions for physical
chemistry in general and for molecular biology in particular. How
do we relate the potential energy to experimental data on structu
ral, dynamic and thermodynamic properties of molecules? What are
the theoretical considerations and which are the computational al
gorithms available? Finally we shall point out the advantages of a
rigorous application of the inductive approach based on objective
search for "consistent force fields" of energy functions and energy
parameters, and of establishing a "bench-mark" for comparing alter
native force fields.
The third part will be devoted to a discussion of the nature
of the hydrogen bond. Is it basically a weak chemical bond? Or is
it a strong non-bonded interaction? And why is this distinction
important for molecular biology? We shall show how an application
of the Consistent Force Field method can give a definite answer to
the above questions, and shall compare this answer with results ob
tained by quantum mechanical methods of calculating the hydrogen
bond and of partitioning the hydrogen bond energy into its various
components.
1. EMPIRICAL POTENTIAL ENERGY FUNCTIONS
The Basic Facts of Life of Molecules
We start our discussion of the use of potential energy func
tions in structural biology by a concise review of the quantum mec
hanical and the empirical basis of our qualitative understanding
and quantitative determination of the potential functions of molecu
lar interactions. Such an introductory discussion is necessary be
cause an intelligent and useful application of potential functions
POTENTIAL ENERGY FUNCTIONS 3
in biology requires a feeling for the power as well as for the limi
tations of both the theoretical and the empirical approaches, and
for the complex and subtle nature of their inter-relations.
The nature of molecular forces is in principle well under
stood, thanks to quantum mechanics, which "made theoretical chemistry
a branch of applied mathematics" according to the famous exagger
ation by Dirac. Atoms and molecules are made of nuclei and electrons,
which carry positive and negative electrostatic charges, respective
ly. The only potential of interaction between nuclei and electrons
which is of relevance to our discussion is therefore the Coulomb
potential. Thus, the potential energy of interatomic and intermo
lecular interactions originates from the Coulomb (electrostatic)
interactions,
v = (1/2) I ..e .e.lr ..• (1 )
Coulomb ~,J ~ J ~J
between the nuclei and electrons which form the atomic and molecular
assemblies. The dynamic behavior of such assemblies is, however,
controlled by the laws of quantum mechanics, i.e. by the Schrodinger
equation.
The solution of the Schrodinger equation is neither needed nor
generally possible for the molecules of interest to our subject of
discussion, namely, structural molecular biology. Yet an understan
ding of some basic properties of the laws of quantum mechanics in
corporated in this equation is essential to the understanding of the
nature of the molecular forces which centrol all life processes.
Such understanding requires no mathematics, yet may be deep and
fundamental. Let us try to put it in the simplest terms compatible
with the purpose of our discussion.
We shall start with an analysis of the nature of the total
energy of an assembly of nuclei and electrons which form a molecule.
The total energy is composed of an electrostatic potential energy
which is given by Eq. (1), and a kinetic energy, given by
2
T(p) = (1/2) I.p./m.. (2)
~ ~ ~
where m. is the mass and p{ is the momentum (mass times velocity)
1 ...
of the i-th particle. The total energy, when given as a function of
the coordinates and momenta of the nuclei and the electrons is the