Molecular Orbital Calculations for Amino Acids and Peptides Anne-Marie Sapse Molecular Orbital Calculations for Amino Acids and Peptides With 32 Figures Springer Science+Business Media, LLC Anne-Marie Sapse John Jay College and Graduate School City University of New York New York, NY 10019 and Rockefeller University New York, NY 10021 USA Library of Congress Cataloging-in-Publication Data Sapse, Anne-Marie. Molecular orbital calculations for amina acids and peptides I Anne-Marie Sapse. p. cm. Includes bibliographical references and index. ISBN 978-1-4612-7109-3 ISBN 978-14612-1354-3 (eBook) DOI 10.1007/978-1-4612-1354-3 1. Amino acids. 2. Peptides. 3. Molecular orbitals. 1. Title. QD431.S257 1999 547'.750448-dc21 99-26375 CIP Printed on acid-free paper. i © 2000 Springer Science+Business Media New York ® Originally published by Birkhăuser Boston in 2000 Softcover reprint ofthe hardcover Ist edition 2000 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as under stood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. ISBN 978-1-4612-7109-3 SPIN 19901572 Typeset by Best-set 'JYpesetter Ltd., Hong Kong. 9 8 7 6 5 432 1 To my husband, Marcel Sapse, and to my daughter, Danielle Sapse, without whose support I could not have written this book. Contents Preface IX Introduction xi Chapter 1 Theoretical Background 1 Chapter 2 Theoretical Calculations on SmallAmino Acids 15 Chapter 3 Gamma-AminobutyricAcid (GABA) 27 Chapter 4 The Diaminobutyric (DABA),Delta Aminopentanoic, and EpsilonAminohexanoicAcids 41 Chapter 5 Ab Initio Studies ofSome Acids and BasicAmino Acids:Aspartic,Glutamic,Arginine,and Deaminoarginine 52 Chapter 6 Proline 63 Chapter 7 Taurine and Hypotaurine 74 Chapter 8 Ab Initio Calculations Related to Glucagon 83 Chapter 9 The Alpha Factor 97 Chapter 10 TightTurns in Proteins 113 Chapter 11 Some Small Peptides 124 Chapter 12 OligopeptidesThatAre Anticancer Drugs 138 Appendix Theoretical Studies ofa Glucagon Fragment: Ser8-Asp9-Tyrl0 150 ANNE-MARIE SAPSE, MIHALY MEZEI,DULl C.JAIN, and CECILLE UNSON Index 165 vii Preface This book is intended mainly for biochemists who would like to augment experimentalresearchinthedomainofaminoacidsandsmallpeptideswith theoretical calculations at the ab initio level. The book does not require a profound knowledge of mathematics and quantum chemistry. It teaches one rather how to use computer software such as the Gaussian programs and gives examples ofproblems treated in this manner. Chapter 1 describes the calculations and one of the programs used for ab initio work. Chapter 2 describes calculations on small amino acids, such as glycine and alanine. Chapter3discussesthe biochemicalpropertiesofGABA (gammaamino butyricacid),whichisoneofthemostimportantaminoacidsofthenervous system.Ab initio calculations performed in order to study the structure of GABA are presented. Chapter 4 discusses an amino acid related to GABA, namely DABA (diaminobutyricacid),presentinginformationaboutitsstructureand trans port properties. A number of amino acids, essentials in the biochemistry of organisms, are discussed in Chapter 5. These acids have been subjected to ab initio investigation. Proline,aspecial amino acid asfar as structure isconcerned, is discussed in Chapter 6. Chapter7discusses twosulfur-containingaminoacids,taurine and hypo taurine,presentingsome experimental studieson their mode ofaction and an ab initio study oftheir structure. StartingwithChapter8,smallpeptidesofgreatimportancearediscussed. Glucagon, a small peptide that plays a role in diabetes, is the subject of Chapter 8. Chapter 9 discusses the pheromone alpha factor, from an experimental and theoretical point ofview. Chapter 10presents calculations on tight turns in proteins. ix x Preface Chapter11 discussessomesmallpeptidesthathave beenstudiedwith ab initio methods. Oligopeptides that feature anticancer activity, such as lexitropsins, are discussed in Chapter 12. The book is addressed to graduate and postgraduate students as well as other researchers in the amino acid and peptide area. NewYork,NY Anne-Marie Sapse Introduction Knowledge about the origin oflife requires the recapitulation ofthe steps of archaic molecular evolution. According to the protenoid model, proteinoids (copolyaminoacids) arose on earth from mixtures of self sequencing amino acids. The structure of amino acids, of the peptides formed bytheirpolymerizationvia theformation ofpeptidicbonds,aswell as the structure of the proteins that are polypeptide chains in various numbers and conformations, have formed the subject of an enormous number ofexperimental and theoretical studies. At present, both theoretical and experimental methods are taken seri ously as useful sources of information.They compare results and confirm or dispute structural findings. While experimental results are usually not doubted, and computational results depend on such parameters as the qualityofthe basis sets used,there have been instances in which computa tional results have contradicted experimental ones regarding structural determination.However,in most instances the two types ofmethods com plement each other. For instance, a laboratory search for intermediates in certain reactionscan be avoided once large basis-setcalculationsshow the intermediates not to be astationary state,more exactly,a minimum on the energy hypersurface. The application of computational methods to biological systems dates from the 1950s,when the pioneeringworkofBernardandAlbertePullman was first published. The biological systems studied with the quantum chemical methods available at that time had to be small, and not all the conclusions derived were correct. However, this work opened the door to a whole new area ofresearch. The basic problem in the determination of the structure of biolog ical systems is their size. In order to be able to handle such molecules as the nucleic acids or the proteins, new theoretical methods had to be developed, and the quantum-chemical methods, ab initio and semi empirical, were augmented by the molecular mechanics method, which uses experimental parameters in order to determine the force fields of the systems. xi xii Introduction Hugestrideshave beenmadein thedevelopmentofcomputerprograms that handle larger systems. Researchers are striving to find the optimum combination of accuracy and expediency,with the ultimate goal being the reduction ofcomputational effort with no loss of accuracy. All three of these types of theoretical methods are used in the descrip tion of amino acids and peptides. The size of proteins precludes the use of ab initio or semiempirical methods, so they are mainly described with computer modeling, with programs such as Sybil, Quanta, and Insight, augmented by energy calculations with the Charmm program and other molecular-mechanic calculations. The primarystructure ofproteins,characterized by the amino acid com position and sequence, is determined experimentally by degradation via hydrolysis of the peptidic bonds. The classic method of determining the sequenceinvolvesEdmandegradation,which isanend-labelingprocedure. Physical methods used include mass spectrometry and nuclear magnetic resonance (NMR). Since the 1980s, sequencing of proteins has been per formed by sequencing its mRNA or gene. Thethree-dimensionalstructuresofabout800proteinshave beendeter mined by Max Perutz and John Kendrew using X-ray crystallography. Recently, NMR methods have also been used.The secondary structure of proteins, with 60% alpha helices or beta sheets and the rest random coils and turns, is determined by the propensity ofthe amino acids constituting the given protein to form either alpha helices or beta sheets. It is recog nized now that the sequence ofa protein determines its three-dimensional structure. Given the size of proteins, quantum-chemical conformational and energycalculationsareatpresentimpossible.Somecalculationsonproteins are being performed at present in Dr. Lothar Schafer's laboratory. Undoubtedly,the increase in computer capacity and progress in computer algorithms will make it possible to perform many such calculations in the not too distant future. The theoretical methods used so far for proteins include molecular-mechanics methods that neglect electrons and describe the motion of nuclei under the influence of an empirical or quantum mechanicallycalculatedpotentialenergyfunction,methods thatdo notuse energy functions except in terms of stereochemical principles, computer graphics methods,and molecular-dynamic methods. Smaller peptides have also been described by the above-mentioned methods,especially the empirical conformational energy program for pep tides (ECEPP), written by Sheraga and his group, which has been applied to a large number ofsmall peptides. Inrecentyearsithasbecomepossibletotreataminoacidsandsmallpep tides with quantum-chemical calculations, as will be described in the next chapters. 1 Theoretical Background Inadequate descriptions of atoms and molecules by the methods ofclassi calphysicsled researcherstoproposenewways todescribe physicalreality, giving birth to a totally new science, quantum mechanics. The methods of quantum mechanics are based on the introduction of a wave function, whose physical meaning is related to the probability of finding a certain particle, at a certain time in a volume element, positioned between x and x + dx in the x =direction, between y and y + dy in the y =direction, and between z and z+dz in the z= direction at certain time t.This wave function 'P satisfies the Schrodinger equation, 2 --1lV2+v)'P=E'P Il=h- ( 2m '21t' or for short, H'P = E'P, where H, the Hamiltonian operator, is defined by the expression h is Planck's constant; V2 is the sum of the partial second derivatives with respect to x, y, and z; m is the mass of the particle; and V is the potential energy of the system. The Hamiltonian H represents the quantum equivalent of the sum of the kinetic energy and potential energy, 2 with V being the potential energy operator and _1l V2 the kinetic energy 2m operator. Finally, E is the total energy of the system and is a number, not an operator. The wave function, satisfying the Schrodinger equation, and the energy containalltheinformationaboutthesystemwithinthelimitsoftheHeisen berguncertaintyprinciple,whichstatesthattheexactmomentumandposi tion of a particle cannot be known simultaneously. This is why the wave function represents a probability and not a certitude. A.-M. Sapse, Molecular Orbital Calculations for Amino Acids and Peptides © Birkhäuser Boston 2000 1