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METHODS OF BIOCHEMICAL ANALYSIS

Edited by DAVID GLICK Cancer Biology Research Laboratory Stanford University Medical Center

Stanford, California

VOLUME 30

An Intersciences Publication

JOHN WILEY & SONS

NewYork Chichester Brisbane Toronto Singapore

M E T H O D S O F B I O C H E M I C A L A N A L Y S I S

Volume 30

Advisory Board

N.G. ANDERSON, Division of Biologkal and Medical Research, Argonne National Laboratories, Argonne, IL 60439

T . H . BUCHER, Institute of Physiologacal Chemistry, and Physical Biochemistry and Cell Biology, University of Munich, 8000 Munich 2, West Germany

W.E. COHN, Oak Rdge Nationul Laboratory, T N 37830 P. DOUZOU, Institute of Physico-Chemical Biology, Edmond de Rothschild Foundation, Paris

S. GATT, Department of Biochemistry, Hebrew University-Hadassah Medical School, Jerusalem,

C. JOLICOEUR, Department of ChemlrtT, University of Sherbrooke, Sherbrooke, Que'bec, J l K

J.H.R. KAGI, Biochemical Institute, University of Zurich, Zurich 8032, Switzerland R.W. LUMRY, Department of Chemistry, University of Minnesota, Minneapolis, M N 55455 B.G. MALMSTROM, Department of Biochemistry and Biophysics, Chalmers University of Technol-

A. MEISTER, Department of Biochemistry, Cornell Medical College, New York, NY 10021 R.S. MELVILLE, Bureau of Medical Services, Food and Drug Administration, Retired, 111 12

M. OTTESEN, Chemical Department, The Carlsberg Research Center, DK 2500 Copenhagen, Valby,

J .E. SCOTT, Department of Medical Biochemistry, University of Manchester, Manchester M l 3 YPT,

E.C. SLATER, Laboratmy of BiochemistT, B.C.P. Jansen Institute University of Amsterdam,

B.L. VALLEE, Center for Biochemical and Biophysical Sciences and Medicine, Harvard University,

P. VENETIANER, Institute of Biochemistry, Hungarian Academy of Sciences, Szeged 6701,

M. WIKSTROM, Department ofhledical Chemistv, University of Helsinki, SF 001 70 Helsinki 17,

K. YAGI, Imtitute of Applied Biochemistry, Y a p Memorial Park, Mitab, Gifu 505-01, Japan

75005, France

Israel

2R1, Canada

ogy, S-412 96 Gotebmg, Sweden

Kenilworth, Garrett Park, MD 20896

Denmark

England

Amsterdam-C., The Netherhnds

Boston, M A 02115

Hungary

Finland

METHODS OF BIOCHEMICAL ANALYSIS

Edited by DAVID GLICK Cancer Biology Research Laboratory Stanford University Medical Center

Stanford, California

VOLUME 30

An Intersciences Publication

JOHN WILEY & SONS

NewYork Chichester Brisbane Toronto Singapore

An Interscience@ Publication

Copyright 0 1984 by John Wiley & Sons, Inc.

All rights reserved. Published simultaneously in Canada.

Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc.

Library of Congress Catalog Card Number: 54-7232

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

ISBN 0-471-80276-X

METHODS OF BIOCHEMICAL ANALYSIS VOLUME 30

PREFACE

Annual review volumes dealing with many different fields of science have proved their value repeatedly and are now widely used and well established. These reviews have been concerned, not only with the results in the developing fields, but also with the techniques and methods em- ployed, and they have served to keep the ever-expanding scene within the view of the investigator, applier, the teacher, and the student.

It is particularly important that review services of this nature should have included the area of methods and techniques, because it is becoming increasingly difficult to keep abreast of the manifold experimental inno- vations and improvements which constitute the limiting factor in many cases for the growth of the experimental sciences. Concepts and vision of creative scientists far outrun that which can actually be attained in present practice. Therefore, an emphasis on methodology and instrumentation is a fundamental need in order for material achievement to keep in sight of the advance of useful ideas.

The volumes in this series are designed to try to meet the need in the field of biochemical analysis. The topics to be included are chemical, physical, microbiological, and if necessary, animal assays, as well as basic techniques and instrumentation for the determination of enzymes, vita- mins, hormones, lipids, carboydrates, proteins and their products, min- erals, antimetabolites, etc.

Certain chapters will deal with well-established methods or techniques which have undergone sufficient improvement to merit recapitulation, reappraisal, and new recommendations. Other chapters will be concerned with essentially new approaches which bear promise of great usefulness. Relatively few subjects can be included in any single volume, but as they accumulate, these volumes should comprise a self-modern- izing encyclopedia of methods of biochemical analysis. By judicious selec- tion of topics it is planned that most subjects of current importance will receive treatment in these volumes.

The general plan followed in the organization of the individual chapters is a discussion of the background and previous work, a critical evalua-

V

vi PREFACE

tion of the various approaches, and a presentation of the procedural details of the method or methods recommended by the author. The presentation of the experimental details is to be given in a manner that will furnish the laboratory worker with the complete information re- quired to carry out the analysis.

Within this comprehensive scheme the reader may note that the treat- ments vary widely with respect to taste, and point of view. It is the Editor’s policy to encourage individual expression in these presentations because it is stifling to originality and justifiably annoying to many authors to submerge themselves in a standard mold. Scientific writing need not be as dull and uniform as it too often is. In certain technical details, a consistent pattern is followed for the sake of convenience, as in the form used for reference citations and indexing.

The success of the treatment of any topic will depend primarily on the experience, critical ability, and capacity to communicate of the author. Those invited to prepare the respective chapters are scientists who either have originated the methods they discuss or have had intimate personal experience with them.

It is the wish of the Advisory Board and the Editor to make this series of volumes as useful as possible and to this end suggestions will be always welcome.

DAVID GLICK


CONTENTS

The pH Jump: Probing of Macromolecules and Solutions by a Laser-Induced, Ultrashort Proton Pulse- Theory and Applications in Biochemistry. By Menachem Gutmun ............................................. 1

Laser Photolysis in Biochemistry. By Shirley S. Chan and Robert H . Austin ..................................................... 105

Density Gradient Electrophoresis of Mammalian Cells. By Abraham Tulp ......................................................... 141

Quantitation of Lipid Transfer Activity. By John R. Wetterau and Donald B. Zalversmit ......................................... 199

Measurement of Oxygen Consumption by the Spectro- photometric Oxyhemoglobin Method. By Octavian Brirzu ...................................................................... 227

Historical Development and Newer Means of Tempera- ture. Measurement in Biochemistry. By Robert L. Berger, Thomas R. Clem, Sr., Victoria A. Harden, and B. W. Mangum ....................................................... 269

Author Index .................................................................. 333

Subject Index ................................................................... 345

Cumulative Author Index, Volumes 1-30 and Supple- mental Volume ...................................................... 353

Cumulative Subject Index, Volumes 1-30 and Supple- mental Volume ..................................................... 965;

vii


The pH Jump: Probing of Macromolecules and Solutions by a Laser-Induced, Ultrashort

Proton Pulse-Theory and Applications in Biochemistry

MENACHEM GUTMAN BiochemGtly, Tel Auiu University, Tel Auiu, Israel

I. Introduction ..................................................................................................

1 . Dynamics of Proton Dissociation from Excited Molecules ............... 2. Dynamics of Protonation mpounds .... .... ... . . . . . ..

A. Excitation Pulse ............. B. Monitoring Light .... ..... ........................ ...

D. Geometry of Excit earns ......................... . , , . . . . . , , . , , . . . . . . . . . . . . . . . . . . . . . . .

1. Determination of the Rate of Proton Dissociation .............. 2. The Effect of pK on Rate of Dissociation ......................................... 3. The Effect of the Solvent on the Rate of Proton Dissociation ......... 4. Proton Dissociation in Concentrated Salt Solution ........................... 5. Conclusion ................................................... ....,..., ....,..

11. Methodology and Instrumentation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C. Measuring Equipment ...... , .............................

111. Kinetics of Proton Dissociation

IV. Detection of the Proton by Its Reaction with the Proton Emitter .......................................

1. Reactions in a Small, Open, Hydrating Microcavity ......................... A. Steady-State Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Time-Resolved Fluorescence ...............................

2. Proton Dissociation in a Poorly Hydrating Site ................................ 3.

4. Discussion and Conch

1.

Proton Dissociation-Recombination in the Inner Space

s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Reaction of the Proton with a Molecular Proton Detector .................

The Detection of Protons by Their Reaction with the Ground- State Anion of the Proton Emitter ...................... ...

of a Liposome ........... .............................. ... . . . . . . . . . . . . . . . . . . . . . . . .

V.

1 3 4 4 5 5 5 6 6 7

10 10 15 21

22 24 24 27

.33

35 38 43

45

1

2 MENACHEM GUTMAN

2. The Reaction of Proton with Indicator ............................................. A.

B.

Dynamics of Proton Cycle in the Absence of Direct Proton Exchange ...................................................................... The Effect of Initial Conditions on the Macroscopic Parameters ............................... .................... , ...............

The Direct Proton Exchange between sand Its Effect on the Dynamics of the Proton Cycle ........................................................... Alkalinization Pulse by the Conjugate Base of the Proton Emitter

3.

4. 5. Limitations and Inaccuracies ...............................................

A. Reactants Concentration ...................... .... ............................... B. Accuracy of the Macroscopic Parameters ..............................

VI. Kinetics of Protonation of High-Molecular-Weight Structures .................. Protonation of Uncharged Target Adsorbed on Uncharged Carrier The Effect of Charge on Rate of Protonation .................................. The Effect of Postprotonation Reaction on the Dynamics ...............

A. B. Classification of Postprotonation Reactions ...........................

VII. Proton Transfer on the Surface of Macromolecular Structure .................. The Effect of Buffer on the Dynamics of the Proton Cycle ......................

Two-Component Systems: Buffer and Proton Emitter ................... Three-Component System: Emitter, Detector, and Buffer .............

A. Simulative Solution ............... ................ B. Effect of Initial Conditions .... .,............... , ..... , ...............

1. 2. 3.

Simulation of Protonation of Adsorbed Bromo Cresol Green

VIII. 1. 2.

. . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

47

51

57 62 63 63 65 66 68 69 73 75 78 84 90 91 94 94 96 96 98 99

100 100 101

I. INTRODUCTION

The chemiosmotic hypothesis, alias the Mitchell theory, was accepted in biochemistry with a whole glossary of new terms: proton-motive force, proteicity, proton well, local pH, proton-driven reaction, protogenic site, proton symport, etc. All these terms were intended to describe a specific thermodynamic parameter, or chemical mechanism, with the assumption that their meaning is well defined in the Biophysical-Biochemzcacal Dictionary. Although these terms are made up of familiar explicit words, the interpretation of some composite terms is only vaguely implicit. Presently, it is generally accepted that the free energy released by proton transfer between phases of different electrochemical proton potential is converted into other forms of chemical energy (ATP synthesis, active transport, redox reaction). Still, the identity of these phases is not agreed upon. The phases are identified with the whole aqueous bulk, a thin nearly

T H E pH JUMP: PROBING OF MACROMOLECULES AND SOLUTIONS 3

unimolecular layer on the surface of a membrane, a single proton trapped in an active site, or even an anhydrous hydrochloric acid in the dry lipid interior of a membrane. The various models describing proton transfer through a transmembranal protein consider an array of hydro- philic semirigid carriers spanning the protein, a water molecule channel, an ice-like microthread, or even approximate the proton channel by Al(0H)s crystal at 300°C.

Proton transfer in biochemical systems is measured, in most cases, as an outcome of external force (ATP, redox potential, etc.) mediated by an enzyme. Enzymic turnover is a million to a billion times slower than the basic events of proton transfer. Because of this huge difference in time scale, enzyme-driven proton transfer is blurred by the noncoherent catal- ysis. By the time the first turnover is completed, the proton had ample time to equilibrate with the whole bulk of the solution.

Because of these reasons, my colleagues and I initiated a few years ago a detailed study of proton transfer in an aqueous system, where the event is synchronized by a laser pulse. This technique, using signal averaging, retains the temporal parameters of the event and allows the evaluation of the probabilities of finding a proton in putative environments assigned for it by the different bioenergetic models.

During these studies, it became apparent that proton transfer is an extremely sharp instrument for gauging the water in the immediate environment surrounding the site of dissociation. It turned out that the general biological solvent, the water, acquires different properties at the site where biochemical reaction takes place-the surface of the enzyme. These local properties of the water can be measured through the technique of the laser-induced proton pulse, free of perturbation caused by the huge mass of the bulk water.

In this chapter, I shall describe the basic methodology of the laser- induced proton pulse. Starting with the initial event of a synchronous proton dissociation, going through the reaction of a proton with other solutes in a true solution, and ending with the complex multiphasic system of protons, macromolecules, and interfaces associated with the real life of biochemical reaction. In each level of complexity, I shall point out the pertinent information available for interpretation and the mode of math- ematical and physical analysis. In some cases, I shall also reflect the conclusions on current hypotheses of biochemical proton transfer.

11. METHODOLOGY AND INSTRUMENTATION

The experiments described in this chapter can be carried out in any laser laboratory equipped for monitoring fast photochemical reactions.

4 MENACHEM GUTMAN

1. Dynamics of Proton Dissociation from Excited Molecules

This reaction is observed through time-resolved fluorescence measurements. The sample is excited by a short laser pulse and the fluorescence intensity at the proper wavelength is followed with time.

Thelifetimeofthemeasuredeventsvariesbetween l00psecto -20nsec. The time constant of the measured reaction limits the duration of the excitation pulse. Unless the pulse is shorter than 10% of the lifetime of the measured reaction, the observed signal must be deconvoluted to correct for the time profile of the perturbing event.

The intensity of the excitation pulse is not critical, yet it is advisable to use low-energy density. High-energy flux enhances the probability of undesired two-photon effects.

The light source for time-resolved fluorescence can be a nanosecond pulse of Blum-line nitrogen laser, triple harmonics of yttrium-aluminum- garnet (YAG) laser, second harmonics of mode-locked dye, or gas laser.

The fluorescence decay can be measured with a streak camera, a very fast photomultiplier tube-like Hamamatsu 1294U attached to Tektronix transient digitizer, a box car integrator, or photon counting.

2. Dynamics of Protonation of Ground-State Compounds

The reaction is followed through transient absorbance measurements. The sample is excited by intensive laser pulse (0.2-2 MW/cm2) and absorbance changes in the irradiated volume (usually 0.05-0.1 ml) are monitored by a probing light beam at the proper wavelength (see Figure 1).

Figure 1. Optical arrangement and elements needed for transient absorbance measurements. C, observation cell; PL, pulse laser; CWL, C W laser; Mr, mirror; F1, filter; MC, monochromator; PM photo multiplier; Trig, triggering photo diode; T R , transient recorder; AV, signal averager; COM, computer; X-Y, XY recorder.

THE pH JUMP PROBING OF MACROMOLECULES AND SOLUTIONS 5

A. EXCITATION PULSE

The excitation pulse should be less than 10% of the fastest time constant that is measured. A pulse of suitable duration (1 - 10 nsec) and energy (0.5- 10 mJ) can be obtained by many commercially available nitrogen or excimer lasers.

High-energy input into the solution (more than 10 mJ) can lead to rapid accumulation of undesired photoproducts. Thus, it is better to use a short (1 -2 nsec), less intensive pulse (0.5-2 mJ) than massive (5-50 mJ) longer ones (5-20 nsec).

The length of the proton cycle is 10-300 pec. Thus, even at high repetition rate (100-400 Hz) available with some gas lasers, the system will relax to its prepulse state before the next pulse. Thus, high repetition rate cannot compensate for low peak power of the laser. I found it practically impossible to use a peak power of less than 50 KW.

B. MONITORING LIGHT

The monitoring light should fulfill the following requirement: Its energy-density modulation at the entrance slit of the monochromator should be higher than the energy of the fluorescence emitted from the observation cell. About 1- 10% of the MW excitation pulse is emitted as fluorescence over a wide spectral range. Even if 0.1% of the fluorescence falls at the wavelength of the monitoring beam, it amounts to 10- 100 W of light energy. To prevent it from saturating the photomultiplier, it must be damped below the energy of the oncoming signal. The simplest way to reduce the fluorescent light is to keep the monochromator far from the reaction cell, 1-3 m. The monitoring beam should probe only the irradiated volume, that is, not more than 1 - 1.5 mm in diameter, and all of its energy should reach the entrance slit of the monochromator-without the assistance of a lens. A lens will focus both monitoring and fluorescent light and no advantage is gained.

The fluorescence spans a wide spectral range, thus the narrower is the wavelength of the probing source, the lesser will be the incremental energy of the fluorescence. Thus the monitoring light should be highly monochromatic collimated intensive beam, that is, the output of a cw laser.

C. MEASURING EQUIPMENT

The measuring equipment needed to follow transient absorbance can be as simple as a fast oscilloscope and a Polaroid camera. But a transient recorder coupled to signal averager, q recorder, and computer have a certain advantage.

6 MENACHEM GUTMAN

The measured signals are small-in most cases less than 2-3 mV deviation from the constant voltage of the photomultiplier (-50 mV at 50 R entrance impedance) which corresponds in the above case to AA = log (50 + 2)/50 = 0.017. Many events (50-5000) should be recorded to obtain a clear signal. A few thousand pulses of a megawatt photon flux can bleach even photostable compounds. To avoid this outcome, it is highly recommended to mix the content of the cell.

As the irradiated volume is rather small (0.05-0.1 ml), moderate stirring can replenish the irradiated volume with fresh reactants. Under such conditions, 10,000-50,000 events can be recorded without decrease of intensity of signal.

Stirring cannot remove transient photoproducts with lifetime of few nanoseconds to -300 Fsec. These photoproducts may appear in varying quantities, depending on the proton emitter, energy density, pH, impurities, etc. Most of these photoproducts, solvated electrons, stable free radicals, and triplets are formed by two-photon reaction and their yield is higher with ground-state ionized emitters (+O-) than with +OH. Thus, it is recommended to keep the pH of the solution below the pK of the proton emitter and to lower the excitation energy density as long as it does not reduce the quality of the measurement. Sometimes these precau- tions are insufficient. Under these conditions a two-channel signal averager can be very useful for subtracting the imprint of the transient photoproducts from the measured event.

D.

The irradiated volume should not be bigger than needed to obtain a good overlap with the probing light. The perpendicular-crossing beams are the geometry of choice (Figure 1), because they allow the use of a constant- length optical path and probing the space very close to the front surface of the cell, where the excitation pulse is at its maximumLThis beam geometry spreads the irradiating beam and lowers the energy density. Lasers with low output should be focused to a small spot that necessitates the colinear alignment of the probing beatn (Figure 1). In such an arrangement, care should be taken that the sample is optically thin. High absorbance of the excitation pulse will render most of the probed space inactive, with con- commitant reduction of the measured signal.

GEOMETRY OF EXCITATION A N D PROBING BEAMS

111. KINETICS OF PROTON DISSOCIATION

In the classical chemistry of aqueous solutions, proton dissociation is treated as a simple first-order reaction. Actually it is a very complex

THE pH JUMP: PROBING OF MACROMOLECULES AND SOLUTIONS 7

reaction involving more than one step (Huppert et al., 1982). The initial event is the charge separations:

AH,, G A;, - - - H+

where the dissociating bond of the proton donor stretches to a distance where charge separation takes place and an ion pair is formed. The lifetime of this transient state is very short-comparable with the vibration time, for an OH bond it is about 30 fsec.

Compounds with low pK will reach the A- - - . H+ state with high frequency whereas those with high pK will have to go through many vibrations until the energy of stretching will overcome the threshold to form the ion pair.

The A- - - H+ state is very unstable, being subjected to enormous electrostatic attraction. Thus, no dissociation will take place without the assistance of the solvent. The positively charged proton interacts with the dipole of the surrounding water molecules, and a hydration shell is formed within a time frame of 20-50 fsec (Rao and Berne, 1981), (War- shel, 1982). The stabilized proton can now diffuse away from its conjugated base, but this diffusion, still within the radius of the Coulomb cage, is subjected to electrostatic forces. The rate of the escape of the proton out of the Coulomb cage (where electrostatic force is higher than the thermal energy) is given by Equation (1) (Hauser et al., 1977; Eigen et al., 1964; Eigen, 1964.)

3 2 D 6 k , = - - 72 1 - e-'

where XD is the sum of the diffusion coefficient of the proton and the conju ate base, T is the radius of encounter, and 6 is given by 6 =

-2, -3, the rate of proton escape out of the Coulomb cage will be 5 x lo", 2 X lo", 0.7 X lo", sec-l, respectively (Eigen et al., 1964).

As the rates of proton hydration and escape are comparable for all acids, the big difference between kdiss (or pK) of acids stems from the probability that the dissociating bond will stretch to its A- - - - H+ state. This correlation between the pK and the rate of dissociation is described by the empirical valance bond formalism of Warshel (1982).

Z I Z p e B lwkT. For r = 5A and residual charge of the conjugate base of - 1,

1. Determination of the Rate of Proton Dissociation

In their first electronic singlet state, hydroxy aromatic compounds are much stronger acids than in their ground state (Weller, 1961; Gutman et al., 1981; Schullman, 1977). The pK shift ApK = pK* - pKo can be

8 MENACHEM CUTMAN

estimated from the wavelength of emission of the neutral and the ionized excited states, using the Forster cycle calculation (Forster, 1950).

where u(+~)-, and u ( + ~ ~ ) are the frequency of maximal emission of 40- and +OH, respectively, (For compilation of pK* of many compounds, see Ireland and Wyatt, 1976).

The rate of proton dissociation can be obtained, either by steady-state or time-resolved measurements. The reaction describing the proton dissociation from the excited molecule is summarized in Scheme I

k

k- 1 +OH & $0-* + H+

Scheme I

The excited molecule can decay, by irradiative ( k ( f ) ) and nonirra- diative (Iqn,.)) processes into its ground state with a time constant 70 = (k(f) + k(nr))-i . Alternately, it may first dissociate and then decay as an excited anion by the same processes (7'0 = (k'(f) + k'("&*).

In a case where dissociation is faster than the decay of +OH*, (Itl>>

k ( f ) + k,,,) the emission of +OH* will decline very rapidly, due to the depletion of population by the dissociation reaction. The steady-state reflection of this rapid dissociation will be a very weak emission of the +OH* species. Slow dissociation of +OH*, or rapid recombination of the excited anion with the proton (H+-kL1>k1) will enhance the emission of +OH* (observed by steady-state fluorescence) and prolong the decay time of +OH* as observed by time-resolved measurements.

The interrelation between the kinetic constants and the steady-state fluorescence of the two species is given by the following equations (Weller, 1961).

where is the ratio between the quantum yield measured under the experimental condition (4) and that measured under conditions where


dissociation is totally supressed (40). This ratio can be approximated by the intensities of the +H* emission measured under experimental conditions and when +OH is dissolved in strong acid or in organic solvent where no dissociation takes place. +'/+A is the ratio of $0-* emission under the experimental conditions (+') and under conditions where no recombination takes place (+A), that is, at pH>>pK*.

T~ and T A are the decay lifetime of +OH* and +O-*, respectively. T~ can be approximated by the decay time of +OH* measured at pH << pK* and 7;) is that measured for +O-* at pH>>pK*. By dividing Equations (3) and (4), we obtain

Drawing the ratio of the quantum yields (or the relative intensities) vs. H+ can yield the rate constants, given that the lifetimes of the two states are known. Because of the simplicity of the measurement and the avail- ability of spectrofluorimeters, this method is readily applicable. Still, the lifetime of +OH* and $0-* should be measured and verified for each experimental system.

The other method for calculation of the rate of proton dissociation calls for time-resolved measurements. The differential rate equations for + OH* and ~$0-*

can be integrated to give the time dependence of these two species.

The apparent, macroscopic time constants y1 and y2 are related with the partial rate constant

10 MENACHEM GUTMAN

According to these expressions, the intensity of the +OH*emission will decay as a biexponent, the rapid initial phase y2 represents the reaction as it proceeds until the velocity of dissociation and recombination become equal. The slower phase y1 represents the decay when the two populations (+OH* and +O-*) are in equilibrium with each other. The relative amplitudes of the two phases A r = (a2, - y1)/(y2 - yl) and the macroscopic rate constants (y1,y2) allow one to calculate the rate of all partial reactions. The agreement between rate constants calculated by time-resolved measurements and steady-state kinetics is usually'good. In a limiting case, where the rate of recombination is much slower than dissociation pKo > pH >> pK*, the amplitude of the slow phase repre- senting recombination will diminish to zero and the emission of the +OH* state will decay in a single exponent curve with a macroscopic rate constant y2 = k l + k(f, , , ) = k l .

2. The Effect of pK on Rate of Dissociation

The rate of proton dissociation is controlled by three parameters: the frequency of ion pair formation, the rate of stabilization of the proton by hydration, and the rate of escape out of the Coulomb cage. Measurements carried out in dilute salt solutions, that is, 10- l O O m M , will not be influ- enced by the two later steps. The activity of the water is invariable whereas the ionic atmosphere will screen the electrostatic attraction. Under such conditions, the rate of dissociation should be a direct function of the probability that the stretching covalent bond will reach the dissociation distance. As demonstrated in Figure 2, this expected correlation is observed over a wide range of pKs. Under these conditions, a reversible dissociation will comply with the relationship Kdiss = k l / k - l . As the recombination reaction for all acids is a diffusion-controlled reaction, we can approximate kl = k-1 - = 10'' * Kdi,,(sec-').

3. The Effect of the Solvent on the Rate of Proton Dissociation

The solvent can affect the rate of dissociation by three independent mechanisms:

1. The rate of proton hydration. 2. The rate of proton diffusion. 3. The dielectric constant of the medium.

The first mechanism has already been discussed. The latter two both affect the rate at which the proton escapes out of the Coulomb cage. Diffusion of proton is mediated through rapid exchange of hydrogen bond-covalent bond through the quasistatic continuous network of hy-


10

Q

2 8 3 A

* B 7

6

5

4

3

2

1

1 2 3 4 6 6 7 8 0 PK

Figure 2. Correlation between rate constant of proton dissociation and pK of acids. (M) 8-hydroxypyrene- 1,3,6-trisulfonate, excited state; (U) 2-naphthol-3,6-disulfonate, excited state; (A) 2-naphthol-6-sulfonate, excited state; (V) 2-naphthol, excited state; (0) Bromo Cresol Green; (0) Bromo Cresol Purple; (V) Bromo Fymole Blue; (A) 8-Hydroxypyrene 1,3,6 trisulfonate, ground state; (8) 2-naphthol 3,6 disulfonate, ground state; (0) 2- naphthol, ground state.

drogen bonds (Belch et al., 1981). Any rupture of the network will shorten the distance over which the proton can migrate at a rate faster than the relaxation time of the network. Thus, organic solvents, may shorten the fast passage stretch, and slow the proton on its way out of the Coulomb cage.

The low dielectric constant of organic solvent will expand the size of the Coulomb cage, which may also lower the probability of successful escape.

T o evaluate the relative contribution of each mechanism, Huppert et al., (1981) and Huppert and Kolodney (1981) measured the rate of proton dissociation in organic solvent-water mixtures.

The effect of organic solvent on proton dissociation is easily demonstrated through the emission spectrum of HPTS (Figure 3). In water, the rate of dissociation is so fast that 95% of the emission is at the wavelength

12 MENACHEM GUTMAN

450 500 555 nm

Figure 3 . (---) and in 40% vollvol ethanol water.

of the anion (~$0~"). Increasing the mole fraction of ethanol in the mixture enhances the emission of the neutral species (@OH*) at the expense of that of @O-*, that is, the rate of dissociation is slowed to the extent that the radiative (plus nonradiative) decay of +OH* can success- fully compete with the dissociation.

The kinetic reflection of the enhanced emission of the neutral form is demonstrated in Figure 4. In pure water, @OH* emission decays rapidly (7 = 100 psec) due to dissociation (Figure 4A), but in 50% (vol/vol) of ethanol in water, it is already 25 times longer (Figure 4B) and so is the rise time of 40-* (Figure 4C).

The dependence of the dissociation rate on the mole fraction of the organic solvent is depicted in Figure 5. As seen in Figure 5 , the rate of dissociation decreases exponentially with the mole fraction of the ethanol. This decrease in rate of dissociation cannot be attributed to the effect of the solvent on the dielectric constant of the solution. At Xethanol = 0.2, the dielectric constant of the mixture is 66.2 (vs. 77.5 of water), but the rate of dissociation is slowed by an order of magnitude. The proton conductivity of the water-ethanol mixture decreases with the mole fraction of the solvent, but this decrease is not steep enough to account for the measured effect on the rate of dissociation (see Figure 5). This reasoning

Fluorescence emission spectra of B-hydroxypyrene-l,3,6-trisulfonate in water

cn- " O S

8 hydroxy p m n e

2.3,6 T r i sulfonate

Time (psec)

(A)

HPS IN E T H A N O L WATER MIXTURE

50 VOL.% E T H A N O L

O B S E R V E D A T 54.7"

L 0 - 2000

T I M E ( psec)

( B)

Figure 4. Time-resolved fluorescence of 8-hydroxypyrene- 1,3,6-trisulfonate in water- ethanol mixture. The samples were excited by a 6-psec laser pulse (352 nm) and the emission was recorded by Hammamatsu C939 streak camera combined with optical multichannel analyzer (PAR 1205 D): (A) the emission of the undissociated state, measured in pure water at the spectral range 400-470 nm; (B) the emission of the undissociated state (400-470 nm) measured in 50% voVvol ethanol-water mixture; (C) fluorescence rise time (540 nm) of the dissociated excited form, 45% voVvol ethanol- water mixture.

13

HPS IN 'ETHANOl! WATER 'MIXTURi 4 5 VOL.% ETHANOL

I

ANION FLUORESCE NC RISE f l

J

I 2 3 4 5 TIME (nsec)

(C)

Figure 4. (Continued)

30

0

3. I

MOL X EtOH

Figure 5. The dependence of the rate of proton dissociation from excited S-hydroxypyrene- 1,3,6-trisulfonate on the mole fraction of ethanol in water, and the respective proton conductivity of the mixtures. The rate of proton dissociation was measured by time resolved (0) or steady-state (D) fluorescence. The proton conductivity of the solutions (A) is normalized for pure water conductivity. Data taken from Erdey-Grutz and Lengyel (1977).

14


suggests that the main effect of the organic solvent is to delay the hydration of the proton, increasing the probability of abortive dissociation attempts. Still the present information is insufficient to state whether the slow hydration is the only mechanism that slows dissociation, or whether the expansion of the Coulomb cage and reduced prototropic mobility contribute also to the observed phenomena.

4. Proton Dissociation in Concentrated Salt Solution

Figure 2 demonstrated the free-energy relationship for proton transfer from various donors to the same acceptor, H20. In the present section, we shall extend these studies by relating the rate to the chemical potential of the acceptor, the water.

The water-alcohol mixtures described above are not convenient for measuring the role of water in the proton dissociation reaction. The large Coulomb cage (3081 for 8-hydroxypyrene- 1,3,6-trisulfonate (HPTS) (Hauser et al., 1977) and its expansion upon lowering of the dielectric constant, introduces a nontrivial contribution of the ion pair recombination to the observed reaction. Concentrated solutions of strong electrolytes are a much better system. At concentrations above 1M of strong electrolyte, the electrostatic screening shrinks the Coulomb cage to be about the molecular diameter of HPTS. This effective electrostatic screening practically eliminates the role of the Coulomb cage in the recombination. The dissociative step itself will already place the proton out of the range of the electrostatic attraction.

Under these conditions, we can investigate the primary event of proton hydration. What is more, as hydration is a femtoseconds event (Rao and Berne, 1981; Warshel, 1982), only those water molecules that are in the range of the hydration shell can stabilize the dissociating proton. Conse- quently such studies may be used to gauge the properties of water in microenvironments, such as the active site of an enzyme.

The effect of salt on the rate of proton dissociation from excited hydroxypyrene trisulfonate is demonstrated in Figure 6. The effect on the steady-state fluorescence is similar to that shown in Figure 3. The emission of the neutral form is intensified while that of the anion decreases.

Figure 7 relates the rates of proton dissociation, as measured by time- resolved fluorescence and steady-state fluorescence with the molar concentrations of LiC104 and MgC12. As in the case of organic solvents (Figure 5) , the decreased proton conductivity is insufficient to account for the decrease in the rate of dissociation. The advantage of the strong electrolyte solution, with respect to organic solvent, is their adherence to Rault’s law. Thus the activity coefficient of the water can be easily obtained from the vapor pressure data (Grollman, 1928; Kracek, 1928).

I I I I I

rF = 180 psec I \ 500 1000 1500 2000 2500 3

TIME (psec) )OO

Figure 6. Time-resolved fluorescence of the neutral form of 8-hydroxypyrene- 1,3,6-trisulfonate in concentrated LiC104 solution. Measurements were carried out as in Figure 4. Line (a) 1M LiCIO,; (b) 2.5 M LiCIO,.

Figure 7. The variation of the rate of proton dissociation from excited hydroxypyrene trisulfonate on the molar concentration of the salt: (0, 0) time-resolved fluorescence measurements; (0, U) steady-state fluorescence measurements; (A) proton diffusion coefficient, normalized for pure water (data from Glietenberg et al. 1968). Open symbols, MgCI,; closed symbols, LiCIO,.

16

THE PH JUMP: PROBING OF MACROMOLECULES AND SOLUTIONS 17

Figure 8 demonstrates the linear log-log correlation between the rate of proton dissociation and the activity coefficient of the water in concentrated solutions of NaCI, LiBr, and MgCI2.

The same correlation has been measured for five more compounds whose kdiss values (measured in pure water) differ by five orders of magnithdes (Figure 9). The slope of the lines vary with the structure of the compound. Compounds which have a hydrophylic moiety (SO;) or polarizable substituent (Br) in ortho position with the dissociating proton (2-naphthol-3,6-disulfonate and Bromocresol Green) are somewhat less affected by water activity than compounds where a hydrophylic moiety is in a more remote position (2-naphthol-6-sulfonate) or no hydrophylic substitution at all @-naphthol).

The realiability of this fluorometric technique for determination of u ( ~ , O ) is demonstrated in Figures 10 and 1 1. Figure 10 relates the activity of water with the molar concentration of NaC1, as determined by the rate

1 I I I

u I 1 46 0.55

acH,O)

Figure 8. The free-energy relationship between rate of proton dissociation from excited 8-hydroxypyrene-l,3,6-trisulfonate and the activity coefficient of the water. Water activity coefficient was varied by concentrated solution of NaCl (El), LiBr(A), and M g C12 (0,O).

18 MENACHEM GUTMAN

t 1

log aH20

Figure 9. The dependence of the proton transfer rate on water activity for various excited hydroxy aromatic compounds. (0) 2-naphthol-3,6-disulfonate; (A) 2-naphthol-6,8-disulfonate; (A) 8-hydroxypyrene- 1,3,6-trisulfonate; (+) 2-naphthol-6-sulfonate; (0) 2-naphthol; (m) Bromo Cresol Green (ground state). Note the discontinuity of the ordinate.

of proton dissociation from two proton emitters or as measured by the colligative properties of the solution.

Figure 1 1 demonstrates the equivalence of u(H?O) as estimated for the same salt solutions by the rate of proton dissociation from two proton emitters. Thus, the kinetic method for determination of u ( H , O ) can be regarded as a reliably accurate technique.

The most trivial explanation for the effect of electrolytes on rate of proton dissociation is to consider the effect of salts on the dielectric constant of the solution (see also Equation 1) . In concentrated salt solutions, a considerable fraction of the water moiecules are oriented in an hydration shell around the ions; thus, their dielectric constant is smaller than in pure water (Hasted et al., 1948). A decreased dielectric constant will accelerate ion-pair recombination and slow down ion-pair separation.


1 2 3 4 5 NaCl (M)

Figure 10. The reduction of water activity by high concentration of NaCI. Water activity was measured by the rate of proton dissociation fromexcited hydroxypyrene trisulfonate (A), excited 2-naphthol-6-sulfonate (O), or using the published vapor pressure (0) (Grollrnan, 1928; Kracek, 1928).

The combination of these two effects will lower the probability of proton dissociation in accord with our observation. Yet, this explanation is not applicable for our case. An appreciable decrease of the solution’s dielectric constant occurs above 1 molar of electrolyte. At such concentration (1M) the ionic atmosphere will effectively screen the proton from the electric charge of the conjugated base at a distance of 3 A. Under such effective screening, the contribution of the 10% decrease of the dielectric constant (at 1M NaCl) will have a trivial contribution.

Apparently neither electrostatic interactions nor reduced diffusibility of protons is the major cause for the decrease in the proton transfer rate. As these effects are dominating in ion-pair recombination and ion-pair separation, we have to focus our attention to the primary event in proton dissociation: ion-pair formation. In this reaction, the hydrogen of the OH bond of the excited parent molecule forms a hydrogen bond with the nearest H 2 0 molecule, which itself is hydrogen bonded to other water

20 MENACHEM GUTMAN

7 1

aH20 (Pyrene)

Figure 1 1. Correlation between water activity coefficient o f MgC1, and NaC104 solutions as estimated from the rate of proton dissociation from two proton emitters, 2-naphthol- 6-sulfonate (ordinate) and hydroxypyrene trisulfonate (abcissa). (0) MgCI,; (m) NaC104.

molecules nearby. If the proton moves by 0.5 A, along the lineconnecting it to the nearest H20, the OH bond breaks and H 3 0 + is formed. The enthalpy of proton hydration is 270 kcal/mol, whereas the enthalpy of formation of H 3 0 + is estimated to be 170 kcal/mol (Conway, 1964). The energy difference of 100 kcal is attributed to further solvation of H 3 0 + by additional water molecules. Within the timeframe of proton dissociation, a stable hydronium ion must be formed: otherwise, the proton will revert to the parent molecule. Molecular dynamic simulations indicate that the formation of a hydration shell around the central ion is completed within 0.05 psec (Rao and Berne, 198 1) . Just because the stabilization of proton in the hydration complex is comparable with the OH vibration time (0.03 psec), any perturbation at this step might be crucial for the rest of the reaction to occur.

The dynamics of proton hydration is too fast to be directly measured, but the thermodynamics of stepwise hydration of proton was measured as clustering of water molecules around free protons in a gas phase (Searcy and Fenn 1974; Kebarle, 1975). Clusters with varying size were observed

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