Cooperative Conformational Changes in Globular Proteins

Cooperative Conformational Changes in Globular Proteins

By Fritz M. Pohl[*]

In globular proteins, the complicated steric arrangement of the polypeptide chain is determined by several interdependent cooperative interactions. These macromolecules are capable of reacting to changes in the environmental conditions such as temperature and pressure or the concentration of a wide range of compounds by changing their conformation and hence their biological and chemical properties. They are thus suitable for regulation processes or information storage in solution with a wide range of time constants. Environmental effects of this kind can be followed and explained in part a t the molecular level by investigation of the time-dependent reversible unfolding of a number of proteins that can be described to a good approximation by a strongly cooperative “all-or-none’’ transition between two states

1. Introduction

Proteins are among the most complicated of all organic molecules, and also among the most fascinating“’. Together with the “linear” macromolecules, the nucleic acids, which serve in particular for the storage and transfer of genetic information, the ‘‘two-dimensional’’ membranes, which serve also as boundaries and partitions for the separation of compartments, and water with its special properties as a solvent[’- ’I, they are responsible for numerous structures and processes in biology. As enzymes, the proteins have the function of accelerating chemical reactions and considerably increasing their specificity. Proteins are important molecules for regulation processes in the cell, without which it would be impossible for the many reactions to proceed in an orderly manner under changing environmental conditions16. ’I.

The large number of natural proteins is understandable from their chemical structure. A very large number of possible sequences can be produced by linking together 20 different amino acids to form polypeptide chains of 100-500 members in most cases. Weak interactions such as hydrogen bonds, “hydrophobic” bonds, van der Waals interactions, and “ionic bonds” occur between the members of the same chain and also between the chain and other small and large molecules~* - ’‘I. These interactions influence one another and lead to thecooperative stabilization of certain steric arrangements. Cooperative effects of this type are familiar for small molecules in the form of phase transitions such as melting and evaporation.

Many biological and biochemical properties of the proteins are associated with one particular three-dimensional arrangement of functional groups, which is often referred to as the “native” form. If this arrangement or “conformation” is changed, the corresponding properties of the proteins are also changed. It is thus possible to build up molecular control and switching circuits in which changes in the environment are reflected in changes in the macro- molecular conformation, often intensified by cooperativ-

[*] Priv.-Doz. Dr. F. M. Pohl Max-Planck-Institut fur Biophysikalische Chemie 34 Gottingen-Nikolausberg (Germany)

ity[”], as for example in a non-linear response to changes in the concentration of small molecules.

The environmental influences can be best summarized by equation (I)[”]. In this equation, AGE is the change in the free energy of a protein upon a change in temperature of AT, in pressure of AP, or in the mole fraction of the i-th type of particle of AMi (effects due to a change in electric field A@ are not taken into account):

(p, are the chemical potentials, S is the entropy of the system, V is the volume). Eq. (1) can be illustrated by the impressions of the senses, such as smell and taste (AMi) , heat and cold (AT), and sound and touch perceptions (AP). In all these cases, a change in the conformation of certain “receptor” proteins, i. e. AG;. is very probably important to the initiation of the stimulus.

In addition to an accurate determination of the native conformation itself, questions of special interest include the extent, the rate, and the reason for the conformational change of a protein on variation of the environment. Apart from general observations on the conformation of globular proteins, problems of conformational changes connected with eq. (1) are discussed here with respect to a particular example, i. e . the kinetics of the reversible unfolding of certain mutually “related proteins[’ 31.

The conformation of a protein is the steric arrangement of the polypeptide chain, which consists of 1000-10000 atoms in many cases. The conformers can be converted into one another by rotation about covalent A conformational change is a change in which no chemical bonds (with the exception of hydrogen bonds) are altered and the torsion angles 8 about the bonds are the essential variables. Figure 1 shows part of a peptide chain with the designations of the principal torsion angles.

Strictly speaking, this definition rules out any change in the bond lengths b and bond angles CL. This is justifiable to a first approximation for the general steric arrangement of the main and side chain^['^,'^]. Thus for an energy consumption of k T , the relative position of a C“ atom, for

894 Angew. Chem. mternat. Edit. Vol. I 1 (1972) / N o . 10

example, changes by _+ 0.04 8, on variation ofb, by 0.15 8, on variation of cc. but by i 1 a on variation of 0. This naturally does not mean that such changes in h or r cannot be of particular importance, e.g. in enzymatic catalysis.

analysis in the crystal. An example is the transition from the arterial form of hemoglobin into the venous form ( A e V ) on release of oxygen[231, which can be compared with transitions between two solid phases.

2. Conformation of Globular Proteins

2.1. Anatomy of Proteins

Two methods complement each other excellently in the determination of the static three-dimensional arrangement of the polypeptide chain :

1. The determination of the electron density distribution with atomic resolution by X-ray diffraction in protein crystal^'^^-^^^. (The distribution of nuclei (mainly hydrogen) can now also be determined by neutron diffraction‘”].)

Ip9[1311

Flg. 1. Schematic representation of part of a polypeptide chain, with designation of the torsion angles about bonds of the main chain (@, j l , o) and of the side chains of phenylalanine ( ~ 1 , ~ 2 ) [14].

2, The determination of the amino acid sequence by chemical methods[”- 301.

This “geometric” definition, which is oriented in particular toward the requirements of the X-ray structure analysis of protein crystals. does not give any lower limit for conformational changes. In this progress report. a change will be referred to as a conformational change only if the torsion angle changes by at least 30”.

The determination of changes in certain torsion angles in solution is stdl rather hopeless for macromolecules, despite the progress that has been made e.g. for cyclic oligopep-

In many cases, an indication of conformational changes in macromolecules is the observation that reaction steps are independent of the protein concentration or that such steps are necessary for the quantitative explmation of the reaction scheme[*8-201.

Reversible conformational changes may involve the rotation of a single side chain or they may involve the collapse of the entire steric structure. I t is therefore often necessary to use very different methods for their measurement. (Conformational changes in which protein properties such as absorption or fluorescence of aromatic side chains are altered can fairly easily be followed directly.) For processes involving a large part of a protein moIecuIe, a t least a rough classification seems justifiable:

1. The change e.g. in the activity is due to a change from the native toa ‘‘flexible” conformation (A*F), the investigation of which is possible practically only in solution. Readily measurable changes e.g. in the hydrodynamic and thermodynamic properties occur here. An example that has been intensively studied is the glyceraldehyde-3-P dehydrogenase (GAPDH) from yeast[20-221. However, this group also includes processes such as reversible denaturation (by extreme temperatures and pH values or by a change of solvent), which can be best compared with transitions between a solid and a liquid phase of the macromolecule.

2. The change is due to the transition from a “relaxed” to a “ locked or “strained” conformation, i. e. both have solid-like properties and can be investigated by X-ray

By means of the two methods together, it is possible to construct models of globular proteins in which the nature and the steric positions of a few thousand atoms are given. The rapid progress in this field is indicated in Figure 2.

zool 100

1 20- 10 -

2 -

/

1 1 I I

1960 1965 1970 (1(9032( +

Fig. 2 Number n of globular proteins whose primary structure (-0-0-) I301 and whose three-dimensional crystal structure wlth an atomic resolution of better than 3.5 A (--a--a-) have been determined in recent years [25, 261. The rapid progress is impressively shown even by the logarithmic plot.

No simple “geometric” structural principles can be deduced from the structures obtained. Even the description of the secondary structure, i. e. the arrangement of small regions of the main chain, by CL (helix) and p (pleated sheet) structures is only a relatively rough approximation; considerable deviations occur from the geometry observed for polyamino acids. An example of the complicated structure of two related enzymes is illustrated in Figure 3, where only the course of the peptide chain is s h o ~ n * ~ ~ - ~ ~ ~ . This great similarity of the conformations. though only 39‘;; of the amino acids are homologous, is also found in other members of this family of proteins, chymotrypsinogen A[341 and t r y p ~ i n ’ ~ ~ ] .

Different crystal forms of the same protein, such as a- and y - ~ h y m o t r y p s i n [ ~ ~ ~ or subtilisin novo and subtilisin

Angeuz. Chem. internat. Edit. 1 Vol. I 1 (1972) / No. 10 895

Fig. 3. Conformation of the polypeptide chain of a-chymotrypsin (top) and of elastase (bottom), two related proteins, as found from X-ray diffraction on protein crystals. The band, which is bent at each C“ atom, represents the main chain (after [33]). Though the two enzymes differ in a number of amino acids, a very similar steric folding is found.

BPN[37. 3 8 1 also show only minor differences in conformation. However, small differences in conformation even within the same crystal can be observed for the two proteins constituting the dimers of m-chymotrypsin or insu-

391. Great similarities, such as have already been found between myoglobin and hemoglobin, suggest that the influence of the exchange of amino acids on the conformation of proteins of various species can be predicted relatively accurately if the fundamental structure is known.

It is interesting to correlate the conformation of dissolved proteins with the conformation in the crystal. Observations so far indicate that under comparable conditions, the two conformations probably often differ only in the mobility of some side chains at the surface of the molecule.

An “energetic” structural principle is confirmed at least as a very good approximation by all X-ray structure analyses. The polar side chains are nearly all in contact with the aqueous solution, while mainly apolar or hydrophobic side chains are arranged in the i n t e r i ~ r ~ ~ . ~ ’ ] . The magnitude of such interactions with water can be estimated from the solubility of amino acids in water and in organic solvents respectively[411. The change in free energy when amino acids are transferred from ethanol into water (AG?)f42,431 is shown in Figure 4 as a functionf7’] of their v0Iume1~~1.

The dangers of the simple application of these numerical values to changes in conformation lie in the fact that it is not entirely certain whether and to what extent the free energy is additive for macromolecules. Models for liquid mixtures suggest e . g . a higher than linear dependence on the relative v0lume~4~]. Moreover, it has not been established how well a thermodynamic description of the interior of the protein as a liquid organic or oily phase fits the facts. The results of X-ray diffraction are more easily reconciled with a “solid” phase and very dense packing of the amino acids[49. 431. Furthermore, the ACP values for the transfer

0 20 40 60 80 100 \I [cm3/moU-

Fig. 4. Change in free energy AG p for the transfer of several amino acids from water into ethanol at 25°C [42,43], plotted as a function [71] of the molecular volume 1443. The curves connect amino acids whose side chains contain no polar atoms (---), one polar atom (-.-.-), or two polar atoms (-. .-) such as nitrogen or oxygen. AG? was deduced from the solubility [43]; the value for glycine was taken as zero. If the solubility differenceofthe peptidegroupas found from thedifference betweenglycine and diglycine is also taken into account, the dotted line roughly represents the zero line for the transfer of a peptide. The parts of the polypeptide chain that have side chains above this dotted line will prefer a nonaqueous environment, while the remainder will prefer contact with water. The amino acids are denoted in accordance with the one-letter code [30]: A (alanine), F (phenylalanine), G (glycine), G, (diglycine), H (histidine), I (isoleucine), L (leucine), M (methionine), N (asparagine), Q (glutamine), S (serine), T (threonine), V (valine), W (tryptophan), Y (tyrosine), and Y’ (dihydroxytyrosine).

896 Angew. Chem. internal. Edit. 1 Vol. I 1 (1972) / N o . 10

of peptide groups are difficult to estimate, and are indicated in Figure 4 only very approximately. However, these values and data on the influence of solvent mixtures on the thermodynamics of conformational changes may allow at least a rough estimation of the number of additional amino acids that come into contact with the s ~ l u t i o n [ ~ ’ ~ ~ ~ !

This example of a “hydrophobicity scale” shows that though the behavior of small molecules is relatively well known, additional problems arise in the application of the data to proteins, and quantitative conclusions can therefore be drawn only with reservations. The same is true of stabilization by hydrogen bonds or electrostatic interaction^[^'.^*!

In this connection, it should be pointed out that practically no systematic investigations on the packing properties of “irregular” polymers have been reported. The minimum free space required in the interior of a polypeptide is unknown. On the other hand, the rules for the tight packing of polypeptide chains are particularly important to the understanding of the conformation of globular proteins[491 since relatively large amounts of energy must be supplied to produce an “empty” volume in water.

Another difficulty in the deduction of thermodynamic stabilities of proteins from the crystal structure is that too little is known, a t least with the required accuracy, about the height of the barriers to rotation about individual bonds in polypeptide chainsr151. Values for several thousand bonds have to be added together and this also presents a difficult problem. A possible simplification by consider- ation of the distribution of the various conformations observed in proteins themselves is discussed in Section 2.2.

2.2. Conformational Analysis

The numerous conformations that have been established experimentally (Fig. 2) allow the derivation of additional information. The most probable conformations around certain bonds can be determined by the use of all the corresponding data found for many proteins at high resolution for the construction of “empirical protein energy

Though peculiarities of a particular protein are lost by this averaging procedure, the underlying “conformation patterns” become very clear.

To illustrate this with an example, Figure 5 shows the distribution of the conformations of aromatic side chains found in eleven proteins for the torsion about the C“-Cp bond, which is described by the torsion angle XI (Fig. 1). A logarithmic plot was chosen, from which a kind of conformation energy E,, can be derived which, apart from a constant (2, is given by

E , , = -R T(ln y x l + In Q) ( 2 )

The relative density of experimental values qxl from as many proteins as possible is equal to the number n,, of Conformations observed in the range of angles XI k A ~ 1 , divided by the total number of observed values N . Figure 5 shows the conformations of N = 230 aromatic side chains

given for intervals of k by superposition of two harmonic functions

The curve shown is obtained

where E3, the three-fold barrier to rotation about the Ca-CB bond, is 8.6 kJ/mol. This is comparable with the values found by very different methods for small molecules[5 ‘ I .

The other contribution to the conformation energy, E, = - 5.4 kJ/mol, represents the interaction between the peptide chain and the aromatic ring. The relative popula- tions of the three conformations I, 11, and 111 are given in Table 1. This distribution is practically the same for the side chains of phenylalanine, tyrosine, histidine, and tryptophan, and agrees well with the values found from NMR measurements on model molecules[521.

II IU N N

O 25

16

I I I I I I

60 120 180 2LU 300 360 r,[”l-

Fig. 5 . Distribution of the conformations of 230 aromatic side chains as found for eleven proteins by X-ray structure analysis with a resolution of 2.8 A or better [ S O ] ; the conformations I. 11, and 111, which differ in torsion about the C“-CB bond, are shown as Newman projections. The observed number of conformations n,, per 20 of the torsion angle x 1 (short dashes) is shown in a logarithmic plot to facilitate comparison with the conformation energies in accordance with eq (2). The continuous curve is the superposition of two harmonic functions in accordance with eq. (3).

An advantage of the method outlined here is that important information can be obtained relatively easily from the immense volume of data on the X-ray structure analysis ofproteins. This is naturally not restricted to rotation about a single bond. When sufficient data are available, correla-

Table 1. Relative abundances of the three conformers I, 11, and 111 (Fig. 5 ) , which differ In rotation about the C”--CB bond, in the side chains of aromatic amino acids. For comparison, data found from NMR spectroscopy for the tripeptide Gly-Phe-Gly in D,O are also given [ S q The data for the side chains (see Fig. 5 ) were obtained from conformations observed in the crystal structure of eleven different proteins PI. ____ ~ ~ -. ~

Number of observations N Pl Pli Plll

Population Side chains of

~~~~ . . -_ . ~

Histidine Tryptophan Tyrosine Phenylalanine

53 0.09 0.36 0.55 34 0.15 0.35 0.50 65 0.11 0.29 0.60 78 0.09 0.37 0.54

230 0.11 0 34 0.55 Total:

Gly-Phe-Gly [52] 0.14 0.34 0.52

Angew. Chem. infernat. Edit. / Vol. 11 (1972) / N o . 10 897

tions in two and more variables can be established; these should be of considerable value in the prediction of unknown conformations, and should contribute to the molecular explanation of conformational changes. Empir- ical distributions of this type can also be compared with calculations of the conformation 53, 541.

3. Reversible Conformational Changes

3.1. Theoretical Considerations

An extensive literature exists on the theory of cooperative structural changes of linear polymers, such as helix-coil transitions of polypeptides; this literature deals both with the statistical mechanics and thermodynamics of such systems and with their kinetics[*’- ’’I. The “linear king model”, in which interactions with nearest neighbors are taken into account, has proved particularly useful.

Numerical calculations have been carried out on a simple three-dimensional Ising model for cooperative transitions of globular proteins1581. However, a complicating factor here is that the state of an element in the three-dimensional network of the interactions not only depends on the state of the nearest neighbors in the chain or in space, but may also be influenced by the state of relatively remote parts of the macromolecule. An example is provided by the changes in the positions of a number of groups in chymotrypsinogen A as a result of the breakage of the peptide chain in positions remote from these groups on acti~ation‘’~!

The folding of proteins can also be regarded as analogous to the nucleation and condensation phenomena in phase transitions‘61 -631.

However, the most serious problems are due to the fact that a large number of parameters must be known before a moderately realistic quantitative description on the molecular level is possible. Moreover, relatively few conformational changes have so far been experimentally studied so systematically as to allow a decision in favor of one of several models[601.

If one disregards “small” conformational changes, such as the reorientation of a single side chain, for which the description normally used for small molecules is adequate, a large number of elementary steps such as opening and closing of hydrogen bonds and simultaneous rotation about one or more bonds must always be expected in cooperative changes. This can be represented in a greatly simplified form by a genera1 conformation coordinate

P,*P,*. . . P,. . .+P, (4)

where the Pi each denote a different conformation. Even if it is assumed that each of the n amino acids can exist in only two conformations, there will be N = 2” possible states; however, these will be occupied with very different weights. Since the conformational changes take place in solution and not in a vacuum, the influence of other molecules must also be taken into a c ~ o u n t ~ ~ ~ , ~ ~ ! This is achiev- ed with the aid of a general concentration coordinate. The two coordinates can be combined to give ( 5 ) :

a,’ Pll =+ pI2 + . . . . . . . . . . . . . . . - + - P l K

Jl

P U N J ph l i= ph,2.. . . . :. . . . . . . . . . . .* conformation coordinate -

The states within a column differ in the number and positions of “ b o u n d water molecules, cations, anions, etc. The relative concentrations of the states and their dependence on external variables are important to the description of such a system. A relaxation spectrum is generally to be

expected for the kinetics if a small sudden disturbance of the equilibrium occurs, i. e. a superposition of exponential functions with different time constants T~ and amplitudes pi should be observed if the various states are present in comparable ~oncentrations[’~1.

n 10-10 r

B Reaction coordinate +

Fig. 6. Schematic representation of a concentration distribution (relative concentration C,,, in arbitrary units) of the distinguishable conformations of a protein as expected if e.g. unfolding at the melting point T,,, can be described as an “all-or-none” process. The states A and B may each represent a collection of somewhat different conformations, which cannot be distinguished experimentally [79].

A significant simplification results if only two states Pij and P,, can be detected, as indicated schematically in Figure 6. If the concentrations of intermediate states and their variation with time can be disregarded, we have an “all- or-none’’ process, which is described by two overall or steady state rate constants:

t; i;

A + B (7)

Information on the individual intermediate states is largely lost here. However, the simplification also allows a closed solution of extensive systems of kinetic differential equations, since under steady-state conditions, the change in the concentration of intermediate states as a function of time is zero; the overall rate constants I; and R are then obtained by straightforward calculations.

898 Angew. Chem. internat. Edit. 1 Vol. I1 (1972) 1 No. 10

3.2. Model Systems

Investigations have so far been carried out in solution only for relatively few cooperative conformational changes in proteins that are fully reversible, i.e. in which the initial state is restored after a disturbance and in which a parameter that directly characterizes the conformation of the protein is followed. Measurements are often hindered by the low concentrations, which are around mol/l in many cases. It is sometimes also difficult to distinguish clearly between changes in the conformation itself and in the bonding of small molecules.

As was mentioned earlier, the cooperative effects are particularly important. Unfortunately, there are no macromolecules with simple structures that exhibit three-dimensional folding similar to that shown by globular proteins, so that it is necessary at present to investigate natural proteins. To observe these cooperative effects within amolecule, there should be no aggregation between the molecules which might mask intramolecular processes. The main problem is that, in many proteins consisting of subunits[65, 661,

cooperative unfolding is often not fully reversible‘671; thermodynamic and kinetic data are then only of limited validity.

The acid denaturation of some intensively studied proteins such as chymotrypsinogen, trypsin, ribonuclease, and lysozyme is a t present the simplest model system for the investigation of cooperative and reversible conformational changes in globular proteins, in which many biologically interesting phenomena can also be simulated. This reaction, which is also known as transition I, can be best described as a transition from a compact to a more mobile conformation, which, however, involves only parts of the protein and apparently does not lead to a completely random coil conf~rmation‘~l .

There are a series of excellent reviews on this transition, which deal in particular with the equilibrium proper-

transition of chymotrypsinogen A in acidic soJution as a function of temperature[70, 71J. The change in the tryptophan absorption of the protein was measured here after equilibrium had been reached at various temperatures.

When the solution is cooled, the original values are restored ; the transition curve can be transversed repeatedly with no deviation from the original curve, i. e. the transition is fully reversible. (In the case of cr-chymotrypsin, the enzymatic properties are also fully restored if the refolding takes place in acidic solution, but only partially in neutral s~ lu t ion‘~’ ] . )

Several properties of the native form A, which exists at low temperatures, change into those of the unfolded form B within a range of about 15°C. The transition may also be regarded as a melting process within the macromolecule[79’. The temperature in the middle of the transition is also referred to as the melting temperature T,.

The transition can be initiated by various experimental methods; changes in the temperature, pH, or the pressure [eq. (1)][70-731 reflect “environmental changes”. Spec- troscopic detection of the conformational change is ad-

ties[9. 68. 691 . A s a typical example, Figure 7 shows the

vantageous e.g. in kinetic measurements down to the nanosecond range. The most important of the methods used so far to follow the equilibrium of transition I. in addition to the measurement of UV and IR absorption, optical rotation, fluorescence, and NMR spectra[68- 741,

include measurements of viscosity, sedimentation behavior, specific volume[751, specific heat1761, solubility[7 ’I, and tritium e~change”~’ .

4u 50 60 T [ T I -

Fig. 7. Equilibrium curve of the transition I of chymotrypsinogen A at pH = 2.0 as a function of the temperature. The percentage decrease in the tryptophan absorption at 293 nm (Iz9,) was measured after equilibrium had been reached. I, and I, (---) are the values for forms A and B in the transition region extrapolated from the optical behavior at low and at high temperatures respectively.

One question is whether this transition can be described as an “all-or-none’’ process between two macroscopic conformations of the protein, i.e. whether half of the molecules are in the form A and the other half in the form B at the temperature Tm, or whether at T, e.g. half of each individual molecule is changed, and very many different conformations are present in measurable concentrations, as is expected for the helix-coil transition of long polypeptides[801. I t is difficult to answer this question on the basis of equilibrium measurements. Important tests are1791:

1. A two-state model may be assumed if several parameters change by the same relative amount when an external variable is changed. The methods mentioned above should therefore give the same equilibrium constant K [eq. (7)] under comparable conditions. Extremely high accuracy of measurement is often necessary for such a comparison ; this criterion is satisfied e.g. by isosbestic points in the protein spectra in the transition region.

2. Another test is the agreement of the enthalpy found by calorimetric measurement with that calculated from the van’t Hoff equation. This test has satisfactorily confirmed a two-state model in acidic solution for the three proteins investigated so far, i. e. chymotryp~inogen[~~I, ribonuclease

and lysozyrneEaz1.

3. A further test, which can also be applied to very small quantities of substance, is the examination of the kinetic behavior after a rapid perturbation of the equilibrium.

A n g w . Chem. internat. Edit. 1 VOI. I I (1972) 1 NO. 10 899

4. Kinetics of Reversible Folding

Kinetic measurements, in addition to the information on the therniodynamics of the system, also provide information on its behavior as a function of time. This is particularly important for biological phenomena, with their strong time dependence. Even intermediate states with very short lifetimes can be detected, and it may thus become easier to decide between several possible reaction mechanisms.

4.1. Methods

As a result of the development of kinetic methods, the variation of the conformation with time after a sudden or periodic disturbance of an external parameter in equation (1) can be followed over many orders of m a g n i t ~ d e [ ~ ~ - ~ ’ ] . For very fast reactions, rapid mixing of solutions in stop- flow apparatus ( A M i ) and relaxation methods, e .g . temperature jump (AT) and pressure jump (AP) methods, are particularly important, as well as ultrasonic and nuclear magnetic resonance measurements.

To follow the kinetics of the transition I (Fig. 7), one need only vary the temperature rapidly enough and follow the establishment of a new equilibrium, e .g . on the basis of the change in absorption. This is a relatively slow process, in the second to minute region. A very simple temperature jump method has proved to be very suitable for this purpose[701.

In this method, the solution to be investigated is placed in a thermostatically controllable microcell, which allows a fast temperature equilibration (half time = 1s) between the thermostat liquid and the solution. The solution can be subjected to positive and negative temperature jumps of any size by the alternate passage of the liquids from two thermostats a t different temperatures through the thermostat jacket of the cell with the aid of magnetic valves. The variation of the absorption, fluorescence, optical rotation, etc. with time is then recorded.

4.2. Kinetic Criteria for an “All-or-None” Process

For a multi-stage reaction system of type ( 5 ) which must certainly be the case for the unfolding of a protein, a relaxation spectrum in accordance with (6) will be expected for a small disturbance of the equilibrium. Such a relaxation spectrum has been observed in the denaturation of high molecular weight DNA[86* ” I . If the measurable concentration distributions before and after the disturbance correspond roughly to those indicated in Figure 5, very stringent conditions must be satisfied for the kinetics (see Fig. 8)[13, 871.

1 . The establishment of the new equilibrium as a function of time after a sudden disturbance follows a simple exponential function, which gives a straight line in a semi- logarithmic plot (Fig. 8a); the relaxation time or time constant T can be determined from the slope of this line. (Changes such as those responsible for the change in the density of the solution after a sudden temperature change or the change in the bonding of small molecules, must be considered separately.)

2. The rexalation time is independent of the parameter followed, e .g . absorption at various wavelengths, solubility, etc.

10 r

t lsl-

22r b I

Fig. 8. “All-or-none” transition of trypsin at pH = 1.8 [87, 131. The relaxation time T is independent of the protein concentration (lo-’ - 10- mol/l). a) Change in the optical rotation at 315 nm (- o -- o -) and in the absorption at 293 nm (- u -c-), divided by the total change between t = O and t=m, as a function of time. (Temperature jump from the transition region at 39°C to20.O’C.) b) lack ofdependence oftherelaxation time T on the initial state (temperature at time zero, T,=,) and on the magnitude of the disturbance. The final temperature is constant at 38.4’C. The varying error limits are due to the different amplitudes of the relaxation curves.

3.Thetimeconstantrdependsonlyon the final statereached after the disturbance, and not on the initial state (Fig. 8b), as is to be expected from the equation[881

which describes the change in the concentration of A as a function of time after a sudden disturbance.

If these criteria are satisfied, as in the transition I discussed here, it is justifiable to describe the conformational change in the approximation of an “all-or-none’’ process. (With very sensitive kinetic methods, it is also possible to detect fast preceding equilibria, though these usually account for only a few percent of the total ~ h a n g e [ ’ ~ ~ ’ ~ ~ ~ . ) The overall rate constants for the folding and for the unfolding R can be determined. The equilibrium constant Kcan be deduced e .g . in accordance with eq. (9)

from the relative amplitude [A], = - [A], = oc, which also contains all the thermodynamic information. Together with the definition of the relaxation time

900 Angew. Chem. internat. Edit. 1 Vol. 11 (1972) / N o . I0

two equations for the determination of the two unknowns and f are given.

These two overall rate constants can be regarded, according to the theory of the activated state[891, as "quasi-thermodynamic quantities" the zero of the free energy of activation (AG or A@ being taken as RTln (kT/h) (where k is Boltz- mann's constant and h is Planck's constant). For the unfolding, this leads to

f= (kTfh )xexp( - A ( ? / R T ) = ( k T J h ) x e x p ( - A @ J R T + A s / R ) (11)

with AHas the enthalpy and Asas the entropy ofactivation. AH can be obtained from the Arrhenius equation or the first derivative of AC with respect to the temperature.

d In E d T

Af? = RT2 ~- RT

If A& itself is temperature-dependent, it is also possible to define a specific heat of activation.

AC = dl?/dT (13)

Similar equations are found for f ; the connection with the usual thermodynamic functions in the case of the equilibrium is provided by eq. (9) and the expression for the free energy AGO:

AGO = - RT In K (14)

4.3. Temperature Dependence

The relaxation time as a function of temperature for the transition I of chymotrypsinogen A, a typical example, is shown in Figure 9[931. (The corresponding dependence of

Lool '0

' 0

'o I 1 I I I , -b

50 40 30 20 10 - T [ " C I

Fig. 9. Relaxation time 7 1-0-0-) for the transition 1 of chymotrypsinogen A at pH = 2.0 as a function of the final temperature, determined by following the change in the tryptophan absorption of the protein as a function of time (70, 711. In the transition region, the overall rate constants for unfolding L(. . . .) and foldtng k (----) are given. The values + and x were obtained by Eisenberg and Sehwert [77] by following the change in the solubility of the protein as a function of time.

the overall rate constants is also given.) It can be seen that below the transition temperature, the reciprocal relaxation time 7-l becomes equal to the rate constant for folding i ; at high temperatures, T-' becomes equal to I;. The experimental values found some 20 years ago by Eisenberg and S ~ h u e r t ~ " ~ are also plotted. Instead of the tryptophan absorption, these authors used the solubility of the protein in a precipitation buffer as the parameter. The good agreement. among other things, supports the proposed course of the transition.

A striking feature in comparison with conventional chemical reactions in this temperature and time range is the high positive activation energy for unfolding (AR and the strong temperature dependence of Ak for folding, with negative values at high temperatures (Fig. 10). Both observations indicate that several elementary steps are necessary for this conformational change"03. lea]. A similar temperature dependence is observed in the denaturing of other hetero- geneous biopolymers such as DNA and ~ o l l a g e n ' ~ ' . ~ 'I, as

0 20 LO 60 0 20 LO 60 TYCI--' T YCI+

C

0 20 LO 60 Ip903101 TPCI-+

Fig. 10. Temperature dependence of the thermodynamic and kinetic parameters for the transition I from chymotrypsinogen A. a) Free energy, b) enthalpy, c) specific heat. The thin lines indicate the extrapolation of the experimental data when thechange in the specific heat ACis described by a linear dependence on temperature. (-a-a-) denotes data from calorimetric measurements [76] and (-) the equilibriumdata determined by optical measurements. The kinetic quantities for unfolding (. ...) and for folding (----) are given. (An error of kO.1 "C in the measurement of the temperature and of 5% in the rate constants over a temperature range of 10°C gives an uncertainty of about t 4 kJ mol- I deg-' for AC.)

well as in phase transition^'^^! The transition I can thus be placed in the larger group of problems of cooperative processes involving nucleation.

An important result is that high positive, but also zero or negative, temperature coefficients are found for the kinetics

Angew. Chem. internaf. Edit. / Vol. I I (1972) / No. 10 901

in such conformational changes of proteins. The negative activation energy of A& at high temperatures can be attri- buted to the fact that several steps are necessary for the nucleation, which for its part determines the rate of the folding. With falling temperature, instead of the formation of a nucleus, the further folding of the polypeptide chain may be rate-determining.

Another explanation is that falling temperatures lead to the formation ofmore and more “false” nuclei, which must be reopened before a successful nucleus is formed. Both can lead to A f i < 0 at high temperatures. The interaction of apolar groups with water, as expressed in the form of the concentration coordinate [see (5)] and the associated contributions to the free energy, may be very important in this respect. Hydrophobic interactions of this type can be responsible for the temperature dependence of the activation energy, since these involve fast pre-equilibria, which enter into the overall rate constants.

Figure 10 shows the currently accepted temperature depend- ences of the thermodynamic and kinetic functions, a linear temperature dependence being assumed for the variation of the specific heat. (The accuracy of measurement is not sufficient to allow a definite decision as to whether and how AC depends on the temperature.) The corresponding functions for theenthalpy and the free energy are then found by integration. If the curves for 2 and E intersect at low temperatures, a cold transition may also be observed[92, 931.

The considerable change in the specific heat was pointed out in particular by Brandt~‘~’~. Corresponding results for a series of protein reactions are summarized in Table 2.

Table 2. The change in the specific heat at constant pressure, ACo, for several protein reactions.

Reaction A Co Ref. -

[kJ m o l - ’ deg-’1 ~ ~ _ _ _ _ _ _ ~ _ _ _ _ Chymotrypsinogen A :

solvation 10 1761 transition I, pH = 2.0, A + B 14 1761

Ribonuclease A: transition I, pH = 2.8 8.2 C811 S-protein + S-peptide-RNase S 2.9 c1121 GAPDH (yeast)+holoenzyme + NAD 2.2 [221 a-Chymotrypsin: dimer-monomer 2.8 11131

(Calorimetric measurements on small molecules, both apolar and polar, show that their interaction with water leads to changes in the specific heatL5].)

4.4. pH Dependence

Not only does the transition I exhibit a strong and complicated temperature dependence, but the pH dependence also reflects the cooperativity of the transition. Thus for the proteins investigated so far, the rate constant for unfolding g increases with the second to third power of the H 3 0 + activity (Fig. 11). Protons influence the native form A as “negative” effectors, since they destabilize this form with increasing concentration[93! The rate constant for folding ,&, on the other hand, changes only slightly; it decreases somewhat. Much more complicated molecules

may act as cooperative effectors (E)‘61 on proteins built up from subunits, and may e.g. stabilize the native form, as in the stabilization of GAPDH from yeast by NAD at high temperatures and pH values[’9!

I I I I , 10F lo-‘ ID-^ lo-’

111903111 [El IrnoL/ll - Fig. 11. Rate constants for the conformational change as a function of the effector concentration [El. (--0--0-) z and I$ for chymotrypsinogen A with H,Oi as the effector. Additional measurements in urea solutions were used for the extrapolation [71, 951. (----) E and & after chemical modification (removal of the negative charge) of 13 of the 16 carboxyl groups of chymotrypsinogen A 197, 711. There are only minor changes in the pH dependence of I;, which is evidence for the stabilization of the form A by special “trigger groups”. ( . . . .) As a comparison, the kinetics of an “allosteric transition” in an enzyme consisting of four identical subunits, i .e. the GAPDH from yeast with NAD as the effector molecule (after [19]).

The dependence of the overall rate constants it, f; of the conformational change can be described in both cases by a very similar reaction scheme. Thus for trypsin with two such peculiar binding sites we havecs7]

2H + A , + B, 1 2 H

H + A , + R , + H

A, f B,

K, ir 8 A h

K, .IF ”?Kb

The concentration dependence of T is found in a closed form in the case of simplifying and well satisfied assump- t i o n ~ ‘ ~ ~ ] . The assumptions are:

1. The binding of the effector is fast in comparison with the conformational change (a bimolecular rate constant of about 10” 1 mol-’s-’ can be expected for protonation

2. The change in the concentration of free effector following the disturbance of the equilibrium and the change in the conformation can be disregarded.

3. Within the forms A and B, all n binding sites have equal binding constants for the particular effector; however, the values for the two forms are different (pK, # pKJC6. 87 . 921.

From the values of I; and ,&, e.g. for the measured pH dependence in the case of chymotrypsinogen or cc-chymotrypsin, it is found, on the assumption of an “all-or-none’’ process, that three binding sites for protons with a disso- ciation constant K, = 0.05 mol/l considerably stabilize the nativeformA in theunprotonated form, byafactorofabout 100-1000 per binding site. The constants Kb (pK values of 3 . 5 4 . 5 ) found for these binding sites in state B are

902 Angew. Chem. internat. Edit. 1 Vof. I 1 (1972) No. 10

close to the values expected for carboxyl groups in water and are accordingly smaller by a factor of 100-1000.

A possible explanation for this effect of protons on the conformation is that ionic bondsare formed between certain carboxyl groups and ammonium groups, e .g . of lysine, which stabilize the form A[931. Up to five such ionic bonds are present in crystalline a-chymotrypsin, two being completely shielded from the s01utionI"~~.

An experimental confirmation of such "trigger groups" is the observation that the pH dependence of the transition I is not appreciably influenced by removal of the negative charge of 13 of the 16 carboxyl groups in chymotrypsinogen A by chemical modification (Fig. 11)[97, 711. This is to be expected if the electrostatic repulsion of the positive net charge of the protein in water contributes only slightly to the destabilization of the form A. For such a general electrostatic effect, a monotic dependence of the rate constants on the ionic strength would be expected, which is not observed (Fig. 12a). Ionic bonds of this nature explain also the very low pK value found for carboxyl groups in form A. The proximity of a positive charge causes a considerable pKshift even in small molecules[981.

1 -

t t- 0 - c -

W

i i

/ I 0 /" ,."

VISaltl' [rnoi/il --j 100/0 - Fig. 12. Influence of monovalent ions (a) and small molecules (b) on the rate constant for unfolding E in 8 x 1 0 - 3 ~ HCI for (-) chymotrypsinogen A, (----) trypsin, and (. . . .) rihonuclease [l?, 931.61n Erepresents the ratio of the rate constant in the corresponding solvent mixture to that in 8 x 10-3M HCI. a) Change on addition of salts such as NaCI, corrected for the secondary salt effect; b) change in solvent mixtures at 3 0 T , plotted against the reciprocal of the macroscopic dielectric constant D of the mixture [93]. (-U-U-) up to 15 vol.% dioxane, (--0--0-)

up to 25% ethanol, and (-A-A-) up to 25% ethylene glycol.

4.5. Salt Effects

The unfolding reaction depends in a complicated manner on the salt concentration. A maximum is found for f ; ,

indicating two factors with opposing effects (Fig. 12a). An explanation for the salt dependence of k is that the ionic bonds (and hence form A) are destabilized at low ionic strengths by binding of counterions, whereas at higher salt concentrations the electrostatic shielding of the net charge of the protein predominates and decreases[931. However, such reasoning, which is familiar and justified for small molecules, is not always permissible for proteinsr941. At very high salt concentrations, destabilization of the native form may also occur because the ions change the structure of waterf99' 51.

4.6. Variation of Solvent

Slight differences in the transition I are observed when it takes place in heavy water instead of in water (see Table 3). The difference in behavior in H,O and D,O found for complicated biological systems['001 may be partly due to the same causes; a possible explanation is provided by small changes in the structure and thermodynamic properties of water upon deuteration["".

The use of solvent mixtures makes it possible to vary the dielectric constant, the viscosity, etc. continuously. The thermodynamic properties of small molecules in these mixtures can be compared with those of the macromole- c ~ l e s [ ~ ~ J .

Figure 12b shows experimental values for f ; in several solvent mixtures. A plot of the relative free energy of activation &? against the reciprocaIofthedielectricconstant D gives a surprisingly good linear relationship, such as one could expect for electrostatic interactions. No such simple relationships are found for the folding, however, particularly at low temperature^[^']. S c depends in a very similar manner on the solvent composition and the temperature as does the solubility of apolar molecules['021. This may be regarded as evidence of the additional interactions of apolar groups with water in the form B[92-931.

4.7. Change in Covalent Structure of Proteins

Quantitative data on the influence ofchemical modifications or the exchange of amino acids on the stability of proteins are important, in particular because of their industrial and medicinal use. The recent successes in the chemical synthesis of proteins offer the possibility of systematically investigating the influence of an amino acid exchange['041. Another, less systematic method is the comparison of families of proteins or proteins of mutants or of different species.

4.7.1. Exchange of Several Amino Acids

An example is the family of serine proteinases such as chymotrypsinogen A and B, trypsin, and elastase, where parts of the amino acid sequence agree with each other. [Their crystal structure is also very similar (Fig. 3).] The stability and the kinetics of the transition I in acidic solution are also very similar for these proteins (Fig. 13 and Table 3).

4.7.2. Chemical Modifications

Several chemical reactions allow a more or less selective, mild, and specific modification of the side chains of proteins['051. A modification of carboxyl groups and its influence on the pH dependence has already been mentioned (Fig. 11).

Another example is the modification of the active site of a-chymotrypsin by a diisopropylphosphoryl (DIP-CT) or an anthraniloyl group (AN-CT), these groups being covalently bonded to the active center. There are differences in stability, which are mainly due to a lower unfolding rate (Table 3). With the aid of the fluorescent AN group, however, it is also possible to follow the transfer of energy from tryptophan side chains to the chromophore. This energy

Ahgew. Chem. internat. Edit. Vol. I 1 (1972) 1 No. 10 903

transfer is very sensitive to distance“ 0 6 ] , so that distance measurements can be carried out within the protein molecule during the unfolding or folding. Kinetic results obtained in this way agree with the behavior expected for an “all-or-none” process[’ ‘1.

Y

0005 -

0.002 c

Fig. 13. Rate constant for folding ( k ) for several members of a family of proteins at pH = 2.0 as a function of the temperature [13, 931 after a change in the covalent structure. Exchange of several amino acids: (-) chymotrypsinogen A, (--.--.-) chymotrypsinogen B, and (--..--..-) trypsin ; specific breakage of the polypeptide chain of chymotrypsinogen A; once: (---) gives 6-chymotrypsin, twice: (. . . . .) a-chymotrypsin. The circles show the middle of the transition (Tm), where E is equal to E. The short lines indicate the dependence of the rate constant for unfolding (E).

The introduction of covalently bonded “reporter groups” also offers the possibility of measuring conformational changes in systems in which other parameters are difficult to follow ~pticalIy[”~J.

Table 3. Kinetic parameters for folding (-) and unfolding (+) in the transition I for several proteins in 0.01M HCI at 30°C [13].

Protein A t

-In.& -In& A H A H ~ k J m o l - l [s-’1 [s-‘1 CkJmol] [kJmol] deg-,l

Chrymotrypsinogen A 11.1 6-Chymotrypsin 6.8 a-Chymotrypsin 6.8 AN-Chymotrypsin [a] 6.8 DIP-Chymotrypsin [b] 7.5 Chymotrypsinogen B 10.8 Trypsin 8.4 Trypsin (D,O) 8.2 Ribonuclease A 6.0

3.90 4.88 4.88 5.10 5.30 4.05 3.17 3.44 3.5

340 230 350 320 330 370 280 190 280

70 6 33 12 33 12 25 14 42 10 80 8 50 14 50 14 20 5

[a] AN = anthraniloyl. [b] DIP = disopropylphoryl

4.7.3. Cleavage of Peptide Chains

If the polypeptide chain in globular proteins is broken, their stability decreases in the cases investigated so far. In the enzymatic activation of chymotrypsinogen A to 6 and a-chymotrypsin, the peptide chain is broken once and twice respectively. The first break also leads to the most important changes in the crystal structure[371. This is also reflected in the kinetics of the transition I. The order of the reaction does not change; the reaction remains intramolecular, since the parts of the chain are still joined by disulfide bridges (Fig. 13 and Table 3).

5. Closing Remarks

With the transition I of some “simple” globular proteins as an example, the influence of “environmental changes” (pH, temperature, etc.) or of a change in the covalent structure of the protein on the thermodynamics and kinetics of cooperative conformational changes in proteins can be relatively easily investigated and described. This is greatly facilitated by the fact that this reversible partial unfolding can be represented to a very good approximation by an “all-or-none’’ process between two macroscopic states of the protein. This approximation is less satisfying in other reversible folding reaction^['^^^ “‘I, so that generalizations are not possible, and are not really to be expected for such complicated systems depending on many parameters. However, reversible transitions of this type are suitable for use as models of “molecular switches”.

In contrast to the cooperative transitions of linear homo- polymers, for which the thermodynamics and kinetics can be described quantitatively on a molecular basis, we are still far from achieving this aim in the case of globular proteins. Even the knowledge of the crystal structure, e.g. of a family of proteins (Fig. 3), does not lead to satis- factory correlations with the observed thermodynamics and kinetics of cooperative transitions in solution.

Because of the many kinds of interactions in the three- dimensional folding ofthe polymer chain, the time constants for various transitions can vary by many orders of magnitude, and may be very appreciably increased or decreased by small external changes due to cooperative effects. It is not only fast conformational changes that are important to biological regulation processes“ ‘‘I. It is conceivable that even processes such as the differentiation of cells, the phenomenon of a biological “clock” or the storage of information in the memory may in part be due to cooperative conformational changes with time constants of seconds - years. A time constant of one yearcorresponds to a difference in the free energy of activation of about - 35 kJ/mol in relation to the values given in Table 3, i. e. a quantity of energy that is compensated e.g. by the transfer of three tryptophan side chains from water into an organic phase (Fig. 4) or by rupture of about three ionic bonds (Fig. 11). Such slow conformational changes, on which very little investigation has been carried out so far, can probably be brought about within a single protein molecule, because of the specific three-dimensional interaction between the parts of the chain.

In biologically important processes, however, coupling with further reactions and interactions with other macromolecules is also to be expected, and the cooperativity and the specificity of responses to changes in the environment can be considerably increased in this way.

This work was partly supported by an EMBO long-term fellowship duringaperiodspent in the Molecular Enzymology Laboratory (University of Bristol) . I am very grateful to all those who have made information available to me before publication.

Received: August 4,1971 [A 903 IE] German version: Angew. Chem. 84,931 (1972)

Translated by Express Translation Service, London

904 Angew. Chem. internat. Edit. 1 Vol. I 1 (1972) / N O . 10

[l] R. E. Dickerson and I. Geis: Struktur und Funktion der Proteine. Verlag Chemie, Weinheim 1971 ; The Structure and Action of Proteins. Harper & Row, New York 1969. [2] J. D. Watson: The Molecular Biology of the Gene. Benjamin, New York 1971. [3] D. Eisenberg and W . Kaurmann: The Structure and Properties of Water. Oxford University Press, London 1969. [4] L. P. Kayushin: Water in Biological Systems. Plenum Publ. Corp , New York 1969. [ S ] E. Wicke, Angew. Chem. 78, 1 (1966); Angew. Chem. internat. Edit. 5 , 106 (1966). [6] J . Monad, J . Wyman, and J . P. Changeux, J . M o l . Biol. 12, 88 (1965). [7] B. Miiller-Hill. Angew. Chem. 83, 195 (1971); Angew. Chem. internat. Edit. 10, 160 (1971).

[8] W . Kaurmann, Advan. Protein Chem. 14, 1 (1959). [9] R. Lumry and R. Biltonen in S. Timasheffand G. Fasman: Structure and Stability of Biological Macromolecules. Dekker, New York 1969. [lo] J . A. Schellman and C. Schelfman in H. Neurath: The Proteins. Vol. 11. Academic Press, New York 1964. [11] M . Eigen, Nobel Symposium 5, Almquist & Wiksell, Stockholm 1966; Angew. Chem. 80, 892 (1968). 1121 K. G. Denbigh: The Principles ofchemical Equilibrium. Cambridge University Press, London 1968. [ 131 F. M . Pohl, Habilitationsschrift, Universitat Konstanz 1970. [14] J. Mol. Biol. 52, 1 (1970). [15] M . Leuitt and S. Lifson, J. Mol. Biol. 46, 269 (1969). [16] G. N . Ramachandran and V. Sasisekharan, Advan. Protein Chem. 23,283 (1968). [17] T. Funk, F. Eggers, and E. Grell, 1. Eur. Biophys. Congress 5, 37 (1971). [18] H . Gutfreund: An Introduction to the Study of Enzymes. Blackwell Scientific Publications, Oxford 1967. [19] J. D. Shore and H. Gutfreund, Biochemistry 9, 4655 (1970).

[20] K. Kirschner, M . Eigen, R . Bittman, and B. Voigl, Proc. Nat. Acad. Sci. USA 56, 1661 (1966). [21] H. Durchschlag, G. Puchwein, 0. Kratky, I. Schuster, and K. Kirsch- ner, Eur. J . Biochem. 19, 9 (1971). [22] S . F. Velick, J . P. Bagott, and J. M . Sturteuanr, Biochemistry 10, 779 (1971). [23] M . Perurr. New Scientist 50, 676 (1971). [24] J . C. Kendrew, Angew. Chem. 75, 595 (1963). [25] D. Eisenberg in L. Boyer: The Enzymes. 2nd Edit., Vol. I, Dekker, New York 1970. 1261 D. M . Blow and T. A. Seirz, Annu. Rev. Biochem. 39, 63 (1970). [27] B. P. Schoenborn, A . C. Nunes, and R . Nathans, Ber. Bunsenges. Phys. Chem. 74, 1202 (1970). [28] B. S. Hartley, Biochem. J . 119, 805 (1970). 1291 S. B. Needleman: Protein Sequence Determination. Chapman & Hall, London, and Springer, Heidelberg 1970. [30] M . 0. Dayhof: Atlas of Protein Sequence and Structure. National Biomedical Research Foundation, Silver Spring, Md. 1969. [31] J . J . Birktoft, B. W . Melrhews, and D. M . Blow, Biochem. Biophys. Res. Commun. 36, 131 (1969). [32] D. M . Shotton and H. C. Watson, Phil. Trans. Roy. SOC. London B257, 111 (1970). 1331 B. S. Hartley and D. M . Shotton In L . Boyer: The Enzymes. 3rd. Edit. Vol. 111, Dekker, New York 1971. [34] S. T . Freer, J. Kraut, J. D. Robertus, H. T. Wright, and Ng. H. Xuong, Biochemistry 9, 1997 (1970). [35] R. M . Stroud, L . M . Kay, and R . E. Dickerson, Cold Spring Harbor Symp. Quant. Biol. 36, 125 (1971). [36] D. M . Segal, G. H. Cohen, J . C. Powers, and P. E Wlcos, Cold Spring Harbor Symp. Quant. Biol. 36, 85 (1971). [371 C . S. Wright. R. A . Alden, and J . Kraut. Nature 221. 236 (1969).

[38] W . G. J . Hal, Dissertation, Universiteit Groningen 1971. [39] T. L. Blundell, J . F. Curfield, S. M . Cutfield, E. J. Dodson, D. C. Hodgkm. D. A Mercola. and M Viiayan. Nature 231. 506 (19711 1401 B LCT and F. M Rirhardq. J . Mol. Blol. 55. 379 (1971).

1411 C 7anford. J . Amer. Chem. SOC. $6. 2050 (1964).

[42] Y . Nozaki and C . Tanford, J. Biol. Chem. 246, 2211 (1971). [431 E. J . Cohn and J . T. Edsall: Proteins, Aminoacids and Peptides. Reinhold, New York 1943. [44] M . H. Klapper, Biochim. Biophys. Acta 229, 557 (1971). 1451 J . S. Rowlinson, Discuss. Faraday SOC. 49, 30 (1970).

[46] R . Biltonen and R. Lumry, J . Amer. Chem. SOC. 93, 224 (1971). [47] A. Rich and N. Dauison: Structural Chemsitry and Molecular Biology. Freeman, San Francisco 1968. [48] P. Flory: Statistical Mechanics of Chain Molecules. Wiley, New York 1969. 1491 A. C. T . North and D. C. Phillips, Progr. Biophys. Mol. Biol. 19, l(1969). [SO] F. M . Pohl, Nature New Biol. 234, 277 (1971). [Sl] E. L . Eliel, N . L . Allinger, S. J . Angyal, and W. A. Morrison: Conformational Analysis. Interscience, New York 1965. 1521 R. A . Newmark and M . A. Miller, J . Phys. Chem. 75, 505 (1971). [53] H . A. Scheraga, Advan. Phys. Org. Chem. 6, 103 (1968). [54] B. Pullmann in D. Daudel and A. Pullmann. Aspects de la Chimie Quantique Contemporiar. Coll. Int. CNRS, Paris 1971. [55] J . Engel and G. Schwarz, Angew. Chem. 82, 468 (1970); Angew. Chem. internat. Edit. 9, 389 (1970). [56] G. Schwarz and J . Engel, Angew. Chem. 84, 615 (1972); Angew. Cbem. internat. Edit. 11, 568 (1972). [57] D . C . Polandand H. A . Scheraga: Theory of Helix-Coil Transitions. Academic Press, New York 1970. [SS] J . Hermanns, D. Lohr. and D. Ferro, Nature 224, 175 (1919). [59] J . Kraut in L. B0J’t-r: The Enzymes. 3rd Edlt., Vol. 111, Dekker, New York 1971 [60] M . Joly: A Physico-Chemical Approach to the Denaturation of Proteins. Academic Press, New York 1965. [61] 0. B. Ptitsyn, A . K. Kron, and Yu. Ye. Eizner, J . Polymer Sci. C 16, 3509 ( I968). [62] G. I . Likhtenshtein and T. V . Troshkina, Mol. Biol. 2, 654 (1968). [63] A. C. Zettlemoyer- Nucleation. Dekker, New York 1969. [64] J . Steinhardr and J. A Reynolds: Multiple Equilibria in Proteins. Academic Press, New York 1969. 1651 H . Sundand K. Weber, Angew. Chem. 78,217(1966); Angew. Chem. internat. Edit. 5,231 (1966). [66] I . M . Klotz, N. R. Langerman, and D. W . Darnall, Annu. Rev. Bio- chem. 39,25 (1970). 1671 J. W. Teipeland D. E. Koshland, Jr., Biochemistry 10, 792 (1971). [68] C. Tanford, Advan. Protein. Chem. 23, 121 (1969). C691 J . F. Brandts in S. Timashefland G. Fasman, Structure and Stability of Biological Macromolecules. Dekker, New York 1969. C701 F. M . Pohl, Eur. J . Biochem. 4,373 (1968). [71] F. M . Pohl, to be published. 1721 J . F. Brandts, R. J. Oliueira, and C. Westort, Biochemistry 9, 1038 (1970). [73] S A. Hawley, Biochemistry 10, 2436 (1971). [74] D. F. Hollis, G. McDonald, and R. Biltonen, Proc Nat. Acad. Sci. USA 58,1038 (1970). [75] D. N. Holcomb and K. E. van Holde, J . Phys. Chem. 66,1999 (1962). [76] W . M . Jackson and J . F. Brandts, Biochemistry 9, 2294 (1970). [77] M . A . Eisenberg and G. W . Schwerr, J . Gen. Physiol. 34, 583 (1951). 1781 A. Rosenberg and C. K. Woodward, J . Biol. Chem. 245,4677 (1970). [79] R. Lumry, R. Biltonen, and J . F. Brandts, Biopolymers 4,997 ( 1066). [SO] D. C. Polandand H. A . Scheraga, Biopolymers 3, 401 (1965). [Sl] T. Y. Tsong, R . P. Hearn, D. P. Wrathall, and J . M . Sturteaant, Biochemistry 9, 2666 (1970). [82] J. M . O’Reilly and F. E. Karasz, Biopolymers 9, 1429 (1970). [83] M . Eigen, Quart. Rev. Biophys. I , 3 (1968). [84] A. N. Schechter, Science 170,273 (1970). [S5] B. Havsteen in S. J . Leach: Physical Principles and Techniques of Protein Chemistry. Academic Press, New York 1969. [86] D. M . Crothers, J . Mol . Biol. 9,712 (1964). [87] F. M . Pohl, Eur. J . Biochem. 7,146 (1968). [88] M . Kunitz, J. Gen. Physiol. 31, 241 (1948). [89] F. H . Johnson, H. Eyring, and M . J. Pollisart Kinetic Basis of Mole- cular Biology. Wiley, New York 1954. [90] J . G. Wetrnur and N. Dauidson, J. Mol. Biol. 31, 349 (1968). [91] W . F. Harrington and G. M . Karr, Biochemistry 9, 3725 (1970). 1921 J. F. Brandts, J . Amer. Chem. SOC. 86, 4291 (1964). [93] F. M . Pohl, FEBS Lett. 3,60 (1969). [94] A. Kurosky, J . E. S. Graham, J. W Dixon, and 7: Hofmann, Can. J . Biochem. 49, 529(1971). [95] C. H . Cheruenka, J . Amer. Chem. SOC. 83,473 (1961). [96] M . Eigen, Angew. Chemie 75,489 (1963). 1973 M . Ladzdunski, M . Delaage, J . P. Abila, and J . P. Vincent: Structure- Function Relationships in Proteolytic Enzymes Munksgaard, Copen- hagen 1969. [98] J . J. Christensen, J. L. Oscarson, and R . M. Izatt, J . Amer. Chem SOC. 90, 5949 (1968). 1991 P. u. Hippel and T. Schleich in S. Timasheff and G. Fasman: Structure and.Stability of Biological Macromolecules. Dekker, New York, p. 417. [loo] E. Lehr, M . Wenzel, and G. Werner, Naturwissenschaften 57, 521 (1970).

Angew. Chem. internat. Edit. / Val. I 1 (1972) / No. 10 905

[ lol l C. Nemethy and H. A . Scheraga, J. Chem. Phys. 41,680 (1964). [lo21 A . Ben-Naim and S. Baer, Trans. Faraday SOC. 89,4826 (1962). [I031 R. CerL C. R. Acad. Sci. Paris 271,60 (1970). [I041 R. B. Merrifield, Advan. Enzymology 32,221 (1969). [lo51 L. A . Cohen, Annu. Rev. Biochem. 37,695 (1968). [lo61 L. Stryer, Science 162, 526 (1968). [lo71 D . J. Birketl, R . A . Dwek, G . K . Radda, R . E . Richards, and A . G . Salmon, Eur. J. Biochem. 20,494(1971). [I081 T E Tsong, R. L. Baldwin, P . McPhie, and E. L. Elson, J . Mol. Biol. 63,453 (1972).

11091 A . N. Schechter, R . F. Chen, and C . 8. An$nsen, Science 167, 886 (1 970).

[llOl M . Brunori, E. Antonini, P . Fasella, J . Wyman, A . Rossi Fanelli, J. Mol. Biol. 34,497 (1968).

[I 113 C. Frieden, J. Biol. Chem. 245,5788 (1970)

[112] R . P . Hearn, F. M . Richards, J . M . Sturtevant, and G. D. Watt , Biochemistry 10,806 (1971).

[I131 K. C. Aune, K . C. Goldsmith, and S. N.Timashefl,Biochemistry 10, 1617(1971).

Crystal Chemistry of Complex Carbides and Related Compounds

By Hans Nowotny[*]

Numerous metal carbides can be discussed in a rather uniform way by means of structural features, mainly characterized by the mode of linking of octahedral and occasionally trigonal prismatic [M6C] groups (M = transition element). From this point of view perovskite carbides (M,M'C, M'= another transition or A-group element) and derivatives, p-Mn carbides (M,M;C), K-carbides, carbides with V,AsC- and Cr,AlC type structures and derivatives, q-carbides (M,M3C) and carbides having the filled Mn,Si, type structure will be treated. The high stability of these complex carbides is due to the strong bonding M - C and additional bonding of M-M' atoms forming an ordered parent lattice. Besides the interstitial principle of filling of lattice holes (by isolated carbon atoms), substitution with A-group elements may also take place. Thus in borocarbides extended structural elements occur.

1. Introduction

The review deals mainly with the structural aspects of some metallic carbides which occur in ternary systems of the type : two transition elements-carbon and transition element-A group element-carbon. The term complex carbide is arbitrarily introduced and stands for a doubfe or higher carbide of intermediate character. There are more reasons than just classification for contrasting complex carbides with pseudoternary or pseudoquaternary compounds having their origin in binary carbides or nitrides such as (Ti,V)C,-, or (Zr,Ta)(C,N) solid solutions. The latter carbonitride is found, for example, to be a constituent in cobalt based superalloys. Considering the compounds such as (Mo, Re)C or (W, Re)C having NaCl type structure"], it is very likely, but not proven, that rhenium is able to stabilize the high-temperature modifications MoC , --* and WC,-, at much lower temperatures. Some kind of ordering may however occur in such solid solutions. Thus metal-metal short range order in carbides was found by analyzing the diffuse X-ray scatteringr2]. Solid solutions of (Hf, Ta)C or (Nb, Mo)C --x apparently exhibit discontinui- ties of the electronic state',], and clustering is indicated by miscibility gaps which have been detected at low temperatures for cubic carbide solid solutions such as Tic-HfC or

[*] Prof. Dr. H. Nowotny Institut fiir Physikalische Chemie der Universitat A-I090 Wien IX, Wahringerstrasse 42 (Austria)

VC-TaC14]. In addition, ordering of carbon (and void) sites can be envisaged as is well known particularly for a number of sub carbide^^'^, carbohydrides etc.

Another peculiar case is encountered with the chromium- iron substitution in Fe,C; chromium enters the lattice only in the eightfold position, thus a partial ordering of the metal atoms takes placer6]. The same seems to occur with Cr,,W,C, within the solid solution (Cr, w),3c6, as one can assume from the numerous borides such as Ni,,Hf2B6 displaying metal ordering"'. There are multicomponent carbides such as Nb,(Ni, Fe,Cr),C, reported as adispersion phase in stainless steels, which obviously derives from the q-carbide['] Nb,Ni,C, and also phases such as Nb,Cr, ,A], - ,C which have been shown to exist only as a quaternary compound[81.

Relatively few true quaternary (and higher) carbides have been characterized so far. A number of metal carbides which correspond to intermediate carbides, develop from binary or ternary intermetallic compounds by uptake of carbon, e. g. Nd,InC,,, or (Cr, W, Fe)l,C[91. An interesting case involves the complete miscibility between rhenium metal and W,C observed by Kuz'ma eta1>'O1 and confirmed by Fackelman et al.[' 'I.

[*] q-carbides, first detected as constituents in high speed steels by A. Wesrgren and G. Phragmen, Jemkontorets Ann. I l l , 525 (1927), are of formula M2 - aM;- ,C o r (M, M'),C, occasionally occurring with less carbon. They are characterized by a cubic cell with lattice parameters around 11 A.

906 Angew. Chem. internat. Edit. 1 Vol. I1 (1972) 1 No. 10

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