Plasticity of crystalline proteins

Plasticity of crystalline proteins Donald L.D. Caspar and John Badger Brandeis University, Waltham, Massachusetts, USA The spatial and temporal correlations of the atomic movements in well ordered protein crystals and the variations in structure among different crystalline environments demonstrate the intrinsic plasticity of hydrated protein molecules. Current Opinion in Structural Biology 1991, 1:877-882

Introduction

the atomic movements are correlated only over short distances, which are roughly the size of amino acid residues.

How are atomic movements in protein molecules correlated and how are the average positions of surrounding water molecules related to the protein structure? We will consider these questions with particular reference to studies on crystalline insulin, lysozyme and myoglobin structures. The experimental evidence demonstrates that although crystallographers' proteins are highly ordered, the thermal fluctuations in the atomic positions are not correlated over large distances in the molecules as might be expected from the Debye-Waller theory [1,2], which describes thermal movements in crystalline elastic solids. Furthermore, solvent molecules in protein crystals beyond the tightly bound hydration shell are not uniformly distributed on the average as in the liquid state. The plasticity of hydrated proteins appears to be dependent on the restrained mobility of the surrounding solvent.

Spatial correlations of atomic fluctuations The mean square amplitudes of the individual atomic displacements in crystalline lysozyme, measured from Bragg X-ray diffraction data in a pioneering study by Artymiuk et aL [3], showed that the fluctuations increased at the molecular surface, and local variations in the mean square amplitudes suggested that surface residues might flap or twist independently relative to the backbone. The Bragg reflections, however, provide direct information only about the average structure of the crystal. Information about the variations from the average, most notably about how the atomic displacements are correlated, is contained in the dilhase background scattering. Analyses of the diffraction from the very open tropomyosin lattice [4,5°] have shown that the predominant component of the diffuse low-resolution X-ray scattering can be accounted for by uncorrelated large ( ~ 5-7& root mean square) amplitude lateral fluctuations in the positions of the ~-helical coiled-coil segments in the crystal net. Streaks of diffuse scattering about the Bragg reflections from some orthorhombic lysozyme crystals have been modeled in terms of rigid-body packing disorder in the lattice [6]. Analysis of the dilhise X-ray scattering resulting from variations of the protein structure in 2Zn insulin crystals [7] has demonstrated that most of

Scattering resulting from variations in the density distribution, p(r), is given by:

Iv(R) = <1 Fr0(r

~2 >

_

lET < p(r) >1 2

where <]FTp(r~2> is the average of the squared Fourier transform of the instantaneous structures, and ]FT < p(r) > 12 is the squared Fourier transform of the average structure (which is the normal Bragg diffraction of a crystal, FZhki, finite only at the reciprocal lattice points Rhkl, where II~ = 2sin0/L). For a Gaussian distribution of displacements of mean square amplitude 152 relative t~ the ideal atomic coordinates, F2(Rhld) = e -(2nRa) F2(Rhkl) where 2(2~i) 2 = B, the Debye temperature factor [1], and FZo(Rhkl) are the squared structure factors "for the ideally ordered crystal. To calculate the variational scattering in terms of the amplitudes and correlations of the fluctuations, Clarage et aZ [8-] represented the average Patterson (autocorrelation) function as the convolution of the peaks in the ideally ordered Patterson with a Gaussian whose variance, ~2(u) = 2~52(1-r(u)), approaches the limiting value 2~52expected for uncorrelated fluctuations at large pair separation, u (i.e., the correlation function F(u) decreases from 1--* 0 as u increases). The variational scattering can then be expressed in terms of convolutions of the ideal Bragg reflections F2o(Rhkl) with a halo function that is the Fourier transform of the correlation function F(u) weighted according to R2 and the mean square amplitude, 82, of the corresponding displacements. This treatment accommodates any functional form for the decay r ( u ) in the correlation among the atomic displacements, ranging from the Einstein crystal model [9] with uncorrelated fluctuations to the Debye-WaUer elastically coupled crystal model [1,2] with long-range correlations that decay algebraically. Information about the correlation geometry of the components of the fluctuations is contained in the halo functions that define the diffuse scattering distribution. Experimental diffuse scattering data from tetragonal and triclinic hen egg-white lysozyme crystals, which have average mean square atomic displacements, ~i2, of 0.25A.2

~) Current Biology Ltd ISSN 0959-440X

877

878

Proteins and 0.13A2, respectively, have both been fitted [8 o] using two component exponentially decaying correlation functions, F ( u ) = e - u/.~ with relaxation distances Ys~6A and YL'-'50& The long-range (YL) correlated component, 52t, corresponding to lattice-coupled displacements, amounts to only 0.01A2 in both crystal forms, whereas the short-range (Ys) correlated component, 82s, accounts for 90 and 95 % of the fluctuations in triclinic and tetragonal lysozymes, respectively. The doubling of the mean square displacements in the tetragonal compared with the more tightly packed triclinic crystal results from the short-range correlated intramolecular movements that are liberated in the more hydrated lattice. Models assuming that the fluctuations are dominated by long wavelength lattice vibrations or hinged movements of two lobes of the molecule do not simulate the observed diffuse scattering distribution. The conclusion, from measurements of diffuse scattering from insulin [7] and lysozyme [8o] crystals, that the major contribution to the atomic temperature factors comes from short-range correlated displacements is at odds with surmises based on normal mode calculations [10] and models with rigid-body movements [11], as well as inferences from measurements of Young's modulus [ 12] and the speed of sound [13] in protein crystals, all of which implicate long=range coupled displacements. These models with long-wavelength vibrations or rigid-body movements predict mean square displacements that can fit the crystallographic temperature factors; however, the mean square displacements measured from the Bragg diffraction data contain no direct information about the spatial correlations in the displacements. Diffuse scattering, measured with a well collimated X-ray beam, has excellent momentum resolution, which gives an accurate estimate of the distance scales involved in the correlation of atomic movements but no information about the time scales.

Relaxation times of atomic fluctuations Inelastic scattering of M6ssbauer radiation, the energy of which is narrowly defined, can discriminate movements with relaxation times
fraction of the total mean square displacement, 82, in protein crystals. The Debye theory [1] of elastic thermal vibrations predicts a linear relationship between 82 and absolute temperature. Below ,-- 200 K, there is a shallow linear increase in 8 2 with temperature f o r the Fe atom in myoglobin; above 200 K, however, this relationship breaks down and the displacements increase much more rapidly as a function of temperature. Extrapolation of the low temperature linear relation for the Fe atom to room temperature gives a value of 52 in agreement with the 0.02 A2 lattice-coupled component measured from all the protein atoms by MOssbauer crystallography [14]. Inelastic neutron scattering from myoglobin powder rehydrated with D20, analyzed by Doster et al. [16], has shown that the temperature dependence of the mean square displacements of the protein hydrogen atoms, measured with a time resolution of 0 . I - l o o p s , resembles that of the heme iron measured by M6ssbauer spectroscopy. The vibrational frequency distribution below 180K [17.] is Debye-like at low frequencies, indicating that the low-temperature small-amplitude atomic movements can be described by a distribution of underdamped vibrational modes. At higher temperatures, the increased mobility of the hydrogen atoms can be accounted for by jumps between distinct sites of different energy corresponding to torsional degrees of freedom and fast dihedral angle fluctuations [16]. Molecular dynamics simulations of solvated myoglobin as a function of temperature [18] gave fair agreement with inelastic neutron scattering data and demonstrated a very large increase in protein dihedral angle transitions above ,-- 180K.

Hydration water structure and dynamics The thermal properties of water in myoglobin crystals and rehydrated powders, studied by calorimetry and infrared spectroscopy, display a glass-like transition from a rigid amorphous solid below ~lSOK to a liquidlike state with substantially increased mobility at higher temperatures [19]. Comparison with the results from M6ssbauer spectroscopy [15], water dielectric relaxation measurements [20] and low-temperature crystallography [21,22], as well as the more recent inelastic scattering data [14,16,17° ] indicates that the rigid hydrogenbonded water networks that exist at low temperatures trap the myoglobin molecules into conformational substates where only small amplitude harmonic vibrations are possible. At higher temperatures, however, when water molecules can undergo larger amplitude movements that appear to be only locally correlated, transitions among different substates of the protein may occur. Saenger [23] has exemplified the nature of the structure and dynamics of water at the surfaces of proteins and nucleic acids with results from detailed crystallographic studies on a-and ~-cyclodextrins, which crystallize as hexa-and undecahydrates. In [3-cyclodextrin.11 H20 , the 11 water molecules are disordered over 16 positions, and 15 of 21 glucose hydroxyl groups are orientationally disordered. Most of these disordered groups are inter-

Plasticity of crystalline proteins Caspar and Badger 879 connected by hydrogen-bonded chains in which orientations may change by a flip-flop switch. A pair of crystals with the same composition, studied by neutron and X-ray diffracton [24°], showed alternative arrangements of the solvent in the [~-cyclodextrins cavity, presumably resulting from slight variations of environmental conditions, which indicate a very delicate balance of forces in the average water structures. Quasi-elastic neutron-scattering measurements made on the crystalline hydrates have been accounted for in terms of reorientational jumps of hydroxyl groups and water protons over distances of -~ 1.5.~ and diffusive motions of water molecules over distances of ,~ 3 A, which occur on a time scale of 5-50 ps at room temperature [25"]. Ordering of water well beyond the tightly bound first hydration shell of a protein has been demonstrated from a map of the electron-density distribution of the solvent in cubic insulin crystals [26"], determined by an iterative difference Fourier method restrained by the refined atomic model of the protein [27°]. Of the ~400 water molecules for each 51-amino-acid protein monomer in the crystal, ,~ 100 are well enough ordered to be located by conventional crystallographic refinement. Fluctuations in density well above the n o i ~ level are observed throughout the 65 % of the crystal volume occupied by solvent, demonstrating that non-random: arrangements of the water molecules extend up to ~ 2 0 A from the ordered water at the protein surface. Because the ionic strength of the crystal solvent lies within the physiological range, this water ordering may be similar to that which occurs in viva A molecular dynamics simulation suggested that the disordered but non-uniform average water structure in the insulin lattice could be accounted for by flickering among related hydrogen-bonded networks anchored by the bound water. Such ordering may account for the 'hydration force' opposing close approach of solvated surfaces [28].

Conservation and variation in crystalline protein structures Protein crystallography has yielded atomic-resolution maps of the density distribution averaged in time over all the molecules in well ordered crystals; these maps have established that many proteins have well defined folding patterns which appear relatively insensitive to environmental conditions. This apparent structural conservatism has suggested that protein molecules might be regarded as elastic solids or, at least, built up of rather rigid domains. The diffuse and inelastic scattering of X-rays or neutrons from insulin [7], lysozyme [8-] and myoglobin [14,16,17.] has shown that the simple solid model cannot represent the dynamic properties of these molecules at room temperature. As yet, only mean magnitudes of the spatial and temporal correlations of the atomic fluctuations have been deduced from the variational scattering, assuming homogeneous disorder; inferences regarding the inhomogeneities in flexibility of these paradigmatic proteins have been drawn from comparison of their Fourier averaged structures in different crystalline environments.

Insulin Insulin molecules can take up two locally different conformations in crystals of hexamers, with the eight residue amino-terminal segment of the B-chain being either extended or folded into an 0t-helix [29]; the conformations with the extended and folded segment have been designated as T and R, respectively [30]. Switching from the T6 conformation to T3/R3 in the transformation of 2Znto 4Zn-insulin crystals [31] is driven by an increase in ionic strength leading to anion binding by tetrahedrally coordinated zinc [32]. In addition, binding of phenol stabilizes an R6 conformation for the hexamer [30] which has been crystallized in two different lattices [33]. The symmetric dimer in the zinc-free cubic crystals has a T conformation, but comparison with the corresponding structure in hexamers shows localized differences with relative main-chain displacements up to 6A and altered side-chain torsion angles [27°]. Analysis of divalent cation binding to 2Zn insulin crystals has shown that Cd 2+, which interacts like Ca2+, must jump among three closely spaced trigonatly related sites that are one-third occupied, inducing a linked conformational change in pairs of the six Glu B13 chains that coordinate the one-third-occupied cation sites [34"]. Monovalent cation binding to cubic insulin crystals also involves localized side-chain displacements [35"]. Comparison of the structure of a completely inactive insulin crosslinked between GlyA1 and LysB29 in a T3/R3 crystalline form [36"] with other insulin crystals has established that the biologically active conformation must differ from all the crystalline structures. Derewenda et aL [36"] concluded that binding to the insulin receptor involves separation of the carboxy-terminal segment of the B-chain from the association with the amino;terminal part of the A-chain that occurs, in the various crystal forms. Chothia et al. [29] have speculated that the large movements involved in switching from the extended to the ~x-helical fold of the amino-terminal B-chain segment (which can be regarded as a model for allosteric transitions and other functional conformational changes) could result from propagation of the response to an initial perturbation at the molecular surface by sequential adjustments rather than by independent fluctuations. However, the evidence that most of the atomic displacements in insulin are only locally correlated [7], and that localized structural variations occur among and within different crystal forms [27.,29,30,34o-36 o] suggests that major conformational rearrangements may proceed by a kind of random walk through possible local substates.

Lysozyme Rigid and flexible regions in hen egg-white lysozyme and invariant features in its hydration shell have been identified by Madhusudan and Vijayan [37 o] from comparisons of the high-resolution structures of five crystal forms. Two of these, the low-humidity tetragonal [38] and monoclinic [37 o] forms are discrete shrinkage stages produced by a water-mediated phase transition at ,-, 90 % relative humidity [39]; together with the native tetragonal and triclinic and the high-pressure tetragonal [40] forms,

880

Proteins these crystals delineate conserved and variable features of the hydrated protein structure. Of the 129 residues, 43 Ca positions differ from each other by <0.5A in the difference distance matrices, constituting the relatively rigid main ~-structure and three ~t-helices; the 22 most flexible main-chain positions (with variations > 1 A) are distributed throughout the molecule. This measure of variability correlates with the temperature factors measured in the low-humidity monoclinic form [37 °] and the earlier analysis of the tetragonal form [3]. Among the five crystal structures, the number of ordered water molecules differ wildly, but there are 30 bound water molecules in common, 22 of which correspond to strongly bound water in human and tortoise lysozymes [41]. The number of water molecules in glutaraldehydefixed triclinic hen egg-white tysozyme crystals was reduced from --~230 for each protein molecule when wet to ,-~36 by drying over silica gel [42]. This dehydration occurs without disordering and with root mean square displacements for all protein atoms of < 1 A. The dispositions of conserved water molecules in the lysozyme crystals [37° ] appear to be similar to those observed among different crystalline environments of insulin [27",43] and myoglobin [44]. A mutant T4 phage lysozyme displays free different crystal conformations, four of these in an orthorhombic lattice with four independent molecules in the asymmetric unit [45°]. The difference-distance matrix shows that the amino-and carboxy-terminal domains are largely invariant with most of the variation localized among six residues in the hinge region connecting these domains. Among the five allomorphs, the hinge-bending angle varies in a continuous range of -~ 30 *with a relative maximum displacement of ~ 9 A on opposite sides of the cleft. Although these observations are compatible with the simple idea that conformational transitions in proteins may involve the relative movement of essentially rigid structural elements [46], what is clearly demonstrated is that localized conformational variations can occur among a range of substates even within an ordered crystalline environment [45°]. Hinge bending alone cannot, however, account for the predominant short-range correlated fluctuations of the atomic positions in crystals of hen egg-white lysozyme [8.1.

Myoglobin and other proteins Comparison of the monoclinic sperm-whale myoglobin structure [21] with the hexagonal crystal form of myoglobin from a synthetic gene [44] shows that the mean square displacements of segments involved in intermolecular contacts in one form but not the other are systematically reduced in the restrained environment [47°]. The maximum displacements measured for the unrestrained segments give a better fit with a molecular dynamics simulation of an isolated myoglobin molecule [48] than the amplitudes measured from either crystal structure [47"]. The observation that packing interactions reduce the atomic mobilities supports the notion that protein motions are heavily damped and largely diffusive, rather than harmonic.

Crystallographic studies on a variety of proteins other than insulin, lysozyme and myoglobin provide further evidence for the plastic adaptability of protein structures. Just two examples are cited here. Firstly, comparison of the structures of two thymidylate synthases with significant sequence differences demonstrated that sequence changes can be accommodated by local adjustments in the positions of the surrounding amino acids, independent of the rest of the structure [49°]. Secondly, structural plasticity of an engineered a-lytic protease led to accommodation of a variety of substates by a combination of alternate side-chain conformations and binding-site flexibility [50]. The ability of one part of a hydrated protein to move relatively independently of another under physiological conditions must play an essential role in the remarkable adaptability of protein structures.

Conclusion Protein folding appears to proceed through an intermediate molten globule state [51]. The distinction between this condensed liquid-like state and the regularly folded conformation in solution may not be as extreme as suggested by the precisely defined structures characterized in well ordered protein crystals. Cooper [52] noted the apparently conflicting views of the physical nature of globular proteins in crystals and in solution: "one, a compact structure in which the polypeptide chain is precisely folded to give a tightly interlocking, rigid molecule; the other, a 'kicking and screaming stochastic molecule' in which fluctuations are frequent and dramatic". He pointed out that these two views may be reconciled by consideration of the inevitable thermodynamic fluctuations inherent in microscopic systems. Protein molecules considered singly can undergo sizeable fluctuations which are not incompatible with the timeaveraged properties of crystalline ensembles. Measurements of the diffuse X-ray scattering [7,8 o] and inelastic scattering of M6ssbauer photons [14] from very well ordered protein crystals at room temperature demonstrate that the correlations of the predominant thermal movements are liquid-like, rather than the more orderly lattice vibrations expected for elastic solids [1]. These studies, together with the characterization of the temperature dependence of inelastic neutron scattering from hydrated powders [16,17.], information from lowtemperature crystallography [21,22] and spectroscow [15,19] of hydrated protein crystals, and analysis of water dynamics in model-hydrated crystals [23,24°,25°], indicate that the predominant short-range correlated atomic movements in protein crystals at room temperature result from fluctuating transitions among similar conformational substates that are dependent on the restrained mobility of the solvent. The range of conformational substrates that occur for protein molecules in solution can be characterized by NMR spectroscopy, but description of such studies is beyond the scope of this review. In solution, the amplitude of the mean square fluctuations about the average atomic positions would be expected to increase compared with such variations in crystals, and positional correlations between some parts of a stably

Plasticity of c r y s t a l l i n e p r o t e i n s C a s p a r a n d B a d g e r

folded protein could blur out as they do for a liquid. Transition to a molten-globule state might only require a graded increase in these local fluctuations. T h e p l a s t i c i t y o f p r o t e i n s t r u c t u r e s , w h i c h is e v i d e n t f r o m d e t a i l e d c r y s t a l l o g r a p h i c a n a l y s e s o f t h e s a m e p r o t e i n in d i f f e r e n t e n v i r o n m e n t s a n d o f d i f f e r e n t s e q u e n c e s in s i m ilar e n v i r o n m e n t s , is a n e s s e n t i a l a t t r i b u t e f o r a d a p t a b i l i t y . The switching among different functional conformations m a y i n v o l v e t h e s a m e t y p e o f l o o s e c o u p l i n g m a n i f e s t at h i g h e r levels o f m a c r o m o l e c u l a r o r g a n i z a t i o n [53].

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Acknowledgement Preparation of this review was facilitated with support from NIH grant CA47439 to DLD Caspar from the National Cancer Institute.

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DLD Caspar and J Badger, Rosenstiel Basic Medical Sciences Research Center, Brandeis University, Waltham, Massachusetts 02254-9110, USA.