doi:10.1016/j.jmb.2004.05.066
`
`J. Mol. Biol. (2004) 341, 565 574
`
`Available online at www.sciencedirect.com
`
`SCIENCE@DIRECTO
`
`ELSEVIER
`
`X-ray and Thermodynamic Studies of Staphylococcal
`Nuclease Variants I92E and I92K: Insights into Polarity
`of the Protein Interior
`
`Duc M. Nguyen, R. Leila Reynald, Apostolos G. Gittis* and
`Eaton E. Lattman
`
`Department of Biophysics
`Johns Hopkins University
`3400 North Charles Street
`Baltimore, MD 21218, USA
`
`We have used crystallography and thermodynamic analysis to study
`nuclease variants I92E and I92K, in which an ionizable side-chain is
`placed in the hydrophobic core of nuclease. We find that the energetic
`cost of burying ionizable groups is rather modest. The X-ray determi-
`nations show water molecules solvating the buried glutamic acid under
`cryo conditions, but not at room temperature. The lysine side-chain does
`not appear solvated in either case.
`Guanidine hydrochloride (GnHCl) denaturation of I92E and I92K, done
`as a function of pH and monitored by tryptophan fluorescence, showed
`that I92E and I92K are folded in the pH range pH 3.5 – 9.0 and pH 5.5 –
`9.5, respectively. The stability of the parental protein is independent of
`pH over a broad range. In contrast, the stabilities of I92E and I92K
`exhibit a pH dependence, which is quantitatively explained by thermo-
`dynamic analysis: the pKa value of the buried K92 is 5.6, while that of
`the buried E92 is 8.65. The free energy difference between burying the
`uncharged and charged forms of the groups is modest, about 6 kcal/mol.
`We also found that 1 app for I92K and I92E is in the range , 10 – 12, instead
`of 2 – 4 commonly used to represent the protein interior.
`Side-chains 92E and 92K were uncharged under the conditions of the
`X-ray experiment. Both are buried completely inside the well-defined
`hydrophobic core of the variant proteins without forming salt-bridges or
`hydrogen bonds to other functional groups of the proteins. Under cryo
`conditions 92E shows a chain of four water molecules, which hydrate
`one oxygen atom of the carboxyl group of the glutamic acid. Two other
`water molecules, which are present in the wild-type at all temperatures,
`are also connected to the water ring observed inside the hydrophobic core.
`The ready burial of water with an uncharged E92 raises the possibility
`that solvent excursions into the interior also take place in the wild-type
`protein, but in a random, dynamic way not detectable by crystallography.
`Such transient excursions could increase the average polarity, and thus
`1 app, of the protein interior.
`
`q 2004 Elsevier Ltd. All rights reserved.
`
`*Corresponding author
`
`Keywords: staphylococcal nuclease; buried water; dielectric constant;
`hydrophobic core; protein polarity
`
`Supplementary data associated with this article can be
`found at doi: 10.1016/j.jmb.2004.05.066
`Present address: D. M. Nguyen, Human Genome
`Sciences, 9410 Key West Avenue, Rockville, MD 20850,
`USA.
`Abbreviations used: GnHCl, guanidinium
`hydrochloride; IR, ionizable residue.
`E-mail address of the corresponding author:
`apo@groucho.med.jhmi.edu
`
`Introduction
`
`In many macromolecular processes (e.g. molecu-
`lar recognition, catalysis, REDOX reactions, photo-
`activation, proton conduction) internal
`ionizable
`residues (IRs) play a key functional role. Such
`critical IRs typically occupy highly evolved micro-
`environments within the molecule. Quantitative
`calculation of the energetics and pKa shifts of IRs
`
`0022 2836/$ see front matter q 2004 Elsevier Ltd. All rights reserved.
`
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`566
`
`Buried Glu and Lys in Staphylococcal Nuclease
`
`remains a challenge, although significant progress
`has been made in recent years.1 In particular, large
`shifts in pKa values are not always reproduced
`faithfully. One difficulty arises from the relatively
`low polarity of the protein interior. This means
`that the electrostatic interactions between buried
`groups and other IRs are weakly shielded, and
`thus rather large. The reaction field effects of
`buried IRs are also large, and difficult to calculate.
`These interaction energies and self energies have
`to be determined with great precision to fix a pKa
`value.
`At this moment the most detailed calculations,
`which would include all atoms, and treat polari-
`zation and dynamic effects explicitly, are beyond
`the state of the art. Investigators are forced to
`subsume some effects into a dielectric constant.
`In order to improve our understanding at
`the
`molecular level of how polar or charged groups
`are accommodated within protein molecules, and
`thus to lay the groundwork for improved compu-
`tational methods, we have been carrying out muta-
`genesis experiments in which large shifts in pKa
`values are produced by burying IRs in the hydro-
`phobic core of a model protein, staphylococcal
`nuclease. The present study focuses on mutations
`of residue I92, a residue deeply buried in the
`molecule’s b-barrel.
`There are not many techniques available for the
`measurement of the local polarity within a protein.
`We have been using thermodynamic analysis to
`relate protein stability, measured as a function of
`pH, to the shift in pKa value of buried ionizable
`groups. As discussed in Materials and Methods,
`this analysis allows us to determine the free energy
`of burying a charge, and serves as one probe of
`polarity.
`In earlier work we have probed the polarity in
`the core of staphylococcal nuclease experimentally,
`using shifts in pKa of IRs introduced by site-
`directed mutagenesis at position 66, which is
`completely buried in the hydrophobic core. For
`the variants V66E and V66K we determined values
`of DGbur, defined as (^ )2.3RT(pKnative
`pKunfolded),
`to be of about 6 kcal/mol.2,3 Through the Born
`formalism these correspond to values of 10 – 12 for
`the apparent dielectric constant 1 app.2 These modest
`energies were surprising in light of the conven-
`tional picture of the protein interior as a largely
`hydrophobic region of low polarizability in which
`dipoles,
`such as peptide groups, have little
`rotational freedom. The very large values of DGbur
`often quoted in the literature are not experimental,
`but are obtained from the Born model using values
`of 80 for the solvent dielectric constant 1 s and of
`2–4 for the apparent protein dielectric constant 1 app.4
`We have also studied the variants at position 66
`by X-ray crystallography. Our initial work was
`done on V66K,3 and this was followed by the struc-
`ture of PHS/V66E.2 The K66 and the E66 side-
`chains are buried in the same space occupied by
`the valine residue in the wild-type, but extend
`into the cavity. However,
`in the E66 protein,
`
`water molecules are visible in the cryo structure,
`connecting the polar group of the side-chain with
`the protein surface.
`No water molecules are seen bound to K66 in the
`cryo or room temperature structures, but dis-
`ordered water molecules would not be visible.
`Thus, our data are not definitive about
`the
`hydration state of K66. All this suggests that the
`energy landscape for burial of water molecules is
`rather flat, and that other methods of dielectric
`compensation are likely to play an important role.
`Although position 66 is completely buried, the
`region around it is not very well packed. One can
`readily imagine that the burial of water molecules
`here represents a special circumstance. Thus, to
`explore the generality of our observations at
`position 66, we have carried out a similar study at
`position 92. Application of an algorithm in which
`layers of atoms are successively peeled off the
`nuclease surface shows that I92 is one of the most
`deeply buried residues in nuclease. The backbone
`at locus 92 is also tightly packed, and distal atoms
`in the side-chain delineate part of the cavity. The
`microenvironments at loci 66 and 92 are quite dis-
`tinct. Thus, studies at position 92 serve to diversify
`the set of conditions we have explored.
`Crystallographically, both variants I92E and I92K
`have the ionizable side-chain group buried com-
`pletely in the hydrophobic core of the protein. The
`values for DGbur were found to be in the range of
`5 – 6 kcal/mol, close to the value found at position
`66. The cryo crystallographic structure of I92E
`shows a ring of water molecules solvating the
`side-chain carboxyl group of the buried glutamic
`acid.
`The IRs we have introduced at positions 66 and
`92 encounter a local environment that is not pre-
`evolved or pre-disposed to provide any sort of
`charge compensation, and nuclease has to find
`other ways to cope with the potentially high
`energetic cost of these events. Our studies suggest
`that nuclease copes, at least in some cases, by
`burying the ionizable groups in a solvated form,
`and by invoking other forms of compensation that
`we have not identified in detail.
`The buried water molecules we see represent a
`new mechanism for increasing the local polarity of
`the protein interior. We will return later to a discus-
`sion of how general or important this mechanism
`may be. Other mechanisms for increasing local
`polarity are certainly in play. The Warshel group5
`for example, has found that explicit consideration
`of protein relaxation leads to a significant increase
`in the apparent dielectric constant 1 app. Also, coher-
`ent clusters of polar and charged amino acid side-
`chains do exist, as in metal binding sites, but these
`are highly evolved functional entities not typical
`of the protein interior as a whole.
`Although we have used the Born formalism to
`derive an apparent dielectric constant from our
`observations, we have focused our presentation on
`measurable quantities, stabilities and DpKa values.
`As advocated by Honig and co-workers, protein
`
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`Buried Glu and Lys in Staphylococcal Nuclease
`
`567
`
`molecules are neither isotropic nor homogen ous,
`so that the idea that the internal screening can be
`represented by a single parameter, an apparent
`dielectric constant eapp, is open to doubt.6 Warshel
`and co-workers have repeatedly emphasized that
`the v alue of the screening parameter to be used
`depends not only on the local environment, but
`also on the observable being calculated, and on
`the s tructural model being used
`to interpret
`energetics.7 This is particularly relevant for the
`highly evolved microenvironments mentioned
`above, in which charges are "solvated" by shells
`of protein dipoles. These issues have been ana(cid:173)
`lyzed extensively elsewhere.8 A fully integrated
`view of polarity of the protein interior is s till to
`emerge.
`
`Results
`pK. values of the buried side-chains of 92E
`and 92K
`
`A hyperstable v ariant of wild-type s taphylo(cid:173)
`coccal nuclease (truncated .i + PHS), w hich we
`term the parental protein (see Materials and
`
`Methods), was used as the starting material for
`making I92E and I92K mutant proteins. Equi(cid:173)
`librium GnHCI denaturations, monitored by fluor(cid:173)
`escence, were then performed for each mutant
`in the appropriate pH range to get accurate .iG'
`values of the unfolding process at different pH
`values, assuming a reversible two-state transition .3
`The results are shown in Figure 1. The s tability of
`the parental protein showed a broad range of
`pH-independence from pH 4.5 to 9.0. In contrast,
`the stability of I92E and I92K exhibited a pro(cid:173)
`nounced pH dependence (Figure 1). This s tron g
`pH dependence is due to the presence of an
`ionizable group, the side-chain of glutamic acid or
`lysine at position 92. It is explained quantitatively
`by thermodynamic analysis, under the assumption
`that the remaining !Rs of the I92E and I92K mutant
`proteins do n ot show differences in behavior from
`those in the parental. The side-chains of 92E and
`92K are deeply buried in the hydrophobic core
`and far way from other polar and ionizable side(cid:173)
`chains in the proteins as shown in the crystal
`s tructures.
`Using thermodynamic analysis (see Materials
`and Methods), we calculated pK~ and pK;>, the
`pKa v alues of the buried and solvent-exposed
`
`12
`
`10
`
`8
`
`-";
`~ 6 -"' C :;; :e C
`
`0
`E
`ni u
`
`::,
`(!)
`<]
`
`4
`
`2
`
`0
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`
`11
`
`pH
`Figure 1. pH dependence of the stability .:iG 0 with respect to denaturation of the parental .:i + PHSt (open circles),
`.:i + PHSt/I92E (filled triangles) and .:i + PHSt/ I92K (squares) proteins as determined from GnHCI titrations
`monitored by fluorescence at 25 °c and in 100 mM NaO .
`
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`568
`
`(a)
`
`MG
`
`(b)
`
`MG
`
`-4
`
`-6
`
`-6
`
`-7
`
`-8
`
`-8
`
`-10
`
`-1 1
`
`-4
`
`-6
`
`-6
`
`-7
`
`-8
`
`-8
`
`-10
`
`-11
`
`Buried Glu and Lys in Staphylococcal Nuclease
`
`• •
`
`•
`
`•
`
`6
`
`8
`
`10
`
`pH
`
`•
`
`Figure 2. pH dependence of the
`relative stability, MG0 = ace ..
`AG~.,., of (a) 6 + PHSt/l92E and
`(b) 6 + PHSt/l92K with respect to
`the stability of the parental protein,
`where AG e .. is the stability of the
`individual variants and AG~ .. is the
`stability of the parental protein.
`The correlation coefficient R2 = 0.98.
`The values of pK);' and pl<!' lie
`at the flex points at both ends of
`each curve.
`
`6
`
`8
`pH
`
`9
`
`10
`
`11
`
`side-chains, for E92 and K92 (Figure 2). There is
`som e uncertainty in d etermining the value of p~
`of the side-chain of 92K because this variant
`is unstable below pH 5.5. Thus, the calculated
`~c0 value, and consequently ~~C0
`, have large
`uncertainties at low pH for 192K. The value of
`p~ of the side-chain of 92K is found to be 5.6
`(Table 1). The pK~ value of the side-chain 92E is
`well determined at 8.65.
`The values we de termined for the p~ of the
`side-chain of both E92 and K92 are different from
`the published values of small molecules. These
`differences are analyzed in Discussion.
`
`Table 1. Calculated values of pK?, pK);' and "•PP for the
`variants l92E and 192K
`
`192E
`
`5.54 (4.4)
`8.65
`14.89
`
`1921<
`
`9.44 (10.2)
`5.62
`12.70
`
`The values in parentheses refer to the pK. values obtained for
`the side chains of the free amino acids in solution.
`
`We used the Born approximation (see Mate rials
`and Methods), to estimate values for "•PP from
`pK~ and pK!_) of the side-chain of either glutarnic
`acid or IX5ine at position 92 (Table 1) as
`described.9 The calculated values of "•PP are in
`the range of 10 to 12 instead of 2 to 4 that are
`commonly associated with the protein interior.
`A careful analysis of errors in the calculation of
`"•PP based on the Born approximation is given by
`Dwyer etal.2
`
`Crystallographic structures of 192E and 192K
`
`To explore the environment of the buried resi(cid:173)
`dues, the structures of mutant I92E (at cryo and
`room temperatures) and 192K (at cryo temperature)
`were determined by X-ray crystallography. The
`crystals of both variants were grown at a pH at
`which the buried side-chains of I92E and 192K
`were uncharged. When the s tructures of these
`variants are superimposed, no apparent backbone
`alte rations are observed. Both side-chains are
`buried completely inside the well-defined hydro(cid:173)
`phobic core of the variant proteins (Figure 3),
`
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`Buried Glu and Lys in Staphylococcal Nuclease
`
`569
`
`(a)
`
`N
`
`C
`
`(b)
`
`Figure 4. Close-up view of the hydrogen bonding
`pattern of the E92 side-chain, the four internal and the
`two bridging water molecules which form a chain from
`the protein interior to the bulk solvent. Atoms are
`colored according to atom type: carbon, grey; nitrogen
`blue; and oxygen, red.
`
`K92 conf.2
`
`C
`
`Figure 3. Ribbon representation of the superposition of
`the I92E cryo (cyan) and (a) I92E room temperature (red)
`structures and (b) the I92K cryo structure. (a) The side-
`chain of 92E in both cryo (blue) and room temperature
`(orange) adopts an identical conformation. The blue
`spheres represent the four completely buried and the
`two bridging water molecules seen in the I92E cryo
`structure. (b) The two conformations of 92K as observed
`in the I92K cryo structure with hydrophobic residues
`that surround conformers 1 (magenta) and conformer 2
`(green) within 4 A˚ .
`
`without forming salt-bridges or hydrogen bonds to
`other functional groups of the protein.
`In the cryo structure of the I92E variant, there is
`a ring of four water molecules, not present in the
`wild-type, which hydrate one oxygen atom of
`the carboxyl group of 92E (Figure 3(a)). The other
`oxygen atom of the side-chain makes only van der
`Waals contacts. These water molecules are held
`together by a network of hydrogen bonds among
`them. They also interact with the side-chain of
`92E, the backbone amide group of residue 18,
`and the carbonyl groups of residues 19 and 20
`(Figure 4). Two other water molecules, which are
`also present in the wild-type, are connected to the
`water ring buried inside the hydrophobic core.
`Thus, a channel of water molecules connects the
`side-chain of glutamic acid at position 92 outward
`to the bulk solvent (Figure 3(a)). The contrast
`with the variant V66E is interesting, since both
`66E carboxylic oxygen atoms are bound to water.
`Interior water molecules have not been visual-
`ized in the I92E variant room temperature struc-
`
`ture, or in the cryo structure of the I92K variant.
`In the case of the I92K variant structure, the lysyl
`group shows conformational variability and high
`mobility, and populates at least two side-chain
`conformations (Figures 3 and 5).
`
`K92 conf.1
`
`......
`
`Figure 5. The two conformations of 92K built into the
`2Fo
`Fc (blue) and Fo
`Fc (magenta) electron density
`maps, contoured at 1s and 3.5s respectively, calculated
`from a model that had alanine at position 92. The sub-
`sequent refinement of the model with the alternate 92K
`conformations showed no electron density for the Cd
`and Nz atoms for conformer 1 or for the Nz for conformer
`2, which is indicative of increased mobility of the 92K
`side-chain. The electron density maps displayed might
`suggest the native isoleucine at this position. The lysine
`mutation was confirmed by DNA sequencing and mass
`spectrometry (data not shown). Moreover, none of the
`four most frequent isoleucine conformers could be built
`into these electron density maps (see Supplementary
`Material).
`
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`570
`
`Discussion
`
`pKa values in the denatured state
`
`The values of pKD
`a of the side-chains of both
`glutamic acid and lysine 92 (Table 1) are different
`from the classic values reported for the free amino
`acids in the literature. These discrepancies may
`indicate that those side-chains are not completely
`exposed to the solvent when the variant proteins
`unfold. This observation is consistent with what
`we know about the unfolding process of staphylo-
`coccal nuclease.10,11 In addition, the variant proteins
`I92E and I92K are denatured at low concentrations
`of GnHCl (1 – 1.5 M). Thus, these values of pKD
`a
`indicate that the variant proteins retain residual
`structure or interactions when they unfold. In con-
`trast, at position 66 the values of pKD
`a measured
`for K and E are very close to these classic values.
`Also, recent studies (E. B. Garcı´a-Moreno, personal
`communication) show that substitutions of K and
`E into many internal sites in nuclease give rise
`to similarly aberrant pKD
`a values. These values are
`determined by the flex points of
`the titration
`curve, and could be biased.
`The use of our experimentally measured pKD
`a
`values to calculate the energy of charge transfer,
`and thus determine the apparent dielectric con-
`stant of the protein via the Born approximation
`requires the value of the dielectric constant of the
`environment surrounding the ionizable residue in
`the denatured state (with presumed residual struc-
`ture). This value is not known. Since the pKa values
`of the completely exposed glutamic acid and lysine
`side-chains are known from the literature, we used
`them in conjunction with the pKN
`a values obtained
`by non-linear least-squares analysis to calculate
`the energy needed to transfer a charge from the
`solvent to the protein interior.
`A key issue in the interpretation of pKN
`is
`a
`whether the charging of the buried group is linked
`to unfolding.3 In the case of locus 66 we deter-
`mined unequivocally that the variant molecules
`the pKN
`remained globally folded at
`a value of
`the buried group. In the case of I92K, however, the
`data suggest that the pKN
`a value is affected by glo-
`bal unfolding. This means that the values of DGbur
`that we have determined represent a lower limit
`for the actual process (an upper limit for 1 app.)
`Heuristically, one can understand the relation
`between all these quantities using the following
`argument. The process of transferring a charged
`group from water to the protein interior can be
`broken up into two steps. First,
`remove the
`charged group from water to the vacuum. Second,
`transfer the charge from the vacuum to the protein
`interior. In step 1, relatively strong electrostatic
`interactions are broken, those between the water
`dipoles and the solvated charge. The process of
`removing the charge is expensive. When the
`charged group is transferred to the protein interior,
`there are two effects. One is geometrical and pH
`independent, arising from the changed shape of
`
`Buried Glu and Lys in Staphylococcal Nuclease
`
`the side-chain. A second is electrostatic: some of
`this energy is recouped through new electrostatic
`interactions between the charged group and
`elements in the protein core. The difference in
`energy between these two steps is DGbur. These
`charge – protein interactions are typically much
`weaker than those in step 1. Their exact strength
`depends on the polarizability of nearby protein
`groups. This polarizability is determined,
`for
`example, by the mobility of fixed dipoles and the
`response of polar side-chains to interaction with
`fixed dipoles. The greater the polarizability the
`more energy is recouped in step 2, and the smaller
`is DGbur. Thus, the higher the protein polarizability,
`the smaller the DGbur value. Finally, the pKa value
`of a group is related to the energy needed to create
`a charge, and a shift in pKa value is proportional to
`DGbur. The more polarizable the protein interior, the
`smaller the shift in pKa value.
`
`Ordered and disordered water molecules in the
`protein interior
`
`The I92E variant shows ordered buried water
`molecules under cryo conditions, but no ordered
`water at room temperature. In the case of the cryo
`structure of the I92K variant, no water molecules
`were observed in the hydrophobic core. However,
`the relatively high polarity of their respective core
`environments, as indicated by the shifts in the pKa
`values of these groups, suggests that there may be
`disordered or transient water molecules present.
`Thus, one must be cautious about this assertion,
`since in I92K charging of the lysyl group is linked
`to global unfolding. The failure to observe water
`molecules in the protein interior of the I92E variant
`room temperature structure may be due to the fact
`that at room temperature, the enthalpy of hydro-
`gen bond formation is not able to overcome the
`loss of entropy of the disordered water, therefore
`implying a rather flat energy profile for water
`ordering. In the case of the I92K variant, the hydro-
`gen bonding propensity of the lysyl side-chain is
`not sufficient to promote the ordering of transient
`water molecules even at cryo temperature. Instead,
`the buried lysyl group lowers its free energy by
`increasing its entropy due to conformational varia-
`bility and mobility. Thus, the two variables that
`seem to determine the order – disorder state of the
`water molecules in the protein interior are the
`identity of the buried amino acid and the tempera-
`ture at which the crystal structure is determined.
`The probes 92E and 92K that we engineered at
`position 92 report an environment of much higher
`polarity than commonly thought, a polarity similar
`to that at locus 66, as revealed by our previous
`measurements.2 This is so despite the difference in
`the microenvironments of the two sites mentioned
`earlier. Indeed, the two extra water molecules that
`are observed at position 92 occupy positions taken
`by carboxyl oxygen atoms in the variant E66. The
`burial of water molecules in association with the
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`Buried Glu and Lys in Staphylococcal Nuclease
`
`571
`
`ionizable side-chains clearly makes a significant
`contribution to this high polarity.
`To address the effect of the observed confor-
`mational variability and mobility on the value of
`the dielectric constant
`in the case of the I92K
`mutant, we must have an estimate of the magni-
`tude of the dipole fluctuations corresponding to
`the two observed conformers. We therefore com-
`pared the root-mean-square (rms) difference in the
`positions of the atoms of the two conformers after
`separate energy minimization. The rms difference
`for all backbone atoms is 0.2 A˚ and for all side-
`chain atoms is 0.56 A˚ . There is practically no
`positional difference for the backbone atoms of the
`two K92 conformers, but a large rms difference of
`3.6 A˚ is found for the side-chain atoms, with the
`largest difference observed between the two Nz
`atoms, which are separated by a distance of
`4.88 A˚ . The rms difference in the positions of the
`side-chain atoms of the two conformers represents
`an upper limit on the magnitude of the positional
`fluctuations of the Nz atom and consequently on
`the fluctuations of the dipole moment. The two
`conformers in fact represent the two most fre-
`quently observed rotamers for the lysyl side-chain
`in crystal structures and, since their interconver-
`sion in the protein interior will require major struc-
`tural
`rearrangements, we may neglect
`the
`positional fluctuations that would arise from such
`transitions and consider only the positional fluctu-
`ations of the side-chain atoms within each confor-
`mer. Thus, the fluctuations in the positions of the
`side-chain atoms in the two observed conformers
`will be much smaller than those estimated from
`the rms difference in the positions of the side-
`chain of the two conformers and will be of the
`order of 1 A˚ . The lysyl side-chain that attains a par-
`ticular rotamer conformation can be considered to
`be in a local energy minimum and cannot undergo
`large displacements (motions). The values of 1 app
`that we have measured represent,
`in a certain
`sense, a spatially averaged quantity (dielectric
`property) of the region that is accessed by the K92
`side-chain. The large positional fluctuations (rela-
`tive to positional fluctuations that are observed for
`atoms in the protein hydrophobic core) are loca-
`lized around the Nz atom and they correspond to
`large dipole fluctuations that undoubtedly contrib-
`ute to the high value of the observed apparent
`dielectric constant. The question is whether they
`account for all of the increase in 1 app from the
`value of 4.
`The effect of the mobility of the lysyl side-chain
`at position 92 on the local 1 app can be estimated by
`either its effect on the microscopic susceptibility
`tensor as described by Simonson et al.12 or by a Fro¨ -
`lich – Kirkwood type of argument as first applied to
`proteins by Gilson & Honig13 and as implemented
`also by Smith et al.14 and Simonson & Perahia.15
`The correlation between the generalized suscepti-
`bility and the local atomic mobility is very difficult
`(or even impossible) to estimate from the crystallo-
`graphic data, since it involves the evaluation of the
`
`the instantaneous
`mean correlation matrix of
`dipoles.16 While it is rather straightforward to esti-
`mate the diagonal element of the dipole correlation
`matrix due to the positional fluctuation of the Nz
`atom, it is impossible to evaluate the off-diagonal
`elements, since this involves the cross-correlation
`of positional displacements (fluctuations) between
`different atoms. As pointed out by Simonson
`et al.,12 based on molecular dynamics simulations
`of tuna ferricytochrome c, the diagonal and off-
`diagonal elements of the dipole – dipole correlation
`matrix tend to cancel each other. Thus, the follow-
`ing discussion will be based on the macroscopic
`theory of dielectrics.13 When we use the expression
`for the dielectric formula (equation (5) or (11)13
`with a value of 3 for the high frequency dielectric
`constant and 4 for the dielectric constant of the pro-
`tein) we find that a twofold increase in the dipole
`moment fluctuation per unit volume due to the
`permanent dipoles in the protein will lead to a
`dielectric constant of 13, a number that coincides
`with the experimentally observed value for the
`two mutants. In addition, when equation (3) of
`Smith et al.17 is used, which relates the dipole
`moment fluctuation density to the static dielectric
`constant, assuming a dielectric constant of 70 for
`the reaction field dielectric and a dielectric constant
`of 4 for the cavity, a fourfold increase in the dipole
`moment fluctuation will result in a dielectric con-
`stant of 13.8.
`Molecular dynamic simulations by Simonson &
`Perahia15 have shown in the case of cytochrome c
`that when charged surface side-chains are included
`as part of the protein, the mean-square dipole fluc-
`tuation of the protein, kDM2l, is five to eight times
`larger than the value when the surface charged
`side-chains are treated as part of the solvent with
`the major contribution coming from the self-
`correlation of the charged side-chains. In addition,
`it was found that some of
`the charged side-
`chains contribute individually to kDM2l as much
`as the uncharged side-chains in total. In the case
`of the I92K mutant where the lysyl side-chain
`adopts two conformations and electron density in
`Fc map, contoured at 1s, is observed up
`the 2Fo
`to and including Cg and Cd atoms for the respective
`conformers and the mobility of the side-chain is
`significantly restricted as compared to a surface
`lysyl side-chain, it is unlikely that the contribution
`of the 92K side-chain to the mean-square dipole
`fluctuation could double its value.
`
`Transiently buried water molecules
`
`These buried water molecules form a charac-
`teristic ring structure. This burial has now been
`observed in both a loosely and a tightly packed
`environment. Furthermore, we have observed the
`association with the side-chains in an un-ionized
`state, when its strength should be much less than
`when the side-chains are ionized. These obser-
`vations have led us to propose a much more
`general hypothesis, that protein molecules in their
`
`Bausch Health Ireland Exhibit 2044, Page 7 of 10
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`572
`
`Buried Glu and Lys in Staphylococcal Nuclease
`
`native state are randomly and transiently pene-
`trated by water molecules, and thus contain, on
`average, more water molecules than is currently
`believed. These water molecules would not be
`site bound, but would penetrate transiently and
`at many locations, so that
`they would not be
`observed by techniques such as X-ray crystallogra-
`phy and NMR that describe an average structure.
`This results in a protein molecule whose interior is
`more polar than expected, and which is subject to
`significant fluctuations in solvent content.
`It is useful to summarize the various experi-
`mental and conceptual points that led us to the
`TBW hypothesis.
`
`second, shallower, minimum occurs when
`two methane molecules are separated by a
`single water molecule. This provides a
`physical
`justification for
`the presence of
`water molecules in hydrophobic clefts in a
`protein molecule.
`
`These points are listed not to prove the hypo-
`thesis but to justify its further consideration.
`In accordance with this hypothesis the ordered
`water molecules that we see in the interior of the
`I92E cryo crystal structure represent typical tran-
`sient solvent penetration, stabilized by interactions
`with the buried ionizable group and that part of
`the protein backbone lining the hydrophobic core.
`
`(1) Support for this idea comes not only from
`our own work but also from computer
`simulations by Angel Garcı´a and Gerhard
`Hummer. Their work has shown that water
`penetrates quite readily into certain regions
`of cytochrome c. They found, for example,
`that in a 1.5 ns trajectory there were over
`200 events in which water molecules made
`their way to the interior of the proteins, and
`stayed there for at least 5 ps. Twenty-seven
`molecules stayed for at least 300 ps.18,19 They
`have obtained similar, unpublished results
`for nuclease.
`(2) Our X-ray studies of nuclease show that well-
`localized water molecules are often seen in
`the hydrophobic core in association with
`polar residues placed there by site-directed
`mutagenesis. How did these water molecules
`get
`there? Obviously what
`is required is
`some sort