doi:10.1016/j.jmb.2009.03.039
`
`J. Mol. Biol. (2009) 389, 34 47
`
`Available online at www.sciencedirect.com
`
`The pKa Values of Acidic and Basic Residues Buried at
`the Same Internal Location in a Protein Are Governed by
`Different Factors
`
`Michael J. Harms1, Carlos A. Castañeda1, Jamie L. Schlessman1, 2,
`Gloria R. Sue1, Daniel G. Isom1, Brian R. Cannon1
`and Bertrand García-Moreno E.1⁎
`
`1Department of Biophysics,
`Johns Hopkins University, 3400
`North Charles Street, Baltimore,
`MD 21218, USA
`2Department of Chemistry,
`United States Naval Academy,
`572 Holloway Road, Annapolis,
`MD 21402, USA
`
`Received 4 December 2008;
`received in revised form
`6 March 2009;
`accepted 11 March 2009
`Available online
`24 March 2009
`
`Edited by C. R. Matthews
`
`Introduction
`
`The pKa values of internal ionizable groups are usually very different from
`the normal pKa values of ionizable groups in water. To examine the
`molecular determinants of pKa values of internal groups, we compared the
`properties of Lys, Asp, and Glu at internal position 38 in staphylococcal
`nuclease. Lys38 titrates with a normal or elevated pKa, whereas Asp38 and
`Glu38 titrate with elevated pKa values of 7.0 and 7.2, respectively. In the
`structure of the L38K variant, the buried amino group of the Lys38 side
`chain makes an ion pair with Glu122, whereas in the structure of the L38E
`variant, the buried carboxyl group of Glu38 interacts with two backbone
`amides and has several nearby carboxyl oxygen atoms. Previously, we
`showed that the pKa of Lys38 is normal owing to structural reorganization
`and water penetration concomitant with ionization of the Lys side chain. In
`contrast, the pKa values of Asp38 and Glu38 are perturbed significantly
`owing to an imbalance between favorable polar interactions and unfavor-
`able contributions from dehydration and from Coulomb interactions with
`surface carboxylic groups. Their ionization is also coupled to subtle struc-
`tural reorganization. These results illustrate the complex interplay between
`local polarity, Coulomb interactions, and structural reorganization as deter-
`minants of pKa values of internal groups in proteins. This study suggests
`that improvements to computational methods for pKa calculations will
`require explicit treatment of the conformational reorganization that can
`occur when internal groups ionize.
`
`© 2009 Elsevier Ltd. All rights reserved.
`Keywords: pKa values; internal ionizable groups; structure/function; energy
`calculations; electrostatics
`
`A small fraction of ionizable residues in proteins
`are sequestered from water and buried in the protein
`interior.1–3 These internal
`ionizable groups are
`essential for catalysis,4–6 H+/e
`transport,7–10 and
`molecular recognition.11 The pKa values of internal
`ionizable groups are usually different from the
`normal pKa values in water12–19 and are often tuned
`
`*Corresponding author. E-mail address:
`bertrand@jhu.edu.
`Abbreviations used: SNase, staphylococcal nuclease;
`THP, thymidine-3′,5′-diphosphate; HSQC, heteronuclear
`single quantum coherence; MCCE, multi-conformer
`continuum electrostatics; PDB, Protein Data Bank.
`
`0022 2836/$ see front matter © 2009 Elsevier Ltd. All rights reserved.
`
`for specific biological purposes.4 Understanding the
`determinants of these pKa values is important for
`quantitative description of the structural basis of
`function in a large variety of biological processes.
`The shift in the pKa of an internal group relative
`to the normal pKa in water is governed by diffe-
`rences in the polarity and polarizability experienced
`by the charge in the two environments (ΔGself) and
`by Coulomb interactions with the charges of other
`ionizable groups. Structural reorganization of the
`protein coupled to the ionization of internal groups
`can also influence their pKa. One of the goals of
`this study was to examine the relative magnitude
`of these three determinants of the pKa values of
`internal groups.
`The polarity and polarizability in the protein
`interior are usually lower than those in bulk water;
`
`Bausch Health Ireland Exhibit 2045, Page 1 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`pKa Values of Internal Groups
`
`35
`
`therefore, ΔGself is generally unfavorable for buried
`ionizable groups. For this reason, the pKa values of
`internal ionizable groups are usually shifted in the
`direction that favors the neutral state (i.e., increase in
`pKa for acidic groups and depression for basic
`ones).12–18 Surprisingly, the apparent polarity and
`polarizability in the protein interior reported by
`internal ionizable groups are not as low as pre-
`viously thought.15–17,20–25 In some cases, hydrogen
`bonds (i.e., high polarity) can actually compensate
`fully for the loss of hydration experienced by a
`charged atom inside a protein (M.J.H., J.L.S., G.R.S.,
`and B.G.-M.E, unpublished results).6,19
`Coulomb interactions between surface charges are
`usually weak because charges are screened effec-
`tively by water.26–30 In contrast, the Coulomb inter-
`action of ion pairs sequestered from bulk solvent
`at protein–protein interfaces can be quite strong
`(3–5 kcal/mol).31 Coulomb interactions between sur-
`face and internal groups in protein active sites have
`never been studied directly. Surface ionizable groups
`have been shown to have small but observable
`effects on enzyme activity.32–34 Even if the effects are
`small, the sum of many small interactions could lead
`potentially to a large effect.35,36 A complete under-
`standing of interactions between internal and surface
`charges is necessary to understand contributions of
`surface ionizable residues to the properties of
`internal groups at active sites and interfaces.4
`Staphylococcal nuclease (SNase) is an excellent
`model system for studying properties of internal
`ionizable groups systematically and for dissecting
`molecular determinants of their pKa values. It has
`been shown that hyperstable variants of SNase
`can tolerate substitutions of 25 internal positions
`with Lys, Asp, Glu, and Arg.37 The majority of
`these internal
`ionizable groups titrate with pKa
`values shifted in the direction that promotes the
`neutral state, some by as much as 5.7 pKa units
`(M.J.H., J.L.S., G.R.S., and B.G.-M.E, unpublished
`results).15,16,22,23,25,38 We have shown previously
`that, although Lys38 in SNase is internal, it titrates
`with a normal or possibly elevated pKa value. The
`pKa is not depressed despite the amino group being
`secluded from bulk water in the crystal structure;
`water penetration facilitated by structural relaxa-
`tion ensures hydration of the charged group.38 In
`contrast, we show here that the pKa of Glu38 and
`Asp38 is shifted significantly. The differences in the
`ionization behavior of Lys, Glu, and Asp at position
`38 in SNase offer opportunities to examine con-
`tributions by the reaction field of bulk solvent, local
`polarity and polarizability, conformational reorga-
`nization, and Coulomb interactions to the pKa
`values of these internal ionizable groups.
`
`Results
`
`Crystal structure of the L38E variant
`
`Two hyperstable variants of SNase were used in
`this study: PHS and Δ+PHS. The structure of the
`
`PHS/L38E variant was solved to 2.0 Å and com-
`pared to the structures of PHS nuclease and the
`PHS/L38K variant.38,39 Refinement statistics are
`shown in Supplementary Table 1. PHS nuclease
`was used for crystallographic studies instead of the
`Δ+PHS form of nuclease that was used for equi-
`librium thermodynamic and NMR spectroscopy
`experiments because PHS/L38E crystallized and
`Δ+PHS/L38E did not. PHS nuclease contains six
`residues (44–49) in a dynamic loop and two point
`mutations (F50G and N51V) that are not present in
`Δ+PHS nuclease. The structures of Δ+PHS and PHS
`variants are superimposable.39,40
`The overall structure of the PHS/L38E variant
`is comparable to the structures of PHS nuclease
`(Cα RMSD = 0.7 Å) and of the PHS/L38K variant
`(Cα RMSD = 0.4 Å), even in the region surrounding
`Glu38 (Fig. 1a). The primary difference between the
`PHS/L38E and PHS/L38K structures is the position
`of Glu122. This residue is in the same position in the
`structure of PHS and PHS/L38E, whereas the Cδ of
`Glu122 is shifted by 1.6 Å to establish a Lys38/
`Glu122 ion pair in the structure of PHS/L38K.38
`Residues 113–115 in the structure of PHS/L38E are
`
`Fig. 1. Crystal structure of PHS/L38E (pink, PDB
`accession code 3D6C) overlaid on the structures of PHS/
`L38K (blue, PDB accession code 2RKS) and PHS nuclease
`(white, PDB accession code 1EY8). (a) The global fold of the
`protein is not perturbed. The Cα atoms of Asp and Glu
`residues are shown as red spheres. Glu38, Lys38, and
`Glu122 are shown as sticks. (b) Microenvironment of
`Glu38 and Lys38. Ionizable residues within 8.4 Å of Glu38
`are shown in stick, and hydrogen bonds are shown as
`broken lines.
`
`Bausch Health Ireland Exhibit 2045, Page 2 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`36
`
`pKa Values of Internal Groups
`
`in a slightly different conformation than in the
`other structures owing to the presence of an inhi-
`bitor [thymidine-3′,5′-diphosphate (THP)] that is
`present in the structure of PHS/L38E nuclease and
`absent in the other structures.
`The oxygen atoms of the Glu38 side chain are
`completely solvent inaccessible in the structure of
`PHS/L38E. The nearest crystallographic water
`molecule is 5.4 Å from the Glu38 Oε1 atom. Thus
`far, this is the only crystal structure of an SNase
`variant with an internal oxygen atom in which the
`atom is not hydrated by an internal water mole-
`cule.16,41 Interactions with internal water molecules
`might be precluded by hydrogen bonds between
`the carboxylic group of Glu38 and the backbone
`amides of Thr120 and His121 and the hydroxyl
`group of Tyr91 (Fig. 1b). The hydrogen bond to
`Tyr91 directly links Glu38 into an extensive hydro-
`gen bond network.29,30,42,43
`Although SNase is a basic protein, the ionizable
`residues nearest to Glu38 in the crystal structure of
`the PHS/L38E variant are acidic: Asp77 (4.0 Å) and
`Glu122 (5.1 Å). The next nearest ionizable residues
`are basic: His121 (6.5 Å) and Arg126 (6.6 Å) (Fig. 1b).
`The proximity of these residues makes them ideal
`for direct measurement of Coulomb interactions
`between surface charges and the carboxylic groups
`of Asp38 and Glu38.
`
`pKa values of Glu38 and Asp38
`
`The pKa values of Glu38 and Asp38 were mea-
`sured by analysis of the pH dependence of protein
`stability. This method takes advantage of
`the
`thermodynamic linkage between proton binding
`and stability.44 Measurement of the unfolding free
`energy (ΔG°H2O) of a protein as a function of pH
`reports on the pKa values of all ionizable residues
`in the protein. The pKa value of a single group
`introduced by mutagenesis can be measured by
`subtracting ΔG°H2O of the background protein (i.e.,
`the variant
`from ΔG°H2O of
`Δ+PHS nuclease)
`protein (i.e., Δ+PHS/L38E). Shifts in the pKa are
`reflected in the characteristic shape of the pH depen-
`dence of ΔΔG°H2O.15,23,25 It was shown previously
`that the pKa of Lys38 was ≥10.4, comparable to the
`normal pKa of a Lys in water.38 In contrast, the pKa
`values of Glu38 and Asp38 were 7.0 ± 0.3 and 6.8 ±
`0.3 pH units, respectively (Fig. 2). Relative to the
`normal pKa values of 4.4 and 4.0 for Glu and Asp in
`water, respectively, this corresponds to shifts in pKa
`of 2.6 and 2.8 pH units.
`The measurement of pKa values by analysis of the
`pH dependence of stability is too imprecise for de-
`tailed investigation of the contribution of Coulomb
`interactions to the observed pKa value. An attempt
`was made to measure the pKa of Glu38 with NMR
`spectroscopy using the pH dependence of the Glu38
`Cδ resonance.40 Although the Cδ resonance could be
`assigned at low pH, the peak entered intermediate
`exchange above pH 5.6 and could not be followed at
`higher pH values. Resonances corresponding to the
`Cγ/Cδ atoms of Glu73, Glu75, Asp77, Asp83, and
`
`Fig. 2. pH dependence of ΔΔG°H2O for the Δ+PHS/
`)
`L38D ( ), Δ+PHS/L38E ( ), and Δ+PHS/L38K (
`variants. Continuous lines are fits to the data (see
`Materials and Methods). Error bars are propagated from
`GdnHCl denaturation fit errors.
`
`Glu122 all showed a secondary apparent titration
`centered at pH 7.0. At positions 75 and 77, the
`magnitude of the secondary transition was greater
`than 0.5 ppm. All of the data from NMR spectro-
`scopy are consistent with a pKa of 7.0 for Glu38.
`The pKa of Glu38 was also obtained by performing
`a global fit to the pH titrations of multiple reso-
`nances.45,46 Specifically, the pKa was obtained by
`analysis of the pH dependence of the 1H chemical
`shift of six backbone amides (Thr33, Phe34, Arg35,
`Glu75, Gly88, and Leu89). The titration events
`monitored by these amide backbone atoms in
`Δ+PHS nuclease are shown in Fig. 3a. No changes
`larger than 0.06 ppm were observed over the pH
`range studied. A small
`transition centered at
`pH 6.3 ± 0.3 is visible for positions 34, 35, 75, and
`89, most likely reflecting the titration of His8 or
`Asp21, whose pKa values are both 6.5 in Δ+PHS
`nuclease.40 In contrast, the pH dependence of the 1H
`chemical shift of the same six amides in the Δ+PHS/
`L38E variant (Fig. 3b) reflects a large transition. A
`global fit of the modified Hill equation to this tran-
`sition yielded a pKa value of 7.0 ± 0.1, in excellent
`agreement with the pKa of Glu38 determined using
`linkage thermodynamics and the value inferred
`from the titration of carboxylic acids. A similar ana-
`lysis of the L38D variant showed that Asp38 has a
`pKa of 7.2 ± 0.1, which is also in agreement with the
`value of 6.8 ± 0.3 obtained by analysis of the pH
`dependence of stability of the Δ+PHS/L38D var-
`iant. The pKa values extracted by global fit of NMR
`spectroscopy data and by linkage analysis are sum-
`marized in Table 1.
`The agreement between the pKa values measured
`from equilibrium thermodynamic data and from the
`global fit of titrations of backbone amide resonances
`suggests that the values obtained by NMR are
`
`Bausch Health Ireland Exhibit 2045, Page 3 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`pKa Values of Internal Groups
`
`37
`
`Table 2. pKa values and Hill coefficients of His residues
`measured using NMR spectroscopy
`
`His8
`
`a
`Variant
`pKa
`Δ+PHS
`6.6
`Δ+PHS/E122Q
`6.5
`Δ+PHS/L38K
`6.5
`Δ+PHS/L38E
`6.5
`Δ+PHS/L38E/E122Q
`6.4
`Δ+PHS/L38D
`6.5
`Δ+PHS/L38D/E122Q
`6.5
`a Uncertainty in pKa value is ±0.1.
`
`n
`1.0
`1.0
`1.0
`1.0
`1.1
`1.0
`1.1
`
`His121
`a
`pKa
`5.4
`5.3
`5.6
`5.7
`5.7
`5.7
`5.8
`
`n
`0.8
`0.9
`1.0
`0.9
`0.9
`0.9
`0.9
`
`This demonstrates that none of these groups are
`responsible for the apparent titration near pH 7
`monitored with NMR spectroscopy. The 1H chemi-
`cal shifts of multiple groups appear to be reporting
`on the proton titration of Asp38 or Glu38.
`
`Spectroscopic probes of structural
`rearrangement
`
`Structural reorganization associated with the sub-
`stitution of Leu38 with Asp or Glu or with the ion-
`ization of Asp, Glu, and Lys at position 38 was
`probed by circular dichroism (CD), Trp fluorescence,
`and NMR spectroscopy. The intrinsic fluorescence of
`Trp140, which caps the C-terminal end of helix 3, has
`been shown to be a robust reporter of the global
`integrity of SNase.47 Trp fluorescence at neutral pH
`was insensitive to the substitution of Leu38 with
`ionizable groups (data not shown). CD spectra of all
`variants in the far-UV range were also indistinguish-
`able from one another at pH 4, 7, and 10 (Fig. 4),
`
`Table 3. pKa values of Asp and Glu residues measured
`using NMR spectroscopy
`
`Δ+PHS/L38E
`b
`c
`pKa
`ΔpKa
`b2.5
`6.6
`3.9
`b2.5
`b2.5
`2.3
`3.8
`3.9
`3.1
`4.4
`4.0
`3.6
`3.8
`3.4
`3.3
`3.9
`3.8
`3.9
`3.8
`4.5
`
`Δ+PHSa
`b
`pKa
`Position
`2.2
`D19
`6.5
`D21
`3.9
`D40
`b2.5
`D77
`b2.5
`D83
`2.2
`D95
`3.8
`D143
`3.9
`D146
`2.8
`E10
`4.3
`E43
`3.9
`E52
`3.5
`E57
`3.8
`E67
`3.3
`E73
`3.3
`E75
`3.8
`E101
`3.9
`E122
`3.8
`E129
`3.8
`E135
`4.5
`E142
`a Castañeda et al.40
`b Uncertainty in pKa value is ±0.1.
`c Uncertainty in ΔpKa value is ±0.1.
`d Acid baseline fixed to Δ+PHS value.
`
`—
`0.0
`0.0
`—
`—
`0.1
`0.0
`0.0
`0.2
`0.0
`0.1
`0.1
`0.1
`0.1
`0.1
`0.1
`−0.1
`0.1
`0.1
`0.0
`
`Δ+PHS/L38K
`b
`c
`pKa
`ΔpKa
`b2.5
`6.5
`3.8
`—
`b2.5
`2.1d
`4.0
`4.0
`3.1d
`4.5
`4.1
`3.6
`3.9
`3.3d
`—
`3.9
`3.9
`3.8
`3.9
`4.6
`
`—
`0.0
`−0.1
`—
`—
`0.0
`0.2
`0.1
`0.2
`0.2
`0.2
`0.1
`0.1
`0.0
`—
`0.0
`0.0
`0.0
`0.1
`0.1
`
`Fig. 3. Apparent titration of 1H backbone resonances
`in Δ+PHS nuclease (a) and the Δ+PHS/L38E variant (b).
`), Arg35 ( ), Glu75 ( ), Gly88
`Series are Thr33 (●), Phe34 (
`(
`), and Leu89 ( ). Lines indicate a global fit to the
`apparent titration of all residues.
`
`accurate. However, the NMR experiment does not
`follow the amino acid of interest directly. Other
`groups could be responsible for the observed
`transition. The pKa values of all residues that titrate
`between pH 4.6 and 8.5 in Δ+PHS nuclease were
`measured in the Δ+PHS/L38E variant to examine
`this possibility. The pKa values of His8, His121, and
`Asp21 were found to be 6.5, 5.7, and 6.5, respec-
`tively, in the Δ+PHS/L38E variant (Tables 2 and 3).
`
`Table 1. Comparison of pKa values determined by linkage
`analysis and NMR spectroscopy
`
`Variant
`Δ+PHS/L38E
`Δ+PHS/L38E/E122Q
`Δ+PHS/L38D
`Δ+PHS/L38D/E122Q
`
`Residue
`Glu38
`Glu38
`Asp38
`Asp38
`
`Linkage
`analysis
`±
`pKa
`7.0
`0.3
`—
`—
`6.8
`0.3
`6.9
`0.3
`
`NMR
`pKa
`7.0
`6.2
`7.2
`6.6
`
`±
`0.1
`0.1
`0.1
`0.1
`
`—, pKa could not be determined using linkage analysis because
`variant unfolds in an apparent three-state manner.
`
`Bausch Health Ireland Exhibit 2045, Page 4 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`38
`
`pKa Values of Internal Groups
`
`At pH 4.5, 137 peaks were evident for Δ+PHS
`nuclease, 138 for the Δ+PHS/L38E variant, and only
`125 for the Δ+PHS/L38K variant. In the spectrum of
`Δ+PHS nuclease, only three peaks in the region of
`interest entered intermediate exchange (i.e., milli-
`second timescale) with increasing pH: Tyr113 dis-
`appeared above pH 5.7; Lys116 and Gly117 dis-
`appeared above pH 7.2. Larger changes were
`observed in the spectrum of
`the Δ+PHS/L38E
`variant. The peaks for seven residues (78, 80, 114,
`and 117–120) all entered exchange above pH 6.3,
`concomitant with ionization of Glu38. Without
`further information, it cannot be determined if this
`is due to structural relaxation or due to the change in
`the electrostatic environment of the groups owing to
`the ionization of Glu38. Changes in proton chemical
`shift as large as 0.4 ppm were also observed in helix
`3 (residues 123–130), around Tyr91 (residues 88–92),
`and in the residues adjacent in sequence to position
`38 (residues 34–39).
`Unlike Glu38 and Asp38, Lys38 was ionized over
`the entire pH range under investigation. Twelve
`peaks are missing in this spectrum at all pH values
`studied. Of
`these, nine peaks correspond to a
`contiguous stretch from Tyr113 to Glu122 (Fig. 4).
`The remaining three missing peaks are Lys38, Lys78,
`and Gln80. Changes in 15N–1H chemical shifts
`should not be overinterpreted;49 however,
`the
`absence of these peaks is consistent with increased
`exchange of the amide protons with solvent. This
`interpretation is also consistent with the previous
`investigation of the L38K variant and with the
`measured pKa value of His121 (see next section).38
`Overall, the changes in chemical shift are smaller in
`the Lys38 variant than in the Glu38 variant, having a
`maximum shift of 0.2 ppm. The largest changes are
`limited to the N-terminal end of helix 3.
`
`Structural reorganization probed with His121
`
`The properties of His residues of SNase have been
`characterized extensively.29,30 Changes in the micro-
`environments of His residues can be probed by
`measuring their pKa values by 1D 1H NMR, a
`method that has high accuracy and precision
`N0.1 pH units. The Δ+PHS variant of nuclease
`only contains two of the four His residues normally
`present in wild-type SNase: His8 and His121. In
`Δ+PHS nuclease, His8 and His121 titrate with pKa
`values of 6.6 and 5.4, respectively. The pKa of His8
`was entirely insensitive to the presence and ioniza-
`tion of Asp, Glu, or Lys at position 38 (Table 2). This
`was expected because His8 is 17 Å from position 38.
`It has been shown previously that the pKa of
`His121 is depressed owing primarily to dehydration
`in a partially buried configuration.30 His121 is 6 Å
`from the Oε1 of Glu38 and 9 Å from the Nζ atom of
`Lys38 (Fig. 1b). In both the L38D and L38E variants,
`the pKa value of His121 was elevated from 5.4 to 5.7
`(Table 2). This cannot be due to a Coulomb inter-
`action because His121 and the internal carboxylic
`groups do not ionize in the same range of pH. It has
`been observed previously that perturbations to the
`
`Fig. 4. Far-UV CD spectra of at pH 4 (a) and pH 7 (b).
`Series are Δ+PHS (▾), Δ+PHS/L38E ( ), Δ+PHS/L38E/
`D77N ( ), Δ+PHS/L38E/E122Q ( ), Δ+PHS/L38E/
`E122D ( ), Δ+PHS/L38E/R126Q ( ), Δ+PHS/L38D ( ),
`and Δ+PHS/L38D/E122Q ( ).
`
`suggesting that none of the substitutions altered
`the secondary structure of the protein significantly,
`even when the internal Lys, Asp, or Glu groups were
`charged. Similarly, 70–90% of the 131 peaks in the
`15N–1H heteronuclear single quantum coherence
`(HSQC) spectrum of Δ+PHS nuclease at pH 4.5
`were identifiable by visual inspection on the spectrum
`of each variant (Fig. 5).40 Overall, the spectroscopic
`probes suggest that the substitutions did not affect
`the structure of the protein over a wide range of pH.
`Although the global structure of the proteins
`remained intact, the previous investigation of the
`Δ+PHS/L38K variant suggested that flexibility of
`the loop containing residues 113–119 allowed water
`to penetrate the protein to solvate the charged
`moiety of the side chain of Lys38. To probe the con-
`formation of this loop in these variants, we used an
`HNN experiment to assign all backbone 15N–1H
`peaks in the HSQC spectra of the Δ+PHS/L38E and
`Δ+PHS/L38K variants at pH 4.6.48 These spectra
`were compared to the spectra of Δ+PHS collected
`previously,40 at pH values between 2.8 and 9.0 in
`steps of ~0.4 pH units.
`
`Bausch Health Ireland Exhibit 2045, Page 5 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`pKa Values of Internal Groups
`
`39
`
`Fig. 5. HSQC spectra of the Δ+PHS (black), Δ+PHS/L38D (red), Δ+PHS/L38E (green), and Δ+PHS/L38K variants
`(blue) at pH 4.6 4.7. The four spectra are overall quite similar. Arrows highlight 4 of the 12 residues that are seen in every
`spectrum except that of Δ+PHS/L38K. Boxes identify residues used in global fits to extract pKa values of groups at
`position 38.
`
`hydrogen bonding network centered on His121
`almost always cause the pKa value of His121 to
`increase relative to its pKa in Δ+PHS.30 Thus, it is
`likely that Glu38 and Asp38 perturb the hydrogen-
`bond network, possibly allowing more water to
`reach His121 than in Δ+PHS nuclease.
`Lys38 is fully charged in the range of pH where
`His121 titrates; therefore, a Coulomb interaction
`between these residues is possible. An unfavorable
`Coulomb interaction would further depress the pKa
`of His121. This was not observed. Instead, as in the
`L38D and L38E variants, the pKa of His121 was
`elevated to 5.6 in the presence of Lys38. This small
`change is consistent with slight structural relaxa-
`tion induced by the substitution of Leu38 with Lys
`or by the ionization of Lys38. This is fully consis-
`tent with the conclusion of our previous study of
`Lys38 and with the evidence from NMR spectro-
`scopy of slight structural reorganization in the L38K
`variant.38
`
`Coulomb interactions between surface and
`internal ionizable groups
`
`Δ+PHS nuclease has 20 Asp and Glu residues. The
`pKa values of these groups are known.40 With the
`
`exception of Asp21, which has an elevated pKa, all
`carboxylic groups titrate with depressed or normal
`pKa values. The pKa values of surface Asp and Glu
`residues in the Δ+PHS/L38E and Δ+PHS/L38K
`variants were measured with NMR spectroscopy
`(Table 3).
`Substitution of Leu38 with Glu did not alter the pKa
`values of any of the Asp or Glu residues (Table 3).
`This does not imply that Glu38 does not interact
`with these groups. Glu38 titrates with a pKa of 7.0,
`while most other acidic groups titrate with pKa
`values near 4.0; therefore, Glu38 is neutral during
`the titration of the other Asp and Glu residues and
`cannot affect their pKa values by Coulomb interac-
`tion. These data also show that the L38E substitu-
`tion has no detectable impact on the structure of the
`protein and, thus, on the electrostatic environments
`of the surface Asp and Glu residues. If Asp21 had a
`significant Coulomb interaction with Glu38, its pKa
`of 6.5 would be affected. The lack of any detectable
`shift
`indicates that any Coulomb interaction
`between these two carboxylic groups is b0.1 kcal/
`mol. Overall, the absence of any measurable impact
`of substitutions of Leu38 on the pKa values of
`surface residues corroborates the results from spec-
`troscopic experiments showing that the structure of
`
`Bausch Health Ireland Exhibit 2045, Page 6 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`40
`
`pKa Values of Internal Groups
`
`Table 4. pKa values of Asp38 and Glu38 measured using
`global fit to 1HN chemical shift data
`
`Variant
`Residue
`Δ+PHS/L38E
`Glu38
`Δ+PHS/L38E/D77N
`Glu38
`Δ+PHS/L38E/E122Q
`Glu38
`Δ+PHS/L38E/E122D
`Glu38
`Δ+PHS/L38E/R126Q
`Glu38
`Δ+PHS/L38D
`Asp38
`Δ+PHS/L38D/E122Q
`Asp38
`a Uncertainty in pKa value is ±0.1.
`
`n
`0.8
`0.7
`0.9
`0.8
`0.9
`0.9
`1.0
`
`a
`pKa
`7.0
`6.1
`6.2
`7.4
`7.2
`7.2
`6.6
`
`ΔpKa
`0.0
`−0.9
`−0.8
`0.4
`0.2
`0.0
`−0.6
`
`the variants is very similar if not identical with the
`structures of the background protein.
`Five double mutants were made (L38E/D77N,
`L38E/E122Q, L38E/E122D, L38E/R126Q, and
`L38D/E122Q) to probe interactions between Asp38
`and Glu38 with neighboring ionizable residues
`directly. The pKa value of the internal Glu38 or
`Asp38 was measured by global fit of the pH
`dependence of 1HN chemical shifts measured with
`NMR spectroscopy. The measured pKa values are
`listed in Table 4. These pKa values can be readily
`converted to apparent ΔGij values by multiplying
`the difference in pKa between the background
`protein and the variants with neutral substitutions
`by RTln(10). To measure the interaction between
`Glu38 and Asp122, we measured ΔpKa using the
`L38E/E122Q variant as a background. The observed
`ΔGij values were strongly distance dependent and
`ranged from 0 to 1.5 kcal/mol (Table 5).
`Unlike Asp38 or Glu38, which are neutral at low
`pH, Lys38 is ionized below pH 10. Any Coulomb
`interaction with Lys38 should therefore alter the pKa
`values of surface carboxylic groups. In particular,
`Lys38 is involved in a 2.7-Å ion pair with Glu122 in
`the crystal structure of the L38K variant. A con-
`servative estimate of the possible pKa shift can be
`made with Coulomb's law using the dielectric
`constant of pure water. This indicates that an inter-
`action of 1.5 kcal/mol between Lys38 and Glu122 is
`possible. This would shift the pKa of Glu122 by
`1.1 units. The measured pKa values of the carboxylic
`groups in the Δ+PHS/L38K variant are shown in
`Table 3. Surprisingly, no shifts in pKa value were
`observed. This experiment demonstrates conclu-
`sively that the ion pair between Lys38 and Glu122
`observed in the crystal structure is not present in
`
`solution and that Lys38 does not interact with any
`carboxylic acid residues in the protein. This behavior
`is fully consistent with a structural rearrangement
`leading to hydration of the charged side chain of
`Lys38.
`
`Structure-based pKa calculations
`
`Reproducing the shifts in pKa values in multiple
`sites in a protein is still a difficult challenge for
`structure-based electrostatics calculations. To test the
`ability of computational methods to calculate Cou-
`lomb interactions accurately, we used five compu-
`tational methods to calculate the pKa of Glu38 in the
`L38E, L38E/D77N, L38E/E122Q, L38E/E122D, and
`L38E/R126Q variants. The pKa values of Asp38 (in
`the L38D variant), His8, and His121 were also calc-
`ulated. Overall, the calculations attempted to repro-
`duce 12 unique pKa values: Glu38 in the five variants
`listed above (Table 4), Asp38 in the L38D variant
`(Table 4), and His8 and His121 in the L38E, L38E/
`E122Q, and L38D variants (Table 2). A variety of diffe-
`rent computational methods were tested: PROPKA,50
`the single site (S/FDPB) and full-site PARSE (F/FDPB)
`implementation of finite difference Poisson–Boltzmann
`electrostatics,51–53 the pH-adapted conformer FDPB
`method (PAC),54,55 and multi-conformer continuum
`electrostatics (MCCE).56,57
`PROPKA uses a set of empirical rules to estimate
`pKa values from structure. The pKa of Glu38 calc-
`ulated with PROPKA was 5.3. The group was
`classified as buried and experienced an unfavorable
`dehydration energy (2.1 kcal/mol) offset by favor-
`able polar interactions with the Tyr91 side chain and
`His121/Glu122 backbone (− 1.3 kcal/mol). No
`Coulomb interactions were calculated because
`PROPKA only treats Coulomb interactions between
`two residues if they are both classified as buried and
`within 7 Å of one another. Only His121 meets both
`criteria, but no interaction energy was calculated
`because the calculated pKa of His121 (5.1) is below
`that of Glu38; the PROPKA algorithm excludes
`possible interaction because the groups are never
`charged simultaneously. The lack of explicit Cou-
`lomb interactions causes PROPKA to be entirely
`insensitive to substitution of residues at position 77,
`122, or 126 with uncharged analogs. The overall
`RMS error for the calculated versus experimental pKa
`values was 1.0 (Table 6).
`
`Table 5. Apparent Coulomb interactions between Glu38 and other ionizable residues
`
`Interaction
`Glu38/Asp122b
`Glu38/Asp77
`Glu38/Glu122
`Glu38/Arg126
`Glu38/Asp21
`Glu38/His8
`
`a (kcal/mol)
`ΔGij
`1.5
`1.2
`1.1
`−0.3
`0.0
`0.0
`
`rij (Å)
`3.6c
`4.0
`5.1
`6.6
`13.1
`15.2
`
`a Uncertainty is 0.1 kcal/mol.
`b ΔpKa estimated using L38E/E122Q variant.
`c Distance estimated using structural model.
`
`Interaction
`
`a (kcal/mol)
`ΔGij
`
`rij (Å)
`
`Asp38/Glu122
`
`Asp38/His8
`
`0.8
`
`0.0
`
`5.3c
`
`18.9c
`
`Bausch Health Ireland Exhibit 2045, Page 7 of 14
`Mylan v. Bausch Health Ireland - IPR2022-00722
`
`

`

`pKa Values of Internal Groups
`
`41
`
`Table 6. Comparison of calculated and measured pKa
`values
`
`Residue
`Glu38
`
`Asp38
`His8
`
`His121
`
`FDPB
`PAC MCCE
`NMR PROPKA S
`F
`Variant
`4.9
`8.5
`7.0
`5.3
`7.0
`7.1
`L38E
`0.0
`5.4
`L38E/D77N 6.1
`5.3
`5.9
`5.7
`2.7
`7.2
`L38E/E122Q 6.2
`5.3
`5.6
`6.0
`6.5
`9.0
`L38E/E122D 7.4
`5.2
`8.2
`7.5
`5.3
`9.0
`L38E/R126Q 7.2
`5.2
`7.5
`8.1
`L38D
`7.2
`5.0
`6.7
`7.4 16.2
`8.7
`L38E
`6.5
`6.5
`6.8
`6.8
`6.5
`6.7
`L38E/E122Q 6.4
`6.5
`6.7
`6.8
`6.6
`6.7
`L38D
`6.5
`6.5
`6.7
`6.8
`6.6
`6.7
`L38E
`5.7
`5.1
`8.0 10.2
`8.3
`7.6
`L38E/E122Q 5.7
`5.1
`8.0 10.0
`8.1
`7.7
`L38D
`5.7
`5.3
`7.9
`9.6
`5.9
`7.7
`RMS
`1.0
`1.2
`2.1
`3.4
`1.4
`
`The results of FDPB calculations were highly de-
`pendent on the choice of protein dielectric constant.
`Using S/FDPB, the calculated pKa of Glu38 ranged
`from 19.2 when εp = 4 to 5.4 when εp = 20. Likewise,
`the pKa of Glu38 calculated using F/FDPB ranges
`from 19.2 when εp = 4 to 5.2 when εp = 20. The pKa
`of 7.0 of Glu38 was reproduced by dielectric cons-
`tants of 12 and 11 with the S/FDPB and F/FDPB
`methods, respectively. The dielectric constant that
`reproduced the experimental pKa value (εapp) was
`used for all
`further calculations. In both types
`of calculations, the pKa at εapp was governed by
`unfavorable dehydration energy (4 kcal/mol), net
`favorable polar interactions (−3 kcal/mol), and net
`unfavorable Coulomb interactions (2.5 kcal/mol).
`The overall RMS for all 13 measured pKa values was
`1.2 and 2.1 for S/FDPB and F/FDPB, respectively
`(Table 6). The relatively large RMS value is due to a
`large error in the calculated pKa value of His121
`(8.0 and 10.2). If this is excluded from the RMS
`calculation, both methods have RMS errors of 0.4.
`S/FDPB and F/FDPB overestimated the apparent
`Coulomb interactions by 75% by 25%, respectively.
`The PAC method generates ensembles of possible
`side-chain positions at pH extremes, calculates
`electrostatic potentials of each configuration using
`FDPB, and Boltzmann weights these ensembles as a
`function of pH. To test the best-case scenario for PAC
`calculations, we used a variety of parameter com-
`binations to maximize agreement with experiment.
`For PAC, it was found that minimizing side-chain
`positions was the most important user-adjustable
`parameter, lowering the RMS error by 20%. Even so,
`the calculations performed poorly. The calculated
`pKa of Glu38 was 4.9 and the overall RMS error of
`the pKa values was 3.4 pH units (Table 6). On aver-
`age, the apparent Coulomb interactions calculated
`using this method were 3.7 times higher than those
`of the experiment.
`MCCE couples conventional FDPB calculations to
`side-chain rotamer sampling with a Monte Carlo
`method. MCCE does not allow for arbitrary adjust-
`ment of the protein dielectric constant without ex-
`tensive reparameterization; therefore, these calcu-
`lations used the default εp values of 4 or 8. The
`
`calculations with εp = 4 failed to converge, giving
`pKa values for Glu38 that were N14. Only calcula-
`tions using εp = 8 are reported here. The calculated
`pKa value of Glu38 was 8.5, and the overall RMS
`error was 1.4 pH units (Table 6). The apparent
`Coulomb interactions reported by MCCE were, on
`average, twice as strong as observed experimentally.
`A corre