Analysis of the Self Association Properties of WT PaDDAH.

6.2.1 - Analytical size exclusion chromatography: WT PaDDAH

A high resolution 10/30 Superdex?5 (S75) analytical gel filtration column was employed to investigate the oligomeric state of WT PaDDAH. 100 pi samples of WT PaDDAH over a 100-fold concentration range (5 mg/ml to 50 pg/ml) were applied to a pre-equilibrated S75 column and the elution of protein followed by absorbance at 280 nm (see ‘Materials and Methods’ Section 3.2.10). At each concentration, the elution profile of WT PaDDAH showed a single peak. As shown in Figures 6.1(a) and 6.1(b) a clear increase in elution volume from 10.23 ± 0.02 ml to 10.64 ± 0.02 ml was observed as the protein concentration is decreased. Over the course of this study, a total of eight separate SEC experiments were recorded per WT PaDDAH concentration and this behaviour was completely reproducible (Figure 6.1(c)).

The crystal structure of PaDDAH shows numerous free cysteine residues at the surface of the protein. To ensure the behaviour observed in SEC analyses was not due to the formation of transient inter-protomer disulphide bonds, analytical SEC runs were repeated in the presence of a reducing agent, p-mercaptoethanol (pME; see ‘Materials and Methods’ Section 3.2.10). The elution volume of WT PaDDAH in reducing solution conditions did not differ from that in non-reducing conditions (data not shown).

6.2.2 - Analytical size exclusion chromatography: ovalbumin and GST

The proteins ovalbumin (43.5 kD), a monomer, and glutathione S-transferase (GST; 51 kD), an obligate homodimer, were chosen for comparison with WT PaDDAH (see Materials and Methods' Section 3.2.10). 100 pi samples of each protein over a 100- fold concentration range (5 mg/ml to 50 pg/ml) were applied to a pre-equilibrated S75 column and protein elution followed by absorbance at 280 nm. The elution profiles of both ovalbumin and GST displayed two peaks (Figures 6.2(a) and 6.2(b) respectively). In both cases, the ratio of peak areas for the major and minor peaks was invariant (data not shown). The subsequent analysis of the hydrodynamic properties of ovalbumin and GST deals only with the major peak in each elution profile. The elution volume of both Ovalbumin and GST, over a similar range of sample

(a) (b) 6 8 10 12 14 1 mg/ml 5 mg/ml 0.5 mg/ml s 0.1 mg/ml 0.5 mg/ml 0.05 mg/ml 9.5 10.0 10.5 11.0 11.5

Elution Volume (ml) Elution Volume (ml)

10.7 10.6-■ B 10.5 ■5 1 0 .3 .. 10.2 - ■ 10.1 0.0 1.0 2.0 3.0 4.0 5.0 6.0 [PaDDAH] (mg/ml)

Figure 6.1. Analytical size exclusion chromatography of WT PaDDAH. (a) Elution profile of WT PaDDAH samples with loading concentrations of 5, 1, 0.5, 0.25, 0.1 and 0.05 mg/ml; (b) expansion of (a) with loading concentrations (mg/ml) annotated; (c) Summary of elution volume compared to loading concentration (mg/ml) for WT PaDDAH. The error bars indicate plus and minus one standard error from the mean with n = 8.

(a) _(b)

"J o

§ o

8 10 12 8 10 12

Elution Vol (ml) Elution Vol (ml)

(c) 10.6 10.4 10.2 i i i 0.0 (d) 1.0 2.0 3.0 [Protein] (mg/ml) 4.0 5.0 6.0 10.6 .9 1 0 .4 -- 10.3 0.0 1.0 2.0 3.0 4.0 5.0 6.0 [Protein] (mg/ml) Figure 6.2. A n a l y t i c a l s i z e e x c l u s i o n c h r o m a t o g r a p h y o f o v a l b u m i n a n d g l u t a t h i o n e S - t r a n s f e r a s e ( G S T ) . E l u t i o n p r o f i l e s o f o v a l b u m i n ( a ) a n d G S T ( b ) s a m p l e s w i t h l o a d i n g c o n c e n t r a t i o n s o f 5 , 1 , 0 . 5 , 0 . 2 5 , 0 . 1 a n d 0 . 0 5 m g / m l ; S u m m a r y o f e l u t i o n v o l u m e ( m l ) c o m p a r e d t o l o a d i n g c o n c e n t r a t i o n ( m g / m l ) f o r o v a l b u m i n ( c ) a n d G S T ( d ) . T h e e r r o r b a r s i n d i c a t e p l u s a n d m i n u s o n e s t a n d a r d e r r o r f r o m t h e m e a n w i t h n = 5 f o r o v a l b u m i n a n d n = 2 f o r G S T .

concentrations and under identical sample conditions to WT PaDDAH, were not dependent on the loading concentration (Figures 6.2(a) to 6.2(d)).

6 .2 .3 - Conversion o f elution volume into apparent molecular weight

Molecular weight gel filtration standards were applied to a pre-equilibrated S75 column and protein elution followed by absorbance at 280 nm. A graph of peak elution volume versus log of the species molecular weight was linear {r = -0.99) between molecular weights of 88 kD and 14.8 kD (Figure 6.3(a) and 6.3(b)). Using these data, an empirical relationship between elution volume (EV; in ml) and molecular weight (MW; in kD) was calculated (Equation 6.1).

M W = 10 [(2 1 .1- E V ) /6.37)] Equation 6.1

Equation 6.1 was used to convert the elution volumes of WT PaDDAH, ovalbumin and GST into apparent molecular weight values (app. MW). For WT PaDDAH, a 100-fold decrease in loading concentration gave a decrease in average app. MW of 7.2 ± 0.1 kD from 51 ± 0.91 kD to 43.8 ± 0.32 kD (Figure 6.3(c)). No such decrease was seen for either ovalbumin or GST (Figure 6.3(d)), which have respective average app. MWs of 47.2 ± 0.2 kD and 48.4 ± 0.2 kD over the concentration range studied.

6.2.4- Estimation o f the dissociation constant o f WT PaDDAH using analytical SEC

During analytical SEC analysis WT PaDDAH eluted as a single peak at all concentrations. Analysis of the peak shape revealed a slight asymmetry around the peak maximum. This asymmetry was probably of experimental origin as the degree was not dependent on concentration (data not shown; Manning et al. 1996).

If the exchange rate between homodimeric and monomeric species is fast with respect to the rate of molecular separation then a single peak is expected in the elution profile (Manning et al. 1996). The app. MW, (MW), of this peak is a function of the mole fraction of homodimer and the mole fraction of monomer and the app. MW of the dimeric (MWd) and monomeric (MWm) species (Equation 6.2)

(MW) = /?j^(MW^) + /?d(MWd) Equation 6.2

(a) (b) Ovalbumin (43kD) S CVJ < _{O v a lb u m in} (8 6 lc D )\ 5 10 15 20 E g 12 g S 10 ; =3 LU 1.0 1.2 1.4 1.6 1.8 2.0 (c)

Elution Volume (ml) log (MW)

52 ■ 44 42 ■■ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 (d) Protein Concentration (mg/ml) 2.0 3.0 4.0 Protein Concentration (mg/ml) Figure 6.3. ( a ) E l u t i o n p r o f i l e o f p r o t e i n m o l e c u l a r w e i g h t s t a n d a r d s a m p l e s w i t h l o a d i n g c o n c e n t r a t i o n o f 4 m g / m l ( s e e ‘ M a t e r i a l s a n d M e t h o d s ’ S e c t i o n 3 . 2 . 1 0 ; ( b ) P l o t o f e l u t i o n v o l u m e ( E V ) v e r s u s l o g m o l e c u l a r w e i g h t f o r e l u t i o n v o l u m e s o f m o l e c u l a r w e i g h t s t a n d a r d s i n ( a ) w i t h c a l c u l a t e d r e g r e s s i o n l i n e ; r = - 0 . 9 9 . G r a p h s h o w i n g a p p a r e n t m o l e c u l a r w e i g h t ( M W ) v e r s u s l o a d i n g c o n c e n t r a t i o n f o r ( c ) W T P A D D A H a n d ( d ) o v a l b u m i n ( b l a c k s y m b o l s ) a n d G S T ( g r e y s y m b o l s ) .

Ao

and /?D, the mole fraction of dimer, as

. 0 =

Ao

Equation 6.3

Equation 6.4

By definition for a homodimer-monomer equilibrium (i.e. with no higher oligomer species)

Equation 6.5 and the total concentration of protein, Ao, is given by

Aq = 2[D] + [M] Equation 6.6

where [M] is the concentration of free monomer and [D] the concentration of homodimer. Ao was defined as such because the concentration of protein in the solution was calculated using an extinction coefficient predicted fi'om the amino acids sequence of a PaDDAH monomer.

Elimination ofp u fi'om Equation 6.2 yields

(MW) = (1 - p ^ (MWj^) + /?d(MWd) Equation 6.7 Defining /?d in terms of Ao and [M] (Equation 6.6) and rearranging now allows (EV) to be solved in terms of [M], MWmand MWd.

Ao - [M]

(MW) = MWm + (MWd - MWm)

The equilibrium dissociation constant Kd, is defined D ^ M + M

[M]2 • • [D]

Combining Equations 6.6 and 6.9 and eliminating [D] gives,

2[ M ] 2 + K J M ] - A o K j = 0

from which [M] can be solved in terms of Kj and Ao - K , ± (K,: + SAoKo)'/' [M] = ---1--- Equation 6.8 Equation 6.9 Equation 6.10 Equation 6.11

[M] can be eliminated from Equation 6.8 with the correct solution of Equation 6.11. Now (MW) is defined in terms of Ao, which is known, and MWm, MWd, and Kd

4Ao-Kd - (K / + S A g K y (MW) = MWw +

4Aq (MWd - M W J

Equation 6.12

An apparent Kd can be estimated by fitting the experimental data to Equation 6.12. If the app. MW of the monomeric or homodimeric species are also unknown these can also be estimated by fitting

In order to estimate Kd from WT PaDDAH analytical SEC data it was necessary to correct Ao to account for the dilution of the sample that occurred during each experiment. The area of the elution peak of a protein should be directly proportional to the loading concentration such that graph of log(peak area) versus loading log(sample concentration) should yield a positive linear relationship with a slope of unity (Manning et al. 1996). For WT PaDDAH, such a graph, gave a positive linear relationship (r = 0.998) with a slope of 1.0 when the relationship was constrained to go through the origin. (Figure 6.4(a)). A dilution factor of 6.4 ±0.16 was calculated from the peak width at half-height (see ‘Materials and Methods’ Section 3.4.5; Manning a/. 1996).

The app. MW data (Section 6.2.3), corrected for the 6.4-fold dilution factor, was fit to Equation 6.12 (see ‘Materials and Methods’ Section 3.4.5). The best-fit values of MWm, MWd and Kd parameters are presented in Table 6.1 with their associated

asymptotic standard errors. The 95 % confidence intervals calculated from the standard errors of the best-fit values revealed a good level of confidence for MWd

(52.2 ± 1.02 kD) but unacceptable levels for MWm(36.3 ± 10.28 kD) and Kd (235 ±

489 nM). Because of the high levels of uncertainty for MWm and Kd, attempts to

evaluate the fit of Equation 6.12 to the experimental data using a Monte-Carlo procedure failed (see ‘Materials and Methods’ Section 3.4.5). Both 3-parameter (MWm, MWd and Kd) and 2-parameter (MWm and Kd, with MWd fixed as 52.2)

(a) 2.5 1.5 -- O) 0.5 -- 0 0.5 1 1.5 2 2.5 (b) (c) 2 0.5 g 0 •o (D Œ -1 Log(Loading [Protein] ) 50 -- 48 -- 46 44 -i; 42 0 5 10 15 20 25 [PaDDAH] (^iM) Q_Q_ _Q_ O 10 15 [PaDDAH] (^iM) 20 25 F i g u r e 6 . 4 . F i t t i n g W T P a D D A H S E C d a t a , ( a ) A p l o t s h o w i n g l o g ( p e a k a r e a ) v e r s u s l o a d i n g l o g ( W T P a D D A H c o n c e n t r a t i o n ) . T h e l i n e o f b e s t f i t i s c o n s t r a i n e d t o g o t h r o u g h t h e o r i g i n , r = 0 . 9 9 8 ; ( b ) W T P a D D A H a n a l y t i c a l S E C d a t a b e s t - f i t t o E q u a t i o n 6 . 1 2 y i e l d i n g f i t t i n g p a r a m e t e r s o f = 2 3 5 n M , M W ^ = 3 6 . 3 a n d M W p = 5 2 . 2 ( s e e T a b l e 6 . 1 ) ; ( c ) t h e r e s i d u a l s o f e x p e r i m e n t a l d a t a f r o m s i m u l a t e d d a t a ( r e s i d u a l = ÿ j - y ^ ) .

in Table 6.1, the function used to optimise the fit of Equation 6.12 to the experimental data was evaluated (see Appendix A.1). Of the three parameters, MWdwas the best

defined. When MWmand Kd were floated and EVdfixed, a large range of possible solutions of MWm and Kd were observed (see Appendix A.2). It was not possible

therefore to independently fix upon MWmand Kd estimates.

Table 6.1. Results of fitting WT PaDDAH analytical SEC data.

Parameter ® Value Error (±) ^ (±) 95% C.I. ®

MWm 36.3 kD 3.23 10.28 kD

MWd 52.2 kD 0.32 1.02 kD

Kd 2.3 X 10''^ M 1.5 X 10'^ 4.9 x lO'^M

“ MWm and MWd are the app MW of PaDDAH monomer and homodimer species, and Kd is the equilibrium dissociation constant. ^ Asymptotic standard errors ; ® 95 % confidence interval (C.I.) calculated using asymptotic standard errors._____________ ____ ___ ___ ___

To obtain a more satisfactory fit required the constraint of both MWmand MWd. In

the absence of experimentally derived values of MWd and MWm, two alternatives

were tried. One possible way was to define these parameters as the values returned from the original fit. With MWmand MWddefined as their respective values in Table

6.1, Kd was estimated to be 218 ± 7 nM following 200 Monte-Carlo simulations (Figure 6.4(b)). Alternatively, MWm and MWdcan be estimated using the predicted

molecular weight of each PaDDAH species. The protomer molecular weight of affinity tagged PaDDAH from the amino acid sequence is 32.2 kD. With these definitions, a single parameter fit of Equation 6 .12 was performed and Kd estimated to be 1.3 ±0.03 pM.

In summary, using a three parameter fit of Equation 6 .12 against the experimental WT PaDDAH SEC data resulted in low levels of confidence for Kd. This uncertainty related to the poor estimations of MWmdue to no experimental estimate of the elution volume of a PaDDAH monomer.

The results presented in Section 6.2 validate the previous observation of a concentration dependent elution volume for PaDDAH and suggestion of a dynamic homodimer-monomer equilibrium. In the following sections, the potential to manipulate this equilibrium is explored by using site-directed point mutations of residues located at the protomer interface to modulate the strength of the dimer interaction. Ultimately, through mutation, it may be possible to manipulate the equilibrium in such a way as to produce a monomeric variant of PaDDAH. Such as species would likely have solution properties more amenable to NMR studies.

6.3. Structural Description of Residues Contributing to the Homodimer Interface