Hyperbolic Pressure-Temperature Phase Diagram of the Zinc-Finger

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Hyperbolic Pressure-Temperature Phase Diagram of the ZincFinger Protein apoKti11 Detected by NMR Spectroscopy Andi Klamt, Kumar Nagarathinam, Mikio Tanabe, Amit Kumar, and Jochen Balbach J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11019 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 7, 2019

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The Journal of Physical Chemistry

Hyperbolic Pressure-Temperature Phase Diagram of the Zinc-Finger Protein apoKti11 Detected by NMR Spectroscopy

Andi Klamt1, Kumar Nagarathinam2,3, Mikio Tanabe2, Amit Kumar1,4*, Jochen Balbach1,*

1

Martin-Luther University Halle-Wittenberg, Institute of Physics, Biophysics, Betty-Heimann Str. 7,

06120 Halle, Germany 2

HALOmem, Membrane Protein Biochemistry, Martin-Luther-University Halle-Wittenberg, Kurt-

Mothes-Str.3, 06120, Halle (Saale), Germany. 3

Institute of Virology, Hannover Medical School, Carl-Neuberg-Straße 1, D-30625, Hannover,

Germany 4

Department of Diabetes, Faculty of Lifesciences and Medicine, King's College London, Great Maze

Pond, London SE1 1UL, UK *Corresponding authors: Amit Kumar

Jochen Balbach

E-mail address: [email protected]

E-mail address: [email protected]

Phone: +44 20 7631 6827

Phone: +493455528550 Fax: +493455527161

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Abstract

For the comprehensive understanding of the thermodynamic state functions describing the stability of a protein, the influence of the intensive properties temperature and pressure has to be known. With the zinc finger-containing Kti11, we found a suitable protein for this purpose, because folding and unfolding transitions occur at an experimentally accessible temperature (280 °K – 330 °K) and pressure (0.1 MPa – 240 MPa) range. We solved the crystal structure of the apo form of Kti11 revealing two disulfide bonds at the metal binding site which seals off a cavity in the β-barrel part of the protein. From a generally applicable proton NMR approach, we could determine the populations of folded and unfolded chains under all conditions leading to a hyperbolic pressure-temperature phase diagram rarely observed for proteins. A global fit of a two-state model to all derived populations disclosed reliable values for the change in Gibbs free energy, volume, entropy, heat capacity, compressibility, and thermal expansion upon unfolding. The unfolded state of apoKti11 has a lower compressibility compared to the native state and at ambient pressure a smaller volume. Therefore, a pressure increase up to 200 MPa reduces the population of the native state and above this value, the native population increases again. Pressure induced chemical shift changes in 2D 1H-15N NMR spectra could be employed for a molecular interpretation of the thermodynamic properties of apoKti11.


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Introduction

The self-assembly process of the polypeptide chain towards the native state follows the energy landscape shaped by the primary sequence and the local environment of the respective protein. This protein folding reaction and the corresponding energy landscapes have been extensively studied in vitro dominated by thermodynamic investigations during heat and denaturant induced un- and refolding 1. Both temperature and denaturant concentration determine the Gibbs free energy of the system, which is the main driving force of folding. Typically, a volume change of the system comes along with the folding reaction which allows shifting of the equilibrium between the folded and unfolded states by changing the physical pressure. The latter has several advantages concerning reversibility and absence of denaturing agents but requires technical equipment to reach several hundred MPa for sufficient shifts in the populations.

Since Bridgman first proposed protein unfolding under high pressure 2, numerous studies manifested the physical basis of this process towards a reduced overall volume of the system by a contribution from the peptide chain which is devoid of cavities in the unfolded state and a contribution from the water solvent, weakening hydrophobic interactions by an increased solvent density at exposed surfaces of the unfolded state as well as electrostriction of polar and charged groups

3-9

. Pressure-induced

folding reactions under NMR detection allows not only the following of shifts in the populations of unfolded, intermediate, and native states

9-11

but also local structural and dynamical adaptations of the

peptide chain 12-16.

The here studied protein Kti11 belongs to the highly conserved family of eukaryotic zinc fingercontaining protein

17, 18

first observed as one of the necessary factors required for maintaining the 3 ACS Paragon Plus Environment


sensitivity of Saccharomyces cerevisiae towards Kluyveromyces lactis zymocin

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19, 20

. Kti11 and

structural homologs play multiple roles in cellular processes including the regulation of transcription by tRNA modification, translation elongation, zymocicity and diphtheria toxicity 18. The structure of Zn2+ bound Kti11 was solved by NMR spectroscopy, revealing conserved cysteine residues C26, C28, C48 and C51 forming the zinc binding site. The recently solved crystal structure of Kti11 in complex with Kti13 showed that this metal binding site facilitates hetero-dimerization 17, 21.

In the present study, we solved the structure of apoKti11 by X-ray crystallography and characterized its thermodynamic stability under a wide range of temperatures and high pressure. In the absence of Zn2+, Kti11 forms two disulfide bonds at the metal binding site burying a small cavity. Thermodynamic parameters including changes in heat capacity, thermal expansion, compressibility, and volume upon unfolding could be quantified by a global data analysis of NMR derived protein populations. Because of the increased compressibility of the native state compared to the unfolded state, apoKti11 has a hyperbolic pressure-temperature phase diagram, which has been to our knowledge experimentally observed only once

22

before. Residues close to the cavity at the substrate-binding site of apoKti11

show large amide proton NMR chemical shift changes upon pressure increase, suggesting a structural plasticity of these residues.


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Experimental Methods

Protein preparation Kti11 was expressed in E. coli and purified as described earlier

18

. In brief, Kti11 was cloned in the

pTrc vector with His6 at the C-terminus. The plasmid was transformed into E. coli BL(21) DE3 cells. The protein was purified from the soluble fraction using Ni-affinity chromatography and further purified by S75 gel filtration chromatography. For

15

N labeling, M9 media supplemented with

15

N

NH4Cl and 200 µM ZnSO4 was used. Metal was removed by dialyzing the holoKti11 in buffer containing 5 M guanidinium thiocyanate and 100 mM EDTA at pH 7.5. This unfolded protein was refolded in the respective buffer (i) 50 mM Tris-HCl, pH 7.5, 50 mM NaCl or (ii) 25 mM sodium phosphate, pH 7.5, 25 mM NaCl by dialysis. The purity of protein was analyzed by 12 % SDS-PAGE.

Crystallization Buffer solution for apoKti11 was exchanged from 25 mM sodium phosphate, pH 7.5, 25 mM NaCl to 25 mM HEPES (pH 7.5), 25 mM NaCl by overnight dialysis prior to crystallization trials. Initial apoKti11 crystal bundles appeared by mixing 100 nl of protein solution with an equal volume of reservoir solution consisting of 0.1 M sodium acetate (pH 5.5), 5 mM CdCl2 and 20% PEG 4000 in a 1:1 ratio. The drop was equilibrated with 70 µl of the reservoir solution for 3 to 4 weeks in a 96-well formatted vapor diffusion sitting drop screening plate. In order to avoid growth of crystals as bundles, micro seeding was performed. The seed stock was prepared by harvesting the crystal bundles of apoKti11from a single drop and crushed using a glass seed bead (Jena bioscience) in 50 µl reservoir solution. For optimization of crystallization conditions, hanging drop vapor diffusion was performed. 0.5 µl of the diluted seed stock (1/1000) was added to 1.5 µl protein and mixed with 1 µl reservoir solution. The drop was equilibrated against 1 ml of reservoir solution. Single crystals of Kti11 appeared 5 ACS Paragon Plus Environment


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within 2 days, growing to a final size of approximately 40 µm × 30 µm × 30 µm by 4 days. The crystals were cryo protected with 30 % glycerol and directly flash cooled and stored in liquid nitrogen.

X-ray diffraction data set was collected at 100K on the X06DA (PXIII) beam line at Swiss Light Source (SLS, Villingen) using a Pilatus 2 M detector. The diffraction data were processed and scaled by the HKL2000 program suite. The initial phase was obtained by the molecular-replacement (MR) method using the partial coordinates (residue number 36-80) of YBL071w-A from S. cerevisiae (PDB ID: 1YWS sequence identity 98%) as a search model with the assistance of Cd2+ single wavelength anomalous diffraction (SAD) anomalous phasing by the Phenix suites

23

. Density modification and

crystallographic refinement procedures were carried out using CCP4 24. Model building was performed using Coot 25. The coordinates of apoKti11 have been deposited in the PDB (accession code 5AX2).

NMR spectroscopy The NMR resonance assignment of metal bound Kti11-Zn2+ has been reported earlier

18

. If not

differently stated, apo- and holoKti11 was studied at 295 K, 50mM Tris-HCl, pH 7.5, 50mM NaCl, and 10% D2O at a protein concentration of 0.5 mM. The backbone assignment of

15

N/13C apoKti11 was

achieved by the standard triple-resonance experiments HN(CO)CACB, HNCACB, HNCO and HN(CA)CO and complemented by side chain assignments from a constant time 13C HSQC 26 and a 3D HCCH-TOCSY experiment

27

at Bruker Avance III 600 (TXI triple resonance probe) and 800

spectrometers (CP–TCI cryoprobe). Heteronuclear Overhauser effects (hetNOE) of backbone amides 28 of holo- and apoKti11 were determined by 3 s proton saturation. High-pressure NMR measurements were performed in a commercial 3 mm ceramic cell (Daedalus Innovations LLC) connected to a home-built pressure generation up to 250 MPa at 600 MHz. 1D 1H spectra under WATERGATE solvent suppression were processed and analyzed by Bruker TopSpin 3.1 6 ACS Paragon Plus Environment

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and 2D 1H-15N HSQC spectra by NMRPipe and NMRview.

Thermodynamics The fractions of native( fn ) and unfolded ( fu ) protein can be quantified from one dimensional (1D) 1HNMR spectra as described previously29. Briefly, two integral regions are set: In(T) comprising native signals only (well separated methylene or methyl groups) and Iu+n(T) comprising a mixture of resonances of the native and unfolded states and where most of the unfolded aliphatic signals appear. ali The sum of In(T) and Iu+n(T) is defined as I tot (T ) used in eq 1 to noramlize In(T). From this ratio, fn and

fu can be derived by I n (T ) ⋅ f n (Tmax ) ali I tot (T ) f n (T ) = I n (Tmax ) ali I tot (Tmax )

and

fu(T) = 1 - fn(T).

(1)

For apoKti11, the integral region for In(T) was set between 0.27 ppm and 0.65 ppm and for Iu+n(T) between 0.65 ppm and 1.24 ppm. A χ2 analysis was performed to determine the temperature Tmax for the maximum of the native fraction fn(Tmax) by fitting eq 1 to the temperature transition. For apoKti11 in 50mM sodium phosphate, pH 7.5, at ambient pressure Tmax was found to be 295 K and fn(Tmax) = 0.88 with an error of 6%. For a two-state protein folding model U ↔ N at equilibrium the standard Gibbs free energy of unfolding ∆Gu° (T ) is given by eq (2):

 f  ∆Gu° (T ) = − RT ln u  .  1 - fu 

(2)

Assuming that the change in heat capacity upon unfolding ∆Cp is not a function of temperature,30 this parameter as well as the change in enthalpy ∆H u° (Tm ) at the mid-point of the temperature transition Tm (corresponding to ∆Gu° (T ) = 0 ) can be derived from the temperature dependence of ∆Gu° (T ) : 7 ACS Paragon Plus Environment


 T −T   T   − ∆Cp  Tm − T + T ⋅ ln   . ∆Gu° (T ) = ∆H u° (Tm ) m    Tm   Tm   

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(3)

The change in entropy is given by ∆S u° (Tm ) = ∆H u° (Tm ) / Tm at Tm. The temperature of maximum stability Tmax corresponds to ∂∆Gu° (T ) / ∂T = 0 . Above Tmax the Tm value corresponds to heat-induced unfolding (Th) and below it corresponds to cold-induced unfolding (Tc). From the intensive state properties pressure and temperature, the difference in the extensive Gibbs free energy relative to T0 and p0 is given by 31, 32

    ∆β ( p − p0 )2 + ∆α ( p − p0 )(T − T0 ) − ∆Cp T ⋅ ln T − 1 + T0  + ∆V0 ( p − p0 ) 2    T0  − ∆S0 (T − T0 ) + ∆G0

∆Gu° ( p, T ) =

(4)

and simplifies by a second order approximation for values close to T0 to

∆Gu° ( p, T ) =

∆C ∆β ( p − p0 )2 + ∆α ( p − p0 )(T − T0 ) − p (T − T0 )2 + ∆V0 ( p − p0 ) − ∆S0 (T − T0 ) + ∆G0 2 2T0

(5)

where α corresponds to the thermal expansion and β to the compressibility. All differences between the native and the unfolded state concerning volume V, entropy S, and Gibbs free energy G are referenced to the arbitrary values of T0 and p0 (here ambient conditions of 295 K and 0.1 MPa if not stated otherwise). Note that the definition of ∆β is not consistent in the literature, which might be

∆β = −(∂∆V / ∂p ) T

33-35

or ∆β = (∂∆V / ∂p ) T

15, 31, 32

and the latter has been used for the here presented

analyses. In the pressure-temperature phase diagram, values of ∆S 0 = 0 and ∆V0 = 0 correspond to the following lines:

p(T ) ∆S0 =0 =

∆C p (T − T0 ) ∆S 0 + + p0 ∆α T0 ∆α

p(T ) ∆V0 =0 = −

∆α (T − T0 ) − ∆V0 + p0 ∆β ∆β 8

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(6)

(7)

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A global fit of eq 4 to all 1D 1H-NMR derived ∆Gu° ( p, T ) values was performed by the program GraFit 5.0 (Erithacus Software). For isothermal experiments, eq 5 simplifies to eq 8 for sole pressure transitions:

∆Gu° ( p ) =

∆β ( p − p0 )2 + ∆V0 ( p − p0 ) + ∆G0 2


(8)


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Results

X-ray structure determination of apoKti11 For a molecular interpretation of the pressure-dependent thermodynamic parameters, the structure of apoKti11 (Figure 1) was solved with initial phases obtained by molecular-replacement using residues 36-80 of YBL071w-A from S. cereviciae (PDB ID: 1YWS, sequence identity 98%) and an additional Cd2+ SAD phasing. Data collection details and refinement statistics are shown in Table S1 (PDB ID: 5AX2). The NMR structure of holoKti11 identified a Zn2+ coordinated by four cysteine residues (Cys26, Cys48, Cys28, Cys 51). To prepare apoKti11, Zn2+was chelated by ethylene diamine tetra acetic acid (EDTA) leading to two disulfide bonds between Cys26 and Cys48 as well as Cys 28 and Cys 51 as shown in the crystal structure upon air oxidation (Figure 1). There was no additional density around the predicted Zn2+ binding site. Crystal contacts between the molecules of apoKti11 are mediated by charged surface residues coordinating two Cd2+ ions. Asp37/Asp38 from molecule A and Asp60/Asp63 from molecule B coordinate the first Cd2+, and Glu43 from molecule A and Glu69 from molecule C coordinate the second ion (Figure S1). The corresponding 1H-15N HSQC spectrum, containing very well-dispersed resonances of the backbone amides, confirms that apoKti11 retains its well defined tertiary structure in solution (Figure S2). No anomalous signal of Zn2+ or other metals was found around the Zn2+ binding site for the protein crystal when we collected data at 1.07 Å. The averaged root mean square (RMS) deviation between the crystal structure of the apo-form and the NMR structure of the holo-form results in 1.94 ± 0.12 Å for all heavy atoms (residues 8-70) and 1.67 ± 0.08 Å for the corresponding backbone. This indicated that Zn2+ release and oxidation of Kti11 does not significantly modify the topology of the native structure besides minor changes in the length of secondary structural elements such as β-strand 1 or the C-terminal α-helix. The additional two cystine bonds in apoKti11 10 ACS Paragon Plus Environment

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may also explain the unmodified low backbone dynamics on a pico- to nanosecond timescale between residues 8-72 of Kti11 (Figure S3).

Figure 1: Structure representations of Kti11. (A) Superposition of apoKti11 (PDB ID 5AX2, cyan) with the lowest energy NMR structure of holoKti11 (PDB ID 1YOP, grey). The two disulfide bonds formed by C26-C48 and C28-C51 in apoKti11 are indicated in yellow. (B) Close up view of apoKti11 showing the 2|Fo|-|Fc| map with electron density countered at 1.0σ in blue. (C) Close-up view showing the four Cys residues coordinated to one Zn2+ in holoKti11. The pictures were prepared in PyMol.

Determination of protein populations by 1D 1H-NMR 1D 1H-NMR of proteins in solution has the advantage that it is a quantitative method for distinct protein populations because some resonances of the native state typically do not overlap with those of the unfolded state. Assuming a two-state model U ↔ N allows one to determine the fraction of 11 ACS Paragon Plus Environment


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unfolded protein chains fu and the fraction of folded chains fn by integrating the 1D 1H-NMR spectrum in the corresponding sections and normalizing by the total integral (see Methods and Materials). This NMR approach has been used previously 29 to follow cold denaturation and the change in heat capacity of the cold shock protein Csp, an archetype protein in the protein folding field.36

Temperature and pressure transitions of apoKti11 A complete profile of the thermodynamic stability of apoKti11 was recorded by varying both temperature and pressure between 280 K – 330 K and 0.1 MPa – 240 MPa. The thermodynamic stability of apoKti11 strongly depends on the pH of the solution, therefore the pH has to be constant under all experimental conditions. The pKa value of phosphate buffer is nearly temperature independent37 but shows a strong pressure dependence

38

whereas Tris-HCl has a strong temperature

dependence of its pKa value 39 but almost no pressure dependence up to 250 MPa38. In a pressure range up to ~ 400 MPa, the pH value of phosphate buffer decreases linearly by 0.4 pH units per 100 MPa 38. Therefore for each temperature series at one particular pressure the phosphate buffer was adjusted at ambient pressure such that it reaches pH 7.5 at the final pressure of the recorded series. One temperature series of 1D 1H NMR spectra at 60 MPa pressure is shown in Figure 2 as representative example and three additional transitions in Figure S4. The decrease of the separated methylene and methyl resonances between -0.1 ppm and 0.6 ppm indicates a heat induced shift of the equilibrium from the native to the unfolded state.


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Figure 2: High-field region of the 1D 1H-NMR spectra of apoKti11 at 60 MPa and various temperatures. The native region (In(T) in eq 1) between 0.27 ppm and 0.65 ppm contains the proton resonances of I8(Hγ2), I10(Hγ13), I34(Hδ1), M39(Hε), V57(Hγ2), and L64(Hδ2). Spectra are referenced to deuterated 2,2-dimethyl-2-silapentane-5-sulfonate (d6-DSS) set to 0 ppm.

The quantification in terms of fraction of unfolded apoKti11 by eq 1 follows our approach established for the cold denaturation of the cold shock protein Csp 29. These fractions (fu) are illustrated in Figure 3 for all 99 investigated temperature and pressure combinations. The standard Gibbs free energy of unfolding ∆Gu° (T ) is given by eq 2. Above 60 MPa, more than 50% of the protein chains can be unfolded by heat or cold induction within the examined temperature range. Fitting eq 3 to each set of temperatures at a fixed pressure revealed the thermodynamic parameters listed in Table 1. Between 0.1 MPa and 180 MPa ∆Gu° (Tmax ) decreases from 4.4 kJ/mol to 0.6 kJ/mol concomitantly with an increase in the midpoint of cold-denaturation and a decrease in the midpoint of heat-denaturation as expected from eq 3 if both the temperature of maximum stability and ∆Cp only marginally change. Both, the differences in enthalpy ∆H u° (Tm ) and entropy ∆Su° (Tm ) between the folded and unfolded state of 13 ACS Paragon Plus Environment


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apoKti11 drop 3-folds in this pressure range whereas the difference in heat capacity ∆Cp slightly drops. Between 180 MPa and 240 MPa ∆Gu° (Tmax ) increases again. We recently made a similar observation by the same NMR approach applied to GB1 at pH 2, which got stabilized with increasing pressure most likely because of electrostriction 9.

Figure 3: Fractions of unfolded apoKti11 depending on temperature and pressure. The pH was adjusted by sodium phosphate to be pH 7.5 at the given pressure. A fit of eqs 2 and 3 (grey line) results in the thermodynamic parameters listed in Table 1. Isobars derived from the results of the global fit (Table 2) are plotted as broken grey line. The dotted line represents fu = fn = 0.5 and errors in the populations are below 0.05 (estimated from double data sets).


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Table 1: Results obtained from fitting eqs 2 and 3 to the fractions of unfolded apoKti11 obtained from temperature transitions at different fixed pressures. Column ‘D’ specifies H – heat- and C– colddenaturation.

To derive changes in volume ∆V0 and compressibility ∆β of apoKti11 upon unfolding, we analyzed from the same dataset the fractions of folded (fn = 1 - fu) (Figure 4, top) and unfolded protein chains at 295 K and increasing pressure. Figure 4 (bottom) shows the ∆Gu° ( p ) values derived by eq 2. Fitting of eq 8 to these energies results in ∆V0 = -42.3 ± 6.4 ml/mol and ∆Gu° ( p ) = 4109 ± 330 J/mol at ambient pressure, the latter in good agreement with the value derived from the temperature transition (Table 1). To our surprise, we found a positive value of ∆β = 0.23 ± 0.03 ml/(mol·MPa) for the compressibility of apoKti11.



1 0,8

f

n

0,6 0,4 0,2 0

uo

[J/mol]

4000

∆G

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3000 2000 1000 0 0

30

60

90 120 150 180 210 240 pressure [MPa]

Figure 4: Pressure transition of apoKti11 at 295K. ∆Gu°(p) (bottom) was calculated from the NMR derived fu fractions (top) and plotted against pressure. The grey line corresponds to a fit of eq 8 and the results are given in the text.

Plotting ∆Gu° ( p, T ) at all investigated temperatures and pressures (Figure S5) results in the stability diagram of apoKti11 depicted in Figure 5A, which can be represented by a contour map in Figure 5B. Starting from the highest stability at 295 K and ambient pressure ∆Gu° ( p, T ) drops up to 180 MPa before reaching a saddle point and slightly increasing again. Also note the contour line at ∆Gu° ( p, T ) = 0 corresponding to fu = fn = 0.5, which determines the protein phase boundary between the

folded and unfolded states.31-33, 35 A global fit of eq 4 to ∆Gu° ( p, T ) at all studied temperatures and pressures revealed the thermodynamic parameters given in the left column in Table 2. A graphical representation of these results are depicted as a stability diagram in Figure 5C and as a comparison with experimental isobars and isotherms at all 16 ACS Paragon Plus Environment

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respective measured temperatures and pressures in Figure 3 and Figure S5.

Figure 5: Protein stability diagrams of apoKti11. (A) Three dimensional representation of the pressure and temperature-dependent Gibbs free energies derived from the fraction of unfolded apoKti11 detected by 1D 1H-NMR. (B) Contour plot of (A) with the same color code indicating isoenergetic ∆Gu° ( p, T ) values. (C) Calculated stability diagram using eq 4 with thermodynamic values derived

from a global fit of all Gibbs free energies given in Table 2. The energy difference between the depicted contour lines is 500 J/mol.

Because of the ln(T/T0-1) term in eq 4, the arbitrary value for T0 has to be below the lowest measured temperature and was set to 270 K. After the second order approximation leading to eq 5, T0 can be any value and setting it to 295 K, which is Tmax at ambient pressure, gives identical values and errors for ∆α and ∆β (right column in Table 2). A plot of the latter fit cannot be differentiated from the given global fits in Figures 3 and S5 according to eq 4 showing that the second order approximation is valid in the 17 ACS Paragon Plus Environment


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studied temperature range.

Table 2: Thermodynamic parameter of apoKti11 in respect to p0 = 0.1 MPa

The solutions of eq 5 for ∆Gu° ( p, T ) = 0 are conic intersections, which can be a line, a circle, of elliptical, parabolic or hyperbolic shape.31,

34

The mathematical criteria are ∆α2 > ∆Cp⋅ ∆β/T0 for an

elliptical shape, ∆α 2 = ∆Cp⋅ ∆β/T0 for a parabolic shape, and ∆α 2 < ∆Cp⋅ ∆β/T0 for a hyperbolic shape. From Table 2, ∆α 2 = 0.18 and ∆Cp⋅ ∆β/T0 = 2.0 confirming the measured and calculated hyperbolic contour lines at ∆Gu° ( p, T ) = 0 (Figures 5B and 5C).

Local pressure effects The chemical shifts of backbone amide NMR resonances in 1H-15N heteronuclear single quantum coherence (HSQC) experiments report about the local chemical environment of each peptide bond along the protein chain. A shift in population towards the unfolded state with increasing pressure at 295 K can be seen in Figure 6 by the built up of lowly dispersed resonances around 8.5 ppm amide proton chemical shifts. The well dispersed cross peaks of the native state show linear and non-linear pressure dependencies for both the 1H and 15N chemical shifts reporting a local adaptation of the native state towards increased pressure (Figures S6 and S7). 18 ACS Paragon Plus Environment

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Figure 6: Superposition of 1H-15N HSQC spectra of apoKti11 between 0.1 MPa and 240 MPa. Spectra were recorded at 295 K, pH 7.5 (Tris-HCl), and increasing pressure in steps of 40 MPa. Residue assignments at 0.1 MPa are given at the respective resonances.

Fitting δnuclei (p) = δnuclei (p0) + b1⋅p + b2⋅p2 to these chemical shift changes reveal linear b1 and quadratic b2 coefficients for all backbone amides (Figures S8 and S9), which could be unambiguously assigned under all conditions, and a structural representation of the proton b1 values is shown in Figure 7. The highest absolute values for b1 were clustered around the only cavity in apoKti11.



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Figure 7: Structural visualization of the linear backbone amide proton b1 coefficients of apoKti11 (PDB ID: 5AX2). Green sections correspond to b1 < - 0.4 ppm/GPa and red residues to b1 > 0.4 ppm/GPa. The blue color represents the boundaries of a cavity of about 3.9 Å diameter mapped by a radius of 1.4 Å with the program PyMol corresponding to a volume of approximately 30 Å3.


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Discussion

Removal of the zinc ion from holoKti11 causes minor structural rearrangements (Figure 1 and Figure S2) because the loss of metal coordination is compensated by two new cystines of the coordinating cysteines by air oxidation. Like the zinc ions, both new covalent bonds connect the loop between βstrand 3 and 4 with the loop between β-strand 5 and 6. Thus a drop in stability and unfolding known from other zinc finger proteins when forming the apo form

40

has not been observed for Kti11. The

local dynamics on a pico- to nanosecond timescale remains also the same for apo- and holoKti11 (Figure S3). Minor structural differences between the NMR structure of holoKti11

18

and the here

determined crystal structure of apoKti11 were observed (Figure 1). For example, apoKti11 comprises an additional β strand (β1) and the length of the respective β3 to β6 strands differ compared to the holoKti11 structure.

Compared to other model proteins for protein folding studies41, apoKti11 revealed a low Gibbs free energy of unfolding ∆Gu° (T ) at ambient pressure below 5 kJ/mol but a reasonable change in heat capacity ∆Cp upon unfolding. Therefore, the temperature profile of ∆Gu° (T ) has a strong curvature (eq 3) and both heat and cold induced unfolding can be studied above the freezing point of water. To derive these and all following thermodynamic parameter we assumed a simplifying two-state model of an unfolded and a folded population, which differ in their 1D 1H-NMR spectra, under all experimental conditions. A comparison of the temperature transitions at increasing pressure (Figure 3 and Table 1) shows that apoKti11 at ambient pressure has a slightly higher ∆Cp value compared to the expected value from the pressure range 30 MPa to 240 MPa. The same holds for ∆Gu° (T ) , obvious from Figures 4 and S5 at temperatures between 285 K and 305 K. There is currently no straight-forward molecular 21 ACS Paragon Plus Environment


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reason for this deviation from a two-state model, which has been assumed as simplifying framework to derive thermodynamic parameters. The low ∆S u (Tm ) values might be explained by the two disulfide bonds constraining the ensemble of unfolded polypeptide chains. A general drop in ∆Cp with increasing pressure results from the reorganization of water molecules near exposed hydrophobic side chains, thus reducing the free energy gain from the hydrophobic effect 33.

The compressibility of apoKti11 in the unfolded state is smaller compared to the folded state because of a positive value for ∆β. This is obvious from the plots of ∆Gu° ( p) in Figure 4 and the saddle shaped ∆Gu° ( p, T ) in Figure 5A. Beside one exception of metmyoglobin, only negative values for the change

in isothermal compressibility of proteins have been measured as reviewed 22, 42. Therefore, only elliptic phase boundaries in pressure-temperature phase diagrams of proteins have been reported

9, 31-35, 43-45

since the condition for this shape of ∆α2 > ∆Cp⋅ ∆β/T0 is always fulfilled by a negative ∆β because ∆Cp is positive for proteins46. ApoKti11 revealed ∆α2 < ∆Cp⋅ ∆β/T0 leading to a hyperbolic phase boundary from a mathematical point of view, which we observed experimentally (Figure 5). It has been argued that this hyperbolic shape is forbidden due to unrelated fluctuations of volume and enthalpy or entropy changes at the folding/unfolding transition of a two-state system

34, 35

. In a molecular picture these

authors claim that the higher compressibility of the unfolded state in respect to the native state results from voids caused by exposed hydrophobic sections decorated by well-ordered water shells. The latter causes the generally observed positive ∆Cp values. Currently we cannot give a full molecular picture for this unexpected hyperbolic phase diagram of apoKti11, but suggest caution when discussing general properties of proteins derived from p/T phase diagrams with only very few experimental data points. Note that our approach to derive the phase diagram does not only rely on values of ∆Gu° ( p, T ) = 0 (black line in Figure 5 or one to two data points per pressure at fu = 0.5 in Figure 3) typically employed 22 ACS Paragon Plus Environment

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for published work by others but on values covering the entire experimentally accessible p/T space with values of about - 4000 J/mol < ∆Gu° ( p, T ) < 4000 J/mol and for 99 combinations of pressure and temperature values. This high number of experimental values results in a converging global fit with a positive value for ∆β independent from the given starting values for Eq. 4 and 5. The crystal structure of native apoKti11 revealed six β-strands wrapping around a cavity terminated by the two disulfide bonds at one side and the α-helices at the opposite side (Figure 7). Inspection of this cavity revealed that predominantly hydrophobic residues (I8, M13, Y24, F32, A45, I55, V57) form this void volume and we assume that water cannot penetrate at ambient pressure. The covalent inter residue bonds of the two cystines might prevent the unfolded state to form a fully extended random coil. Both effects together might result in a positive ∆β value. The crystal structure of native apoKti11 also revealed that the employed side chain NMR resonances for the 1D 1H-NMR approach to determine the ∆Gu° ( p, T ) values (Figure 2) are well distributed: I8(Hγ2) in β-strand 1, I10(Hγ13) in a loop between β-strands 1 and 2, I34(Hδ1) in β-strand 4, M39(Hε) in α-helixes 1, V57(Hγ2) in β-strand 6, and L64(Hδ2) in αhelixes 2. This good coverage of the entire apoKti11 structure by reporting side chains verifies that this 1D 1H-NMR approach characterizes global protein properties.

Several further features of the hyperbolic p/T phase diagram of apoKti11 can be verified by the results from individual measurements and analyses of single properties and confirm the derived global thermodynamic parameters. In Table 1, the temperature of maximal stability increases from 295 K to 302 K between 0.1 MPa and 240 MPa in accordance to the dotted line in Figure 5C representing

p(T ) ∆S0 =0 because ∆S0 = 0 at Tmax under all conditions. This separates the phase diagram in the left part at low temperatures corresponding to ∆S0 < 0 and the right part at high temperatures and ∆S0 > 0. Therefore, ∆S0 is close to zero for the global fit with eq 5 and T0 = 295 K as reference point and drops 23 ACS Paragon Plus Environment


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to -318 J/(mol⋅K) for the global fit with eq 4 and T0 = 270K (Table 2). The broken dotted line in Figure 5C represents p (T ) ∆V0 =0 leading to ∆V0 < 0 below this line at lower pressures fitting to a value of ∆V0 = -31 ml/mol found at 295 K and ambient pressure from the ∆Gu° ( p ) values shown in Figure 4. A negative ∆V0 corresponds to a smaller volume of the unfolded state compared to the native form of apoKti11 and thus a destabilization according to the Le Chatelier’s principle with increasing pressure up to the p (T ) ∆V0 =0 line, which corresponds to the minima of ∆Gu°(p) isotherms shown in Figure S5. We expect that the negative ∆V0 value results mainly from the hydrophobic cavity of apoKti11 in the native state. Electrostriction should play a minor role because all charged side chains are exposed to the solvent in the native structure of the protein.

The thermal expansion of the volume of apoKti11 with temperature is bigger in the unfolded state compared to the native state because of a positive value of ∆α = 0.43 ml/(mol⋅K). This corresponds to a tilt of the p/T phase diagram because p (T ) ∆S0 =0 has a positive slope of ∆Cp/ ∆α and p (T ) ∆V0 =0 a negative slope of - ∆α/ ∆β. Both, positive

31, 45

and negative

34

values for ∆α have been reported for

other proteins. A positive ∆α implies that the hydration shell around exposed hydrophobic sections of the unfolded protein is more susceptible to expand with increasing temperature compared to the hydration shell of the native state burying these sections.

Because of its favorable thermodynamic properties, both the unfolded and folded state of apoKti11 can be studied at residue-to-residue resolution between ambient and 240 MPa pressure, because both states are significantly populated and exchange slow on the NMR chemical shift time scale. At 295 K the ratio fn/fu shifts from 0.86/0.14 (0.1 MPa) to 0.55/0.45 (240 MPa). For the unfolded state, both 1H and 15

N chemical shifts show only marginal pressure dependencies (δnuclei (p)) and therefore it is unlikely 24 ACS Paragon Plus Environment

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that this state buries voids at exposed hydrophobic sections.35 This is in line with a positive ∆β value as discussed above. In contrast, 1H and

15

N resonances of the native state of apoKti11, are pressure

dependent (Figures 6, S6, S7, S8, S9). Linear contributions to δnuclei (p) are discussed to report about conformational rearrangements along the protein chain with increasing pressure.47, 48 After correction for the individual pressure dependencies of each residue

49

, high positive linear b1 values of amide

protons cluster around the hydrophobic cavity (red in Figure 7). The majority of large negative b1 values (green in Figure 7) correspond to protons in secondary structures, which also show high positive b2 values (Figure S8). The former might arise from a stabilization of hydrogen bonds 14, 47, 48, the latter have been attributed to correlated motions during fluctuations between different conformations Conformational plasticity can correlate with protein function

13

47, 48

.

and for Kti11, indeed NMR chemical

shift mapping upon titration with the natural binding partner Kti13 revealed residues not only close to the Zn2+ binding cysteine residues but propagated towards residues surrounding the cavity

17

. V45 at

the N-terminal end of β-strand 5 stands out with the highest value for all derived b values. A correlation between the contact order of hydrogen bonds and their stability as found for ubiquitin 14 is not obvious from the here derived b1,2 coefficients probably because of the two disulfide bonds. The linear and nonlinear δnuclei (p) contributions of the 15N chemical shifts are not related to the here discussed structural properties. A straight forward correlation between b1,2 coefficients and ∆V0 or ∆β as found recently 50 was not possible because the relation |∆G0|

Hyperbolic Pressure-Temperature Phase Diagram of the Zinc-Finger

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