Open Access Article
Davide
Brasili‡
a,
Joanna
Watly‡
b,
Eyal
Simonovsky
cd,
Remo
Guerrini
a,
Nuno A.
Barbosa
b,
Robert
Wieczorek
b,
Maurizio
Remelli
*a,
Henryk
Kozlowski
*b and
Yifat
Miller
*cd
aDepartment of Chemical and Pharmaceutical Sciences, University of Ferrara, via Fossato di Mortara 17, I-44121 Ferrara, Italy. E-mail: rmm@unife.it
bDepartment of Chemistry, University of Wroclaw, F. Joliot-Curie 14, 50-383 Wroclaw, Poland. E-mail: henryk.kozlowski@chem.uni.wroc.pl
cDepartment of Chemistry, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
dIlse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel. E-mail: ymiller@bgu.ac.il
First published on 17th February 2016
Polyhistidine-tags are often used for the affinity purification of polyhistidine-tagged recombinant proteins. These sequences are also found in nature and are often highly conserved across different species. However, their exact role in the biological systems is not clear. The purpose of this work is to shed light on the behavior of poly-His sequences in their interactions with metal ions. This work illustrates the first study of novel poly-(His–Ala) peptides that bind Cu(II) applying both experimental techniques and extensive computational tools. The studied novel peptides are analogues of the short protected fragment of the pHpG (EDDH9GVG10) peptide, which was found in the venom of Atheris squamigera. Our study presents the properties of metal ion binding-histidine tag complexes and their mutated derivatives. The Cu(II) binding ability in pHG (Ac-EDDH9G-NH2) is more efficient than in the mutated derivatives, although the number of imidazoles that bind to Cu(II) ions are similar. Finally, the formation of an α-helical structure is observed in pHG and in one of the mutated derivatives, indicating the importance of the sequence in the poly-(His-Ala) tags.
Recently, the interest in HRP studies has been increased, especially for a large class of proteins with poly-His–poly-Gly (pHpG) sequences, which are found in the venom of snakes.3,9 For example, the EDDHHHHHHHHHGVGGGGGGGGGG (pHpG) sequence appears in the venom of Atheris squamigera, an African viper. It has been proposed that such peptides may block the metalloproteinases contained in the poison, and therefore do not cause damage to the venom gland.3,10
Recently, we have studied the short protected fragment of the pHpG peptide from the Atheris squamigera venom: Ac-EDDHHHHHHHHHG-NH2 (pHG) using experimental techniques and computational tools.11 We have shown that the multiple histidine residues in this peptide fragment are very efficient metal ion chelators with very high affinities toward Cu(II), Ni(II) and Zn(II) ions in comparison with other histidine rich proteins. Furthermore, the interactions of metal ions with the pHG peptide have shown a very unusual behavior of this system.11 First, various sets of three imidazoles from the His9-tag in pHG can bind metal ions in different ways along the sequence and consequently form polymorphic binding states. Second, the formation of a regular α-helical structure has been observed when a metal binds to the peptide molecule. Polymorphism allows metal ions to ‘move along’ the polyhistidine fragments, which serve as a metal ion transporting pathway. Our previous studies on copper complexes with the His6-tag have shown similar results: the presence of polymorphic binding states (with the participation of maximum two His residues in metal ion binding) and the formation of helical structures for some binding modes.12,13
Since our recent studies on the specificity of the metal ion interactions with His-tags containing 6 or 9 His residues have shown very unusual behavior and incredible efficiency of binding metal ions,11,12,14 this work extends our studies to new analogues in which the His residues mutated to Ala residues. Therefore the aim of this study is to examine the properties and the structural characterization of these new poly-(His–Ala) analogues of the pHG peptide.
To provide an insight into the mechanisms through which the Cu(II) binds non-adjacent His or alternate His residues in poly-His peptides, this study is focused on two new poly-His peptides that are derived from mutations of Ala of the pHG peptide. The first peptide consists of four His residues alternating with five Ala residues: Ac-EDDAHAHAHAHAG-NH2 (L1) and the second peptide consists of five His residues alternating with four Ala residues: Ac-EDDHAHAHAHAHG-NH2 (L2). These two analogues contain a lower number of histidines with respect to the original peptide pHG; but, more importantly, histidines are not consecutive. In fact, it has been already reported in the literature that not only the number of histidines in the sequence, but also their relative position influences the stability and the structure of the complexes.15–18
This work presents a combination of experimental techniques and computational tools used to investigate the interactions of Cu(II) with each one of these two peptides. This is the first study that shows the coordination abilities of mutated sequences of pHG peptide derivatives towards the Cu(II) ion and the comparison of their properties to the original sequence with consecutive histidines.
| Species | Log β |
pKa | Residue |
|---|---|---|---|
| LH2− | 7.89 (6) | 7.89 | His |
| LH2− | 14.47 (6) | 6.58 | His |
| LH3 | 20.98 (7) | 6.51 | His |
| LH4+ | 26.59 (7) | 5.61 | His |
| LH52+ | 30.9 (1) | 4.3 | Glu |
| LH63+ | 34.5 (1) | 3.6 | Asp |
| LH74+ | 37.2 (1) | 2.7 | Asp |
| Species | Log β |
pKa | Residue |
|---|---|---|---|
| LH2− | 7.72 (3) | 7.72 | His |
| LH2− | 14.54 (3) | 6.82 | His |
| LH3 | 21.17 (4) | 6.63 | His |
| LH4+ | 27.14 (4) | 5.97 | His |
| LH52+ | 32.75 (5) | 5.61 | His |
| LH63+ | 37.01 (6) | 4.26 | Glu |
| LH74+ | 40.70 (7) | 3.69 | Asp |
| LH85+ | 43.24 (1) | 2.53 | Asp |
:
L1 and Cu(II)
:
L2 in solution are 1
:
1
:
1.1, millimolar concentrations) revealed seven protonated mononuclear Cu(II) complexes for each one of the peptides L1 and L2. The distribution diagrams are shown in Fig. 1 and 2 and the corresponding stability constants are reported in Tables S1 and S2.† The formation of some of these seven protonated mononuclear Cu(II) complexes has been confirmed by the mass spectra (MS) (Fig. S3–S11†). Under conditions of metal excess (M
:
L = 2
:
1) protonated binuclear Cu(II) complexes were formed (Fig. S7 and S11, ESI†). This result is not surprising due to the relatively large number of donor sites that are available in the two peptides, and this finding can be the subject of a further investigation. However, when the metal-to-peptide ratio is approximately 1
:
1, as it is the case for the thermodynamic measurements performed in the current study, no polynuclear complex has been detected.
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Fig. 1 Representative distribution diagram for the peptide L1 with Cu(II); = 6 × 10−4 mol dm−3; metal/peptide ratio = 1 : 1.1. | ||
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Fig. 2 Representative distribution diagram for the peptide L2 with Cu(II); = 6 × 10−4 mol dm−3; metal/peptide ratio = 1 : 1.1. | ||
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Fig. 3 UV-Vis spectra at different pH values for the system Cu(II)/L1; = 5 × 10−4 mol dm−3; M/L ratio = 1.1.1. | ||
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Fig. 4 CD spectra at different pH values for the system Cu(II)/L1; = 5 × 10−4 mol dm−3; M/L ratio = 1.1.1. | ||
In the complex [CuLH] prevailing at pH ≈ 6, L1 is monoprotonated. The fourth His is still protonated, i.e. cannot bind Cu(II). A pKa value of 6.82 characterizes the deprotonation of the species [CuLH] to form the species [CuL]−, which is the most abundant complex at physiological pH. This pKa value is compatible with the coordination to Cu(II) either by an amide nitrogen or by His11 (Tables S1 and S2†). The latter hypothesis implies that the species [CuL]− has a coordination of Cu(II) with four imidazoles (4Nim). However, observing the visible portion of the CD spectra for the system Cu(II)/L1, at a pH higher than 5 the onset of a weak but detectable d–d band at 570–580 nm can be observed (Table S4†). This may be a clue that an amide nitrogen is involved in the coordination. Since the amides are closer to the chiral centers of the peptide more than the imidazole side chains, it is expected to get more intense CD signals. At the same time, the UV-Vis spectra show a further blue-shift of the absorption band to 603 nm (pH 7.2–7.9) and the EPR AII value increases from 173 to 186 G. Therefore, the coordination mode proposed for the species [CuL]− of L1 is (3Nim, N−), where N− refers to the deprotonated nitrogen of a peptide bond. It is therefore proposed that the fourth His residue should remain protonated. The deprotonation of [CuL]−, leading to the formation of the subsequent [CuLH−1]2− species, is characterized by a pKa value of 7.87 which is very close to the value that is measured for His11 in the free peptide (7.89, Table 1). This value suggests that no interaction occurs between this imidazole and Cu(II) and that the complex geometry remains with three imidazoles and a nitrogen (3Nim, N−). Finally, at higher pH values the species [CuLH−2]3− and [CuLH−3]4− are formed. Spectroscopic data suggest that at these higher pH values the deprotonated amides gradually substitute imidazole nitrogens, forming a (2Nim, 2N−) and (Nim, 3N−) complex, respectively.
In the case of L2, the first species which is formed is the complex [CuLH4]3+ (Fig. 2). Also in this case, the coordination hypothesis is 2Nim, as suggested by spectroscopic data (Table S4,†Fig. 5, 6 and S13†).
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Fig. 5 UV-Vis spectra at different pH values for the system Cu(II)/L2; = 5 × 10−4 mol dm−3; M/L ratio = 1.1.1. | ||
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Fig. 6 CD spectra at different pH values for the system Cu(II)/L2; = 5 × 10−4 mol dm−3; M/L ratio = 1.1.1. | ||
In this case, CD spectra suggest that the first coordination of an amide nitrogen occurs only at pH 8.5 (Table S4†). The species [CuLH] which is formed at around pH 5 (corresponding to [CuL]− in the case of L1) is expected to exhibit a coordination of four imidazoles (4Nim) with Cu(II) and not with three imidazoles and nitrogen (3Nim, N−), as proposed for L1. This can suggest that the interactions between Cu(II) and the backbone of the peptide is shielded by the additional histidine residue in L2.
The pKa value of 6.43 characterizes the formation of the species [CuL]− of L2 (Fig. 2). Two possible coordination modes are available: first, an axial coordination should take place, to form a square pyramidal species (5Nim). Second, the substitution of a Nim donor atom in the equatorial position would occur, with the possible shift of the latter to the axial position, to form a square pyramid again but with the (3Nim, N−) coordination in the equatorial plane, similarly as seen for L1 at physiological pH. On the basis of the available spectroscopy data, the second possible coordination mode is more likely at physiological pH.
In summary, at physiological pH, the spectroscopy data suggest that in peptide L1 the Cu(II) binds either to (2Nim, 2N−) or (3Nim, N−), in a preference to the coordination mode of (3Nim, N−). In peptide L2 the Cu(II) binds to (3Nim, N−) at physiological pH.
The minimized structures of L1a and L1b exhibited interactions of Cu(II) with two and three imidazole groups, respectively. In L1a, Cu(II) strongly binds two histidines: His7 and His11 (Cu(II)–His7 and Cu(II)–His11 distances are: 1.832 Å and 1.835 Å, respectively). In L1b, Cu(II) binds three histidines: two histidines His7 and His11 strongly interact Cu(II) (Cu(II)–His7 and Cu(II)–His11 distances are: 1.849 Å and 1.841 Å, respectively) and a third histidine His5 binds to Cu(II) with relatively lower interactions than His7 and His11 (Cu(II)–His5 distance is ∼0.5 Å longer than those of His7 and His11) (Table S5†). Yet, the third imidazole group of His5 that binds Cu(II) in L1b provides a better stabilization, as we obtained from the DFT calculations: L1b is relatively more stable than L1a by 47.2 kcal mol−1.
The minimized structure of peptide L2 illustrated three imidazole groups that bind Cu(II): Cu–His4 and Cu–His10 with bond lengths of around 1.9 Å and Cu–His6 with a slightly longer bond length: 2.1 Å (Table S6†). It should be noted here that the bond length ranges of all Cu(II)–His that have been found in L1a, L1b and L2 peptides demonstrate the typical strong bonds of Cu(II) that bind residues in peptide complexes, as we also previously have shown.11,12,14,25 Interestingly, the DFT predictions show an excellent agreement with the experimental observation for both peptides at physiological pH.
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| Scheme 1 Hydrogen bond networks (blue arrows) in the structural models of L1a and L1b. Orange dots illustrate the residues that bind Cu(II). Red arrows show a regular helix. | ||
The minimized structure L2 shows a more branched network of hydrogen bonds: ten hydrogen bonds, almost twice than the structural models L1a and L1b (Scheme 2). Most of the hydrogen bond networks contribute to the formation of helical structures: both 310 helix and α-helical structures (Table S8†). L2 illustrates two cooperative hydrogen bond chains: one is a typical of 310 helix: D3–A5–A7–A9 and the second typical of the α-helical structure: H4–H6–H8.
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| Scheme 2 Hydrogen bonds and metal–peptide connections (orange dots). Red arrows show regular helix hydrogen bonds. | ||
Similarly as we found for L1a and L1b, in the minimized structure L2 all the hydrogen bonds are formed in the domains along the peptide that the Cu(II) binds (Scheme 2). According to the DFT calculations, ∼50% of the domains in L2 exhibit 310 helix properties. We expect α-helical regular structures in peptides longer than 19–21 residues, but the 310 helices shall be energetically preferred over α-helixes.26
The DFT calculations for the structural models of L1a, L1b and L2 were performed in the gas phase; nevertheless, they can provide good initial structures to run MD simulations for solvated Cu(II)–peptide complexes and mimic the experimental conditions. The simulated structural models can then be compared to the experimental observations performed in solution.
The simulated models for the complexes formed by L1 and L2 peptides are shown in Fig. 8. We applied the DSSP analysis to determine the properties of the secondary structure of these complexes. One can see that during the MD simulations of L1a there are no properties of the α-helical structure, while L1b has slight properties of the α-helical structure that appears at the end of the simulations (Fig. S14†). On the other hand, the complex L2 shows α-helical properties that appear along most of the MD simulations (Fig. S14†). The percentages of the α-helical properties for each residue along these structures are seen in Fig. 9. While the complex L1b demonstrates a small percentage of a short α-helix structure in the N-terminal (Asp2–His5), the complex L2 shows a relatively large percentage of a relatively long α-helical structure in the C-terminal (Ala7–His12). The α-helical structures of these peptides in the domains along the sequences can also be seen from the STRIDE analysis (Fig. 8), which is similar to the DSSP analysis.
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| Fig. 9 The percentage of α-helical properties of residues for the peptide models using the DSSP analysis. | ||
An estimation of the energies and the populations of L1a and L1b indicates that the structure of L1b is strongly more stable than the structure of L1a (Fig. S15 and Table S9†), as predicted by the DFT level of theory. Therefore, we suggest that there is a slight preference for the formation of an α-helix structure in the N-terminal of the L1 peptide, when it binds to Cu(II). Finally, the MD simulations illustrate the formation of an α-helix structure in the C-terminal of the L2 peptide when it binds to Cu(II).
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| Fig. 10 A snapshot from the MD simulations for peptide L1a illustrates coordination with Glu1, His7 and His11 (His5 is replaced by Glu1). | ||
Fig. 11 illustrates the competition between L1 and L2 to form complexes with Cu(II). One can see that L2, which contains five His residues, forms distinctly more stable complexes than L1 along the whole pH range. This result confirms our previous observation that larger numbers of His residues reveal a better coordination with metals.11,12,14 Interestingly, the experimental data, the DFT calculations and the MD simulations have shown that Cu(II) is more likely to interact with three histidines in L2 than in L1. The three histidines coordinated and slightly more branched than hydrogen bond networks contribute to a higher stability of the complex Cu(II)–L2.
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| Fig. 11 A competition plot for a ternary solution containing equimolar concentrations (1 mM) of Cu(II), L1 and L2. | ||
In order to better shed light on the role of the number of His residues in the ability of Cu(II) to bind the peptide, we further investigated the competition between each one of the studied peptides L1 and L2 with other similar peptides with poly-His sequences. Four poly-His peptides were studied: (i) the peptide Ac-THHHHAHGG-NH2, which is a protected fragment of the Hpn protein that is secreted by Helicobacter pylori18 and consists of five His residues, four of which are consecutive (Fig. S18†); (ii) a fragment of the prion protein of zebrafish (zp-PrP63-87),27 which consists of seven His residues, six of which are separated by two amino acids (Fig. S19†); (iii) a pHG peptide,11 which consists of nine consecutive His residues (His9-tag) (Fig. 12) and (iv) a His6-tag,12 commonly used in IMAC chromatography (Fig. S20†).
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| Fig. 12 Competition plot for a ternary solution containing equimolar concentrations (1 mM) of: (a) Cu(II), L1 and Ac-EDDH9G-NH2 (pHG); (b) Cu(II), L2 and Ac-EDDH9G-NH2 (pHG). | ||
One can see from Fig. 12 and S18–S20† that the peptides with a larger number of histidines in the sequence have a better ability to bind the Cu(II) ion. For example, the competition plots that compare the pHG peptide with peptides L1 and L2 show that pHG binds Cu(II) ions more effectively than L1 and L2 (Fig. 12). It is important to note that in pHG with L1 and L2 peptides Cu(II) binds a maximum of three imidazole groups. Interestingly, in all peptides metal ions induce the formation of α-helix. The surprising difference in the efficiency of metal ion binding may be due to the occurrence of polymorphic states in the case of Cu(II)–pHG (twelve of various structures) and a much better defined secondary structure of the α-helix, stabilized by the richer network of hydrogen bonds between the imidazole rings in most of these complexes.11
Similar effects are observed when comparing L1 and L2 complexes with the Cu(II)–His6-tag system (Fig. S20†). The peptide with six histidines is the most effective, but more interestingly, in these complexes we have differences in coordination modes before involvement of the amide nitrogen in the metal ion binding: {2Nim} (His6-tag) and {3Nim} (L1 and L2). The MD simulations and DFT calculations have shown an ensemble of polymorphic states for the Cu(II)–His6-tag complex and a preference for the formation of the α-helix structure.12
Finally, for peptides with a similar number of His residues, the alternate sequence of His and Ala as in peptide L2 provides a more stable complex than the non-alternating sequence His and Ala, as seen in peptide Ac-THHHHAHGG-NH2 (Fig. S18b†). It is likely that in the peptide Ac-THHHHAHGG-NH2 the His residues are too close to each other to contemporarily bind Cu(II), while in L2 the His residues that bind Cu(II) are not close to each other, i.e. not continuous.
On the basis of the obtained results we suggest that there are strong dependencies between the number and positions of histidines along the histidine-rich sequences and their ability to coordinate metal ions and the stability of the complexes. Furthermore, in longer sequences of poly-His peptides the quantity of possible polymorphic states and the possibility to induce the formation of helical structures are increased. Finally, we propose that the extremely efficient metal ion binding properties that induce the formation of a regular helical structure in the unstructured His-tag peptides may be important for the biological behavior of peptides and proteins containing such sequences.
:
1 v/v; 2 mL/0.2 g of resin) as the last synthetic step.
The protected peptide-resin was treated with reagent B29 (trifluoroacetic acid (TFA)/H20/phenol/triisopropylsilane 88
:
5
:
5
:
2; v/v; 10 mL/0.2 g of resin) for 1.5 h at room temperature. After filtration of the resin, the solvent was concentrated in vacuo and the residue triturated with ethyl ether. Crude peptides were purified by preparative reversed-phase HPLC using a Water Delta Prep 3000 system with a Jupiter column C18 (250 × 30 mm, 300 A, 15 μm spherical particle size). The column was perfused at a flow rate of 20 mL min−1 with a mobile phase containing solvent A (5%, v/v, acetonitrile in 0.1% TFA), and a linear gradient from 0 to 20% of solvent B (60%, v/v, acetonitrile in 0.1% TFA) over 25 min for the elution of peptides. Analytical HPLC analyses were performed on a Beckman 116 liquid chromatograph equipped with a Beckman 166 diode array detector. The analytical purity of the peptides was determined using a Luna C18 column (4.6 × 100 mm, 3 μm particle size) with the above solvent system (solvents A and B) programmed at a flow rate of 0.5 mL min−1 using a linear gradient from 0% to 40% B over 25 min. All analogues showed ≥95% purity when monitored at 220 nm. The molecular weight of the final compounds was determined by using a mass spectrometer ESI Micromass ZMD-2000.
:
1.1. CuCl2 was an extra pure product (Sigma-Aldrich); the concentration of its stock solution was determined by ICP-MS. The carbonate-free stock solution of NaOH 0.1 mol dm−3 was purchased from Sigma-Aldrich and then potentiometrically standardized with potassium hydrogen phthalate as the primary standard. The HCl stock solution was prepared by diluting concentrated HCl (Sigma-Aldrich) and then standardized with NaOH. All sample solutions were prepared with freshly doubly distilled water. The ionic strength was adjusted to 0.1 mol dm−3 by adding KCl (Sigma-Aldrich). Grade A glassware was employed throughout.
The standard potential and the slope of the electrode couple were computed by means of Glee31 or SUPERQUAD32 programs. The purities and the exact concentrations of the peptide solutions were determined either by the Gran method33 or by using the SUPERQUAD program. The HYPERQUAD program34 was instead employed for the calculation of the overall (β) stability constant, referred to the following equilibrium (1):
| pM + qL + rH ⇄ MpLqHr | (1) |
The associated standard deviations (referring to random errors only), are reported in parentheses in the Tables below as uncertainties on the last significant figure. The speciation and competition diagrams were computed with the HYSS program.35
:
1.1. Ethylene glycol (30%) was used as a cryoprotectant for EPR measurements. The EPR parameters were analysed by computer simulation of the experimental spectra using Bruker's WIN-EPR SIMFONIA Software Version 1.2. The pH was adjusted with appropriate amounts of HCl and NaOH solutions.
The concentration of solutions used for UV-Vis and CD studies was similar to those employed in the potentiometric experiment. The UV-Vis, CD and EPR spectroscopic parameters were calculated from the spectra obtained at the pH values corresponding to the maximum concentration of each particular species, on the basis of distribution diagrams.
:
1.1 stoichiometry, [peptide]tot = 5 × 10−4 mol dm−3) were prepared in a 1
:
1 MeOH–H2O mixture at pH 4.5. The samples were infused at a flow rate of 3 μL min−1. The instrument was calibrated externally with the Tunemix™ mixture (Bruker Daltonik, Germany) in the quadratic regression mode. Data were processed by using the Bruker Compass Data Analysis 4.0 program. The mass accuracy for the calibration was better than 5 ppm, enabling together with the true isotopic pattern (using SigmaFit) an unambiguous confirmation of the elemental composition of the obtained complex.
:
1 complex with capped Ac-EDDAHAHAHAHAG-NH2 (L1) and Ac-EDDHAHAHAHAHG-NH2 (L2) peptides. The starting structure of the peptide for DFT calculations was generated on the basis of the amino acid sequence after 75 ps simulation at 300 K, without cutoffs using BIO+ implementation of the CHARMM force field. All calculations were performed with the Gaussian 09
42 suite of programs using the M06
43 hybrid functional and the triple-zeta 6-311G basis set. In the peptide structures imidazole nitrogens are not protonated and thus available for coordination, while amide nitrogens bear their proton and cannot bind the metal ion. This situation is similar to that of a metal/peptide solution at pH approximately 5.
The equations of motion were integrated using the leapfrog integrator with a step of 1 fs. The solvated systems were energy minimized for 2000 conjugated gradient steps, where the hydrogen bonding distance between the β-sheet in each oligomer was fixed in the range 2.2–2.5 Å. The counter ions and water molecules were allowed to move. The hydrogen atoms were constrained to the equilibrium bond using the SHAKE algorithm.60
The minimized solvated systems were energy minimized for 5000 additional conjugate gradient steps and 20
000 heating steps at 250 K, with all atoms being allowed to move. Then, the system was heated from 250 K to 310 K for 300 ps and equilibrated at 310 K for 300 ps. All simulations were run for 30 ns at 310 K. The temperature of 310 K had been applied to test the stabilities of all the variant models. Parameterizations for the Cu(II)–peptide complexes had been performed for all MD simulations. The force constant values for the Cu(II)–N atom and Cu(II)–O atom are in the range of 25–50 kcal mol−1 Å−2.
In the GBMV calculations, the dielectric constant of water was set to 80. The hydrophobic solvent-accessible surface area (SASA) term factor was set to 0.00592 kcal (mol Å)−1. Each conformation was minimized using 1000 cycles, and the conformational energy was evaluated by grid-based GBMV.
A total of 1000 conformations (500 for each model) were used to construct the energy landscapes of the two models and to evaluate the conformer probabilities by using Monte Carlo (MC) simulations. In the first step, one conformation of conformer i and one conformation of conformer j were randomly selected. Then, the Boltzmann factor was computed as e−(Ej−Ei)/kT, where Ei and Ej are the conformational energies evaluated using the GBMV calculations for conformations i and j, respectively, k is the Boltzmann constant and T is the absolute temperature (298 K used here). If the value of the Boltzmann factor was larger than the random number, then the move from conformation i to conformation j was allowed. After 1 million steps, the conformations ‘visited’ for each conformer were counted. Finally, the relative probability of model n was evaluated as Pn = Nn/Ntotal, where Pn is the population of model n, Nn is the total number of conformations visited for model n, and Ntotal is the total steps. The advantages of using MC simulations to estimate conformer probability lie in their good numerical stability and the control that they allow for transition probabilities among several conformers.
A total of 1000 conformations of these two models (500 conformations for each model) were used to construct the energy landscape (Table S9†). The pair of these two models is likely to present may be only a very small percentage of the ensemble. Nevertheless, the carefully selected models cover the most likely structures.
The DSSP algorithm provides information on specific domains that illustrate an α-helix and a β-sheet. It does not distinguish between various types of α-helixes, such as the 310 helix, α-helix, etc.
Footnotes |
| † Electronic supplementary information (ESI) available: Spectroscopy measurement, DFT and MD data. See DOI: 10.1039/c5dt04747a |
| ‡ These authors contributed equally to this work. |
| This journal is © The Royal Society of Chemistry 2016 |