Letter pubs.acs.org/JPCL
Tightening and Untying the Knot in Human Carbonic Anhydrase III Joachim Dzubiella* Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Germany Department of Physics, Humboldt-University Berlin, Newtonstr. 15, 12489 Berlin, Germany ABSTRACT: The forced mechanical unfolding of the knotted protein Human Carbonic Anhydrase (HCA) III is examined by steered, explicit-water molecular dynamics computer simulations. In agreement with previous indications from experiments and coarse-grained simulations, knot tightening by pulling near-terminal amino acids (4 and 267) leads to a much higher resistance to unfolding than for knot untying, where pulling amino acids 4 and 253 untangles the knot by threading the Cterminal end out of the knotting loop. In particular, the resistance during knot tightening is observed to diverge due to a tightly tied-up enzymatic core of the HCA if it is coordinated by the catalytically important zinc ion. The underlying structural pictures are presented and discussed. SECTION: Biophysical Chemistry and Biomolecules
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n the last two decades several protein folds have been discovered that contain a knot in their native structure.1−8 The question of the physiological relevance of protein knots is still under debate.9−28 One interesting proposal is that the entangled structure might have a stabilizing effect against thermal or mechanical protein unfolding.4,6,10,17,27 This could be relevant in vivo during protein translocation and threading through the tiny pores of biological membranes or proteasomes.29 In this respect, it is tempting to speculate that the steric blocking of narrow pathways by a strongly localized or tightly pulled knotted structure may have biological significance.4,19,20 Indeed Wang and Ikai showed for a protein of the carbonic anhydrase family that due to the presence of a trefoil knot the mechanical unfolding by atomic force microscopy (AFM) was almost impossible,9 likely originating from knot tightening when pulling at the terminal ends. Consistent with that view, the resistance to unfolding was much weaker when pulled at different sites to untie the knot.10 In contrast with the large resistance found by Wang and Ikai during knot tightening, Bornschlögl et al. did not observe any enhanced resistance in the knot tightening in phytochrome when compared with “normal” proteins.18 The structural mechanisms leading to this discrepancy are not well understood. A possible reason could be the distinct core structure of the carbonic anhydrase family, where a zinc ion coordinated to a central β-sheet structure establishes the catalytically active site;13,30 see Figure 1a. This rigid structure may act as a local catcher for the tightening knot, as demonstrated for the first time by coarse-grained computer simulations.16 To address these issues we investigate the resistance against unfolding and structural features in the forced unfolding of the trefoil-knotted Human Carbonic Anhydrase (HCA) III, as a representative example of the knotted carbonic anhydrase family, using detailed explicit-water molecular dynamics (MD) computer simulations. These are the first all-atom simulations of knot tightening in a complete protein from the native to the © XXXX American Chemical Society
Figure 1. (a) Native structure of HCA III explicitly showing the pulled amino acids (aa’s) near the N-terminus (aa 4), the C-terminus (aa 267), and the aa 253. The zinc ion is rendered as gray sphere. (b) Illustration of the shallow knot structure: pulling at aa 4 and 267 tightens the knot, while pulling at aa 4 and 253 unthreads part of the protein through a knotting loop and unties the knot.9,10,24
totally stretched state. In these steered MD simulations we pull the protein at two sites in opposite directions as in AFM and unfold it with a constant pulling velocity between 1 and 2 nm/ ns. First, we investigate the involvement of the zinc ion on the force response during knot tightening. We will provide unprecedented evidence that distinctively different resistances Received: April 8, 2013 Accepted: May 15, 2013
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peak, however, the knot involvement is large (cf. Figure 3b): the knot wraps around the inner β-sheet structure and seemingly ties it together. However, further pulling unfolds this inner structure and stretching can proceed until the chain is fully extended; see Figure 2a. Roughly the same resistive signature is found if zinc is included with nonbonded (purely van der Waals and electrostatic) interactions, apart from the occurrence of a third peak at ∼82 nm extension. In fact, we observe that the initially coordinated zinc ion relatively quickly (in a few nanoseconds) leaves the natively bound state to interact with other charged groups or even diffuses into bulk water. Hence, it is not involved anymore in the unfolding process, similarly as in the case without zinc above. Note that Ohta et al.13 observed involvement of zinc also for larger extensions, but they pulled 50−100 times faster so that the whole protein was unfolded in 1 to 2 ns. The peak at 82 nm is due to wrapping of the knot around a final remaining α-helical peptide part (not shown). The latter shows in agreement with coarse-grained simulations16 that a tightening knot can be locally captured by structural obstacles in the chain. Moreover, while our simulations show reproducible features most of the time, structural fluctuations in the unfolding process can have large mechanical consequences due to the presence of the tightening knot. In a larger ensemble of simulations the knot may be localized at different, partially unfolded locations during the final stages of tightening, as predicted by coarse-grained simulations.16 The situation significantly changes if we coordinate the zinc properly by “covalently” binding it to its native coordinations sites. The corresponding force−extension curves are also plotted in Figure 2a, now for two different pulling rates 2 and 1 nm/ns. Both simulations provide the same result within the statistical fluctuations, showing reproducibility of the major features of the MD protocol. While the first peak of the “no zinc” simulations can also be found, at the second peak location at ∼50 nm extension, however, divergence of the resistance is observed. Similarly as in the previous cases here the knot wraps around the inner enzymatic core of the HCA, as shown in Figure 3c. However, the coordinated zinc ion additionally stabilizes (and entangles) this region so that its unfolding or escape from the knot becomes impossible. The divergence is in agreement with AFM experiments on knot tightening in carbonic anhydrase,9 where probably the same structural mechanisms played a role. Notably, we find that the aa’s adjacent to the tied-up coordinated region remain unstretched during the full run, in contrast with peptides in regions outside the tightening knot. Hence, the knot seem to adsorb most of the stress and the coordinated region appears to remain essentially stress-free. Regarding the overall tightening behavior, in all runs we observe that the knot gets tightened on the chain and does not slide along the unfolded peptide, as observed, for instance, on DNA or simple homopolymers.9,31−34 The reason is likely that it wraps around the relatively rigid core of the protein, which prevents the knot from diffusing away. As suggested by Sulkowska et al. and others,16,19 knot diffusion along unfolded peptides seems unlikely in general due to strong intrapeptide interactions and geometric constraints. We now compare knot tightening versus knot untying. The corresponding force−extension curves are plotted in Figure 2b for the same rate of 1 nm/ns. In both cases the zinc is fully coordinated. Importantly, one can see that on average the
may occur if zinc is properly coordinated to the protein core or not. In the second step, we explore the quantitative difference in resistance between knot tightening and untying, as inspired by the previous AFM experiments9,10 and the systematic coarse-grained computer simulations by Sulkowska et al.16,24 Untying simulations using explicit-water were pioneered by Ohta et al.,13 albeit with 50 to 100 times larger pulling rates. We find that untying is indeed accompanied by much less resistance and therefore the complete unfolding is easily executable. A few underlying structural details will be presented and discussed. The protein HCA III [Protein Data Base (PDB) entry 1Z97]30 is shown in Figure 1, together with an illustrative sketch of the shallow trefoil knot structure. If the amino acids (aa’s) very close to the termini are pulled, the knot will be tightened, while a change from aa 267 to 253 threads the Cterminal region out of a knotting loop and unties the knot.9,10,24 We first discuss the results for various involvements of the zinc ion in knot tightening. The corresponding force−extension curves are plotted in Figure 2a. In the case of no zinc involved,
Figure 2. (a) Force−extension curves for knot tightening. The case of no zinc ion present at all (“no zinc”) is compared with the cases of zinc with “nonbonded” and fully coordinated (“zinc bonded”) interactions at a pulling rate of 1 nm/ns. For the bonded case results for a higher rate of 2 nm/ns are also shown. (b) The force from knot tightening is compared with untying at a pulling rate of 1 nm/ns for the zinccoordinated case.
we find that the protein can be completely unfolded into a stretched configuration with a tightly pulled knot, as previously demonstrated for other proteins by AFM18 and coarse-grained simulations.16 The divergence of the force at an extension of ∼90 nm starts when the contour length of the completely unfolded chain is reached. Two distinct peaks occur before: one at about 25 nm, the second at about 45−50 nm. The first peak is due to the unfolding of the N and C terminal topologies before reaching the inner core, as shown in the snapshot of Figure 3a. We will see below that this signature also appears in untying, as already nicely discussed by Ohta et al.,13 and thus the knot involvement is small in this stage. In the second largest 1830
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Figure 3. Simulation snapshots of the unfolded protein HCA III for (a) knot tightening at an extension of ∼30 nm corresponding to the first peak in Figure 2a, (b) knot tightening at the second peak at ∼50 nm in Figure 2a for “no zinc”, (c) knot tightening at ∼50 nm corresponding to the divergence in Figure 2a for the coordinated zinc, (d) untying at an extension of ∼15 nm corresponding to the first peak in Figure 2b, and (e) untying at an extension of ∼60 nm corresponding to the last peak in the untying curve in Figure 2b. The zinc ion in panels c−e is rendered as a white-gray sphere coordinated by three histidine groups (liquorice rendering).
overall resistance against unfolding is about two to three times higher in the case of knot tightening. The first peak in the untying case is for the same reason as in the tightening case; see the snapshot in Figure 3d and the discussion of the “17 nm peak” by Ohta et al.13 The remaining three peaks are at about 36, 48, and 60 nm and are due to successive ruptures of secondary structure. We find that the former two correspond essentially to unfolding mechanisms discussed by Ohta et al.13 for their “40 nm peak” and “53 nm peak”, respectively. The last peak at 60 nm, not observed by Ohta et al.13 for technical reasons, involves the rupture of a remaining α−β structure around β-sheets S7 and S8 and the helix H5, according to the nomenclature by Ohta et al.13 (involving aa’s 140 to 180), as shown in Figure 3e. In this snapshot also the still-intact peptide part around the coordinated zinc can be seen. In summary, we have examined the role of zinc and different pulling sites on the resistance and structure in the mechanical unfolding of the knotted carbonic anhydrase. Knot tightening during unfolding increases the mechanical force significantly when compared with “normal” proteins through tying-up locally rigid structures by the knot. We demonstrated for the first time that in HCA the zinc ion in the catalytic center plays an extra stabilizing role and leads to a diverging resistance to forced unfolding. Future work may elucidate if such mechanisms can be generalized to other knotted proteins. The tied-up and rigid structure may have biological significance
by inhibiting transport through narrow pores of biological membranes or proteasomes.29
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METHODS The computer simulations have been performed using the Gromacs simulations package 35 version 4.5 employing AMBER’s ff03 force field 36 for the protein and the uncoordinated zinc ion, together with the SCP/E water model.37 The protein structure including the zinc ion has been taken from PDB 1Z97,30 where the first three aa’s of the N-terminus are missing. In the runs with a coordinated zinc ion we adapted the partial charges and bonded force-field parameters suggested by Merz et al. for HCA,12,38 where the zinc ion is harmonically (“covalently”) linked to the three histidine groups 94, 97, and 119 and one water molecule. The simulations have been performed in the Gibbs (NPT) ensemble at constant pressure of P = 1 bar and a temperature T = 300 K using a Parrinello−Rahman barostat and the “V-rescale” thermostat, respectively, as included in Gromacs. A constant number N of atoms in a periodically repeated rectangular simulation box with the size of about 40 × 6 × 6 nm including 46 766 water molecules has been considered. Electrostatic interactions have been evaluated by the particle-mesh Ewald (PME) summation method with 336 × 50 × 50 vectors for the calculation of the Fourier part of the electrostatics. The realspace parts for nonbonded interactions were cutoff at 0.9 nm. Gromacs’ umbrella pulling protocol “direction-periodic” has 1831
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(14) Mallam, M. L.; Jackson, S. E. Folding Studies on a Knotted Protein. J. Mol. Biol. 2005, 346, 1409−1421. (15) Wallin, S.; Zeldovich, K. B.; Shakhnovich, E. I. The Folding Mechanics of a Knotted Protein. J. Mol. Biol. 2007, 368, 884−893. (16) Sułkowska, J. I.; Sułkowski, P.; Szymczak, P.; Cieplak, M. Tightening of Knots in Proteins. Phys. Rev. Lett. 2008, 100, 058106-1− 058106-4. (17) Sułkowska, J. I.; Sułkowski, P.; Szymczak, P.; Cieplak, M. Stabilizing Effect of Knots on Proteins. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 19714−19719. (18) Bornschlögl, T.; Anstrom, D.; Dzubiella, J.; Rief, M.; Forest, K. T. Tightening the Knot in Phytochrome by Single Molecule Atomic Force Microscopy. Biophys. J. 2009, 96, 1508−1514. (19) Dzubiella, J. Sequence-Specific Size, Structure, and Stability of Tight Protein Knots. Biophys. J. 2009, 96, 831−839. (20) Huang, L.; Makarov, D. E. Translocation of a Knotted Polypeptide Through a Pore. J. Chem. Phys. 2008, 129, 121107-1− 121107-4. (21) Sułkowska, J. I.; Sułkowski, P.; Onuchic, J. Dodging the Crisis of Folding Proteins with Knots. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 3119−3124. (22) Noel, J. K.; Sułkowska, J. I.; Onuchic, J. Slipknotting upon native-like loop formation in a trefoil knot protein. Proc. Natl. Acad. Sci. U.S.A. 2009, 107, 5403Đ15408. (23) Sułkowska, J. I.; Noel, J. K.; J. N. Onuchic, J. N. Energy Landscape of Knotted Protein Folding. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 17783−17788. (24) Sułkowska, J. I.; Szymczak, P. S. P.; Cieplak, M. Untying Knots in Proteins. J. Am. Chem. Soc. 2010, 132, 13954−13956. (25) Sułkowska, J. I.; Rawdon, E. J.; Millett, K.; Onuchic, J. N.; Stasiak, A. Conservation of Complex Knotting and Slipknotting Patterns in Proteins. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, E1715− E1723. (26) He, C.; Genchev, G. Z.; Lu, H.; Li, H. Mechanically Untying a Protein Slipknot: Multiple Pathways Revealed by Force Spectroscopy and Steered Molecular Dynamics Simulations. J. Am. Chem. Soc. 2012, 34, 10428−10435. (27) Sayre, T. C.; Lee, T. M.; King, N. P.; Yeates, T. O. Protein Stabilization in a Highly Knotted Protein Polymer. Protein Eng., Des. Sel. 2011, 24, 627−630. (28) Andrews, B. T.; Capraro, D. T.; Sulkowska, J. I.; Onuchic, J. N.; Jennings, P. A. Hysteresis as a Marker for Complex, Overlapping Landscapes in Proteins. J. Phys. Chem. Lett. 2013, 4, 180−188. (29) Prakash, S.; Matouschek, S. Protein Unfolding in the Cell. Trends Biochem. Sci. 2004, 29, 593−600. (30) Duda, D. M.; Tu, C.; Fisher, I. Z.; An, H.; Yoshioka, C.; Govindasamy, L.; Laipis, P. J.; Agbandje-McKenna, A.; Silverman, D. N.; McKenna, R. Human Carbonic Anhydrase III: Structural and Kinetic Study of Catalysis and Proton Transfer. Biochemistry 2005, 44, 10046−10053. (31) Bao, X. R.; Lee, H. J.; Quake, S. R. Behavior of Complex Knots in Single DNA Molecules. Phys. Rev. Lett. 2003, 91, 265506-1− 265506-4. (32) Vologodskii, A. Brownian Dynamics Simulation of Knot Diffusion along a Stretched DNA Molecule. Biophys. J. 2006, 90, 1594−1597. (33) Huang, L.; Makarov, D. E. VMD: Langevin Dynamics Simulations of the Diffusion of Molecular Knots in Tensioned Polymer Chains. J. Phys. Chem. A 2007, 111, 10338−10344. (34) Metzler, R.; Reisner, W.; Riehn, R.; Austin, R.; Tegenfeldt, J. O.; Sokolov, I. M. Diffusion Mechanisms of Localised Knots along a Polymer. Europhys. Lett. 2006, 76, 696−702. (35) Spoel, D. V. D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, and Free. Comput. Chem. 2005, 26, 1701−1708. (36) Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Merz, K. M.; Pearlman, D. A.; Crowley, M.; et al. AMBER9.0; University of California: San Francisco, 2006.
been employed with a pull vector along the longest box diagonal to avoid self-interactions of the unfolded protein with its periodic images. The pull spring constant has been fixed to 36 kJ/mol/nm2 while the pull rate has varied between 2 and 1 nm/ns. Note that these pulling rates are many orders of magnitude faster than those in experimental AFM setups,9,18 and hence the MD simulation results are probably not representing a full equilibrium sampling. However, given the reproducibility in the force extension curves for the different setups and the qualitative agreement of some of our force peaks with those of Ohta’s previous simulations, our findings seem to provide a reasonable picture of the overall mechanical behavior of the protein under forced unfolding. Snapshots have been generated using VMD.39 Calculations have been performed on 16 to 48 cores in parallel on a computing cluster.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS J.D. thanks Matthias Rief for inspiring discussions, the Deutsche Forschungsgemeinschaft (DFG) for support within the Emmy-Noether-Program and the SFB 863, and the Leibniz Rechenzentrum (LRZ) München for computing time.
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REFERENCES
(1) Mansfield, M. L. Are There Knots in Proteins? Nat. Struct. Biol. 1994, 1, 213−214. (2) Taylor, W. R.; Lin, K. A Tangled Problem. Nature 2003, 421, 25. (3) Lua, R. C.; Grosberg, A. Y. Statistics of Knots, Geometry of Conformations, and Evolution of Proteins. PLOS Comput. Biol. 2006, 2, 350−357. (4) Virnau, P.; Mirny, L. A.; Kardar, M. Intricate Knots in Proteins: Function and Evolution. PLOS Comput. Biol. 2006, 2, 1074−1079. (5) Taylor, W. R. Protein Knots and Fold Complexity: Some New Twists. Comput. Biol. Chem. 2007, 31, 151−162. (6) Yeates, T.; Norcross, S.; King, N. P. Knotted and Topologically Complex Proteins as Models for Studying Folding and Stability. Curr. Opinion Chem. Biol. 2007, 11, 595−603. (7) Virnau, P.; Mallam, A.; Jackson, S. Structures and Folding Pathways of Topologically Knotted Proteins. J. Phys.: Condens. Matter 2011, 23, 033101-1−033101-17. (8) Bölinger, D.; Sułkowska, J. S.; Hsu, H.-P.; Mirny, L. A.; Kardar, M.; Onuchic, J. N.; Virnau, P. A Stevedore’s Protein Knot. PLOS Comput. Biol. 2010, 6, e1000731-1−e1000731-6. (9) Wang, T.; Ikai, A. Protein Stretching III: Force-Extension Curves of Tethered Bovine Carbonic Anhydrase B to the Silicon Substrate under Native, Intermediate and Denaturing Conditions. Jpn. J. Appl. Phys. 1999, 38, 3912−3917. (10) Alam, M. T.; Yamada, T.; Carlsson, U.; Ikai, A. The Importance of Being Knotted: Effects of the C-Terminal Knot Structure on Enzymatic and Mechanical Properties of Bovine Carbonic Anhydrase II. FEBS Lett. 2002, 519, 35−40. (11) Wang, T.; Arakawa, H.; Ikai, A. Reversible Stretching of a Monomeric Unit in a Dimeric Bovine Carbonic Anhydrase B with the Atomic Force Microscope. Ultramicroscopy 2002, 91, 253−259. (12) Toba, S.; Colombo, G.; Merz, K. M., Jr. Solvent Dynamics and Mechanism of Proton Transfer in Human Carbonic Anhydrase II. J. Am. Chem. Soc. 1999, 121, 2290−2302. (13) Ohta, S.; Alam, M. T.; Arakawa, H.; Ikai, A. Origin of Mechanical Strength of Bovine Carbonic Anhydrase Studied by Molecular Dynamics Simulation. Biophys. J. 2004, 87, 4007−4020. 1832
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(37) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular-Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684−3690. (38) Peters, M. B.; Yang, Y.; Wang, B.; Füsti-Molnár, L.; Weaver, M. N.; Merz, K. M., Jr. Structural Survey of Zinc-Containing Proteins and Development of the Zinc AMBER Force Field (ZAFF). J. Chem. Theory Comput. 2010, 6, 2935−2947. (39) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38.
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Tightening and Untying the Knot in Human Carbonic Anhydrase III Joachim Dzubiella* Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Germany Department of Physics, Humboldt-University Berlin, Newtonstr. 15, 12489 Berlin, Germany ABSTRACT: The forced mechanical unfolding of the knotted protein Human Carbonic Anhydrase (HCA) III is examined by steered, explicit-water molecular dynamics computer simulations. In agreement with previous indications from experiments and coarse-grained simulations, knot tightening by pulling near-terminal amino acids (4 and 267) leads to a much higher resistance to unfolding than for knot untying, where pulling amino acids 4 and 253 untangles the knot by threading the Cterminal end out of the knotting loop. In particular, the resistance during knot tightening is observed to diverge due to a tightly tied-up enzymatic core of the HCA if it is coordinated by the catalytically important zinc ion. The underlying structural pictures are presented and discussed. SECTION: Biophysical Chemistry and Biomolecules
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n the last two decades several protein folds have been discovered that contain a knot in their native structure.1−8 The question of the physiological relevance of protein knots is still under debate.9−28 One interesting proposal is that the entangled structure might have a stabilizing effect against thermal or mechanical protein unfolding.4,6,10,17,27 This could be relevant in vivo during protein translocation and threading through the tiny pores of biological membranes or proteasomes.29 In this respect, it is tempting to speculate that the steric blocking of narrow pathways by a strongly localized or tightly pulled knotted structure may have biological significance.4,19,20 Indeed Wang and Ikai showed for a protein of the carbonic anhydrase family that due to the presence of a trefoil knot the mechanical unfolding by atomic force microscopy (AFM) was almost impossible,9 likely originating from knot tightening when pulling at the terminal ends. Consistent with that view, the resistance to unfolding was much weaker when pulled at different sites to untie the knot.10 In contrast with the large resistance found by Wang and Ikai during knot tightening, Bornschlögl et al. did not observe any enhanced resistance in the knot tightening in phytochrome when compared with “normal” proteins.18 The structural mechanisms leading to this discrepancy are not well understood. A possible reason could be the distinct core structure of the carbonic anhydrase family, where a zinc ion coordinated to a central β-sheet structure establishes the catalytically active site;13,30 see Figure 1a. This rigid structure may act as a local catcher for the tightening knot, as demonstrated for the first time by coarse-grained computer simulations.16 To address these issues we investigate the resistance against unfolding and structural features in the forced unfolding of the trefoil-knotted Human Carbonic Anhydrase (HCA) III, as a representative example of the knotted carbonic anhydrase family, using detailed explicit-water molecular dynamics (MD) computer simulations. These are the first all-atom simulations of knot tightening in a complete protein from the native to the © XXXX American Chemical Society
Figure 1. (a) Native structure of HCA III explicitly showing the pulled amino acids (aa’s) near the N-terminus (aa 4), the C-terminus (aa 267), and the aa 253. The zinc ion is rendered as gray sphere. (b) Illustration of the shallow knot structure: pulling at aa 4 and 267 tightens the knot, while pulling at aa 4 and 253 unthreads part of the protein through a knotting loop and unties the knot.9,10,24
totally stretched state. In these steered MD simulations we pull the protein at two sites in opposite directions as in AFM and unfold it with a constant pulling velocity between 1 and 2 nm/ ns. First, we investigate the involvement of the zinc ion on the force response during knot tightening. We will provide unprecedented evidence that distinctively different resistances Received: April 8, 2013 Accepted: May 15, 2013
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peak, however, the knot involvement is large (cf. Figure 3b): the knot wraps around the inner β-sheet structure and seemingly ties it together. However, further pulling unfolds this inner structure and stretching can proceed until the chain is fully extended; see Figure 2a. Roughly the same resistive signature is found if zinc is included with nonbonded (purely van der Waals and electrostatic) interactions, apart from the occurrence of a third peak at ∼82 nm extension. In fact, we observe that the initially coordinated zinc ion relatively quickly (in a few nanoseconds) leaves the natively bound state to interact with other charged groups or even diffuses into bulk water. Hence, it is not involved anymore in the unfolding process, similarly as in the case without zinc above. Note that Ohta et al.13 observed involvement of zinc also for larger extensions, but they pulled 50−100 times faster so that the whole protein was unfolded in 1 to 2 ns. The peak at 82 nm is due to wrapping of the knot around a final remaining α-helical peptide part (not shown). The latter shows in agreement with coarse-grained simulations16 that a tightening knot can be locally captured by structural obstacles in the chain. Moreover, while our simulations show reproducible features most of the time, structural fluctuations in the unfolding process can have large mechanical consequences due to the presence of the tightening knot. In a larger ensemble of simulations the knot may be localized at different, partially unfolded locations during the final stages of tightening, as predicted by coarse-grained simulations.16 The situation significantly changes if we coordinate the zinc properly by “covalently” binding it to its native coordinations sites. The corresponding force−extension curves are also plotted in Figure 2a, now for two different pulling rates 2 and 1 nm/ns. Both simulations provide the same result within the statistical fluctuations, showing reproducibility of the major features of the MD protocol. While the first peak of the “no zinc” simulations can also be found, at the second peak location at ∼50 nm extension, however, divergence of the resistance is observed. Similarly as in the previous cases here the knot wraps around the inner enzymatic core of the HCA, as shown in Figure 3c. However, the coordinated zinc ion additionally stabilizes (and entangles) this region so that its unfolding or escape from the knot becomes impossible. The divergence is in agreement with AFM experiments on knot tightening in carbonic anhydrase,9 where probably the same structural mechanisms played a role. Notably, we find that the aa’s adjacent to the tied-up coordinated region remain unstretched during the full run, in contrast with peptides in regions outside the tightening knot. Hence, the knot seem to adsorb most of the stress and the coordinated region appears to remain essentially stress-free. Regarding the overall tightening behavior, in all runs we observe that the knot gets tightened on the chain and does not slide along the unfolded peptide, as observed, for instance, on DNA or simple homopolymers.9,31−34 The reason is likely that it wraps around the relatively rigid core of the protein, which prevents the knot from diffusing away. As suggested by Sulkowska et al. and others,16,19 knot diffusion along unfolded peptides seems unlikely in general due to strong intrapeptide interactions and geometric constraints. We now compare knot tightening versus knot untying. The corresponding force−extension curves are plotted in Figure 2b for the same rate of 1 nm/ns. In both cases the zinc is fully coordinated. Importantly, one can see that on average the
may occur if zinc is properly coordinated to the protein core or not. In the second step, we explore the quantitative difference in resistance between knot tightening and untying, as inspired by the previous AFM experiments9,10 and the systematic coarse-grained computer simulations by Sulkowska et al.16,24 Untying simulations using explicit-water were pioneered by Ohta et al.,13 albeit with 50 to 100 times larger pulling rates. We find that untying is indeed accompanied by much less resistance and therefore the complete unfolding is easily executable. A few underlying structural details will be presented and discussed. The protein HCA III [Protein Data Base (PDB) entry 1Z97]30 is shown in Figure 1, together with an illustrative sketch of the shallow trefoil knot structure. If the amino acids (aa’s) very close to the termini are pulled, the knot will be tightened, while a change from aa 267 to 253 threads the Cterminal region out of a knotting loop and unties the knot.9,10,24 We first discuss the results for various involvements of the zinc ion in knot tightening. The corresponding force−extension curves are plotted in Figure 2a. In the case of no zinc involved,
Figure 2. (a) Force−extension curves for knot tightening. The case of no zinc ion present at all (“no zinc”) is compared with the cases of zinc with “nonbonded” and fully coordinated (“zinc bonded”) interactions at a pulling rate of 1 nm/ns. For the bonded case results for a higher rate of 2 nm/ns are also shown. (b) The force from knot tightening is compared with untying at a pulling rate of 1 nm/ns for the zinccoordinated case.
we find that the protein can be completely unfolded into a stretched configuration with a tightly pulled knot, as previously demonstrated for other proteins by AFM18 and coarse-grained simulations.16 The divergence of the force at an extension of ∼90 nm starts when the contour length of the completely unfolded chain is reached. Two distinct peaks occur before: one at about 25 nm, the second at about 45−50 nm. The first peak is due to the unfolding of the N and C terminal topologies before reaching the inner core, as shown in the snapshot of Figure 3a. We will see below that this signature also appears in untying, as already nicely discussed by Ohta et al.,13 and thus the knot involvement is small in this stage. In the second largest 1830
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Figure 3. Simulation snapshots of the unfolded protein HCA III for (a) knot tightening at an extension of ∼30 nm corresponding to the first peak in Figure 2a, (b) knot tightening at the second peak at ∼50 nm in Figure 2a for “no zinc”, (c) knot tightening at ∼50 nm corresponding to the divergence in Figure 2a for the coordinated zinc, (d) untying at an extension of ∼15 nm corresponding to the first peak in Figure 2b, and (e) untying at an extension of ∼60 nm corresponding to the last peak in the untying curve in Figure 2b. The zinc ion in panels c−e is rendered as a white-gray sphere coordinated by three histidine groups (liquorice rendering).
overall resistance against unfolding is about two to three times higher in the case of knot tightening. The first peak in the untying case is for the same reason as in the tightening case; see the snapshot in Figure 3d and the discussion of the “17 nm peak” by Ohta et al.13 The remaining three peaks are at about 36, 48, and 60 nm and are due to successive ruptures of secondary structure. We find that the former two correspond essentially to unfolding mechanisms discussed by Ohta et al.13 for their “40 nm peak” and “53 nm peak”, respectively. The last peak at 60 nm, not observed by Ohta et al.13 for technical reasons, involves the rupture of a remaining α−β structure around β-sheets S7 and S8 and the helix H5, according to the nomenclature by Ohta et al.13 (involving aa’s 140 to 180), as shown in Figure 3e. In this snapshot also the still-intact peptide part around the coordinated zinc can be seen. In summary, we have examined the role of zinc and different pulling sites on the resistance and structure in the mechanical unfolding of the knotted carbonic anhydrase. Knot tightening during unfolding increases the mechanical force significantly when compared with “normal” proteins through tying-up locally rigid structures by the knot. We demonstrated for the first time that in HCA the zinc ion in the catalytic center plays an extra stabilizing role and leads to a diverging resistance to forced unfolding. Future work may elucidate if such mechanisms can be generalized to other knotted proteins. The tied-up and rigid structure may have biological significance
by inhibiting transport through narrow pores of biological membranes or proteasomes.29
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METHODS The computer simulations have been performed using the Gromacs simulations package 35 version 4.5 employing AMBER’s ff03 force field 36 for the protein and the uncoordinated zinc ion, together with the SCP/E water model.37 The protein structure including the zinc ion has been taken from PDB 1Z97,30 where the first three aa’s of the N-terminus are missing. In the runs with a coordinated zinc ion we adapted the partial charges and bonded force-field parameters suggested by Merz et al. for HCA,12,38 where the zinc ion is harmonically (“covalently”) linked to the three histidine groups 94, 97, and 119 and one water molecule. The simulations have been performed in the Gibbs (NPT) ensemble at constant pressure of P = 1 bar and a temperature T = 300 K using a Parrinello−Rahman barostat and the “V-rescale” thermostat, respectively, as included in Gromacs. A constant number N of atoms in a periodically repeated rectangular simulation box with the size of about 40 × 6 × 6 nm including 46 766 water molecules has been considered. Electrostatic interactions have been evaluated by the particle-mesh Ewald (PME) summation method with 336 × 50 × 50 vectors for the calculation of the Fourier part of the electrostatics. The realspace parts for nonbonded interactions were cutoff at 0.9 nm. Gromacs’ umbrella pulling protocol “direction-periodic” has 1831
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(14) Mallam, M. L.; Jackson, S. E. Folding Studies on a Knotted Protein. J. Mol. Biol. 2005, 346, 1409−1421. (15) Wallin, S.; Zeldovich, K. B.; Shakhnovich, E. I. The Folding Mechanics of a Knotted Protein. J. Mol. Biol. 2007, 368, 884−893. (16) Sułkowska, J. I.; Sułkowski, P.; Szymczak, P.; Cieplak, M. Tightening of Knots in Proteins. Phys. Rev. Lett. 2008, 100, 058106-1− 058106-4. (17) Sułkowska, J. I.; Sułkowski, P.; Szymczak, P.; Cieplak, M. Stabilizing Effect of Knots on Proteins. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 19714−19719. (18) Bornschlögl, T.; Anstrom, D.; Dzubiella, J.; Rief, M.; Forest, K. T. Tightening the Knot in Phytochrome by Single Molecule Atomic Force Microscopy. Biophys. J. 2009, 96, 1508−1514. (19) Dzubiella, J. Sequence-Specific Size, Structure, and Stability of Tight Protein Knots. Biophys. J. 2009, 96, 831−839. (20) Huang, L.; Makarov, D. E. Translocation of a Knotted Polypeptide Through a Pore. J. Chem. Phys. 2008, 129, 121107-1− 121107-4. (21) Sułkowska, J. I.; Sułkowski, P.; Onuchic, J. Dodging the Crisis of Folding Proteins with Knots. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 3119−3124. (22) Noel, J. K.; Sułkowska, J. I.; Onuchic, J. Slipknotting upon native-like loop formation in a trefoil knot protein. Proc. Natl. Acad. Sci. U.S.A. 2009, 107, 5403Đ15408. (23) Sułkowska, J. I.; Noel, J. K.; J. N. Onuchic, J. N. Energy Landscape of Knotted Protein Folding. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 17783−17788. (24) Sułkowska, J. I.; Szymczak, P. S. P.; Cieplak, M. Untying Knots in Proteins. J. Am. Chem. Soc. 2010, 132, 13954−13956. (25) Sułkowska, J. I.; Rawdon, E. J.; Millett, K.; Onuchic, J. N.; Stasiak, A. Conservation of Complex Knotting and Slipknotting Patterns in Proteins. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, E1715− E1723. (26) He, C.; Genchev, G. Z.; Lu, H.; Li, H. Mechanically Untying a Protein Slipknot: Multiple Pathways Revealed by Force Spectroscopy and Steered Molecular Dynamics Simulations. J. Am. Chem. Soc. 2012, 34, 10428−10435. (27) Sayre, T. C.; Lee, T. M.; King, N. P.; Yeates, T. O. Protein Stabilization in a Highly Knotted Protein Polymer. Protein Eng., Des. Sel. 2011, 24, 627−630. (28) Andrews, B. T.; Capraro, D. T.; Sulkowska, J. I.; Onuchic, J. N.; Jennings, P. A. Hysteresis as a Marker for Complex, Overlapping Landscapes in Proteins. J. Phys. Chem. Lett. 2013, 4, 180−188. (29) Prakash, S.; Matouschek, S. Protein Unfolding in the Cell. Trends Biochem. Sci. 2004, 29, 593−600. (30) Duda, D. M.; Tu, C.; Fisher, I. Z.; An, H.; Yoshioka, C.; Govindasamy, L.; Laipis, P. J.; Agbandje-McKenna, A.; Silverman, D. N.; McKenna, R. Human Carbonic Anhydrase III: Structural and Kinetic Study of Catalysis and Proton Transfer. Biochemistry 2005, 44, 10046−10053. (31) Bao, X. R.; Lee, H. J.; Quake, S. R. Behavior of Complex Knots in Single DNA Molecules. Phys. Rev. Lett. 2003, 91, 265506-1− 265506-4. (32) Vologodskii, A. Brownian Dynamics Simulation of Knot Diffusion along a Stretched DNA Molecule. Biophys. J. 2006, 90, 1594−1597. (33) Huang, L.; Makarov, D. E. VMD: Langevin Dynamics Simulations of the Diffusion of Molecular Knots in Tensioned Polymer Chains. J. Phys. Chem. A 2007, 111, 10338−10344. (34) Metzler, R.; Reisner, W.; Riehn, R.; Austin, R.; Tegenfeldt, J. O.; Sokolov, I. M. Diffusion Mechanisms of Localised Knots along a Polymer. Europhys. Lett. 2006, 76, 696−702. (35) Spoel, D. V. D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, and Free. Comput. Chem. 2005, 26, 1701−1708. (36) Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Merz, K. M.; Pearlman, D. A.; Crowley, M.; et al. AMBER9.0; University of California: San Francisco, 2006.
been employed with a pull vector along the longest box diagonal to avoid self-interactions of the unfolded protein with its periodic images. The pull spring constant has been fixed to 36 kJ/mol/nm2 while the pull rate has varied between 2 and 1 nm/ns. Note that these pulling rates are many orders of magnitude faster than those in experimental AFM setups,9,18 and hence the MD simulation results are probably not representing a full equilibrium sampling. However, given the reproducibility in the force extension curves for the different setups and the qualitative agreement of some of our force peaks with those of Ohta’s previous simulations, our findings seem to provide a reasonable picture of the overall mechanical behavior of the protein under forced unfolding. Snapshots have been generated using VMD.39 Calculations have been performed on 16 to 48 cores in parallel on a computing cluster.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS J.D. thanks Matthias Rief for inspiring discussions, the Deutsche Forschungsgemeinschaft (DFG) for support within the Emmy-Noether-Program and the SFB 863, and the Leibniz Rechenzentrum (LRZ) München for computing time.
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