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Ligand diffusion in globins: simulations versus experiment
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Ligand diffusion in globins: simulations versus experiment Ron Elber Computer simulations in molecular biophysics describe in atomic detail the structure, dynamics, and function of biological macromolecules. To assess the quality of these models and to pick up new mechanisms, comparisons with experimental measurements are made. Most comparisons examine thermodynamic and average structural properties. Here we discuss studies of dynamics and fluctuations in a protein. The diffusion of a small ligand between internal cavities in myoglobin, and its escape to solvent are considered. Qualitative and semi-quantitative agreements between experiment and simulation are obtained for the identities of the cavities that physically trap the ligand and for the connections between them. However, experimental and computational ‘doors’ are at significant variance. Simulations suggest multiple gates while kinetic experiments point to one dominant exit. Address Department of Chemistry and Biochemistry, Institute of Computational Engineering and Sciences (ICES), 1 University Station, ICES, C0200, The University of Texas at Austin, Austin, TX 78712, United States Corresponding author: Elber, Ron ([email protected])
continuous flow of theoretical and experimental studies of this system followed these original investigations. This paper provides an overview on the field with a focus on recent computational investigations. Other influential papers from the past to which frequent references are made are (i) the identification of the Xenon cavities in the protein structure and the use of a small computational probe to study them [5] and (ii) the first systematic search of diffusion pathways of a diatomic ligand in a thermally fluctuating protein matrix [6]. Ligand diffusion into and from buried active sites is of wide interest. The Locally Enhanced Sampling (LES) method, for searching diffusion pathways, was introduced for myoglobin [6]. However, it was used to investigate other proteins, for example, the diffusion of oxygen and hydrogen in hydrogenase [9], of oxygen in dioxygenase [10], and of nitric oxide in nitrile hydratase [11]. Interestingly, more accurate variant of LES is available [12,13], but so far it was not used widely. Other examples in which Molecular Dynamics provided insight to ligand permeation problems are of flavoenzyme [14] and catalase [15].
Current Opinion in Structural Biology 2010, 20:162–167 This review comes from a themed issue on Theory and simulation Edited by Chandra Verma and Juan Ferna´ndez Recio Available online 29th January 2010 0959-440X/$ – see front matter # 2010 Elsevier Ltd. All rights reserved. DOI 10.1016/j.sbi.2010.01.002
In addition to a deeper understanding of molecular biophysics events that are relevant to molecular function, thermally assisted diffusion is an ideal system for a straightforward study by Molecular Dynamics (MD). The mantra for accurate application of the MD approach is (i) force field and (ii) sampling. Both items seem in place for the task at hand. The forces involved are physical, and no formation or breaking of chemical bonds is present. This observation suggests that traditional and readily available mechanical force fields are a reasonable match.
Introduction After the determination of the globin structures by X-ray crystallography [1,2] it was quickly established that thermal fluctuations of the protein matrix must assist the penetration of the small ligand in and out of the protein. Visual inspection of the X-ray structure suggests no obvious way for a ligand to enter or escape. Indeed a pioneering computational work by Case and Karplus [3] examined two routes between the binding site and the solvent just below the E helix (Figure 1) exiting through the so-called histidine gate. This study illustrates significant energy barriers for the ‘door’ and a mechanism in which side chain fluctuations are coupled to ligand escape and to partial protein fluidity [4]. It is amusing that this particular path, after significant debate and suggestions for alternatives in the literature [5,6], recently received a strong endorsement from experimental studies [7,8]. A Current Opinion in Structural Biology 2010, 20:162–167
The sampling requirement is somewhat more complex. The time scale of the events of interest (migration of the ligand to alternative cavities in the protein and to the solvent) is pretty long compared to the basic time step of MD (femtoseconds). Ligand hops between cavities and escapes at time scales that are measured in hundreds of nanoseconds [7,8,16]. This makes it necessary to execute hundreds of millions of time steps to observe (frequently) the events of interest. Moreover, to obtain quantitative description of ligand migration, multiple trajectories are required. The diffusion is a non-equilibrium process (once the ligand leaves the protein matrix it is unlikely to return on the simulation time scale) and an average over initial conditions must be performed to obtain quantitative results. The requirement for multiple trajectories and ensemble average makes the calculation more www.sciencedirect.com
Ligand diffusion in globins: simulations versus experiment Elber 163
Figure 1
compared quantitatively to experiment. Hence, the results of ligand diffusion in myoglobin provide a strict test of the way we investigate kinetic mechanisms by computer simulations and are useful probes of anisotropic dynamic fluctuations in well-defined three-dimensional structures of proteins [20,21].
Experimental analysis of ligand diffusion
Myoglobin and the Xenon cavities (detected by free volume calculations in red). The heme is in blue and the red spot attached to it from above is the distal pocket. Above the distal pocket one finds the Xe4 cavity and below the heme is the Xe1 binding site. Xe2 and Xe3 are to the left. The E helix is drawn in the back from the lower left to the upper right of the protein, touching in the figure the cavities Xe2–Xe4. The figure was prepared by the program zmoil http://clsb.ices.utexas.edu/prebuilt/.
expensive by orders of magnitude compared to a single trajectory. This computational task was considered formidable until recently. Past studies were therefore primarily qualitative. Even recently a few approximate approaches to the problem were explored. For example, estimates of free energy landscapes using meta-dynamics or particle insertion methods. Nevertheless, and as argued below, the qualitative computational picture of ligand diffusion in myoglobin did not deviate much from the earlier studies. Arguably, the major remaining qualitative puzzle of the kinetics of ligand diffusion in myoglobin is the identification of the escape pathway from the protein. At present there is a sharp disagreement between simulations and experiments (but there is a reasonable agreement between different simulations). The source of the significant qualitative difference is not clear.
Historically, the dominant experiment for studying ligand diffusion in myoglobin was of geminate recombination kinetics. The iron–ligand bond is broken by light or by other means and the recombination time of the dissociated ligand to the iron is followed by spectroscopy of the heme [22]. The diffusion of the ligand away from the iron and in the protein matrix causes delay in re-binding, allowing for interesting kinetic analysis. The data are interpreted in terms of a competition between (i) reformation of ligand–iron bond, (ii) diffusion between internal protein cavities (the so-called DP—the distal pocket and the Xe1–Xe4 cavities [5], see also Figure 1), and (iii) escape from the protein matrix to the solvent. It is important to separate these steps both in application and analyses of theory and in experiment to make the comparison meaningful. Other types of experiments are available that probe the ligand motions directly and help establish a more complete picture of the diffusion (e.g. time resolved crystallography [23–25] and time resolved vibrational spectroscopy [26,27]). Significant credit to the broader and renewed interest in myoglobin kinetics is due to the spectacular snapshots in time of ligand migration between internal cavities such as the DP, Xe4, and Xe1 [5,23– 25,28–32]. Nevertheless, studies of kinetics remain a crucial component. This is due to the relative ease of experimental kinetics and the ability to probe ligand escape to the solvent (the time scale in which the reaction becomes concentration dependent). After all, kinetics and thermodynamics are the prime determinants of biological function. Kinetics was measured for a wide range of myoglobin mutants, and for different solution conditions such as (Xe) pressure. We can divide the type of computations probing ligand diffusion into two main categories: (i) Approximate calculations of diffusion rate and free energy landscape, and (ii) Straightforward Molecular Dynamics trajectories. Below we discuss both of them.
Approximate calculations of diffusion rate Of course considerably more work remains to be done to make the agreement between experiment and theory quantitative. Advances in software and hardware [17– 19] made it possible to run a significant number of straightforward MD trajectories for substantial lengths of time. These trajectories observed migration events at room temperature that with sufficient statistics can be www.sciencedirect.com
The approximate procedures aim at better sampling of the free energy landscape for ligand diffusion. This is achieved by making plausible assumptions on the system dynamics, assumptions that greatly simplify the computational cost of computing the free energy landscape. Such approaches are important even now in qualitative understanding of the dynamics and interpreting complex Current Opinion in Structural Biology 2010, 20:162–167
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motions in a simpler form. We therefore discuss some of these ideas below. One approach of the so-called metadynamics [33] or local elevation [34] was used to investigate carbon monoxide diffusion in myoglobin [35,36]. The overall diffusion patterns between myoglobin cavities were similar to other studies. Free energies of wells and of barriers between the minima were estimated. The calculated barriers vary between zero and 14.5 kT in one of the studies [36], and are larger than expected from experiment. The time scale of escape to the solvent measured experimentally is about 100 nanoseconds [7,8] while the above barrier is likely to yield longer time scales. Taking the free diffusion time scale to be t0 2 ps, the activated time, t a , according to the above estimated barrier height is ta ¼ t0 expðB=kT Þ 1 ms. Interestingly, a second meta-dynamics study [37] finds significantly lower barriers suggesting that convergence of quantitative free energy map for diffusion was not reached. For example, the barrier between the Xe4 and the Xe1 cavities in the last study, which are on opposite sides of the heme, is surprisingly small. It is estimated as 2.17 kT, corresponding to tens of picoseconds migration time at room temperature. We note that both simulations used the AMBER force field [38] so the variations are likely to be caused by different sampling. A third and recent simulation of the free energy landscape of CO diffusion in myoglobin [39] was conducted with the TAMD (Temperature Accelerated Molecular Dynamics) and the single sweep methods [40]. This time the CHARMM force field was used, and the free energy values were close to the study of Nishihara et al. [36].
proposed as the exit gate at the very beginning of the field [3,44]. So far this coupling has not been demonstrated to be wrong. A slow variable based only on the ligand coordinate may be an oversimplification. Finally, the escape pathway from the Xe3 cavity proposed in reference [36] is in disagreement with experiment that strongly suggests an escape pathway from the distal pocket (DP) [7,16]. The escape pathway(s) is at variance with experiment in essentially all simulations that searched for it, and is not specific to the meta-dynamics calculations. Another intriguing computational probe of ligand diffusion is the treatment of the ligand as a perturbation. Plausible pathways are then determined by the static structure and protein fluctuations computed without the ligand. The free energy landscape is estimated by one-step insertion of the ligand to pre-existing tunnels within the protein matrix [45,46,47]. The calculations are very efficient and make it possible to probe different globins and their alternate internal diffusion network. The underlying assumption is that the small (but hard) ligand does not significantly push protein atoms while moving around.
Straightforward molecular dynamics Given that different approximate theories (and even the same theory) provide quantitatively different results it is necessary to re-evaluate the basic model (i.e. the force field) as well as the approximations that are part of the above theories. From this perspective it is useful to perform the most straightforward calculation possible in which approximations are eliminated allowing for better evaluation of agreement (or disagreement) between simulations and experiments.
Two issues make the quantitative application of metadynamics difficult. The first is that the diffusion is a nonstationary process. A number of studies were conducted on relaxation processes of the protein molecule that happen simultaneously and may induce significant nonequilibrium aspects to the diffusion [21,41–43]. As long as the ligand is trapped in the protein matrix it may be considered in local equilibrium. However, an escape to the solvent interrupts this equilibrium process. Ligands that exit to the aqueous solution may not return to the protein on the simulation time scale. Given that the computed barrier heights for ligand migration (internally and to the solvent) are not so different, for example, 13.7 kT versus 14.5 kT [36], the equilibrium assumption may require further investigations. In contrast to metadynamics the single sweep method [39] computes rigorously the equilibrium free energy surface.
For diatomic molecules such as oxygen or carbon monoxide molecules the prime interaction with other protein atoms (or solvent molecules) is of excluded volume. This interaction is typically modeled as a Lennard Jones potential. Small dipole (or more significant) quadrupole moments are used less frequently, even though welltested parameterization is available [48,49]. The overall diffusion pattern of the diatomic ligand in the protein matrix seems similar with or without the quadrupole moments (see for instance [50]. However, for quantitative description and for (perhaps) solving the gate puzzle, careful investigation of different energy parameterizations are very much to be desired.
Furthermore, in meta-dynamics and the single sweep method it is necessary to decide on slow coordinates that require a ‘speed-up’ or flattening of the energy surface. In all of the above studies the coordinates were the Cartesian position of the CO molecule. This choice is intuitive; however, it may be insufficient. Coupling between the ligand motions and activated transitions of side chains was
In an ideal computer simulation, efforts are made to reproduce the experimental set-up as accurately as possible. A ligand is placed in the heme pocket, bonded or restrained to remain at the binding site. It is kept that way for an equilibrium simulation in which water and protein are allowed to relax to an equilibrium state appropriate to the force field used. The structures of
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Ligand diffusion in globins: simulations versus experiment Elber 165
the bound state generated at equilibrium are sampled to initiate trajectories of ligand diffusion and recombination. In most of the conducted simulations the trajectories are purely diffusive [24,50,51,52], but in some cases they include detailed description of recombination events (reformation of ligand–heme bond [48,53]). Simulations on multiple electronic energy surfaces that describe the bound and unbound ligand–protein state provide a complete computational description of recombination measurements [54]. They make it possible to describe the photo-dissociation, energy relaxation, ligand diffusion, and re-binding in a single computational framework. This approach is most appropriate for direct comparison with flash photolysis and geminate recombination experiments. In [48] correct ordering of nitric-oxide recombination-rates of myoglobin mutants were obtained. Recently however, the focus was on one component of the experiment, that of ligand diffusion between internal cavities. The availability of time resolved FTIR spectroscopy and X-ray crystallography experiments that watch the build up of ligand densities at different locations in the protein matrix (Figure 1) makes direct comparison with experiment possible. A number of computational groups have taken on themselves the task of simulating the ligand diffusion in and out of myoglobin using straightforward tools of Molecular Dynamics without additional physical assumptions that enhance the computational efficiency. Of the studies mentioned above perhaps the most comprehensive is the investigation by Ruscio et al. [51] which, as described, should have put to rest many of the lingering questions about links between experiment and theory in this comprehensively studied system. Sixty-eight trajectories were conducted for ninety nanoseconds each providing ample evidence and statistics for ligand migration in the protein and escape. Moreover, since the simulated system is ‘small’ (or the concentration of myoglobin in the simulated system is very high), entry events from solvent to protein were also observed. The time scale is in overall agreement with rates measured experimentally (about 100–200 nanoseconds) and the diffusion pathways are in remarkable agreement with the emerging consensus of ligand hopping between the Xenon sites [5]. Nevertheless, one qualitative question remains and with this question I wish to conclude the present Opinion.
Conclusion In a beautiful series of experiments Scott et al. showed that the dominant escape pathway for a diatomic ligand from the protein matrix is the histidine gate [7] including an in depth examination of ligand movement in W29 mutant of myoglobin by time resolved X-ray crystallography [55]. This study was further confirmed by a series of mutations to tryptophan residues at crucial points along the ligand diffusion pathway, a study that is summarized www.sciencedirect.com
in a review [16]. These observations appear to contradict all simulations which have searched for escape pathways (rather than assuming them). A recent study in the laboratory of the author [52] observed two non-classical (not histidine) exits and the study by Ruscio et al. [51] proposed nine gates (with different surface residues). The simulation results, of multiple roughly equivalent exit pathways, are not supported by current experiments [7,16]. Kinetic analysis indicates that 70-80% of the ligands enter and exit from the distal histidine gate.
Acknowledgements This research was supported by NIH grant GM059796. Useful discussions and suggestions by John Olson and Quentin Gibson are gratefully acknowledged.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: of special interest of outstanding interest 1.
Perutz M: Structure of hemoglobin. Brookaven Symposia in Biology 1960, 13:165-183.
2.
Kendrew JC, Bodo G, Dintzis HM, Parrish RG, Wyckoff H, Phillips DC: A three-dimensional model of the myoglobin molecule obtained by X-ray analysis. Nature 1958, 181:662-666.
3.
Case DA, Karplus M: Dynamics of ligand-binding to hemeproteins. Journal of Molecular Biology 1979, 132:343-368.
4.
Elber R, Karplus M: A method for determining reaction paths in large molecules—application to myoglobin. Chemical Physics Letters 1987, 139:375-380.
5.
Tilton RF, Kuntz ID, Petsko GA: Cavities in proteins—structure of a metmyoglobin-xenon complex solved to 1.9-A. Biochemistry 1984, 23:2849-2857.
6.
Elber R, Karplus M: Enhanced sampling in moleculardynamics—use of the time-dependent hartree approximation for a simulation of carbon-monoxide diffusion through myoglobin. Journal of the American Chemical Society 1990, 112:9161-9175.
7.
Scott EE, Gibson QH, Olson JS: Mapping the pathways for O-2 entry into and exit from myoglobin. Journal of Biological Chemistry 2001, 276:5177-5188.
8.
Scott EE, Gibson QH: Ligand migration in sperm whale myoglobin. Biochemistry 1997, 36:11909-11917.
9.
Cohen J, Kim K, King P, Seibert M, Schulten K: Finding gas diffusion pathways in proteins: application to O-2 and H-2 transport in Cpl [FeFe]-hydrogenase and the role of packing defects. Structure 2005, 13:1321-1329.
10. Xu L, Liu X, Zhao WJ, Wang XC: Locally enhanced sampling study of dioxygen diffusion pathways in homoprotocatechuate 2,3-dioxygenase. Journal of Physical Chemistry B 2009, 113:13596-13603. 11. Kubiak K, Nowak W: Molecular dynamics simulations of photoactive protein nitrile hydratase. Biophysical Journal 2008, 94:3824-3838. 12. Ulitsky A, Elber R: Application of the locally enhanced sampling (LES) and a mean field witha binary collision correction (cLES) to the simulation of Ar diffusion and NO recombination in myoglobin. Journal of Physical Chemistry 1994, 98(3):1034-1043. 13. Ulitsky A, Elber R: The thermal equilibrium aspects of the timedependent hartree and the locally enhanced sampling approximations—formal properties, a correction, and computational examples for rare gas clusters. Journal of Chemical Physics 1993, 98:3380-3388. Current Opinion in Structural Biology 2010, 20:162–167
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14. Baron R, Riley C, Chenprakhon P, Thotsaporn K, Winter RT, Alfieri A, Forneris F, van Berkel WJH, Chaiyen P, Fraaije MW et al.: Multiple pathways guide oxygen diffusion into flavoenzyme active sites. In Proceedings of the National Academy of Sciences of the United States of America 2009, 106:10603-10608. 15. Amara P, Andeolei P, Jouve P, Martine MJ: Ligand diffusion in the catalase from Proteus mirabilis. Protein Science 2001, 10:1927-1935. 16. Olson JS, Soman J, Phillips GN: Ligand pathways in myoglobin: a review of Trp cavity mutations. IUBMB Life 2007, 59:552-562. 17. Stone JE, Phillips JC, Freddolino PL, Hardy DJ, Trabuco LG, Schulten K: Accelerating molecular modeling applications with graphics processors. Journal of Computational Chemistry 2007, 28:2618-2640. 18. Ensign DL, Kasson PM, Pande VJ: Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece. Journal of Molecular Biology 2007, 374:806-816. 19. Shaw DE, Deneroff MM, Dror RO, Kuskin JS, Larson RH, Salmon JK, Young C, Batson B, Bowers KJ, Chao JC et al.: Anton, a special-purpose machine for molecular dynamics simulation. Communications of the ACM 2008, 51:91-97. 20. Tomita A, Saro T, Ichiyanagi K, Nozawa S, Ichikawa H, Chllet M, Kawai F, Park SY, Tsuduki T, Yamato T et al.: Visualizing breathing motion of internal cavities in concert with ligand migration in myoglobin. In Proceedings of the National Academy of Sciences of the United States of America 2009, 106:2612-2616. 21. Takayanagi M, Okumura H, Nagaoka M: Anisotropic structural relaxation and its correlation with the excess energy diffusion in the incipient process of photodissociated MbCO: highresolution analysis via ensemble perturbation method. Journal of Physical Chemistry B 2007, 111:864-869. 22. Austin RH, Beeson KW, Eisenstein L, Frauenfelder H, Gunsalus IC: Dynamics of ligand-binding to myoglobin. Biochemistry 1975, 14:5355-5373. 23. Bourgeois D, Vallone B, Arcovito A, Sciara G, Anfinrud PA, Brunori M: Extended subnanosecond structural dynamics of myoglobin revealed by Laue crystallography. In Proceedings of the National Academy of Sciences of the United States of America 2006, 103:4924-4929. 24. Hummer G, Schotte F, Anfinrud PA: Unveiling functional protein motions with picosecond x-ray crystallography and molecular dynamics simulations. In Proceedings of the National Academy of Sciences of the United States of America 2004, 101:15330-15334. 25. Srajer V, Teng TY, Ursby T, Pradervand C, Ren Z, Adach S, Schildkamp W, Bourgeois D, Wuff M, Moffat K: Photolysis of the carbon monoxide complex of myoglobin: nanosecond time-resolved crystallography. Science 1996, 274:1726-1729. 26. Nienhaus K, Nienhaus GU: Influence of distal residue B10 on CO dynamics in myoglobin and neuroglobin. Journal of Biological Physics 2007, 33:357-370. 27. Nienhaus K, Palladino P, Nienhaus GU: Structural dynamics of myoglobin: FTIR-TDS study of NO migration and binding. Biochemistry 2008, 47:935-948. 28. Srajer V, Ren Z, Teng TY, Schmidt M, Ursby T, Bourgeois D, Pradervand C, Schildkamp W, Wuff M, Moffat K: Protein conformational relaxation and ligand migration in myoglobin: a nanosecond to millisecond molecular movie from time-resolved Laue X-ray diffraction. Biochemistry 2001, 40:13802-13815. 29. Schotte F, Soman J, Olson JS, Wulff M, Anfinrud PA: Picosecond time-resolved X-ray crystallography: probing protein function in real time. Journal of Structural Biology 2004, 147:235-246. 30. Schotte F, Lim MH, Jackson TA, Smirnov AV, Soman J, Olson JS, Phillips GN, Wulff M, Anfinrud PA: Watching a protein as it functions with 150-ps time-resolved X-ray crystallography. Science 2003, 300:1944-1947. Current Opinion in Structural Biology 2010, 20:162–167
31. Brunori M, Bourgeois D, Vallone B: Structural dynamics of myoglobin. Globins and Other Nitric Oxide-Reactive Proteins, Part B. 2008:. pp. 397–416. 32. Aranda R, Levin EJ, Schotte F, Anfinrud PA, Phillips GN: Timedependent atomic coordinates for the dissociation of carbon monoxide from myoglobin. Acta Crystallographica Section DBiological Crystallography 2006, 62:776-783. 33. Laio A, Parrinello M: Escaping free-energy minima. In Proceedings of the National Academy of Sciences 2002, 99:12562-12566. 34. Huber T, Torda A, van Gunsteren WF: Local elevation—a method for improving the searching properties of molecular-dynamics simulation. Journal of Computer Aided Molecular Design 1994, 8:695-708. 35. Nishihara Y, Hayashi S, Kato S: A search for ligand diffusion pathway in myoglobin using a metadynamics simulation. Chemical Physics Letters 2008, 464:220-225. An intriguing application of meta-dynamics to ligand diffusion with considerable future potential. 36. Ceccarelli M, Anedda R, Casu M, Ruggerone P: CO escape from myoglobin with metadynamics simulations. Proteins-Structure Function and Bioinformatics 2008, 71:1231-1236. Another intriguing application of meta-dynamics to ligand diffusion in myoglobin in which we learned about the capabilities of meta-dynamics and its limitation. 37. Scorciapino MA, Robertazzi A, Casu M, Ruggerone P, Ceccarelli M: Breathing motions of a respiratory protein revealed by molecular dynamics simulations. Journal of the American Chemical Society 2009, 131:11825-11832. 38. Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA: A 2nd generation force-field for the simulation of proteins, nucleicacids, and organic-molecules. Journal of the American Chemical Society 1995, 117:5179-5197. 39. Maragliano L, Cottone G, Ciccotti G, Vanden-Eijnden E: Mapping the network of pathways of CO diffusion in myoglobin. The Journal of the American Chemical Society, 2009, doi:10.121/ ja905671x, in press. An application of the single sweep method (see also ref. [40]) for ligand diffusion in myoglobin that provides sensible values for free energy well depths and barrier heights. 40. Maragliano L, Vanden-Eijnden E: A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chemical Physics Letters 2006, 426(1–3):168-175. 41. Kondrashov DA, Montfort WR: Nonequilibrium dynamics simulations of nitric oxide release: comparative study of nitrophorin and myoglobin. Journal of Physical Chemistry B 2007, 111(31):9244-9252. 42. Banushkina P, Meuwly M: Diffusive dynamics on multidimensional rough free energy surfaces. Journal of Chemical Physics 2007, 127(13). 43. Zhang Y, Fujisaki H, Straub JE: Molecular dynamics study on the solvent dependent heme cooling following ligand photolysis in carbonmonoxy myoglobin. Journal of Physical Chemistry B 2007, 111:3243-3250. 44. Kottalam J, Case DA: Dynamics of ligand escape from the heme pocket of myoglobin. Journal of the American Chemical Society 1988, 110:7690-7697. 45. Cohen J, Olsen KW, Schulten K: Finding gas migration pathways in proteins using implicit ligand sampling. Globins and Other Nitric Oxide-Reactive Proteins, Part B. 2008, pp. 439–457. [36] Cohen. An interesting and elegant way for estimating the free energy landscape of ligand diffusion through globin. The technique is based on ligand insertion into existing tunnels within the protein matrix. 46. Cohen J, Schulten K: O-2 migration pathways are not conserved across proteins of a similar fold. Biophysical Journal 2007, 93:3591-3600. 47. Cohen J, Arkhipov A, Braun R, Schulten K: Imaging the migration pathways for O-2, CO, NO, and Xe inside myoglobin. Biophysical Journal 2006, 91:1844-1857. www.sciencedirect.com
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48. Li HY, Elber R, Straub JE: Molecular-dynamics simulation of no recombination to myoglobin mutants. Journal of Biological Chemistry 1993, 268:17908-17916.
52. Elber R, Gibson QH: Toward quantitative simulations of carbon monoxide escape pathways in myoglobin. Journal of Physical Chemistry B 2008, 112(19):6147-6154.
49. Straub JE, Karplus M: Molecular-dynamics study of the photodissociation of carbon-monoxide from myoglobin— ligand dynamics in the 1st 10 ps. Chemical Physics 1991, 158:221-248.
53. Schaad O, Zhou HX, Szabo A, Eaton WA, Henry ER: Simulation of the kinetics of ligand-binding to a protein by moleculardynamics—geminate rebinding of nitric-oxide to myoglobin. In Proceedings of the National Academy of Sciences of the United States of America 1993, 90:9547-9551.
50. Anselmi M, Di Nola A, Amadei A: The kinetics of ligand migration in crystallized myoglobin as revealed by molecular dynamics simulations. Biophysical Journal 2008, 94:4277-4281. 51. Ruscio JZ, Kumar D, Shukla M, Prisant MG, Murali TM, Onufriev AV: Atomic level computational identification of ligand migration pathways between solvent and binding site in myoglobin. In Proceedings of the National Academy of Sciences of the United States of America 2008, 105:9204-9209. A straightforward and comprehensive Molecular Dynamics investigation of ligand diffusion through myoglobin. Clearly illustrating the conflict about the escape pathway.
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54. Gibson QH, Regan R, Elber R, Olson JS, Carver TE: Distal pocket residues affect picosecond ligand recombination in myoglobin—an experimental and molecular-dynamics study of position 29 mutants. Journal of Biological Chemistry 1992, 267(31):22022-22034. 55. Schmidt M, Nienhaus K, Pahl R, Krasselt A, Anderson S, Parak F, Nienhaus GU, Srajer V: Ligand migration pathway and protein dynamics in myoglobin: a time-resolved crystallographic study on L29W MbCO. In Proceedings of the National Academy of Sciences of the United States of America 2005, 102:11704-11709.
Current Opinion in Structural Biology 2010, 20:162–167
Ligand diffusion in globins: simulations versus experiment Ron Elber Computer simulations in molecular biophysics describe in atomic detail the structure, dynamics, and function of biological macromolecules. To assess the quality of these models and to pick up new mechanisms, comparisons with experimental measurements are made. Most comparisons examine thermodynamic and average structural properties. Here we discuss studies of dynamics and fluctuations in a protein. The diffusion of a small ligand between internal cavities in myoglobin, and its escape to solvent are considered. Qualitative and semi-quantitative agreements between experiment and simulation are obtained for the identities of the cavities that physically trap the ligand and for the connections between them. However, experimental and computational ‘doors’ are at significant variance. Simulations suggest multiple gates while kinetic experiments point to one dominant exit. Address Department of Chemistry and Biochemistry, Institute of Computational Engineering and Sciences (ICES), 1 University Station, ICES, C0200, The University of Texas at Austin, Austin, TX 78712, United States Corresponding author: Elber, Ron ([email protected])
continuous flow of theoretical and experimental studies of this system followed these original investigations. This paper provides an overview on the field with a focus on recent computational investigations. Other influential papers from the past to which frequent references are made are (i) the identification of the Xenon cavities in the protein structure and the use of a small computational probe to study them [5] and (ii) the first systematic search of diffusion pathways of a diatomic ligand in a thermally fluctuating protein matrix [6]. Ligand diffusion into and from buried active sites is of wide interest. The Locally Enhanced Sampling (LES) method, for searching diffusion pathways, was introduced for myoglobin [6]. However, it was used to investigate other proteins, for example, the diffusion of oxygen and hydrogen in hydrogenase [9], of oxygen in dioxygenase [10], and of nitric oxide in nitrile hydratase [11]. Interestingly, more accurate variant of LES is available [12,13], but so far it was not used widely. Other examples in which Molecular Dynamics provided insight to ligand permeation problems are of flavoenzyme [14] and catalase [15].
Current Opinion in Structural Biology 2010, 20:162–167 This review comes from a themed issue on Theory and simulation Edited by Chandra Verma and Juan Ferna´ndez Recio Available online 29th January 2010 0959-440X/$ – see front matter # 2010 Elsevier Ltd. All rights reserved. DOI 10.1016/j.sbi.2010.01.002
In addition to a deeper understanding of molecular biophysics events that are relevant to molecular function, thermally assisted diffusion is an ideal system for a straightforward study by Molecular Dynamics (MD). The mantra for accurate application of the MD approach is (i) force field and (ii) sampling. Both items seem in place for the task at hand. The forces involved are physical, and no formation or breaking of chemical bonds is present. This observation suggests that traditional and readily available mechanical force fields are a reasonable match.
Introduction After the determination of the globin structures by X-ray crystallography [1,2] it was quickly established that thermal fluctuations of the protein matrix must assist the penetration of the small ligand in and out of the protein. Visual inspection of the X-ray structure suggests no obvious way for a ligand to enter or escape. Indeed a pioneering computational work by Case and Karplus [3] examined two routes between the binding site and the solvent just below the E helix (Figure 1) exiting through the so-called histidine gate. This study illustrates significant energy barriers for the ‘door’ and a mechanism in which side chain fluctuations are coupled to ligand escape and to partial protein fluidity [4]. It is amusing that this particular path, after significant debate and suggestions for alternatives in the literature [5,6], recently received a strong endorsement from experimental studies [7,8]. A Current Opinion in Structural Biology 2010, 20:162–167
The sampling requirement is somewhat more complex. The time scale of the events of interest (migration of the ligand to alternative cavities in the protein and to the solvent) is pretty long compared to the basic time step of MD (femtoseconds). Ligand hops between cavities and escapes at time scales that are measured in hundreds of nanoseconds [7,8,16]. This makes it necessary to execute hundreds of millions of time steps to observe (frequently) the events of interest. Moreover, to obtain quantitative description of ligand migration, multiple trajectories are required. The diffusion is a non-equilibrium process (once the ligand leaves the protein matrix it is unlikely to return on the simulation time scale) and an average over initial conditions must be performed to obtain quantitative results. The requirement for multiple trajectories and ensemble average makes the calculation more www.sciencedirect.com
Ligand diffusion in globins: simulations versus experiment Elber 163
Figure 1
compared quantitatively to experiment. Hence, the results of ligand diffusion in myoglobin provide a strict test of the way we investigate kinetic mechanisms by computer simulations and are useful probes of anisotropic dynamic fluctuations in well-defined three-dimensional structures of proteins [20,21].
Experimental analysis of ligand diffusion
Myoglobin and the Xenon cavities (detected by free volume calculations in red). The heme is in blue and the red spot attached to it from above is the distal pocket. Above the distal pocket one finds the Xe4 cavity and below the heme is the Xe1 binding site. Xe2 and Xe3 are to the left. The E helix is drawn in the back from the lower left to the upper right of the protein, touching in the figure the cavities Xe2–Xe4. The figure was prepared by the program zmoil http://clsb.ices.utexas.edu/prebuilt/.
expensive by orders of magnitude compared to a single trajectory. This computational task was considered formidable until recently. Past studies were therefore primarily qualitative. Even recently a few approximate approaches to the problem were explored. For example, estimates of free energy landscapes using meta-dynamics or particle insertion methods. Nevertheless, and as argued below, the qualitative computational picture of ligand diffusion in myoglobin did not deviate much from the earlier studies. Arguably, the major remaining qualitative puzzle of the kinetics of ligand diffusion in myoglobin is the identification of the escape pathway from the protein. At present there is a sharp disagreement between simulations and experiments (but there is a reasonable agreement between different simulations). The source of the significant qualitative difference is not clear.
Historically, the dominant experiment for studying ligand diffusion in myoglobin was of geminate recombination kinetics. The iron–ligand bond is broken by light or by other means and the recombination time of the dissociated ligand to the iron is followed by spectroscopy of the heme [22]. The diffusion of the ligand away from the iron and in the protein matrix causes delay in re-binding, allowing for interesting kinetic analysis. The data are interpreted in terms of a competition between (i) reformation of ligand–iron bond, (ii) diffusion between internal protein cavities (the so-called DP—the distal pocket and the Xe1–Xe4 cavities [5], see also Figure 1), and (iii) escape from the protein matrix to the solvent. It is important to separate these steps both in application and analyses of theory and in experiment to make the comparison meaningful. Other types of experiments are available that probe the ligand motions directly and help establish a more complete picture of the diffusion (e.g. time resolved crystallography [23–25] and time resolved vibrational spectroscopy [26,27]). Significant credit to the broader and renewed interest in myoglobin kinetics is due to the spectacular snapshots in time of ligand migration between internal cavities such as the DP, Xe4, and Xe1 [5,23– 25,28–32]. Nevertheless, studies of kinetics remain a crucial component. This is due to the relative ease of experimental kinetics and the ability to probe ligand escape to the solvent (the time scale in which the reaction becomes concentration dependent). After all, kinetics and thermodynamics are the prime determinants of biological function. Kinetics was measured for a wide range of myoglobin mutants, and for different solution conditions such as (Xe) pressure. We can divide the type of computations probing ligand diffusion into two main categories: (i) Approximate calculations of diffusion rate and free energy landscape, and (ii) Straightforward Molecular Dynamics trajectories. Below we discuss both of them.
Approximate calculations of diffusion rate Of course considerably more work remains to be done to make the agreement between experiment and theory quantitative. Advances in software and hardware [17– 19] made it possible to run a significant number of straightforward MD trajectories for substantial lengths of time. These trajectories observed migration events at room temperature that with sufficient statistics can be www.sciencedirect.com
The approximate procedures aim at better sampling of the free energy landscape for ligand diffusion. This is achieved by making plausible assumptions on the system dynamics, assumptions that greatly simplify the computational cost of computing the free energy landscape. Such approaches are important even now in qualitative understanding of the dynamics and interpreting complex Current Opinion in Structural Biology 2010, 20:162–167
164 Theory and simulation
motions in a simpler form. We therefore discuss some of these ideas below. One approach of the so-called metadynamics [33] or local elevation [34] was used to investigate carbon monoxide diffusion in myoglobin [35,36]. The overall diffusion patterns between myoglobin cavities were similar to other studies. Free energies of wells and of barriers between the minima were estimated. The calculated barriers vary between zero and 14.5 kT in one of the studies [36], and are larger than expected from experiment. The time scale of escape to the solvent measured experimentally is about 100 nanoseconds [7,8] while the above barrier is likely to yield longer time scales. Taking the free diffusion time scale to be t0 2 ps, the activated time, t a , according to the above estimated barrier height is ta ¼ t0 expðB=kT Þ 1 ms. Interestingly, a second meta-dynamics study [37] finds significantly lower barriers suggesting that convergence of quantitative free energy map for diffusion was not reached. For example, the barrier between the Xe4 and the Xe1 cavities in the last study, which are on opposite sides of the heme, is surprisingly small. It is estimated as 2.17 kT, corresponding to tens of picoseconds migration time at room temperature. We note that both simulations used the AMBER force field [38] so the variations are likely to be caused by different sampling. A third and recent simulation of the free energy landscape of CO diffusion in myoglobin [39] was conducted with the TAMD (Temperature Accelerated Molecular Dynamics) and the single sweep methods [40]. This time the CHARMM force field was used, and the free energy values were close to the study of Nishihara et al. [36].
proposed as the exit gate at the very beginning of the field [3,44]. So far this coupling has not been demonstrated to be wrong. A slow variable based only on the ligand coordinate may be an oversimplification. Finally, the escape pathway from the Xe3 cavity proposed in reference [36] is in disagreement with experiment that strongly suggests an escape pathway from the distal pocket (DP) [7,16]. The escape pathway(s) is at variance with experiment in essentially all simulations that searched for it, and is not specific to the meta-dynamics calculations. Another intriguing computational probe of ligand diffusion is the treatment of the ligand as a perturbation. Plausible pathways are then determined by the static structure and protein fluctuations computed without the ligand. The free energy landscape is estimated by one-step insertion of the ligand to pre-existing tunnels within the protein matrix [45,46,47]. The calculations are very efficient and make it possible to probe different globins and their alternate internal diffusion network. The underlying assumption is that the small (but hard) ligand does not significantly push protein atoms while moving around.
Straightforward molecular dynamics Given that different approximate theories (and even the same theory) provide quantitatively different results it is necessary to re-evaluate the basic model (i.e. the force field) as well as the approximations that are part of the above theories. From this perspective it is useful to perform the most straightforward calculation possible in which approximations are eliminated allowing for better evaluation of agreement (or disagreement) between simulations and experiments.
Two issues make the quantitative application of metadynamics difficult. The first is that the diffusion is a nonstationary process. A number of studies were conducted on relaxation processes of the protein molecule that happen simultaneously and may induce significant nonequilibrium aspects to the diffusion [21,41–43]. As long as the ligand is trapped in the protein matrix it may be considered in local equilibrium. However, an escape to the solvent interrupts this equilibrium process. Ligands that exit to the aqueous solution may not return to the protein on the simulation time scale. Given that the computed barrier heights for ligand migration (internally and to the solvent) are not so different, for example, 13.7 kT versus 14.5 kT [36], the equilibrium assumption may require further investigations. In contrast to metadynamics the single sweep method [39] computes rigorously the equilibrium free energy surface.
For diatomic molecules such as oxygen or carbon monoxide molecules the prime interaction with other protein atoms (or solvent molecules) is of excluded volume. This interaction is typically modeled as a Lennard Jones potential. Small dipole (or more significant) quadrupole moments are used less frequently, even though welltested parameterization is available [48,49]. The overall diffusion pattern of the diatomic ligand in the protein matrix seems similar with or without the quadrupole moments (see for instance [50]. However, for quantitative description and for (perhaps) solving the gate puzzle, careful investigation of different energy parameterizations are very much to be desired.
Furthermore, in meta-dynamics and the single sweep method it is necessary to decide on slow coordinates that require a ‘speed-up’ or flattening of the energy surface. In all of the above studies the coordinates were the Cartesian position of the CO molecule. This choice is intuitive; however, it may be insufficient. Coupling between the ligand motions and activated transitions of side chains was
In an ideal computer simulation, efforts are made to reproduce the experimental set-up as accurately as possible. A ligand is placed in the heme pocket, bonded or restrained to remain at the binding site. It is kept that way for an equilibrium simulation in which water and protein are allowed to relax to an equilibrium state appropriate to the force field used. The structures of
Current Opinion in Structural Biology 2010, 20:162–167
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Ligand diffusion in globins: simulations versus experiment Elber 165
the bound state generated at equilibrium are sampled to initiate trajectories of ligand diffusion and recombination. In most of the conducted simulations the trajectories are purely diffusive [24,50,51,52], but in some cases they include detailed description of recombination events (reformation of ligand–heme bond [48,53]). Simulations on multiple electronic energy surfaces that describe the bound and unbound ligand–protein state provide a complete computational description of recombination measurements [54]. They make it possible to describe the photo-dissociation, energy relaxation, ligand diffusion, and re-binding in a single computational framework. This approach is most appropriate for direct comparison with flash photolysis and geminate recombination experiments. In [48] correct ordering of nitric-oxide recombination-rates of myoglobin mutants were obtained. Recently however, the focus was on one component of the experiment, that of ligand diffusion between internal cavities. The availability of time resolved FTIR spectroscopy and X-ray crystallography experiments that watch the build up of ligand densities at different locations in the protein matrix (Figure 1) makes direct comparison with experiment possible. A number of computational groups have taken on themselves the task of simulating the ligand diffusion in and out of myoglobin using straightforward tools of Molecular Dynamics without additional physical assumptions that enhance the computational efficiency. Of the studies mentioned above perhaps the most comprehensive is the investigation by Ruscio et al. [51] which, as described, should have put to rest many of the lingering questions about links between experiment and theory in this comprehensively studied system. Sixty-eight trajectories were conducted for ninety nanoseconds each providing ample evidence and statistics for ligand migration in the protein and escape. Moreover, since the simulated system is ‘small’ (or the concentration of myoglobin in the simulated system is very high), entry events from solvent to protein were also observed. The time scale is in overall agreement with rates measured experimentally (about 100–200 nanoseconds) and the diffusion pathways are in remarkable agreement with the emerging consensus of ligand hopping between the Xenon sites [5]. Nevertheless, one qualitative question remains and with this question I wish to conclude the present Opinion.
Conclusion In a beautiful series of experiments Scott et al. showed that the dominant escape pathway for a diatomic ligand from the protein matrix is the histidine gate [7] including an in depth examination of ligand movement in W29 mutant of myoglobin by time resolved X-ray crystallography [55]. This study was further confirmed by a series of mutations to tryptophan residues at crucial points along the ligand diffusion pathway, a study that is summarized www.sciencedirect.com
in a review [16]. These observations appear to contradict all simulations which have searched for escape pathways (rather than assuming them). A recent study in the laboratory of the author [52] observed two non-classical (not histidine) exits and the study by Ruscio et al. [51] proposed nine gates (with different surface residues). The simulation results, of multiple roughly equivalent exit pathways, are not supported by current experiments [7,16]. Kinetic analysis indicates that 70-80% of the ligands enter and exit from the distal histidine gate.
Acknowledgements This research was supported by NIH grant GM059796. Useful discussions and suggestions by John Olson and Quentin Gibson are gratefully acknowledged.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: of special interest of outstanding interest 1.
Perutz M: Structure of hemoglobin. Brookaven Symposia in Biology 1960, 13:165-183.
2.
Kendrew JC, Bodo G, Dintzis HM, Parrish RG, Wyckoff H, Phillips DC: A three-dimensional model of the myoglobin molecule obtained by X-ray analysis. Nature 1958, 181:662-666.
3.
Case DA, Karplus M: Dynamics of ligand-binding to hemeproteins. Journal of Molecular Biology 1979, 132:343-368.
4.
Elber R, Karplus M: A method for determining reaction paths in large molecules—application to myoglobin. Chemical Physics Letters 1987, 139:375-380.
5.
Tilton RF, Kuntz ID, Petsko GA: Cavities in proteins—structure of a metmyoglobin-xenon complex solved to 1.9-A. Biochemistry 1984, 23:2849-2857.
6.
Elber R, Karplus M: Enhanced sampling in moleculardynamics—use of the time-dependent hartree approximation for a simulation of carbon-monoxide diffusion through myoglobin. Journal of the American Chemical Society 1990, 112:9161-9175.
7.
Scott EE, Gibson QH, Olson JS: Mapping the pathways for O-2 entry into and exit from myoglobin. Journal of Biological Chemistry 2001, 276:5177-5188.
8.
Scott EE, Gibson QH: Ligand migration in sperm whale myoglobin. Biochemistry 1997, 36:11909-11917.
9.
Cohen J, Kim K, King P, Seibert M, Schulten K: Finding gas diffusion pathways in proteins: application to O-2 and H-2 transport in Cpl [FeFe]-hydrogenase and the role of packing defects. Structure 2005, 13:1321-1329.
10. Xu L, Liu X, Zhao WJ, Wang XC: Locally enhanced sampling study of dioxygen diffusion pathways in homoprotocatechuate 2,3-dioxygenase. Journal of Physical Chemistry B 2009, 113:13596-13603. 11. Kubiak K, Nowak W: Molecular dynamics simulations of photoactive protein nitrile hydratase. Biophysical Journal 2008, 94:3824-3838. 12. Ulitsky A, Elber R: Application of the locally enhanced sampling (LES) and a mean field witha binary collision correction (cLES) to the simulation of Ar diffusion and NO recombination in myoglobin. Journal of Physical Chemistry 1994, 98(3):1034-1043. 13. Ulitsky A, Elber R: The thermal equilibrium aspects of the timedependent hartree and the locally enhanced sampling approximations—formal properties, a correction, and computational examples for rare gas clusters. Journal of Chemical Physics 1993, 98:3380-3388. Current Opinion in Structural Biology 2010, 20:162–167
166 Theory and simulation
14. Baron R, Riley C, Chenprakhon P, Thotsaporn K, Winter RT, Alfieri A, Forneris F, van Berkel WJH, Chaiyen P, Fraaije MW et al.: Multiple pathways guide oxygen diffusion into flavoenzyme active sites. In Proceedings of the National Academy of Sciences of the United States of America 2009, 106:10603-10608. 15. Amara P, Andeolei P, Jouve P, Martine MJ: Ligand diffusion in the catalase from Proteus mirabilis. Protein Science 2001, 10:1927-1935. 16. Olson JS, Soman J, Phillips GN: Ligand pathways in myoglobin: a review of Trp cavity mutations. IUBMB Life 2007, 59:552-562. 17. Stone JE, Phillips JC, Freddolino PL, Hardy DJ, Trabuco LG, Schulten K: Accelerating molecular modeling applications with graphics processors. Journal of Computational Chemistry 2007, 28:2618-2640. 18. Ensign DL, Kasson PM, Pande VJ: Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece. Journal of Molecular Biology 2007, 374:806-816. 19. Shaw DE, Deneroff MM, Dror RO, Kuskin JS, Larson RH, Salmon JK, Young C, Batson B, Bowers KJ, Chao JC et al.: Anton, a special-purpose machine for molecular dynamics simulation. Communications of the ACM 2008, 51:91-97. 20. Tomita A, Saro T, Ichiyanagi K, Nozawa S, Ichikawa H, Chllet M, Kawai F, Park SY, Tsuduki T, Yamato T et al.: Visualizing breathing motion of internal cavities in concert with ligand migration in myoglobin. In Proceedings of the National Academy of Sciences of the United States of America 2009, 106:2612-2616. 21. Takayanagi M, Okumura H, Nagaoka M: Anisotropic structural relaxation and its correlation with the excess energy diffusion in the incipient process of photodissociated MbCO: highresolution analysis via ensemble perturbation method. Journal of Physical Chemistry B 2007, 111:864-869. 22. Austin RH, Beeson KW, Eisenstein L, Frauenfelder H, Gunsalus IC: Dynamics of ligand-binding to myoglobin. Biochemistry 1975, 14:5355-5373. 23. Bourgeois D, Vallone B, Arcovito A, Sciara G, Anfinrud PA, Brunori M: Extended subnanosecond structural dynamics of myoglobin revealed by Laue crystallography. In Proceedings of the National Academy of Sciences of the United States of America 2006, 103:4924-4929. 24. Hummer G, Schotte F, Anfinrud PA: Unveiling functional protein motions with picosecond x-ray crystallography and molecular dynamics simulations. In Proceedings of the National Academy of Sciences of the United States of America 2004, 101:15330-15334. 25. Srajer V, Teng TY, Ursby T, Pradervand C, Ren Z, Adach S, Schildkamp W, Bourgeois D, Wuff M, Moffat K: Photolysis of the carbon monoxide complex of myoglobin: nanosecond time-resolved crystallography. Science 1996, 274:1726-1729. 26. Nienhaus K, Nienhaus GU: Influence of distal residue B10 on CO dynamics in myoglobin and neuroglobin. Journal of Biological Physics 2007, 33:357-370. 27. Nienhaus K, Palladino P, Nienhaus GU: Structural dynamics of myoglobin: FTIR-TDS study of NO migration and binding. Biochemistry 2008, 47:935-948. 28. Srajer V, Ren Z, Teng TY, Schmidt M, Ursby T, Bourgeois D, Pradervand C, Schildkamp W, Wuff M, Moffat K: Protein conformational relaxation and ligand migration in myoglobin: a nanosecond to millisecond molecular movie from time-resolved Laue X-ray diffraction. Biochemistry 2001, 40:13802-13815. 29. Schotte F, Soman J, Olson JS, Wulff M, Anfinrud PA: Picosecond time-resolved X-ray crystallography: probing protein function in real time. Journal of Structural Biology 2004, 147:235-246. 30. Schotte F, Lim MH, Jackson TA, Smirnov AV, Soman J, Olson JS, Phillips GN, Wulff M, Anfinrud PA: Watching a protein as it functions with 150-ps time-resolved X-ray crystallography. Science 2003, 300:1944-1947. Current Opinion in Structural Biology 2010, 20:162–167
31. Brunori M, Bourgeois D, Vallone B: Structural dynamics of myoglobin. Globins and Other Nitric Oxide-Reactive Proteins, Part B. 2008:. pp. 397–416. 32. Aranda R, Levin EJ, Schotte F, Anfinrud PA, Phillips GN: Timedependent atomic coordinates for the dissociation of carbon monoxide from myoglobin. Acta Crystallographica Section DBiological Crystallography 2006, 62:776-783. 33. Laio A, Parrinello M: Escaping free-energy minima. In Proceedings of the National Academy of Sciences 2002, 99:12562-12566. 34. Huber T, Torda A, van Gunsteren WF: Local elevation—a method for improving the searching properties of molecular-dynamics simulation. Journal of Computer Aided Molecular Design 1994, 8:695-708. 35. Nishihara Y, Hayashi S, Kato S: A search for ligand diffusion pathway in myoglobin using a metadynamics simulation. Chemical Physics Letters 2008, 464:220-225. An intriguing application of meta-dynamics to ligand diffusion with considerable future potential. 36. Ceccarelli M, Anedda R, Casu M, Ruggerone P: CO escape from myoglobin with metadynamics simulations. Proteins-Structure Function and Bioinformatics 2008, 71:1231-1236. Another intriguing application of meta-dynamics to ligand diffusion in myoglobin in which we learned about the capabilities of meta-dynamics and its limitation. 37. Scorciapino MA, Robertazzi A, Casu M, Ruggerone P, Ceccarelli M: Breathing motions of a respiratory protein revealed by molecular dynamics simulations. Journal of the American Chemical Society 2009, 131:11825-11832. 38. Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA: A 2nd generation force-field for the simulation of proteins, nucleicacids, and organic-molecules. Journal of the American Chemical Society 1995, 117:5179-5197. 39. Maragliano L, Cottone G, Ciccotti G, Vanden-Eijnden E: Mapping the network of pathways of CO diffusion in myoglobin. The Journal of the American Chemical Society, 2009, doi:10.121/ ja905671x, in press. An application of the single sweep method (see also ref. [40]) for ligand diffusion in myoglobin that provides sensible values for free energy well depths and barrier heights. 40. Maragliano L, Vanden-Eijnden E: A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chemical Physics Letters 2006, 426(1–3):168-175. 41. Kondrashov DA, Montfort WR: Nonequilibrium dynamics simulations of nitric oxide release: comparative study of nitrophorin and myoglobin. Journal of Physical Chemistry B 2007, 111(31):9244-9252. 42. Banushkina P, Meuwly M: Diffusive dynamics on multidimensional rough free energy surfaces. Journal of Chemical Physics 2007, 127(13). 43. Zhang Y, Fujisaki H, Straub JE: Molecular dynamics study on the solvent dependent heme cooling following ligand photolysis in carbonmonoxy myoglobin. Journal of Physical Chemistry B 2007, 111:3243-3250. 44. Kottalam J, Case DA: Dynamics of ligand escape from the heme pocket of myoglobin. Journal of the American Chemical Society 1988, 110:7690-7697. 45. Cohen J, Olsen KW, Schulten K: Finding gas migration pathways in proteins using implicit ligand sampling. Globins and Other Nitric Oxide-Reactive Proteins, Part B. 2008, pp. 439–457. [36] Cohen. An interesting and elegant way for estimating the free energy landscape of ligand diffusion through globin. The technique is based on ligand insertion into existing tunnels within the protein matrix. 46. Cohen J, Schulten K: O-2 migration pathways are not conserved across proteins of a similar fold. Biophysical Journal 2007, 93:3591-3600. 47. Cohen J, Arkhipov A, Braun R, Schulten K: Imaging the migration pathways for O-2, CO, NO, and Xe inside myoglobin. Biophysical Journal 2006, 91:1844-1857. www.sciencedirect.com
Ligand diffusion in globins: simulations versus experiment Elber 167
48. Li HY, Elber R, Straub JE: Molecular-dynamics simulation of no recombination to myoglobin mutants. Journal of Biological Chemistry 1993, 268:17908-17916.
52. Elber R, Gibson QH: Toward quantitative simulations of carbon monoxide escape pathways in myoglobin. Journal of Physical Chemistry B 2008, 112(19):6147-6154.
49. Straub JE, Karplus M: Molecular-dynamics study of the photodissociation of carbon-monoxide from myoglobin— ligand dynamics in the 1st 10 ps. Chemical Physics 1991, 158:221-248.
53. Schaad O, Zhou HX, Szabo A, Eaton WA, Henry ER: Simulation of the kinetics of ligand-binding to a protein by moleculardynamics—geminate rebinding of nitric-oxide to myoglobin. In Proceedings of the National Academy of Sciences of the United States of America 1993, 90:9547-9551.
50. Anselmi M, Di Nola A, Amadei A: The kinetics of ligand migration in crystallized myoglobin as revealed by molecular dynamics simulations. Biophysical Journal 2008, 94:4277-4281. 51. Ruscio JZ, Kumar D, Shukla M, Prisant MG, Murali TM, Onufriev AV: Atomic level computational identification of ligand migration pathways between solvent and binding site in myoglobin. In Proceedings of the National Academy of Sciences of the United States of America 2008, 105:9204-9209. A straightforward and comprehensive Molecular Dynamics investigation of ligand diffusion through myoglobin. Clearly illustrating the conflict about the escape pathway.
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54. Gibson QH, Regan R, Elber R, Olson JS, Carver TE: Distal pocket residues affect picosecond ligand recombination in myoglobin—an experimental and molecular-dynamics study of position 29 mutants. Journal of Biological Chemistry 1992, 267(31):22022-22034. 55. Schmidt M, Nienhaus K, Pahl R, Krasselt A, Anderson S, Parak F, Nienhaus GU, Srajer V: Ligand migration pathway and protein dynamics in myoglobin: a time-resolved crystallographic study on L29W MbCO. In Proceedings of the National Academy of Sciences of the United States of America 2005, 102:11704-11709.
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