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Sampling-Based Motion Planning for Tracking Evolution of Dynamic Tunnels in Molecular Dynamics Simulations

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Abstract

Proteins are involved in many biochemical processes. The behavior of proteins is highly influenced by the presence of internal void space, in literature denoted as tunnels or cavities. Tunnels are paths leading from an inner protein active site to its surface. The knowledge about tunnels and their evolution over time, captured in molecular dynamics simulations, provides an insight into important protein properties (e.g., their stability or activity). For each individual snapshot of molecular dynamics, tunnels can be detected using Voronoi diagrams and then aggregated over time to trace their behavior. However, this approach is suitable only when a given tunnel is detected in all snapshots of molecular dynamics. This is often not the case of traditionally used approaches to tunnel computation. When a tunnel becomes too narrow in a particular snapshot, the existing approaches cannot detect this case and the tunnel completely disappears from the results. On the other hand, this situation can be quite common as tunnels move, disappear and appear again, split, or merge. Therefore, in this paper we propose a method which enables to trace also tunnels in those missing snapshots. We call them dynamic tunnels and we use the sampling-based motion planning to compute them. The Rapidly Exploring Random Tree (RRT) algorithm is used to explore the void space in each frame of the protein dynamics. The void space is represented by a tree structure that is transferred to the next frame of the dynamics and updated to remove collisions and to cover newly emerged free regions of the void space. If the void space reaches the surface of the protein, a dynamic tunnel is reconstructed by tracking back in the tree towards a desired place (i.e., the active site). To efficiently sample the narrow void space inside proteins, a Voronoi diagram of the static protein frames is used. The results of the proposed method are demonstrated on an exemplary dataset obtained from the domain experts and the results are compared with the classic aggregation-based tunnel detection performed using the state-of-the-art CAVER 3.0 tool.

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References

  1. Al-Bluwi, I., Siméon, T., Cortés, J.: Motion planning algorithms for molecular simulations: a survey. Comput. Sci. Rev. 6(4), 125–143 (2012)

    Article  MATH  Google Scholar 

  2. Albou, L.-P., Schwarz, B., Poch, O., Wurtz, J.M., Moras, D.: Defining and characterizing protein surface using alpha shapes. Proteins: Struct. Funct. Bioinf. 76(1), 1–12 (2009)

    Article  Google Scholar 

  3. Amato, N.M., Bayazit, L.K., Dale, O.B., Jones, C., Vallejo, D.: OBPRM: an obstacle-based PRM for 3D workspaces. In: Workshop on the Algorithmic Foundations of Robotics (WAFR), pp. 155–168, Natick, MA, USA. A. K. Peters, Ltd (1998)

  4. Amato, N.M., Song, G.: Using motion planning to study protein folding pathways. J. Comput. Biol. 9(2), 149–168 (2002)

    Article  Google Scholar 

  5. Bayazit, O.B., Song, G., Amato, N.M.: Ligand binding with OBPRM and user input. In: IEEE International Conference on Robotics and Automation, vol. 1, pp. 954–959 (2001)

  6. van den Bergen, G.: Efficient collision detection of complex deformable models using aabb trees. J. Graph. Tool 2(4), 1–13 (1997)

    Article  MATH  Google Scholar 

  7. Bohlin, R., Kavraki, L.E.: Path planning using lazy prm. In: IEEE International Conference on Robotics and Automation (ICRA), vol. 1, pp. 521–528 (2000)

  8. Branicky, M.S., LaValle, S.M., Olson, K., Yang, L.: Quasi-randomized path planning. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 1481–1487 (2001)

  9. Bruce, J., Veloso, M.: Real-time randomized path planning for robot navigation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol. 3, pp. 2383–2388 (2002)

  10. Chovancová, E., Pavelka, A., BeneCs, P., Strnad, O., Brezovský, J., Kozlíková, B., Gora, A., CSustr, V., KlvaCna, M., Medek, P., Biedermannová, L., Sochor, J., Damborský, J.: CAVER 3.0: A tool for the analysis of transport pathways in dynamic protein structures. PLoS Comput. Biol. 8(10) (2012)

  11. Cortés, J., Jaillet, L., Siméon, T.: Molecular disassembly with RRT-like algorithms. In: Proceedings 2007 IEEE International Conference on Robotics and Automation, pp. 3301–3306 (2007)

  12. Cortés, J., Jaillet, L., Siméon, T.: Molecular disassembly with RRT-like algorithms. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 3301–3306 (2007)

  13. Cortés, J., Le, D.T., Iehl, R., Siméon, T.: Simulating ligand-induced conformational changes in proteins using a mechanical disassembly method. Phys. Chem. Chem. Phys. 12(29), 8268–8276 (2010)

    Article  Google Scholar 

  14. Cortés, J., Siméon, T., Remaud-Siméon, M., Tran, V.: Geometric algorithms for the conformational analysis of long protein loops. J. Comput. Chem. 25(7), 956–967 (2004)

    Article  Google Scholar 

  15. Ruiz de Angulo, V., Cortés, J., Siméon, T.: BioCD: an efficient algorithm for self-collision and distance computation between highly articulated molecular models. In: Robotics: Science and Systems (2005)

  16. Denny, J., Greco, E., Thomas, S., Amato, N.M.: MARRT: medial axis biased rapidly-exploring random trees. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 90–97 (2014)

  17. Denny, J., Sandström, R., Bregger, A., Amato, N.M.: Dynamic region-biased rapidly-exploring random trees. In: Twelfth International Workshop on the Algorithmic Foundations of Robotics (WAFR) (2016)

  18. Edelsbrunner, H., Kirkpatrick, D., Seidel, R.: On the shape of a set of points in the plane. IEEE Trans. Inf. Theory 29(4), 551–559 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ericson, C.: Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3-D Technology). Morgan Kaufmann Publishers Inc., San Francisco (2004)

    Google Scholar 

  20. Ferguson, D., Kalra, N., Stentz, A.: Replanning with RRTs. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 1243–1248 (2006)

  21. Ferguson, D., Stentz, A.: Anytime, dynamic planning in high-dimensional search spaces. In: Proceedings 2007 IEEE International Conference on Robotics and Automation, pp. 1310–1315 (2007)

  22. Gora, A., Brezovský, J., Damborský, J.: Gates of Enzymes. Chem. Rev. 113(8), 5871–5923 (2013)

    Article  Google Scholar 

  23. Guieysse, D., Cortés, J., Puech-Guenot, S., Barbe, S., Lafaquière, V., Monsan, P., Siméon, T., André, I., Remaud-Siméon, M.: A structure-controlled investigation of lipase enantioselectivity by a path-planning approach. ChemBioChem 9(8), 1308–1317 (2008)

    Article  Google Scholar 

  24. Holleman, C., Kavraki, L.E.: A framework for using the workspace medial axis in PRM planners. In: International Conference on Robotics and Automation (ICRA), vol. 2, pp. 1408–1413 (2000)

  25. Hsu, D.: The bridge test for sampling narrow passages with probabilistic roadmap planners. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 4420–4426 (2003)

  26. Hsu, D., Kindel, R., Latombe, J.-C., Rock, S.: Randomized kinodynamic motion planning with moving obstacles. Int. J. Robot. Res. 21(3), 233–255 (2002)

    Article  MATH  Google Scholar 

  27. Jaillet, L., Yershova, A., LaValle, S.M., Simeon, T.: Adaptive tuning of the sampling domain for dynamic-domain RRTs. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2851–2856 (2005)

  28. Jurčík, A., Parulek, J., Sochor, J., Kozlíková, B.: Accelerated visualization of transparent molecular surfaces in molecular dynamics. In: IEEE Pacific Visualization Symposium (Pacificvis), pp. 112–119 (2016)

  29. Kalisiak, M., van de Panne, M.: RRT-blossom: RRT with a local flood-fill behavior. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 1237–1242 (2006)

  30. Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30 (7), 846–894 (2011)

    Article  MATH  Google Scholar 

  31. Kavraki, L.E., Svestka, P., Latombe, J.-C., Overmars, M.: Probabilistic roadmaps for path planning in high dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566–580 (1996)

    Article  Google Scholar 

  32. Kirillova, S., Cortés, J., Stefaniu, A., Siméon, T.: An NMA-guided path planning approach for computing large-amplitude conformational changes in proteins. Proteins Structure, Function, and Bioinformatics 70 (1), 131–143 (2008)

    Article  Google Scholar 

  33. Koudeláková, T., Chaloupková, R., Brezovský, J., Prokop, Z., Šebestová, E., Hesseler, M., Khabiri, M., Plevaka, M., Kulik, D., Kutá-Smatanová, I., Řezáčová, P., Ettrich, R., Bornscheuer, U.T., Damborský, J.: Engineering enzyme stability and resistance to an organic cosolvent by modification of residues in the access tunnel. Angewandte Chemie International Edition 52(7), 1959–1963 (2013)

    Article  Google Scholar 

  34. Kozlíková, B., CSebestová, E., CSustr, V., Brezovský, J., Strnad, O., Daniel, L., Bednář, D., Pavelka, A., Maňák, M., Bezděka, M., Beneš, P., Kotry, M., Wiktor Gora, A., Damborský, J., Sochor, J.: CAVER Analyst 1.0: Graphic tool for interactive visualization and analysis of tunnels and channels in protein structures. Bioinformatics, 30(18) (2014)

  35. Kurniawati, H., Hsu, D.: Workspace importance sampling for probabilistic roadmap planning. In: International Conference on Intelligent Robots and Systems (IROS), vol. 2, pp. 1618–1623 (2004)

  36. Latombe, J.-C.: Motion planning: a journey of robots, molecules, digital actors, and other artifacts. Int. J. Robot. Res. 18, 1119–1128 (1999)

    Article  Google Scholar 

  37. LaValle, S.M.: Rapidly-exploring random trees: A new tool for path planning. Technical report 98-11 (1998)

  38. LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  39. Li, Y., Littlefield, Z., Bekris, K.E.: Asymptotically optimal sampling-based kinodynamic planning. Int. J. Robot. Res. 35(5), 528–564 (2016)

    Article  Google Scholar 

  40. Lindemann, S.R., LaValle, S.M.: Incrementally reducing dispersion by increasing Voronoi bias in RRTs. In: IEEE International Conference on Robotics and Automation (ICRA), vol. 4, pp. 3251–3257 (2004)

  41. Lindow, N., Baum, D., Bondar, A., Hege, H.-C.: Dynamic channels in biomolecular systems path analysis and visualization. In: IEEE Symposium on Biological Data Visualization (Biovis), pp. 99–106 (2012)

  42. Liu, H., Deng, X., Zha, H., Ding, D.: A path planner in changing environments by using W-C nodes mapping coupled with lazy edges evaluation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4078–4083 (2006)

  43. Marques, S.M., Dunajová, Z., Prokop, Z., Chaloupková, R., Brezovský, J., Damborský, J.: Catalytic cycle of haloalkane dehalogenases toward unnatural substrates explored by computational modeling. J. Chem. Inf. Model. 57(8), 1970–1989 (2017)

    Article  Google Scholar 

  44. Moll, M., Schwarz, D., Kavraki, L.E.: Roadmap methods for protein folding. In: Protein Structure Prediction, pp. 219–239. Springer (2008)

  45. Novinskaya, A., Devaurs, D., Moll, M., Kavraki, L.E.: Improving protein conformational sampling by using guiding projections. In: IEEE International Conference on Bioinformatics and Biomedicine Workshops (2015)

  46. Overmars, M.H.: The Gaussian sampling strategy for probabilistic roadmap planners. In: International Conference on Robotics and Automation (ICRA), pp. 1018–1023 (1999)

  47. Pavelka, A., Šebestová, E., Kozlíková, B., Brezovský, J., Sochor, J., Damborský, J.: CAVER: algorithms for analyzing dynamics of tunnels in macromolecules. IEEE/ACM Trans. Comput. Biology Bioinformatics 13(3), 505–517 (2015)

    Article  Google Scholar 

  48. Pavlová, M., Klvaňa, M., Chaloupková, R., Banáš, P., Otyepka, M., Wade, R., Nagata, Y., Damborský, J.: Redesigning dehalogenase access tunnels as a strategy for degrading an anthropogenic substrate. Nat. Chem. Biol. 5, 727–733 (2009)

    Article  Google Scholar 

  49. Petřek, M., Košinová, P., Koča, J., Otyepka, M.: MOLE: A Voronoi diagram-based explorer of molecular channels, pores, and tunnels. Structure 15(11), 1357–1363 (2007)

    Article  Google Scholar 

  50. Petřek, M., Otyepka, M., Banáš, P., Košinová, P., Koča, J., Damborský, J.: CAVER: A new tool to explore routes from protein clefts, pockets and cavities. BMC Bioinforma., 7 (2006)

  51. Pomârlan, M., Sucan, I.A.: Motion planning for manipulators in dynamically changing environments using real-time mapping of free workspace. In: 2013 IEEE 14th International Symposium on Computational Intelligence and Informatics (CINTI), pp. 483–487. IEEE (2013)

  52. Raveh, B., Enosh, A., Schueler-Furman, O., Halperin, D.: Rapid sampling of molecular motions with prior information constraints. PLos Comput. Biol. 5(2), e1000295 (2009)

    Article  Google Scholar 

  53. Rodriguez, S., Tang, X., Lien, J., Amato, N.M.: An obstacle-based rapidly-exploring random tree. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 895–900 (2006)

  54. Rosell, J., Roa, M., Pérez, A., García, F.: A general deterministic sequence for sampling d-dimensional configuration spaces. J. Intell. Robot. Syst. 50(4), 361–373 (2007)

    Article  MATH  Google Scholar 

  55. Sehnal, D., Svobodová Vařeková, R., Berka, K., Pravda, L., Navrátilová, V., Banáš, P., Ionescu, C.-M., Otyepka, M., Koča, J.: Mole 2.0: advanced approach for analysis of biomacromolecular channels. J Cheminformatics 5, 39 (2013)

    Article  Google Scholar 

  56. Song, G., Amato, N.M.: A motion planning approach to folding: from paper craft to protein folding. In: IEEE International Conference Robotics Automation (ICRA), pp. 948–953 (2001)

  57. Szadeczky-Kardoss, E., Kiss, B.: Extension of the rapidly exploring random tree algorithm with key configurations for nonholonomic motion planning. In: IEEE International Conference on Mechatronics, pp. 363–368 (2006)

  58. van den Berg, J.P., Nieuwenhuisen, D., Jaillet, L., Overmars, M.H.: Creating robust roadmaps for motion planning in changing environments. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1053–1059 (2005)

  59. Vonásek, V.: A guided approach to sampling-based motion planning. Phd thesis Czech Technical University in Prague (2016)

  60. Vonásek, V., Faigl, J., Krajník, T., Přeučil, L.: RRT-path — a guided rapidly exploring random tree. In: Robot Motion and Control (Romoco), pp. 307–316. Springer (2009)

  61. Vonásek, V., Kozlíková, B.: Tunnel detection in protein structures using sampling-based motion planning. In: 2017 11Th International Workshop on Robot Motion and Control (Romoco), pp. 185–192 (2017)

  62. Vonásek, V., Kozlíková, B.: Application of sampling-based path planning for tunnel detection in dynamic protein structures. In: 2016 21St International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 1010–1015 (2016)

  63. Wilmarth, S.A., Amato, N.M., Stiller, P.F.: MAPRM: a probabilistic roadmap planner with sampling on the medial axis of the free space. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 1024–1031 (1999)

  64. Yaffe, E., Fishelovitch, D., Wolfson, H.J., Halperin, D., Nussinov, R.: Molaxis: efficient and accurate identification of channels in macromolecules. Proteins: Struct. Funct. Bioinf. 73(1), 72–86 (2008)

    Article  Google Scholar 

  65. Yershova, A., Jaillet, L., Simeon, T., LaValle, S.M.: Dynamic-domain RRTs: efficient exploration by controlling the sampling domain. In: IEEE ICRA (2005)

  66. Yershova, A., LaValle, S.M.: Improving motion-planning algorithms by efficient nearest-neighbor searching. IEEE Trans. Robot. 23(1), 151–157 (2007)

    Article  Google Scholar 

  67. Zhang, L., Manocha, D.: An efficient retraction-based RRT planner. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 3743–3750 (2008)

  68. Zhou, W., Hong, Y.: Alpha shape and delaunay triangulation in studies of protein-related interactions. Briefings in Bioinformatics, pp. bbs077 (2012)

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Acknowledgments

The presented work has been supported by the Czech Science Foundation (GAČR) under research project No. 17-07690S.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27, Prague 6, Czech Republic

    Vojtěch Vonásek

  2. Faculty of Informatics, Masaryk University, Botanická 68a, 602 00, Brno, Czech Republic

    Adam Jurčík, Katarína Furmanová & Barbora Kozlíková

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  1. Vojtěch Vonásek
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Vonásek, V., Jurčík, A., Furmanová, K. et al. Sampling-Based Motion Planning for Tracking Evolution of Dynamic Tunnels in Molecular Dynamics Simulations. J Intell Robot Syst 93, 763–785 (2019). https://doi.org/10.1007/s10846-018-0877-6

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