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Cell Movement pp 77–102Cite as

Birkhäuser

Bayesian Uncertainty Quantification for Particle-Based Simulation of Lipid Bilayer Membranes

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Abstract

A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to Bayesian uncertainty quantification using transitional Markov chain Monte Carlo (TMCMC) is extremely parallelizable and has opened the door to a variety of applications which were previously too computationally intensive to be practical. In this chapter, we first explore the machinery required to understand and implement Bayesian uncertainty quantification using TMCMC. We then describe dissipative particle dynamics, a computational particle simulation method which is suitable for modeling biological structures on the subcellular level, and develop an example simulation of a lipid membrane in fluid. Finally, we apply the algorithm to a basic model of uncertainty in our lipid simulation, effectively recovering a target set of parameters (along with distributions corresponding to the uncertainty) and demonstrating the practicality of Bayesian uncertainty quantification for complex particle simulations.

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References

  1. D.F. Anderson and T.G. Kurtz, Stochastic Analysis of Biochemical Systems. (Springer, New York, 2015)

    Chapter  Google Scholar 

  2. P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos: Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework. J. Chem. Phys. 137, 144103 (2012)

    Article  Google Scholar 

  3. P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos: X-TMCMC: Adaptive Kriging for Bayesian inverse modeling. Comput. Methods Appl. Mech. Engrg. 289, 409–428 (2015)

    Article  MathSciNet  Google Scholar 

  4. D. Barber, Bayesian Reasoning and Machine Learning. (Cambridge University Press, 2012)

    Google Scholar 

  5. J.L. Beck, K.V. Yuen: Model selection using response measurements: Bayesian probabilistic approach. J. Eng. Mech. 130 (2) 192–203 (2004)

    Article  Google Scholar 

  6. Z. Chen, K. Larson, C. Bowman, P. Hadjidoukas, C. Papadimitriou, P. Koumoutsakos, and A. Matzavinos: Data-driven prediction and origin identification of epidemics in population networks. Submitted. (2018)

    Google Scholar 

  7. B. Efron and T. Hastie, Computer Age Statistical Inference: Algorithms, Evidence, and Data Science. (Cambridge University Press, 2016)

    Google Scholar 

  8. J.Y. Ching, Y.C. Chen: Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133 816–832 (2007)

    Article  Google Scholar 

  9. P. Español and P. Warren: Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30, 191–196 (1995)

    Article  Google Scholar 

  10. V.A. Frolov. A.V. Shnyrova, and J. Zimmerberg. Lipid polymorphisms and membrane shape. CSH Perspect. Biol. 3 (11): a004747 (2011)

    Article  Google Scholar 

  11. L. Gao, J. Shillcock, and R. Lipowsky: Improved dissipative particle dynamics simulations of lipid bilayers. J. Chem. Phys. 126, 015101 (2007)

    Article  Google Scholar 

  12. R.D. Groot and P.B. Warren: Dissipative particle dynamics – bridging the gap between atomistic and mesoscopic simulations. J. Chem. Phys. 107, 4423–4435 (1997)

    Article  Google Scholar 

  13. H. Haario, M. Laine, A. Mira and E. Saksman: DRAM: Efficient adaptive MCMC. Stat. Comput. 16, 339–354 (2006)

    Article  MathSciNet  Google Scholar 

  14. P.E. Hadjidoukas, P. Angelikopoulos, C. Papadimitriou, P. Koumoutsakos: Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models. J. Comput. Phys. 284 1–21 (2015)

    Article  MathSciNet  Google Scholar 

  15. B. Hajek: Cooling schedules for optimal annealing. Math. Oper. Res. 13 (2), 311–329 (1988)

    Article  MathSciNet  Google Scholar 

  16. R. Holley and D. Stroock: Simulated annealing via Sobolev inequalities. Comm. Math. Phys. 115 (4), 553–569 (1988)

    Article  MathSciNet  Google Scholar 

  17. I.K. Jarsch, F. Daste, and J.L. Gallop. Membrane curvature in cell biology: an integration of molecular mechanisms. J. Cell. Biol. 214 (4) 375–387 (2016)

    Article  Google Scholar 

  18. G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation. (Springer, New York, 2005)

    Google Scholar 

  19. E. Keaveny, I. Pivkin, M. Maxey, and G. Karniadakis: A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows. J. Chem. Phys. 123, 104107 (2005)

    Article  Google Scholar 

  20. D. Kim, C. Bowman, J.T. Del Bonis-O’Donnell, A. Matzavinos, and D. Stein: Giant acceleration of DNA diffusion in an array of entropic barriers. Phys. Rev. Lett. 118, 048002 (2017)

    Article  Google Scholar 

  21. O.P. Le Maître and O.M. Knio, Spectral Methods for Uncertainty Quantification. (Springer, New York, 2010)

    Google Scholar 

  22. H. Lei and G.E. Karniadakis: Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations. PNAS 110 (28), 211–227 (2013)

    Article  Google Scholar 

  23. B. Leimkuhler and C. Matthews, Molecular Dynamics: With Deterministic and Stochastic Numerical Methods. (Springer, New York, 2015)

    MATH  Google Scholar 

  24. B. Leimkuhler and X. Shang: On the numerical treatment of dissipative particle dynamics and related systems. Journal of Computational Physics 280, 72–95 (2015)

    Article  MathSciNet  Google Scholar 

  25. H. Matsuo et al. Role of LBPA and Alix in multivesicular liposome formation and endosome organization. Science 303 531534 (2004)

    Article  Google Scholar 

  26. F. Milde, G. Tauriello, H. Haberkern, and P. Koumoutsakos: SEM++: A particle model of cellular growth, signaling and migration. Comp. Part. Mech. 1 (2), 211–227 (2014)

    Article  Google Scholar 

  27. N. Phan-Thien, Understanding Viscoelasticity: An Introduction to Rheology, 2nd edn. (Springer, Berlin, 2013)

    Book  Google Scholar 

  28. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117, 1–19 (1995)

    Article  Google Scholar 

  29. D. C. Rapaport, The Art of Molecular Dynamics Simulation, 2nd edn. (Cambridge, UK, 2004)

    Book  Google Scholar 

  30. P. Salamon, P. Sibani, and R. Frost, Facts, Conjectures, and Improvements for Simulated Annealing. (SIAM, 2002)

    Google Scholar 

  31. T. Shardlow and Y. Yan: Geometric ergodicity for dissipative particle dynamics. Stoch. Dyn. 6, 123–154 (2006)

    Article  MathSciNet  Google Scholar 

  32. R. Smith, Uncertainty Quantification: Theory, Implementation, and Applications. (Society for Industrial and Applied Mathematics, Philadelphia, 2014)

    Google Scholar 

  33. M.A. Stolarska, Y. Kim, H.G. Othmer: Multi-scale models of cell and tissue dynamics. Phil. Trans. R. Soc. A 367, 3525–3553 (2009)

    Article  MathSciNet  Google Scholar 

  34. D. Stroock, An Introduction to Markov Processes, 2nd edn. (Springer, 2014)

    Google Scholar 

  35. Y.-H. Tang, L. Lu, H. Li, C. Evangelinos, L. Grinberg, V. Sachdeva, and G.E. Karniadakis: OpenRBC: A fast simulator of red blood cells at protein resolution. Biophysical Journal 112 (10), 2030–2037 (2017)

    Article  Google Scholar 

  36. A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation. (Society for Industrial and Applied Mathematics, Philadelphia, 2005)

    Google Scholar 

  37. K.-V. Yuen,Bayesian Methods for Structural Dynamics and Civil Engineering. (Wiley Verlag, 2010)

    Google Scholar 

  38. M.W. Vanik, J.L. Beck, S.K. Au: Bayesian probabilistic approach to structural health monitoring. J. Eng. Mech. 126, 738–745 (2000)

    Article  Google Scholar 

  39. A. Vrugt, C. J. F. ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman, and D. Higdon: Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling, Int. J. Non. Sci. Num. Sim. 10, 273 (2011).

    MATH  Google Scholar 

  40. S. Wu, P. Angelikopoulos, C. Papadimitriou, R. Moser, and P. Koumoutsakos: A hierarchical Bayesian framework for force field selection in molecular dynamics simulations. Phil. Trans. R. Soc. A 374, 20150032 (2016)

    Article  MathSciNet  Google Scholar 

  41. D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach. (Princeton University Press, 2010)

    Google Scholar 

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Acknowledgements

Part of this research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University. CB was partially supported by the NSF through grant DMS-1148284. AR was supported in part by the Simons Foundation under Collaboration Grant 359575. DS acknowledges support from NSF under awards 1409577 and 1505878. KL and AM were partially supported by the NSF through grants DMS-1521266 and DMS-1552903. The authors gratefully acknowledge discussions with Petros Koumoutsakos and his group during the preparation of this chapter. AM thanks the Computational Science and Engineering Laboratory at ETH Zürich for their warm hospitality during a sabbatical semester.

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Author notes

  1. Clark Bowman

    Present address: Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA

Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Clark Bowman, Karen Larson & Anastasios Matzavinos

  2. Department of Mathematics, Iowa State University, 50011, Ames, Iowa, USA

    Alexander Roitershtein

  3. Department of Physics, Brown University, 02912, Providence, RI, USA

    Derek Stein

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  1. Clark Bowman
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  2. Karen Larson
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  4. Derek Stein
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  5. Anastasios Matzavinos
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Corresponding author

Correspondence to Clark Bowman .

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Editors and Affiliations

  1. Mathematics, University of St. Thomas, Saint Paul, MN, USA

    Magdalena Stolarska

  2. Mathematics, Purdue University Northwest, Hammond, IN, USA

    Nicoleta Tarfulea

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Bowman, C., Larson, K., Roitershtein, A., Stein, D., Matzavinos, A. (2018). Bayesian Uncertainty Quantification for Particle-Based Simulation of Lipid Bilayer Membranes. In: Stolarska, M., Tarfulea, N. (eds) Cell Movement. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-96842-1_4

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