Theoretical and Computational Methods Working Group

Working Group Leads:

Lead: Bill Cannon (

Co-Lead: Brian Drawert (

Senior Advisors: George Em Karniadakis ( and Linda Petzold (


Goals and Objectives:

The goals of the Theoretical and Computational Working Group are to:

• Provide a clear understanding of state-of-the-art theoretical and computational methods for stochastic multiscale modeling of biological systems and networks. Included in this are both hierarchical and concurrent scale coupling approaches as well as their hybrids.

• Focus on methods with strong mathematical foundations. Identify efficient and reliable techniques for multiscale error estimation, uncertainty quantification, inference, and stability analysis.

• Introduce new parallel computational frameworks and emerging paradigms, such as multi-fidelity techniques and machine learning. 

• Showcase clear examples of methods that have demonstrated strong potential for success in the solution of biological problems.

• Provide links to existing software related to multiscale modeling methods.

• Provide a fertile ground for discussion on current challenges and opportunities.

• Work with the other workgroups to identify problems and then posing them to the theoretical and computational modeling community.

• Organizing talks, symposia and conferences in the area of theoretical and computational multiscale modeling methods.


Methods Literature (click on Mendeley link below)

Mendeley Group on Methods in Multiscale Modeling in Biology

Discussion Forum (LinkedIn request membership -

LinkedIn Group Discussion of Methods

Check out on Twitter #MultiScaleModeling







New software from Linda Petzold:

StochSS is an integrated development environment (IDE) for simulation of biochemical networks


A paper on the occasion of 111 years since Einstein's paper on Brownian motion.

It provides a hydrodynamics perspective and summarizes all known results and controversies, includingexperimental results.


MSM 2017 (10th Anniversary) meeting Discussion Items

1. What are the new trends in multiscale methods?

2. Continuum vs. Atomistic methods.

3. Choosing the new leadership of this WG.

Please attend Theme 5 on an exciting workshop on statistical learning (March 24, 10-12:30 pm)



July 21, 2016  -- Multi-fidelity stochastic modeling with Gaussian processes

April 29, 2014 -- Biocellion: Accelerating Computer Simulation of Multicellular Biological System Models


MSM 2015 Discussion:




MSM 2014 Discussion:




Additional Information


  1. Karniadakis George
  2. Petzold Linda
  3. Oden Tinsley 
  4. De Suvranu
  5. Marmarelis Vasilis
  6. Peng Grace
  7. Hwang Wonmuk
  8. Buehler Markus
  9. Shephard Mark
  10. Picu Catalin
  11. Kuhl Ellen
  12. David Daryn
  13. Bassingthwaighte Jiim
  14. Thompson Elaine
  15. Katzper Meyer
  16. McQueen Philip
  17. Liu Delong
  18. Gregurick Susan
  19. Shum Lillian
  20. Dura-Bernal Salvador
  21. Peng Grace
  22. Sanger Terence tsanger@
  23. mazurchuk Richard
  24. Ashikaga Hiroshi
  25. Krauss Susan
  26. Wang Xujing
  27. Pflieger Mark
  28. Pepper John
  29. Neymotin Sam
  30. Srivastava Ranjan
  31. Radhakrishnan Ravi
  32. Cannon William
  33. Fourkal Eugene
  34. Candia Julián
  35. Swat Maciek
  36. Buehler Markus J.
  37. Linderman Jennifer
  38. Finley Stacey
  39. Chu Liang-Hui
  40. Zhang Le
  41. Wang Jun
  42. Sun Yuekai
  43. Hormuth David
  44. Andasari Vivi
  45. Peng Huiming
  46. Stamatelos Spyros
  47. Lin Ching-Long
  48. Kirschner Denise
  49. Anderson Warren
  50. Makadia Hirenkumar
  51. McDougal Robert
  52. Cook Daniel
  53. Brown David
  54. Lazzi Gianluca
  55. Kuttippurathu Lakshmi
  56. Ropella Glen
  57. Tartibi Mehrzad
  58. Shams Hengameh
  59. Miga Michael
  60. Verma Aalap
  61. Randles Amanda
  62. Frometa-Castillo, Terman:
  63. Dao Ming
  64. Vekilov Peter
  65. Xuejin Li
  66. Ahmad Raeisi Najafi
Working Group Activities

Current Projects:

1. Multiscale Universal Interface

2. Inference inn Stochastic Networks

3. Data-driven Multi-fidelity strategies

4. Rigorous coarse-graining formulations

5. Jacobian-free multiscale method [RaDe11]

6. Multiscale modeling of hydroxyapatite nanocrystals [ZaDe11]

7. Multiscale modeling of bionanoporous materials [ZaDe10]

8. Finite element framework for scaffolded DNA origami structure, dynamics, and mechanics [CaKi11]

9. Finite element framework for protein dynamics and mechanics [Ba08, KiAl11, SeBa10]

10. Coarse grained molecular dynamics for biofilaments including: collagen, amyloid, microtubule, and alpha-helical filaments [Hw10,Hw07,LaHw09a, LaHwa09b,PaHw06,RaHw08,RaHw07]

11. Validation and Uncertainty Quantification of Multiscale Models. Developing methods of statistical calibration and validation based on Bayesian inference to account for uncertainty in parameters and quantities of interests calculated in multiscale models. [OdPrRo10, BaOdPr09, OdPrBaCh09, ChPruDhBaOd10, ChOdPr08]

12. Mathematical Framework for the Adaptive Modeling of Biopolymers [Kurt Anderson]


[edit]Current State of the Art:

LinkedIn Group Discussion of Methods

1. Tang, Y. H., Kudo, S., Bian, X., Li, Z., & Karniadakis, G. E. (2015). Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solversJournal of Computational Physics297, 13-31.

2. Li, Z., Bian, X., Caswell, B., & Karniadakis, G. E. (2014). Construction of dissipative particle dynamics models for complex fluids via the Mori–Zwanzig formulationSoft matter10(43), 8659-8672.

3. [OdMoGh10] Oden, J.T.; Moser, R.; and Ghattas, O. “Quantification of uncertianty in computer predictions”, SIAM News, v. 43, no. 9-10, 2010.

4. [A review of global local multiscale methods]

5. Gillespie, D. T., Hellander, A. & Petzold, L. R. (2013). Perspective: Stochastic Algorithms for Chemical Kinetics. J. Chem. Phys. 138, 170901.


[edit]Challenges and Opportunities:

1. [Oden] Estimation and Control of Errors generated in multiscale models remains a central, open challenge in multiscale modeling. Multiscale modeling, by definition, is the transition from one scale to another. As one goes from fine scale to coarser scales, information is lost. This is a fundamental defect in most multiscale methodologies. To regain lost information, one must carefully define specific quantities of interest and estimate and control the error in these quantities in the transition from one scale to the other.

2. [Oden] Validation – MS modeling. The question of validation and the quantification of multiscale models is a highly complex and essentially open issue. Identifying parameters that control models of behavior at different scales is a major challenge in multiscale modeling.

3. [Hwang] "As the scale increases, the complexity of the system also increases. Thus meso- to macro-scale descriptions may be effective only for certain aspects of the system rather than realistically capturing experimental results as a whole. As multiscale modeling of biological systems is a new area, I believe the first step would be to link between atomistic and the next level of coarse graining. Through such a careful bottom-up approach,systematic ways of describing larger scale biological phenomena based on the molecular-level interactions may be possible."

4. [Anderson]I) Reintroduction of energy back into system to correctly account for added fidelity of finer grain models II) Correctly dealing with non-uniqueness of transitioning to finer-grain III) need to develop appropriate domain specific multirate temporal integration methods to better deal with local temporal scales in a multibody context.


[edit]Journal Articles:

[Ba08] Bathe, M. A Finite Element framework for computation of protein normal modes and mechanical response. Proteins: Structure, Function, and Bioinformatics, 70: 1595–1609 (2008).

[BaOdPr09]Bauman, Paul T.; Oden, J. T.; and Prudhomme, Serge. “Adaptive Multiscale Modeling of Polymeric Materials with Arlequin Coupling and Goals Algorithms,” Computer Methods in Applied Mechanics and Engineering, v. 198, issues 5-8, pp. 799-818, 2009.

T. Knowles, M.J. Buehler , “Nanomechanics of functional and pathological amyloid materials,” Nature Nanotechnology, accepted for publication

A. Gautieri, S. Vesentini , A. Redaelli, M.J. Buehler , “Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up,” Nano Letters, Vol. 11(2), pp. 757-766, 2011. PMID: 21207932

S. Keten, M.J. Buehler, “Nanostructure and molecular mechanics of dragline spider silk protein assemblies,” Journal of the Royal Society Interface, Vol. 7(53), pp. 1709-1721, 2010. PMID: 20519206

S. Keten, Z. Xu, B. Ihle, M.J. Buehler, “Nanoconfinement controls stiffness, strength and mechanical toughness of beta-sheet crystals in silk,” Nature Materials, Vol. 9, pp. 359-367, 2010. PMID: 20228820

A. Gautieri, S. Uzel, S. Vesentini, A. Redaelli, M.J. Buehler, “Molecular and mesoscale disease mechanisms of Osteogenesis Imperfecta,” Biophysical J., Vol. 97(3), pp. 857-865, 2009 PMCID: PMC2718154

A. Nova, S, Keten, N. Pugno , A. Redaelli , M.J. Buehler , “Molecular and nanostructural mechanisms of deformation, strength and toughness of spider silk fibrils,” Nano Letters , Vol. 10(7), pp. 2626-2634, 2010 PMID: 20518518

M.J. Buehler, Y. Yung, “Deformation and failure of protein materials in extreme conditions and disease,” Nature Materials, Vol. 8(3), pp. 175-188, 2009. PMID: 19229265

S. Keten, M.J. Buehler, “Geometric confinement governs the rupture strength of H-bond assemblies at a critical length scale,” Nano Letters, Vol. 8(2), pp. 743-748, 2008. PMID: 18269263

M.J. Buehler, “Nature designs tough collagen: Explaining the nanostructure of collagen fibrils,” Proc. Nat’l Academy of Sciences USA, Vol. 103 (33), pp. 12285-12290, 2006. PMCID: PMC1567872

[CaKi11] Castro, C.E., Kilchherr, F., Kim, D.N., Lin Shiao, E., Wauer, T., Wortmann, P., Bathe, M., and Dietz, H. A primer to scaffolded DNA origami. Nature Methods, 8:221-229 (2011)

[ChPruDhBaOd10] Chamoin, L.; Prudhomme, S.; Ben Dhia, H.; Bauman, P.T.; and Oden, J. T. “Ghost forces and spurious effects in atomic-to-continuum coupling methods by the Arlequin approach,” Int. J. Numerical Methods in Engineering, published online:, March 2010.

[ChOdPr08]Chamoin, Ludovic; Oden, J. Tinsley; and Prudhomme, Serge. “A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations”, Computer Methods in Applied Mechanics and Engineering, Special Issue. Edited by Nicholas Zabaras, v. 197, issues 43-44, pages 3530-3546, 2008.

[Hw10] Hwang, W. ``Ch. 18: How to measure biomolecular forces: A ``Tug-of-war approach, in Computational Modeling in Biomechanics (S. De, M. R. K. Mofrad, and F. Guilak, eds.) (Springer, 2010).

[Hw07] Hwang, W., ``Calculation of conformation-dependent biomolecular forces, J Chem Phys. 127 175104 (2007)

[KiAl11] Kim, D.N., Altschuler, J., Strong, C., McGill, G., and Bathe, M. Conformational dynamics data bank: a database for conformational dynamics of proteins and supramolecular protein assemblies. Nucleic Acids Research, 39: D451-455 (2011)

[LaHw09a] Lakkaraju, S.K. and Hwang, W., ``Critical buckling length versus persistence length: What governs biofilament conformation? Phys Rev Lett. 102 118102 (2009)

[LaHw09b] Lakkaraju, S.K. and Hwang, W., ``Modulation of elasticity in functionally distinct domains of the tropomyosin coiled-coil. Cell Molec Bioeng. 2 57--65 (2009)

[OdPrBaCh09]Oden, J.T.; Prudhomme, S.; Bauman, P.; and Chamoin, Ludovic. “Estimation and Control of Modeling Error: A General Approach to Multiscale Modeling “, in Bridging the Scales in Science and Engineering, Edited by Jacob Fish, Oxford University Press, Section 4, Chapter 10, 2009.

[OdPrRo10] Oden, J.T.; Prudhomme, S.; Romkes, A.; and Bauman, P. “Multi-scale modeling of physical phenomena: Adaptive control of models,” SIAM Journal on Scientific Computing, v.28, no. 6, pp. 2359-2389, 2006.

[PaHw06] Park, J., Kahng, B., Kamm, R.D., and Hwang, W., ``Atomistic simulation approach to a continuum description of self-assembled beta-sheet filaments, Biophys J. 90 2510-2524 (2006).

[RaDe11] Rahul, and De, S., “Efficient preconditioning for Jacobian-free multiscale methods”, International journal for Numerical Methods in Engineering, in press.

[RaHw08] Ravikumar, K.M., and Hwang, W., ``Region-specific role of water in collagen unwinding and assembly, Proteins, 72 1320--1332 (2008).

[RaHw07] Ravikumar, K.M., Humphrey, J.D., and Hwang, W., ``Spontaneous unwinding of a labile domain in a collagen triple helix, J Mech Mater Struct. 2 999-1010 (2007)

[SeBa10] Sedeh, R., Bathe, M., and Bathe, K.J. The subspace iteration method in protein normal mode analysis.Journal of Computational Chemistry, 31: 66–74 (2010).

[ZaDe11] Zamiri, A., and De, S., “Mechanical properties of hydroxyapatite single crystals from nanoindentation data”, Journal of the Mechanical Behavior of Biomedical Materials, in press.

[ZaDe10] Zamiri, A., and De, S., “Modeling the mechanical response of tetragonal lysozyme crystals”, Langmuir, 26(6), 4251-4257, 2010.

[edit]Related websites:




4. ICES multiscale modeling group website

5. Buehler Lab




1. USERMESO GPU-accelerated DPD package for LAMMPS, Subversion server: 

2. Multiscale Universal Interface library, Subversion server:



[edit]Past Conferences:

Multiscale Methods and Validation in Medicine and Biology I: Biomechanics and Mechanobiology