Theoretical and Computational Methods Working Group

The Theory and Methods Working Group discusses, promotes, and organizes activities and events about theory in biology and methods used to model biological systems. 

Working Group Leads:

Lead: Bill Cannon (

Co-Lead: Brian Drawert (

Past Leads: George Em Karniadakis ( and Linda Petzold (

(at bottom of page)

Several members of the Theory and Methods working group are helping to organize the 2021 Annual Meeting of the Society for Mathematical Biology - Join us an propose a session!

New methods workshop: Machine Learning in Genomics: Tools, Resources, Clinical Applications, and Ethics Workshop

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 #MultiScaleModelingMSM 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:



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.


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.

Working Group Activities

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.


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.


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.

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