Finite-Element Analysis of Microbiological Structures

The recent development of nanomanipulation tools such as optical tweezers or atomic force microscopes has paved the way to the exploration of the mechanical properties of biological material at the micro- and nanometric scale. The use of these instruments is nowadays generalized, however, the interpretation of the results remains a challenge. It is well known that the deformation of an object under a load depends not only on the mechanical properties of the material but also on its geometry. This factor seriously hinders the interpretation of these measurements. To master this complexity, it is nowadays possible to numerically simulate the measuring experimental procedure with various parameters until the simulation fits the measurement results. In this chapter we briefly explain this analysis technique, review its application domains, and mention some recent works that employed this approach.

[1]  Christoph F Schmidt,et al.  Elastic response, buckling, and instability of microtubules under radial indentation. , 2006, Biophysical journal.

[2]  T. Hisada,et al.  An integrated finite element simulation of cardiomyocyte function based on triphasic theory , 2015, Front. Physiol..

[3]  H Tashiro,et al.  Buckling of a single microtubule by optical trapping forces: direct measurement of microtubule rigidity. , 1995, Cell motility and the cytoskeleton.

[4]  M. Dembo,et al.  On the mechanics of the first cleavage division of the sea urchin egg. , 1997, Experimental cell research.

[5]  G. W. Brodland,et al.  Mechanical evaluation of theories of neurulation using computer simulations , 2022 .

[6]  D. Johansson,et al.  Modeling and simulation of the mechanical response from nanoindentation test of DNA-filled viral capsids , 2013, Journal of biological physics.

[7]  V. Thomée From finite differences to finite elements a short history of numerical analysis of partial differential equations , 2001 .

[8]  C. Schönenberger,et al.  Nanomechanics of microtubules. , 2002, Physical review letters.

[9]  Ray Keller,et al.  How we are shaped: the biomechanics of gastrulation. , 2003, Differentiation; research in biological diversity.

[10]  M. Raimondi,et al.  Bio-chemo-mechanical models for nuclear deformation in adherent eukaryotic cells , 2014, Biomechanics and Modeling in Mechanobiology.

[11]  Z. Donhauser,et al.  Mechanics of microtubules: effects of protofilament orientation. , 2010, Biophysical journal.

[12]  S Chien,et al.  Spectrin properties and the elasticity of the red blood cell membrane skeleton. , 1997, Biorheology.

[13]  Q. Cui,et al.  A finite element framework for studying the mechanical response of macromolecules: application to the gating of the mechanosensitive channel MscL. , 2006, Biophysical journal.

[14]  M. S. Steinberg,et al.  Cadherin-mediated cell-cell adhesion and tissue segregation in relation to malignancy. , 2004, The International journal of developmental biology.

[15]  Cwj Cees Oomens,et al.  Mechanical and failure properties of single attached cells under compression. , 2005, Journal of biomechanics.

[16]  J. W. Grant,et al.  A finite-element model of inner ear hair bundle micromechanics , 1997, Hearing Research.

[17]  E. Nogales,et al.  High-Resolution Model of the Microtubule , 1999, Cell.

[18]  M. Cooling,et al.  Computational models of the primary cilium and endothelial mechanotransmission , 2015, Biomechanics and modeling in mechanobiology.

[19]  George Oster,et al.  How nematode sperm crawl. , 2002, Journal of cell science.

[20]  Philippe Tracqui,et al.  Mechanical Instabilities as a Central Issue for InSilico Analysis of Cell Dynamics , 2006, Proceedings of the IEEE.

[21]  Computational models of hair cell bundle mechanics: III. 3-D utricular bundles , 2004, Hearing Research.

[22]  Alf Samuelsson,et al.  History of the stiffness method , 2006 .

[23]  N. Caille,et al.  Contribution of the nucleus to the mechanical properties of endothelial cells. , 2002, Journal of biomechanics.

[24]  J. Heck,et al.  Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum. , 2004, Cell motility and the cytoskeleton.

[25]  J. Schoenung,et al.  An integrated approach for probing the structure and mechanical properties of diatoms: Toward engineered nanotemplates. , 2015, Acta biomaterialia.

[26]  Daniel A. Fletcher,et al.  A multi-structural single cell model of force-induced interactions of cytoskeletal components. , 2013, Biomaterials.

[27]  Vince Adams,et al.  Building Better Products with Finite Element Analysis , 1998 .

[28]  Yves Engelborghs,et al.  Dynamical and mechanical study of immobilized microtubules with atomic force microscopy , 1996 .

[29]  Ridha Hambli,et al.  Physically based 3D finite element model of a single mineralized collagen microfibril. , 2012, Journal of theoretical biology.

[30]  M. Dembo,et al.  Mechanics of neutrophil phagocytosis: experiments and quantitative models , 2006, Journal of Cell Science.

[31]  J. Morrow,et al.  Spectrin tethers and mesh in the biosynthetic pathway. , 2000, Journal of cell science.

[32]  R. Fettiplace,et al.  The sensory and motor roles of auditory hair cells , 2006, Nature Reviews Neuroscience.

[33]  Haoran Wang,et al.  Nanomechanical characterization of rod-like superlattice assembled from tobacco mosaic viruses , 2013 .

[34]  Alex Mogilner,et al.  Multiscale Two-Dimensional Modeling of a Motile Simple-Shaped Cell , 2005, Multiscale Model. Simul..

[35]  G. Oster,et al.  How do sea urchins invaginate? Using biomechanics to distinguish between mechanisms of primary invagination. , 1995, Development.

[36]  T. Collins,et al.  Hemodynamics, Endothelial Gene Expression, and Atherogenesis a , 1997, Annals of the New York Academy of Sciences.

[37]  Marc Herant,et al.  The mechanics of neutrophils: synthetic modeling of three experiments. , 2003, Biophysical journal.

[38]  S. Suresh,et al.  Cell and molecular mechanics of biological materials , 2003, Nature materials.

[39]  Ray W. Clough,et al.  Early history of the finite element method from the view point of a pioneer , 2004 .

[40]  R. Melosh BASIS FOR DERIVATION OF MATRICES FOR THE DIRECT STIFFNESS METHOD , 1963 .

[41]  G Wayne Brodland,et al.  The Differential Interfacial Tension Hypothesis (DITH): a comprehensive theory for the self-rearrangement of embryonic cells and tissues. , 2002, Journal of biomechanical engineering.

[42]  Paul J. Kolston,et al.  Finite-element modelling: a new tool for the biologist , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[43]  G W Brodland,et al.  The mechanics of heterotypic cell aggregates: insights from computer simulations. , 2000, Journal of biomechanical engineering.

[44]  David Barlam,et al.  Mechanical properties of murine leukemia virus particles: effect of maturation. , 2006, Biophysical journal.

[45]  G. Cao,et al.  Evaluating the nucleus effect on the dynamic indentation behavior of cells , 2013, Biomechanics and modeling in mechanobiology.

[46]  Zhiping Xu,et al.  Alzheimer's abeta(1-40) amyloid fibrils feature size-dependent mechanical properties. , 2010, Biophysical journal.

[47]  Mechanical double layer model for Saccharomyces Cerevisiae cell wall , 2013, European Biophysics Journal.

[48]  Victor Smetacek,et al.  Architecture and material properties of diatom shells provide effective mechanical protection , 2003, Nature.

[49]  Subra Suresh,et al.  The biomechanics toolbox: experimental approaches for living cells and biomolecules , 2003 .