Download COMPUTATIONAL MODELLING OF CELL AND TISSUE

COMPUTATIONAL MODELLING OF CELL AND TISSUE MECHANORESPONSIVENESS
Patrick J Prendergast
Trinity Centre for Bioengineering, School of Engineering, Parsons Building, Trinity College, Dublin 2, Ireland
ABSTRACT
Tissues have adapted to sustain the mechanical forces
encountered in the earth’s gravitational field. Furthermore
tissues remodel to the prevailing mechanical environment during
the lifetime of the individual, i.e. ontogenic adaptation. If the
mechanical environment changes, it is to be expected that not
only would the degree of optimality achieved during evolution
would be lost but the ontogenic processes that ‘tune’ the
organism to the prevalent mechanical loading would cause
further adaptation. These are among the reasons that it is
interesting to examine tissue response to mechanical stress, and
the cellular responses governing such responses. This paper
presents an overview of computational approaches used to
analyse the regulatory effect of mechanical forces on the
musculoskeletal system. In particular work done on the
computational modelling of cell/tissue responses is presented
together with some experiments corroborating these models. The
paper concludes by returning to the issue of mammalian cell
responses in ontogeny and how that might be extrapolated to
predict ontogenic and phylogenetic responses in low gravity
environments.
INTRODUCTION
Mammalian musculoskeletal systems are geared to
gravity – they have evolved under natural selection to
allow the species to survive in the terrestrial or aquatic
gravitational environment of earth (Carter and Beaupré,
2001; Currey, 2002). It is well known that the tissues of
the skeleton, particularly bone and muscle, respond
during life to the prevailing mechanical forces applied to
them. This ontogenic ‘fine-tuning’ to mechanical loading
can readily be observed in humans who suddenly become
physically active, and it has been quantified in animals;
perhaps the best-known studies are the mouse hindlimb
suspension experiments (van der Meulen et al., 1995;
Hardiman et al., 2005). Such experiments have shown
that skeletal structures change shape, and the bone tissue
within them changes stiffness, when the average
mechanical load is changed. Responses are subject to
great variation even between individuals of the same
species, and experiments on different strains of mice have
attempted to elucidate a genetic basis for this (e.g.,
Amblard et al., 2003). Therefore, not only is the final
shape of the skeletal structure subject to variation, but the
mechano-responsiveness is also subject to variation
among individuals (Prendergast, 2002).
____________________
* Correspondence to: Prof. Patrick J. Prendergast
Trinity Centre for Bioengineering
School of Engineering
Parsons Building / Trinity College
Dublin 2, Ireland
Email: [email protected]
Phone: +353 1 896 2061; Fax: +353 1 679 5554
Computational models have been developed which can
simulate the ontogenic adaptation in response to
mechanical loads. Two processes have been examined in
detail: bone remodelling whereby bones adapt their shape
and internal structure in response to changing loads
(Huiskes et al., 2000; Hart, 2001) and mechanoregulation
of tissue differentiation whereby mechanical forces
regulate tissue differentiation from one phenotype to
another (Prendergast and van der Meulen, 2001). Such
computational models have shown that relatively simple
algorithms can simulate the tissues’ responses to changes
in forces. However, the algorithms take no account of the
genetic basis of the adaptations – in this respect they are
deterministic and would not account for the variation in
the response by different members of the population if the
population was subjected to a new environment. Another
issue with such predictive models is that it has proven
difficult to corroborate them against animal experiments
because this problem of variability between individuals is
compounded by problems relating to differences in
loading and skeletal geometry.
In this article the author presents current research on
computing the response of cells, tissues, and skeletal
elements to the mechanical loading environment. Given
the volume of work in this field it is not possible to be
comprehensive but it is possible to describe some current
research and to highlight future research directions that
may be relevant to gravitational and space biology.
CELLS RESPOND TO FORCES
The cells in the human body are subjected to mechanical
stimulation and to fluid shearing forces. The cells from
load-bearing tissues – such as skeletal (Carter and
Beaupré, 2001), vascular (Rachev, 2005) and mesentery
(Gregersen, 2002) tissues – have been studied intensively
in respect of their mechanosensitivity. The experiments
on cells can be listed as:
(i)
single cell biomechanics, viz. micro-pipette
experiments where single cells are sucked into a pipette
under known pressure with simultaneous video recording
of cell deformation (e.g. Jones et al. 1999) or, more
recently, indenting the cell using the atomic force
microscope and measuring both cell expression and cell
stiffness (e.g. Charras and Horton, 2002; Maguire et al.
2007).
(ii) cells in monolayer experiments, such as substrate
stretch and fluid flow over confluent layers of cells (e.g.
Bacabac et al. 2004; Klein-Nulend et al. 2003; McGarry
et al, 2005).
Gravitational and Space Biology 20(2) June 2007
43
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
These experiments show unequivocally that mechanical
stressing elicits expression of signalling and matrix
molecules. The experiments on cells in a confluent layer
have been important because they have shown that the
magnitude of stimuli acting due to physiological
mechanical loading can cause cells to signal with Nitric
Oxide (NO) and prostaglandin E2 (PGE2) molecules. If
forces on the skeleton reduce and cause the biophysical
stimuli in the tissue to reduce correspondingly then the
tissue would react in some way via cell
mechanoresponsiveness. This clearly establishes that
mechanosensitive cells have the potential to maintain
tissue structure; it is highly likely that this system ensures
that the healthy skeleton is attuned to the mechanical
environment in which it must function.
In an attempt to better understand what causes cellular
mechanosensation, modelling of cells in these
experiments was presented by McGarry et al. 2005. This
study describes a computational model of a cell subject to
fluid flow and substrate strain. The model (described in
detail by McGarry and Prendergast, 2004) was developed
using the finite element method and it creates a complex
geometry of a cell attached to a substrate; the cell has a
spread configuration, and the cytoskeleton of
microtubules and actin elements is configured as a
tensegrity structure within a solid cytosol; the nucleus is
also included (see Fig. 1). It was found that substrate
strain and fluid flow resulted in mechanical stress in all
elements in the model but manifest as very different
biophysical stimuli at the membrane indicating an
independent role for these stimuli in attuning cells to their
mechanical environment. It was further predicted that the
nucleus is subject to a degree of mechanical stress that
depends on the nature of the biophysical stimulus (Fig. 2)
and, given that DNA is known to deform in response to
forces, this could be an issue worth further investigation.
Figure 1: A finite element model of a single cell in a spread configuration on a substrate; half of the cell membrane and cytosol are
removed to reveal the tensegrity-based cyctoskeletal framework of microtubules and microfilaments (actin elements) The finite element
model was generated using the ANSYS software. Various different element types are used, as described on the figure.
44 Gravitational and Space Biology 20(2) June 2007
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
Figure 2: Predicted 1st principal stress (units: N/µm2) in the nucleus of a eukaryotic cell under mechanical forces applied in experiments
(detailed in McGarry et al. 2005) of (a) a substrate strain of 1,000µε and (b) a fluid flow generating a shear stress of 0.6 Pa. Note the
order of magnitude higher stressing under fluid flow in these experiments.
Turning to atomic force microscope (AFM) experiments,
these have shown that mechanical probing of the cell
membrane can elicit responses – typical of these studies is
the report by Charras and Horton (2002) who measure
intracellular calcium levels and find that the number of
reacting cells increases with the strain applied by AFM,
and also that cellular responses could be modulated by
disrupting cytoskeletal components. Recent work by our
group using the AFM in microscope mode has shown that
rat mesenchymal stem cells respond to their extracellular
environment by adapting their cytoskeletal structures.
Maguire et al. (2007) have reported that, if plated on
glass, such stem cells develop internal geodesic F-actin
structures (see Fig. 3). Although these structures have
been observed previously (Boal, 2002), use of AFM has
also allowed measurement of mechanical properties (by
dynamic mode AFM) at the indentation site where the
nodes of the structure are found to be the most flexible
part of the cytoskeleton, indicating a different
composition of the nodes relative to the actin of the
tension elements themselves. Therefore single cell
biomechanics supports theories relating mechanical
stimulation to cell responses, and further suggests
complex cytoskeletal reactions occur as part of the
process.
Given then that cells are mechanosensitive and respond to
mechanical forces, it has been hypothesised that if cells
are disturbed from their customary mechanical
environment a reaction to return the cells to their original
state is created. In mathematical terms this is a negative
‘feedback loop’ where cells use the difference between
their actual stimulus level and a preferred target level as a
homeostatic driver to change the extracellular matrix to
regain the normal mechanical milieu. Not only may a
change in matrix strain or insterstitial fluid flow disturb
the homeostatic mechanical milieu, but damage to the
extracellular matrix will also cause changes in the local
mechanical environment and create an adaptation at the
tissue level (Hart, 2001; van der Meulen and Huiskes,
2002). However, such a ‘control system’ for tissue
stability may become a positive feedback loop if the aim
of the cell is to maximize the level of stimulus received
(Weinans and Prendergast, 1996).
Figure 3: Scan of the periphery of a rat mesenchymal stem cell
showing the emergence of geodesic F-actin structures (image
shows the phase angle in degrees obtained using Atomic Force
Microscopy, after Maguire et al., 2007)
COMPUTING RESPONSES TO MECHANICAL
FORCES – FEEDBACK LOOPS
The adaptation of the skeleton during life to the prevailing
mechanical forces has been one of the classical problems
of biology, beginning with the German anatomists at the
end of the 19th Century. Roesler (1987) gives the most
complete introduction to the historical view. The German
Gravitational and Space Biology 20(2) June 2007
45
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
Figure 4: A diagrammatic representation of a mechanoregulation concept. At time=0 the tissue is a low-stiffness precursor tissue
consisting of stem cells and it is subject to a particular mechanical stimulus, represented here as a combination of strain and fluid flow.
Over time the stem cells differentiate and the tissue begins to get stiffer. If the increase in tissue stiffness reduces the strain then the dashed
line is followed leading, ultimately, to bone. Alternatively, under displacement-control, the increase in tissue stiffness has no effect on
strain and the mechanical stimulus will remain high maintaining a soft-tissue phenotype.
orthopaedic surgeon Friedrich Pauwels (Pauwels, 1965)
brought the subject into a more modern context by
postulating that precursor mesenchymal stem cells
(MSCs) differentiated according to the following rule:
Hydrostatic pressure stimulates MSC differentiation into
chondrocytes to form cartilage, shearing stimulates MSC
differentiation into fibroblasts to form fibrous connective
tissue, combinations of the two stimulate fibrocartilage
formation (as in discs and menisci), and only when a soft
tissue has stabalized the environment is MSC
differentiation into osteoblasts favoured leading to the
formation of bone.
These concepts received great attention many years later
when a better understanding of the influence of
mechanical forces on tissue phenotype became crucial for
the design of medical devices, in particular tissueengineered implants created using bioreactors (Kelly and
Prendergast, 2006).
One of the key issues of the mechanical loading
environment is whether or not the stimulation of the tissue
is controlled by displacement (displacement-controlled)
or controlled by force (force-controlled). The forces that
act in the bones of the appendicular skeleton are
determined by the weight of the body and/or the
acceleration of the limbs – thus they are subject to forcecontrolled stimulation and, as a consequence, increasing
stiffness of these tissues means that the strain experienced
reduces. Displacement-control will act whenever tissues
are subject to a given displacement no matter what the
46 Gravitational and Space Biology 20(2) June 2007
tissue’s stiffness is: typically ligaments and muscles are
subject to displacement-control. It should however be
noted that in terms of actually sensing mechanical load,
cells or tissue can only directly measure displacement and
infer the force from this strain. Computational simulations
can account for force- vs. displacement-controlled
environments (Prendergast et al., 1997) and predict that,
where stiffening of the tissue can reduce the mechanical
stimulation felt by the cells (whether strain or fluid flow)
then a mechanical milieu in the tissue favouring
osteoblast differentiation from the precursor cells will
emerge (see Fig. 4 dashed line); otherwise high
strain/fluid flow environments will emerge maintaining
the soft tissue of fibrous connective tissue or cartilage
(see Fig. 4 full line).
Mechanobiological computer simulations have been
performed to establish if such theories can predict the
deposition and resorption of tissue during fracture healing
(Lacroix and Prendergast, 2002), osteochondral defect
healing (Kelly and Prendergast, 2004) and bone chamber
experiments (Geris et al., 2004).
A satisfactory
correspondence between simulation and experiment has
been found, and thus a kind of collaboration has been
achieved at a functional level. However, for many
researchers such a collaboration or ‘validation’ is
inadequate. Instead it might be preferred if a model for
mechano-regulation could be built up from knowledge of
cell mechanoresponsiveness. The development of such
experiments would require the ability to compute the celllevel stimuli in a tissue when the applied
force/displacement is known; such computations would
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
Figure 5: There may be a selection pressure in favour of mechanosensitive genes during evolution. If mechanical forces during life
increase/decrease we may hypothesise that the flow of mechanosensitive genes will increase/decrease.
require micromechanical
(Prendergast, 2004).
finite
element
models
The above discussion may be summarized as follows:
tissues react to the mechanical environment via
mechanosensation by cells. Such mechanosensitive cells
either signal activity in other cells or change phenotype
(differentiate) themselves. The predictive power of
computational models is somewhat limited even yet
because of the difficulties in corroboration against
experiment (Currey, 1995). In particular, experiments on
cells cannot be easily used to corroborate models because
of the difficulty of relating forces acting on the organ (e.g.
a bone) to stimuli acting within the tissue at the cell level.
A further issue not addressed in current computational
models is variability. Experiments show that individuals
in a population show considerable variability in their
response to mechanical loading; for example, the
experiments quantifying bone loss in hindlimb-suspended
mice show this (van der Meulen et al. 1995, Hardiman et
al., 2005). Therefore, if we aim to predict how an
individual, or indeed a population, will respond when
subject to a new mechanical environment, a relationship
between mechanoregulation and genetics will be required,
e.g. Nowlan and Prendergast (2005).
MECHANICAL EFFECTS IN PHYLOGENY
Based on the mechanobiological model presented in Fig.
4, inferences can be made about how tissues would adapt
if the animal were to move from one mechanical
environment to another, such as the phylogenetic move
from terrestrial to aquatic environments of the Cetaceans
(whales). Those parts of the skeleton that have evolved
under force-control would be most affected because, for
example in, say, a low gravity environment, the cells
within them would not be mechanically stimulated (by
strain or interstitial fluid flow) to the same degree. In
particular the cartilages and fibrocartilage structures of
the appendicular skeleton (discs, menisci) might not be
subject to a level of mechanical stimulation that would
maintain them; fibrous connective tissues on the other
hand (tendon, ligament) that are mainly in a
displacement-controlled regime, would be maintained.
It is interesting to discuss this idea with the concept of
‘fitness’ – according to van der Meulen and Huiskes
(2002) mechanobiological process render tissues fit for
their mechanical function; fitness is increased when
‘mechanosensitive genes’ are selected during evolution. A
mechanosensitive gene is one expressed by a cell in
response to mechanical stimulation, and they have
emerged because of the advantage they give the animal in
growing and remodelling tissues suited to function under
mechanical forces. Novel genes would emerge through
mutation, duplication and/or co-optation of existing genes
and their alleles. Figure 5 attempts to illustrate the
regulatory effect of the strength of gravitational
environment on the emergence of mechanosensitive
genes; selection pressure for the emergence of such genes
will be related to the forces acting on the skeletal
Gravitational and Space Biology 20(2) June 2007
47
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
elements so that species that are highly active will require
the ‘tuning’ to mechanical loading that mechanosensitive
genes bring.
ACKNOWLEDGEMENTS
The author’s research is funded from a range of sources,
including a Science Foundation Ireland (SFI) Investigator
grant
titled
“Computational
Mechanobiology:
fundamental advances and implementation for medical
device engineering”, the European Commission projects
BITES and SmartCAP, and the Programme for Research
in Third Level Institutions administered by the Higher
Education Authority in Ireland. Ms Niamh Nowlan, Ms
Brianne Mulvihill, and Dr Andrew Jackson and Dr Alex
Lennon are thanked for comments on the draft of this
paper.
REFERENCES
Amblard, D., Lafage-Proust M.H., Liab A, Thomas T.,
Ruegsegger P., Alexandre C., Vico, L. 2003. Tail
suspension induces bone loss in skeletally mature mice in
the C57BL/6J strain but not in the C3H/HeJ strain.
Journal of Bone and Mineral Research 18: 561-569.
Bacabac, R.G., Smit, T.H., Mullender, M.G., Dijks, S.J.,
van Loon, J.J.W.A., Klein-Nulend, J. 2004. Nitric oxide
production by bone cells in fluid shear stress dependent.
Biochemical and Biophysical Research Communications
315: 823-829.
Boal, D. 2002. Mechanics of the Cell. Cambridge
University Press: Cambridge.
Carter, D.R., Beaupré, G.S. 2001. Skeletal Form and
Function, Cambridge University Press: Cambridge
Charras, G.T., Horton, M.A. 2002. Single cell
mechanotransduction and its modulation analyzed by
atomic force microscopy indentation. Biophysical Journal
82: 2970-2981.
Currey, J.D. 1995. The validation of algorithms used to
explain adaptive bonde remodelling. In Bone Structure
and Remodelling. A. Odgaard, H. Weinans, Eds., World
Scientific: Singapore, pp. 9-13.
Currey, J.D. 2002. Bones. Princeton University Press:
Princeton
Geris, L., Andreykiv, A., Van Oosterwyck, H., Sloten,
J.V., van Keulen, F., Duyck, J., Naert, I. 2004. Numerical
simulation of tissue differentiation around loaded titanium
implants in a bone chamber. Journal of Biomechanics 37:
763-769.
Gregersen, H. 2002. Biomechanics of the gastrointestinal
tract. Springer: Berlin
48 Gravitational and Space Biology 20(2) June 2007
Hardiman, D.A., O’Brien, F.J., Prendergast, P.J., Croke,
D.T., Staines, A. and Lee, T.C. 2005. Tracking the
changes in unloaded bone: morphology and gene
expression, European Journal of Morphology 42: 208216.
Hart, R.T. 2001. Bone modelling and remodelling:
theories and computation. In Bone Mechanics Handbook
(Cowin, S.C., Ed.) CRC Press: Boca Raton, Chapter 31.
Huiskes, R., Ruimerman, R., van Lenthe, G.H., Janssen,
J.D. 2000. Effects of mechanical forces on maintenance
and adaptation of form in trabecular bone. Nature 405:
704-706.
Jones, W.R., Ting-Beall, H.P., Lee, G.M., Kelley, S.S.,
Hochmuth, R.M., Guilak, F. 1999. Alterations in the
Young's modulus and volumetric properties of
chondrocytes isolated from normal and osteoarthritic
human cartilage. Journal of Biomechanics 32: 119-127.
Kelly, D.J., Prendergast, P.J. 2006. Prediction of optimal
mechanical properties for a scaffold used in osteochondral
defect repair. Tissue Engineering 12: 2509-2519.
Klein-Nulend, J., Bacabac, R.G., Veldhuijzen, J.P., van
Loon, J.J.W.A. 2003. Microgravity and bone cell
mechanosensitivity. Advances in Space Research 32:
1551-1559.
Lacroix, D., Prendergast, P.J. 2002. A mechanoregulation model for tissue differentiation during fracture
healing: analysis of gap size and loading. Journal of
Biomechanics 35: 1163-1171.
Maguire, P., Kilpatrick, J.I., Kelly, G., Prendergast, P.J.,
Campbell, V.A., O’Connell, B.C., Jarvis, S.P. 2007.
Direct mechanical measurement of geodesic structures in
rat mesenchymal stem cells. HFSP Journal. (submitted)
McGarry, J.G., Klein-Nulend, J., Mullender, M.G.,
Prendergast, P.J. 2005. A comparison of strain and fluid
shear stress in stimulating bone cell responses - a
computational and experimental study. The FASEB
Journal 19: 482-484.
McGarry, J.G., Prendergast, P.J. 2004. A threedimensional computational model of an adherent
eukaryotic cell. European Cells and Materials 7: 27-34.
Nowlan, N.C., Prendergast, P.J. 2005. Evolution of
mechanoregulation of bone growth will lead to nonoptimal bone phenotypes. Journal of Theoretical Biology
235: 408-418.
Pauwels, F. 1965. Gesammelte Abhandlungen zur
funktionellen Anatomie des Bewegungsapparates.
Springer: Berlin (Translated as Biomechanics of the
Locomotor Apparatus. by P. Maquet and R. Furlong
Springer: Berlin, 1980).
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
Prendergast, P.J. 2002. Mechanics applied to skeletal
ontogeny and phylogeny. Meccanica 37: 317-334.
Prendergast, P.J. 2004. Mechanobiology: experiment and
computation. In Topics in Biomechanical Engineering.
(Prendergast, P.J. and McHugh, P.E., Eds.) TCBE &
NCBES: Dublin, pp. 41-57.
Prendergast, P.J., Huiskes, R., Søballe, K. 1997.
Biophysical stimuli on cells during tissue differentiation
at implant interfaces. Journal of Biomechanics 30: 539548.
Prendergast, P.J., van der Meulen, M.C.H. 2001.
Mechanics of bone regeneration. In Bone Mechanics
Handbook. (Cowen, S.C., Ed.) CRC Press: Boca Raton,
Chapter 32, pp. 32.1-32.19.
Rachev, A. 2005. Introduction to the remodelling of
arteries. In Tissue Remodelling. (Piekarski, J., Ed.) Centre
of Excellence in Applied Biomedical Modelling and
Diagnostics: Warsaw, pp. 241-300.
Roesler, H. 1987. A history of some fundamental
concepts in bone biomechanics. Journal of Biomechanics
20: 1025-1034.
van der Meulen, M.C.H., Huiskes, R. 2002. Why
mechanobiology? Journal of Biomechanics 35: 401-414.
van der Meulen, M.C.H., Morey-Holton E.R., Carter D.R.
1995. Hindlimb suspension diminishes femoral crosssectional growth in the rat. Journal of Orthopaedic
Research 13: 700-707.
Weinans H., Prendergast PJ. 1996. Tissue adaptation as a
dynamical process far from equilibrium. Bone 19: 143149.
Gravitational and Space Biology 20(2) June 2007
49
P.J. Prendergast - Cell and Tissue Mechanoresponsiveness
50 Gravitational and Space Biology 20(2) June 2007