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INVESTIGATING THE MECHANICAL PROPERTIES OF LIVING HUMAN CELLS. Mark Murphy: GERI & BML Catherine Randall: GERI Alexis Guillaume: Université Claude Bernard, Lyon. PROJECT BREAKDOWN. Mark Murphy Cell Biology Atomic Force Microscopy Fluorescence microscopy. Catherine Randall

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investigating the mechanical properties of living human cells

INVESTIGATING THE MECHANICAL PROPERTIES OF LIVING HUMAN CELLS

Mark Murphy: GERI & BML

Catherine Randall: GERI

Alexis Guillaume: Université Claude Bernard, Lyon

slide2

PROJECT BREAKDOWN

  • Mark Murphy
  • Cell Biology
  • Atomic Force Microscopy
  • Fluorescence microscopy
  • Catherine Randall
  • Force Data Analysis
  • Image Processing
  • Alexis Guillaume
  • Computer Modelling
  • Simulation
slide3

WHAT DO WE ALREADY KNOW ABOUT CELL MECHANICS?

  • Very Little!
  • Cytoskeleton
  • Microtubules, Actin Filaments, Intermediate Filaments & Associated Proteins
  • Changes in the cytoskeleton occur during most normal cellular processes
slide6
WHY SHOULD WE STUDY CELLMECHANICS?
  • Changes in the cytoskeleton are associated with many human diseases, such as:
  • Cancer
  • Heart Disease
  • Premature Aging
  • Skin Fragility
  • Liver Disease
  • Such pathologies were first interpreted as ‘Mechanical Weakness Disorders’
slide8

Laser

Photo Detector

Z-piezo

Sample

X-Y Stage

Objective Lens

THE ATOMIC FORCE MICROSCOPE

slide10

Indentation (nm)

Deflection (nm)

2

1

Non-contact region

0

0

Z-Movement (µM)

1

2

AFM FORCE CURVES

slide11

LIVE HUMAN LUNG FIBROBLAST CELL

AFM Deflection Image of Human Lung Cell

3-D Image of Human Lung Cell

(Reconstructed From Height Image)

the hertz model1
THE HERTZ MODEL
  • Describes simple elastic deformations for perfectly homogeneous smooth surfaces

Fcone = 2/π · E / (1-v2) · tan(α) · δ2

Fparabola = 4/3 · E / (1-v2) · √R · δ3/2

  • Two Unknown Values
  • Powell\'s minimization method
results using the hertz model
RESULTS USING THE HERTZ MODEL

Parabolic tip

Conical tip

problems with the hertz model
PROBLEMS WITH THE HERTZ MODEL
  • Cells are not planar and do not extend infinitely in all directions
  • The cantilever is not infinitely stiff
  • Data is not linear
  • Cells are not perfectly elastic

Must consider other possible solutions

viscoelastic cells
VISCOELASTIC CELLS
  • Constitutive equation
  • Linear Elastic
  • Non-Linear Viscous
strain hardening
STRAIN HARDENING
  • Cells get stiffer with increased applied force
  • Possibly a similar mathematical model to those used in materials science
slide18

CELL INDENTATION OVER TIME WITHOUT SPHERE (n=4)

Applied force = Approx 1.5 nN

Time = 8.5 min

Voltage conversion 1 V/65 nm

  • The tip indents the cell (roughly 400 nm) and does not seem to push back but reaches a plateau
  • This trend is consistent and repeatable
cell indentation over time using attached sphere n 4
CELL INDENTATION OVER TIME USING ATTACHED SPHERE (n =4)

Applied force = Approx 1.5 nN

Time = 8.5 min

Voltage conversion 1 V/65 nm

slide20

ADAPTIVE EVIDENCE!

  • The sphere indents the cell and after a couple of minutes the cell seems to be pushing back
  • This trend is consistent and repeatable when using an attached sphere
how a simulation can help
HOW A SIMULATION CAN HELP
  • Similar experiments without bias
  • New experiments
  • Observe what you can not measure
  • Generally : test some hypothesis
what is simulated
WHAT IS SIMULATED?
  • Adhesion with other cells
  • Lipidic bilayer
  • Actin cortex
  • Cytoskeleton
  • Nucleus
  • Cytoskeleton
  • Actin cortex
  • Lipidic bilayer
  • Focal adhesion complex
  • Substrate
how is the cell simulated
HOW IS THE CELL SIMULATED?
  • Continuum Mechanics :
    • Equations describing the behaviour of the smallest amount of matter that can be seen as continous.
  • Finite Elements Method :
    • A node = an equation
    • Huge system to solve
  • Well-known mechanical materials
  • Realism
  • Slow
results
RESULTS
  • Fairly reproduce experimental conditions ;
  • Displacement, speed and acceleration for each node of the simulation
  • The future : from continuous materials to living materials
slide25

CONCLUSIONS

  • The cells in this study exhibit viscoelastic properties and exhibit strain hardening
  • They Show adaptive behaviour over time when an external force is applied
  • The cell behaves differently when a global force is applied compared to a local force
current future work
CURRENT & FUTURE WORK
  • Develop a model to analyse the force data
  • Disrupt cytoskeleton to determine contribution of each filament type
  • Disrupt cytoskeleton to see how the cell behaves over time
current future work1
CURRENT & FUTURE WORK
  • Compare mechanical properties of normal and pathological cells (cancer)
  • Determine mechanical properties of other cellular components
  • Compare mechanical properties of cells growing on different substrates
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