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INVESTIGATING THE MECHANICAL PROPERTIES OF LIVING HUMAN CELLS

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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

- Mark Murphy
- Cell Biology
- Atomic Force Microscopy
- Fluorescence microscopy

- Catherine Randall
- Force Data Analysis
- Image Processing

- Alexis Guillaume
- Computer Modelling
- Simulation

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

ACTIN (green) & TUBULIN (red) CYTOSKELETON OF HUMAN LUNG FIBROBLAST CELL (LL24)

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’

25 µM

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 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

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

- Constitutive equation
- Linear Elastic
- Non-Linear Viscous

STRAIN HARDENING

- Cells get stiffer with increased applied force
- Possibly a similar mathematical model to those used in materials science

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)

Applied force = Approx 1.5 nN

Time = 8.5 min

Voltage conversion 1 V/65 nm

- 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

- Similar experiments without bias
- New experiments
- Observe what you can not measure
- Generally : test some hypothesis

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?

- 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

- Fairly reproduce experimental conditions ;
- Displacement, speed and acceleration for each node of the simulation
- The future : from continuous materials to living materials

- 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

- 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 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

THANK YOU FOR YOUR TIME!

QUESTIONS ?

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