Biljana Stojković Mentor: Prof. Dr Igor Poberaj

1. University of Ljubljana Faculty of Mathematics and Physics Microrheology with optical tweezers Biljana Stojković Mentor: Prof. Dr Igor Poberaj Ljubljana, December 4th, 2012

2. Outline • Introduction • Microrheology • Optical tweezers • Passive Microrheology • Active Microrheology • Rheology of bacterial network • Future work

3. Microrheology • Rheology Rheology is the study of the deformation and flow of a material in response to applied force. solid DNA V I S K O E L A S T I C materials properties polymers gels foams bacteria fluid

4. Applying oscillatory shear strain: Resultant shear stress:

5. Microrheology is “rheology on the micrometer length scale” • Microscopic probe particles • Locally measure viscoelastic parameters • Study of heterogeneous environments • Requires less than 10 microliters of sample • Biological samples – limited amount of material • Important for fundamental reaserch and in industrial applycations • Current techniques can be divided into two main categories: • active methods that involve probe manipulation • passive methods that rely on thermal fluctuations of the probe

6. Technique in microrheology

7. Optical tweezers technique • Tightly focused laser beam • Dielectric particles with higher refraction index that of surrounding medium • Wavelength of the laser  size of the object being trapped • Maximum force strenght is in the range of 0.1-100 pN • Powerful laser beam (power on sample 10 − 100 mW) • Microscope objective with high numerical aperture ()

8. How we could describe the trapping of dielectric bead? • R<<λ, point dipol λ R • R>>λ, ray optics

9. Optical tweezers set-up

10. Force calibration • Bead is held in stationary trap • Equation of motion: • Power Spectral Density (PSD):

11. Force calibration • Boltzman statistic • In the equilibrium, the probability density of the 1D particle position: • Trap potential can be obtained from normalization histogram of trapped particle postition as: • Fit parabola with:

12. Passive microrheology • Brownian motion • Two ways for determination shear modulus: 1. Linear response theory: 2.

13. Active microrheology • One-particle active Oscillations of trap: The response of the bead is: The equation of motion: The viscoelastic moduli are calculated as:

14. Active microrheology • Two-particle active • The displacements od the probe particle: • The same displacements can be also expressed directly as:

15. Active microrheology Mutual response functions: Single particle response functions: Complex viscoelastic modulus:

16. Rheology of bacteria network Bacteria – single cell organisms • Different modes: • Free floating mode • Formation of biofilms

17. Biofilms Free-floating organisms attach to a surface Colonies of bacteria embedded in an extracellular matrix (EPS) • EPS consist of: • Polymers and proteins • accompanied with nucleic acids and lipids • EPS: • Protect microorganisms from hostile enviroment • Support cells with nutrients • Allow comunication between cells

18. Biofilm development Stationary phase Death phase Log phase Lag phase

19. Complexity of biofilm arises: • Spatial heterogeneities in extracellular chemical concentration; • Regulation of water content of the biofilm by controling the composition of EPS matrix; • Spatial heterogeneities on gene expression creates heterogeneities in polymer and surfactant production The production and assembly of cells, polymer, cross-links and surfactants result in a structure that is heterogeneous and dynamic.

20. Why is this study important • Biofilm mechanics is important for survival in some enviroments • Well-known viscoelasticity of bioflims can provide insight into the mechanics of biofilms • Quantitative measure of the “strength” of a biofilm could be useful for: • Development of drugs for inhibition of biofilm growth • In identifying drug targets • Characterizing the effect of specific molecularchanges of biofilms.

21. Future work We will use optical tweezers to study viscoelastic properties of different biological samples; • We want to understand fundamentally how the viscoelasticity changes on different lenght scales on different frequencies; • Themethods willbe firsttested on water; • The final testground will be viscoelastic characterization of bacterial biofilms at different stages of biofilm evolution.

22. References • Annu. Rev. Biophys. Biomol. Struct. 1994. 23.’247-85 • Annu. Rev. Condens. Matter Phys. 2010.1:301-322. • Natan Osterman,Study of viscoelastic properties, interparticlepotentials and selfordering in soft matter with magneto-optical tweezers, Doctoral thesis, University Ljubljana, 2009. • Natan Osterman, TweezPal – Optical tweezers analysis and calibration software, Computer Physics Communications 181 (2010) 1911–1916 • Oscar Björnham, A study of bacterial adhesion on a single – cell level by means of force measuring optical tweezers and simulations, Department of Applied Physics and Electronics, Umeå University, Sweden 2009 • Mark C. Williams, Optical Tweezers: Measuring PiconewtonForces, Northeastern University