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

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Biljana stojkovi mentor prof dr igor poberaj

University of Ljubljana

Faculty of Mathematics and Physics

Microrheology with optical tweezers

Biljana Stojković

Mentor: Prof. Dr Igor Poberaj

Ljubljana, December 4th, 2012


  • Introduction

    • Microrheology

    • Optical tweezers

  • Passive Microrheology

  • Active Microrheology

  • Rheology of bacterial network

  • Future work

Biljana stojkovi mentor prof dr igor poberaj

  • Rheology

Rheology is the study of the deformation and flow of a material in response to applied force.






















Biljana stojkovi mentor prof dr igor poberaj

Applying oscillatory shear strain:

Resultant shear stress:

Biljana stojkovi mentor prof dr igor poberaj

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

Biljana stojkovi mentor prof dr igor poberaj

  • 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


Biljana stojkovi mentor prof dr igor poberaj

How we could describe the trapping of dielectric bead?

  • R<<λ, point dipol

λ R

  • R>>λ, ray optics

Biljana stojkovi mentor prof dr igor poberaj

Force calibration

  • Bead is held in stationary trap

  • Equation of motion:

  • Power Spectral Density (PSD):

Biljana stojkovi mentor prof dr igor poberaj

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:

Biljana stojkovi mentor prof dr igor poberaj

  • Brownian motion

  • Two ways for determination shear modulus:


Linear response theory:


Active microrheology
Active microrheology

  • One-particle active

Oscillations of trap:

The response of the bead is:

The equation of motion:

The viscoelastic moduli are calculated as:

Active microrheology1
Active microrheology

  • Two-particle active

  • The displacements od the probe particle:

  • The same displacements can be also expressed directly as:

Active microrheology2
Active microrheology

Mutual response functions:

Single particle response functions:

Complex viscoelastic modulus:

Biljana stojkovi mentor prof dr igor poberaj

Rheology of bacteria network

Bacteria – single cell organisms

  • Different modes:

  • Free floating mode

  • Formation of 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

Biofilm development
Biofilm development

Stationary phase

Death phase

Log phase

Lag phase

Complexity of biofilm arises
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.

Why is this study important
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.

Future work
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.


  • 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