PowerPoint Presentation

Biljana Stojkovi

Mentor: Prof. Dr Igor Poberaj

University of LjubljanaFaculty of Mathematics and Physics

Microrheology with optical tweezersLjubljana, December 4th, 2012IntroductionMicrorheologyOptical tweezers

Passive Microrheology

Active Microrheology

Rheology of bacterial networkFuture workOutlineToday you will here what is microrheology and I will describe optical tweezers technique, technique that we use in our experiment.Than I will say something about passive and active methods that we are goning to use, we are interested in rheology of bacterial network, and on the end my future work.2

MicrorheologyRheology is the study of the deformation and flow of a material in response to applied force.materials properties solidfluidVISKOELASTIC

polymers

foams

bacteriagels

DNARheologyWe want to know what is microrheology, but first we need to define what is rheology. That word comes from Greek words rheos, meaning flow, and ology, meaning study of. Material properties we could classified on way how they behave...Or they have solid like behaviour, that means that they have elastic response to applied stress, described by Hooks law, relationship between applied stress and resultant strain is linear, where E is elastic modulus.Or materials could behave like fluid, they have completely viscous response to applied stresswe could write Newtons formula, where ratio between stress and strain rate represents viscosity.Many materials, and esspetially soft materials (liqids, colloids, polymers, foams, gels, granular materials, and a number of biological materials) exhibit both elastic and viscous responses and are therefore called viscoelastic.

3

Applying oscillatory shear strain:4Microrheology isMicroscopic probe particlesLocally measure viscoelastic parametersStudy of heterogeneous environmentsRequires less than 10 microliters of sampleBiological samples limited amount of materialImportant for fundamental reaserch and in industrial applycations

rheology on the micrometer length scaleCurrent techniques can be divided into two main categories: active methods that involve probe manipulationpassive methods that rely on thermal fluctuations of the probe Now when we define all important terms which we use in rheology we could say thatFor Microrheology is characteristic that we usehow and why I will say you laterWe requiredAnd that is important forwhere we haveyou couldThis study is very5Technique in microrheology

On this graph are schematically illustrated techniques with their typical frequency and viscoelastic modulus range (Note: contours show minimum/maximum ranges of the techniques).Schematic illustrations of (a) active microrheology using optical tweezers (b) Passive two-point microrheology using image-based particle tracking. (c) Dynamic material deformation using atomic force microscopy (AFM). (d) Oscillatory macrorheology.6Optical tweezers techniqueOptical tweezers are a powerful tool for manipulating microscopic particles by exerting forces via a highly focused laser beam. Trapping, amnipulating and measuring dorces on micron-sized dielectric particle...The instrument is capable of precise manipulating and detection of sub-nanometer displacement of micrometer dielectric particles.

High NA- to create the large spatial gradient in light intensity necessary to form a stable trap.

7How we could describe the trapping of dielectric bead?R, ray optics

R

There are three waysFirst one is Rayleigh regime, where size of the particle is much smaller of wavelength of the laser. Here dielectric particle can be treated as point dipole in light field. Trapping force can be decompose into two components: Scattering and gradient force. Gradient force acting on the dipole induced by light field, in the direction of the field gradient. Scattering force points along the direction of propagation of incident light.

Second approach is ray optics treatment, beam can be considered as a collection of rays, but for simplicity only two rays are shown, indicates by R1 and R2. Acording to Snells law, because of different refractive index between bead and surrounding media, we going to have change in direction of both rays. Photons carries a momentum, and change in the direction of the ray implies a proportional change in momentum. As consequence of law of conservation of momentum, this means that the bead experiences a change in momentum equal to the change in momentum of the ray but in the opposite direction. (The corresponding arrow from ray R1 cancels the lateral contribution of the momentum and doubles the restoring effect in the axial direction on the bead). The force on sphere is thus given by the rate of momentum change, force is proportional to light intensity.

In our case where size of bead is comparable with wavelength of laser, the calculations of optical force on trapped particle is quite complex, but for most applications we dont need to calculate the force, we calibrate the force for each type of the trapped object. Trapping force is proportional to displacement of bead from equilibrium position. We model optical trap as a Hookean spring characterizied by a single isotropic trap stiffness or spring constant.

Optical tweezers set-upOur optical tweezer is built around optical microscope. We using two lasers-fiber lasers with laser waveleght with 1064 nm, and how you can se we have counter-propagating beams and in this case scattering forces from both beams cancels each other, and we have stiffer and more stable 3D trappening. Our lasers are contoled by AOD which are driven by beam stearing controler which enables creation of multiple traps and their precise positioning. PC is connected with beam steering controler and CMOS camera, which we using for recording our videos.9Power Spectral Density (PSD):Force calibration

10Force calibration

We could also calibrate force using Boltzman statistics. Thermally driven position fluctuations can give us information on the trapping potential.In the equilibrium we expect the probability dennsity of the particle postition to be established by Boltzman statistics.

C normalization constant

In the our case of useing TEM00 Gaussian trapping beam, which results in a harmonic trapping potential, we can fit parabola and get stiffness of the trape.

11 Passive microrheologyBrownian motionTwo ways for determination shear modulus:1.2.Linear response theory:

12

Active microrheologyOne-particle activeOscillations of trap:Optical tweezers can be used to drive the probe particle and thereby actively deform the media and on that way we localy measure properties of medium.Oscilations of the trap is given by this formula, then respons of the bead to applied force is...how you can see we have some phase shift---Motion of our bead we can described by this formula(here we neglect inetrial term and termal fluctuations)

When we have information of amplitude and phase of oscilations of our bead we couls calculate viscoelastic modulus on this way...where this letter d represents ratio between oscillation amplitudes of the bead and the trap. We have few disandvatages of this method, we get viscoelasticity of madium on length scales comparable to probe size, also chemical interactions between the probes and a surrounding medium have also strong influence on MR analysis, e.g. either probes can adsorb molecules of the medium or a depletion layer is created.13

The displacements od the probe particle:Active microrheologyTwo-particle activeThe same displacements can be also expressed directly as:All this limitations are not present in two particle microrheology...So we have two trapped bead...the left, passive one is held in fixed position in weak trap...The right bead is held in trap which stiffness is set on maximum and we harmonicaly oscilating bead, either in direction of line conecting the beads (x-direction) or in perpendicular dorection (y-direction).Why we held this passive one in trap? Because if it is not held in trap, could be happen that bead go out from field of view and the measurement of bead fluctuations are not goodso we held it in week trap and we need to account influence of trap potential.Complex response function is conected with mutual complex function of beads, and single complex particle response, also we need to take in acount the trap effect.In active microrheology frequency dependent response functions are measured and from that you can get information about stiffnes of medium and their voscosity.

14Active microrheology

Complex viscoelastic modulus:Mutual response functions:Single particle response functions:

Rheology of bacteria networkDifferent modes:Free floating modeFormation of biofilmsBacteria single cell organismsMy future work is related with studing of rheological properties of bacteria network...Bacteri is...here you can see some basic part of bacteria cell:

You can find bacteria in two different modes:And we are interested in this where she form a biolfilm...BiofilmsFree-floating organisms attach to a surfaceColonies of bacteria embedded in an extracellular matrix (EPS)

EPS consist of:Polymers and proteinsaccompanied with nucleic acids and lipidsProtect microorganisms from hostile enviromentSupport cells with nutrientsAllow comunication between cellsEPS:Biofilms are formed when free-floating organisms attach to a surfaceAreEPS is product of bacteriaConsist of polymers and proteinsPolysaccharide...

Biofilm formation presents serious problems in industry cousing, for example, product contamination and corrosion. In medical field, biofilms can cause infection of indwelling devices such as catheters. Dental plaque biofilms lead to cavities and gingivitisBiofilm development

Lag phaseLog phaseStationary phaseDeath phaseBiofilm development starting by attaching bacteria on some surface. In this first, so called lag phase, the population remains temporarly unchanged, there is no apparent cell division occuring, the cells maybe growing in volume or mass, synthesizing enzymes, proteins, RNA... And increasing in metabolic activity...

Next phase is lag phase, where number of cells growing by exponential function. Here all the cells are dividing regulary by binary fission, and in this phase starts production of ECP...

In stationary phase, growth of bacteria is stoped, or because there is no more space or no more nutrients, or because of toxic metabolic products.

After this comming death phase, where number of cells decreasing.

In all three phases we have local heterogenities, creation of localized zones and they tipically show a very complex time-dependent behaviour related to their intrinsic lenght scales ranging from nm to micro-meter.

So we can conclude that... -> Complexity of biofilm arises:The production and assembly of cells, polymer, cross-links and surfactants result in a structure that is heterogeneous and dynamic.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

....-> Biofilms are complex biological systems...Spatial heterogeneities in the extracellular chemical concentration, including nutrient, oxygen, or intracellular signaling molecules, can resultin corresponding heterogeneities in polymer production, cell proliferation rate, and biosurfactant excretion.Bacteria regulate the water content of the biofilm by controlling the composition of the extracellular matrix.

Distribution of cells and EPS secretions is a manifestation of complex physical, chemical, and biological organization of the biofilms.

19Why is this study important

Biofilm mechanics is important for survival in some enviromentsWell-known viscoelasticity of bioflims can provide insight into the mechanics of biofilmsQuantitative 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 molecular changes of biofilms.

Why studing of mechanical properties are important:

A better characterisation of the mechanical properties of biofilms ... will

Particle-tracking microrheology provides a quantitative measure of...20Future workWe want to understand fundamentally how the viscoelasticity changes on different lenght scales on different frequencies;

The methods will be first tested on water;

The final testground will be viscoelastic characterization of bacterial biofilms at different stages of biofilm evolution.We will use optical tweezers to study viscoelastic properties of different biological samples;by varing the distance between particles.

The amplitude and the phase shift of the particles motions provide a complete description of the correlated motion.

We will compare results from PMR an AMR how we could quantify nonthermal forces.

21ReferencesAnnu. Rev. Biophys. Biomol. Struct. 1994. 23.247-85

Annu. Rev. Condens. Matter Phys. 2010.1:301-322.

Natan Osterman, Study of viscoelastic properties, interparticle potentials and self ordering 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) 19111916

Oscar Bjrnham, 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, Ume University, Sweden 2009

Mark C. Williams, Optical Tweezers: Measuring Piconewton Forces, Northeastern University

22