EXAM IN COURSE TFY4265 AND FY8906 BIOPHYSICAL MICRO METHODS 6. Des hours written exam. Fasit

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1 NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF PHYSICS Contact during exam: Associate Professor Marit Sletmoen Department of Physics, Realfagbygget Phone / EXAM IN COURSE TFY4265 AND FY8906 BIOPHYSICAL MICRO METHODS 6. Des hours written exam Fasit Permitted aids: Simple calculator according to NTNU regulations No written books or papers Oppgave 1 a Focal length - distance required for a lens to bring the light to a focus (usually measured in microns) Focal point/focus - point at which the light from a lens comes together Magnification - product of the magnifying powers of the objective and eyepiece lenses Numerical aperture - measure of the light-collecting ability of the lens Resolution - the closest two objects can be before they're no longer detected as separate objects (usually measured in nanometers) 1 b Upon transit through a phase object an incident wavefront of an illuminating beam becomes divided into two components: an undeviated wave or surround wave (S wave) that passes through the specimen but do not interact with it, and a deviated or diffracted wave (D wave) that becomes scattered in many directions. Typically only a minority of incident waves are diffracted by cellular objects. Both S and D waves are collected by the objective lens and focused in the image plane where they undergo interference due to the difference in optical pathway, and generate a resultant particle wave (P wave). The relationship among waves is thus described as P=S+D. Detection of the object image depends on the intensities, and hence on the amplitudes of the P and S waves. Only when the amplitudes of the P and S waves are signiffcantly different in the image plane we can see the object in the microscope. The key elements of the optical design have to 1) isolate and separate the undeviated surround and diffracted rays emerging from the specimen so that they occupy different locations in the diffraction plane at the back aperture of the objective lens, and 2) advance/ retard the phase ±_/2 (in addition to the ±_/2 phase shift obtained through the sample) to obtain constructive or destructive interference and reduce the amplitude of the surround light, in order to maximize di_erences in amplitude between the object and background in the image plane. This is achieved by inserting in the optical path of the microscope: 1

2 * The standard circular front aperture diaphragm of the condenser is exchanged with a ring shaped aperture diaphragm. * A modulator made of a glass plate with a partly transparent ring (also called phase plate) is located in the back focal plane of the objective. The partly transparent ring is giving rise to a damping of the light and a phase shift of λ/2 relative to light passing outside this ring. The specimen is thus illuminated by beams from light emanating from a ring, and under conditions of Köhler illumination S waves that do not interact with the specimen are focused as a bright ring in the back focal plane of the objective (the diffraction plane). Light that is diffracted by the specimen (D waves) reaches the diffraction plane at various locations across the entire back aperture. The amount and location depends on the number, size, and refractive index differential of light-scattering objects in the specimen. The D wave emergent from the object plane is changed by λ/4 relative to the phase of the S wave. The manipulation of relative phase advancement is however not suffcient to generate a high contrast image, because the amplitude of the S wave is too high to allow suffcient contrast. For this reason, the ring in the phase plate is darkened with a semitransparent metallic coating to reduce the amplitude of the S wave by about 70 %. Since P=S+D, interference in the image plane generates a P wave with an amplitude that is now considerably less than that of S. Thus the difference in phase induced by the specimen is transformed into a difference in contrast, and we can now observe the object in the microscope. In a phase-contrast microscope, the annular rings in the objective lens and the condenser separate the light. The light that passes through the central part of the light path is recombined with the light that travels around the periphery of the specimen. The interference produced by these two paths produces images in which the dense structures appear darker than the background. 2

3 1c Filterkubus ved epi-fluorescensmikroskopi: For å avbilde fluorescein benyttes som eksitasjonsfilter (1) et båndpassfilter BP nm. Dette skal sørge for at lys med riktig bølgelengde eksiterer fargestoffet. For å separere eksitasjonslys og emisjonslys benyttes et dikromatisk filter (beam splitting mirror) med bølgelende ca 510 nm. Dette sørger for at bare den mer langbølgete fluorescensen kan passere. Som emisjonsfilter (2) benyttes BP Dette sørger for at kun fluorescenslys når detektor (øyet). 1d) Fordeler med multifoton mikroskopi sammenliknet med konfokal laser scanning mikroskopi: Bleking reduseres. Bare bleking i fokalplanet Penetrasjon gjennom vev øker. Ingen absorpsjon utenfor fokalplanet. Mer langbølget lys Fotoskade på celler indusert av UV lys unngås Mer effektiv deteksjon mulig. Bruk av direkte detektorer Oppgave 2 a) The abreviation STED is applied for a particular high resolution optical microscopy method. What is the full name the technique abbreviated STED? Stimulated emission depletion microscopy b) Describe briefly three essential consequtive events taking place in STED microscopy. Step 1: (Red line in figure 2A): Intensity profile for the excitation light: The excitation light will give rise to a diffraction limited spot obtained by irradiation a small area of the sample with the use of an intense laserbeam. The minimal size of a focused light spot is limited by diffraction to about half the wavelength used. Laser-scanning microscopes can therefore not decrease the size of the excitation spot for fluorescent dyes further than approximately 200 nm. Step 2: (Blue line in figure 2A): doughnut-shaped de-excitation spot: Instead of spontaneous relaxation and fluorescence emission, a molecule can also return to its ground state by stimulated emission. If an excited dye molecule is irradiated with light of similar wavelength compared to the fluorescence light, it can immediately return to the ground state 3

4 and emits a photon of exactly the same wavelength and momentum of the light used. Furthermore the molecule is prevented from the spontaneous emission of a fluorescence photon after stimulated emission. Fluorescent dyes can therefore be switched off by additional irradiation of a red-shifted 'de-excitation' beam. The light originating from the spontaneous decay and from the stimulated emission can also be spectrally separated from the fluorescent light by using appropriate color filters. In a STED microscope the excited molecules in the outer rim of the excitation spot are switched off by stimulated emission. This is obtained by employing a second, red-shifted 'deexcitation' laser beam whose wavefront is altered so that a ring-like intensity profile is achieved. This depletion light causes almost all of the excited molecules to return to the ground state, leaving only the region of the sample very close to the center of the excitation spot excited. Fluorescence from the remaining excited dye molecules is then detected by the microscope. Step 3: Black line in figure 2A): remaining area allowing fluorescence: The size of the spot where molecules are still allowed to fluoresce gets smaller with increasing intensity of the deexcitation light. This size corresponds to the achievable resolution. Therefore the resolution is controlled by the brightness of the de-excitation beam. The resolution can become much better than the diffraction-limit, indeed an arbitrary good resolution is possible provided that one can apply such a very high de-excitation beam intensity. STED: By switching-off the excited molecules in a saturated manner, only a fraction of molecules in an area much smaller than the original focused excitation spot can fluoresce. Therefore structures which are smaller than the diffraction-limit can be made visible with STED. Position Figure 2A: Illustration of the three consecutive steps in STED microscopy c) Coherent light are light waves that are "in phase" with one another. For example, two waves are coherent if the crests of one wave are aligned with the crests of the other and the troughs of one wave are aligned with the troughs of the other. Otherwise, these lightwaves are considered incoherent. In a laser, excited atoms loose their energy by induced or stimulated emission. Stimulated emission has the same phase, direction, spectral and polarization properties as the stimulating field and both are indistinguishable in all aspects. It is this stimulated emission that comes out of the laser device as a coherent, high intensity beam of light. 4

5 d) 1 Sample 2 Sheath 3 hydrodynamic focusing 4 fluorescence 5 scattered light 6 light source 7 deflection plates 8 sorted cells 9 waste Oppgave 3 A Definition of r f Direct measurements of the strength of both covalent and non-covalent interactions can be performed using sensitive force probes, i.e. AFM or optical tweezers. In such measurements, the force transducer is moved vertically with respect to the sample, giving what is called a force-distance curve. In a typical force unbinding processes, the linear rise of force with time is set by the product of separation speed vt and transducer spring constant k, which is called the loading rate: r f = k v t When investigating intermolecular bonds, the loading rate, abreviated r f, describes the speed by which the force is applied onto the intermolecular bond. Definition of k off : k off describes the rate of escape from bound to unpopulated free states under force and is described by the following expression: Here, k off is the rate of dissociating events, D/l c l ts is referred to as the attempt frequency which is the inverse of a characteristic time. In general terms, one can state that applying an external force to the interacting molecules adds a mechanical potential that tilts the energy landscape. This results in a reduction in the energy barrier at the transition state. K off thus increases exponentially with the applied force. Definition of x β : x β is the distance from the deep energy minimum to the rate limiting activation barrier in the energy landscape of an interaction, determined along the direction of the reaction path x. Two alternative approaches to determine this parameter based on a set of 1000 force curves revealing 1200 forced unbinding events. Approach 1: In the dynamic force spectra, obtained by plotting the most likely detachment force F* vs. rate of ln (loading rate), a linear spectrum is predicted for a single energy barrier. The predicted linear rise of force with log (r f ) is equal to k B T/ x β. 5

6 Illustration of approach 1 Approach 2: Illustration of approach 2 The experimental observations of unbinding force are regrouped into subgroups based on defined intervals along the axis of increasing loading rate. For each subdistribution a mean loading rate is calculated, so that within each subgroup we treat the loading rate as a constant. When the loading rate is constant, the probability to observe a bond rupture at the force f is expressed by By fitting this equation to the histogram showing the number of observations as a function of unbinding force for each subgroup we determine x β the position of the activation barrier needed to be crossed for the molecules to detach from each other, and koff which is the dissociation rate constant in absence of pulling force. The maximum in this histogram will reect the most probable unbinding force. Axial trapping in optical tweezers: The physical basis for optical tweezers is based on conservation of total momentum of photons when reflected/refracted in surfaces. For a photon that has no mass E = pc. Using the relation between the photon energy and its frequency and wavelength, one gets: p = E/c = hν/c = h/_λ, where h is Planck s constant. There is momentum transfer associated with reflection and or refraction of photons. This is due to the change of direction of propagation. 6

7 Axial trapping: Ray optics explanation (focused laser). In addition to keeping the bead in the center of the laser, a focused laser also keeps the bead in a fixed axial position: The momentum change of the focused rays causes a force towards the laser focus, both when the bead is in front (left image) or behind (right image) the laser focus. So, bead will stay slightly behind the focus, where this force compensates the scattering force. Calculation of trapping force: F = Spring constant x Detector sensitivity x Detector reponse Q x prior to rupture = nn = 12 pn. How would you expect these values to change if you double the laser intensity? (is is sufficient to describe if you expect the values to increase or decrease or remain unchanged, absolute values not required). Answer: Spring constant: increase Detector sensitivity: unchanged Detector reponse Q x prior to rupture = decreased Exercise 4: a) Explain the main components that an AFM consists of. The main parts of an AFM, shown in figure 10.2, are the pizoelectic scanner, the tip and tip holder constituting the cantilever, and the detector system, as well as the feedback system. The scanner controls the position of the tip relative to the specimen. The function of the tip is to transform the minute interaction forces to a signal that can be further analysed. The tip holder places the tip in an appropriate position relative to the sample and together with the scanner it allows correct mutual positioning. The tip deflection detection system transforms the mechanically induced cantilever deflection to an electronic signal. The detection system is normally based on a laser beam reflected from the back side of the cantilever combined with a detection of the position of the reflected laser by a position sensitive photodiode. Other detector systems are based on the principle of interferometry, or using tunnelling current to a conducting top located on the opposite side of the cantilever relative to the tip. Furthermore, the electronics is controlling the feedback of the system to maintain either constant probespecimen force or constant height as the operating signal. Fig a. shows a schematic illustration of an AFM. 7

8 AFM b) The isoforce curves obtained over a substrate does not only depend on the charge, but also on e.g. the other topographic variations. If there is a height difference in addition to an altered surface charge density between the two parts of the surface, this simplest variation of the technique does not afford information of the surface charge density. To discern between height and surface charge differences, it has been proposed to determine the isoforce curves in two different electrolyte solutions with different Debye screening lengths, yielding the ratios of the isoforce conditions for the force curves above the two parts of the surface. The decomposition of the total spatially resolved force signal to topographic distributions in height and surface charge density is carried out using model substrates with height differences and constant surface charge density as well as more complex substrates. Oppgave 5: Elektronmikroskopi a) Oppløsning Oppløsningen (d) til et lysmikroskopi er bestemt av lysets diffraksjon og gitt ved Rayleigh kriteriet: Airy-disk beskriver diffraksjonsmønsteret for en sirkulær åpning. Radien er gitt ved r airy 0, 61 NA der λ= bølgelenden NA=nsinθ=numerisk apertur der n er refraktiv indeks og θ maksimum vinkel lysetstråler treffer objektvet under. 8

9 Typisk verdi for de beste objektiv med NA=1,6 og bølgelende 500 nm er 200nm Oppløsningen til et elektronmikroskop er bestemt av elektronets diffraksjon og gitt ved samme likning som over men med en bølgelende for elektroner som i følge de Broglie er: h h h 1,23nm p m v 2meV V 0,61 0,75nm volt d NA V volt Typisk teoretisk verdi er 0,025Å dersom NA=1 og V=60kV I praksis er d 1-2 Å ca 1000x bedre enn for lysmikroskopi Forskjell teoretisk-praktisk oppløsning skyldes: 1. Elektromagnetiske linsene har ekstremt liten romvinkel slik at NA liten. Nødvendig for å redusere sfæriske aberrasjoner 2. Linsefeil som kromatisk aberrasjon og astigmatisme 3. Diffraksjon b) Oppbyggingen av et transmisjon elektronmikroskop Belysningskilde elektronkanon Kondensorlinse: fokuserer e på prøven. Består av to linser. Linse1 forminsker, linse2 forstørrer. Til sammen kontrollerer mengde e som treffer prøven og størrelse på spot. Objektivlinse: Danner bildet som siden forstørres. Store krav til kvalitet, minimalt med aberrasjoner Intermediærlinse forstørrer bildet. Forstørrelse reguleres av strøm gjennom spole Prosjektørlinse. Vanligvis 2 linser som forstørrer bildet. Har stor dybdefokus. Totalt 4 linser på avbildingssiden av preparatet. Vanligvis benyttes bare 3. Ved svært store forstørrelse benyttes alle 4. Belysningskilde elektronkanon: Katode som emitterer e som akselereres til anode 9

10 1. Elektroner forlater katodefilament ved termisk emisjon. 2. Fokuseres ved Wehnelt sylinder med mer negativ ladning enn e 3. Elektroner tiltrekkes anode koplet til jord Wehnelt sylinder og anode fungerer som elektrostatisk linse slik at elektronstrålen får diameter ca 50 μm Elektromagnetiske linser: Linsene er elektromagnetiske linser bestående av en spole som danner et magnetisk felt. Elektroner kommer inn i feltet og går i en helix-bane og fokuseres Avbildingssystem og kamera: Avbildingssystem under mikroskopering = fosforescerende skjerm Bildet avbildes også på fotografisk film eller på CCD kamera. Vakuumsystem: Hele elektronmikroskopet, fra elektronkanon til avbilding er i vakuum. Formålet med vakuum er at e ikke skal kollidere med gassmolekyler 10