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Does the use of UV light beam lead to poorer contrast in optical microscopy of cells than the higher wavelengths visible light?

Does the use of UV light beam lead to poorer contrast in optical microscopy of cells than the higher wavelengths visible light?


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I am reading about "diffraction-limited system" on Wikipedia, which mentioned

"To increase the resolution, shorter wavelengths can be used, such as UV and X-ray microscopes. These techniques offer better resolution but are expensive, suffer from lack of contrast in biological samples and may damage the sample."

without giving a more detailed explanation for why the higher energy EM waves might lead to poor contrast. I have tried to search on Google, but still can't find a satisfying answer. Can anyone here kindly refer me to more detailed discussion on this question? Thank you.


Contrast in optical microscopy typically depends on different substances having different absorption spectra. Practically everything absorbs UV light, so there tends to be less contrast in that range than in the visible spectrum where there is a bit more selectivity. All of this changes when there are contrast-enhancing substances added. For example, molecules that absorb in one wavelength and emit at a different wavelength via fluorescence, attached to antibodies that bind selectively to specific cell components, can provide very high contrast. E.g., see [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2156041/].

An alternative optical microscopy technique is phase-contrast microscopy which does not use absorption at all. Instead, it measures the effective optical path length through the sample, which depends on local refractive index of the sample.

Yet another alternative is x-ray fluorescence microscopy, which can identify specific elements in the composition of a sample. See, for example,[https://www.americanlaboratory.com/913-Technical-Articles/18833-Three-Dimensional-Elemental-Imaging-Using-a-Confocal-X-Ray-Fluorescence-Microscope/].


UV spectroscopy is type of absorption spectroscopy in which light of ultra-violet region (200-400 nm.) is absorbed by the molecule. Absorption of the ultra-violet radiations results in the excitation of the electrons from the ground state to higher energy state. The energy of the ultra-violet radiation that are absorbed is equal to the energy difference between the ground state and higher energy states (deltaE = hf).
Generally, the most favoured transition is from the highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO). For most of the molecules, the lowest energy occupied molecular orbitals are s orbital, which correspond to sigma bonds. The p orbitals are at somewhat higher energy levels, the orbitals (nonbonding orbitals) with unshared paired of electrons lie at higher energy levels. The unoccupied or antibonding orbitals (pie * and sigma * ) are the highest energy occupied orbitals.
In all the compounds (other than alkanes), the electrons undergo various transitions. Some of the important transitions with increasing energies are: nonbonding to pie * , nonbonding to sigma * , pie to pie * , sigma to pie * and sigma to sigma * .

UV spectroscopy obeys the Beer-Lambert law, which states that: when a beam of monochromatic light is passed through a solution of an absorbing substance, the rate of decrease of intensity of radiation with thickness of the absorbing solution is proportional to the incident radiation as well as the concentration of the solution.
The expression of Beer-Lambert law is-
A = log (I0 /I) = Ecl
Where, A = absorbance
I0 = intensity of light incident upon sample cell
I = intensity of light leaving sample cell
C = molar concentration of solute
L = length of sample cell (cm.)
E = molar absorptivity

From the Beer-Lambert law it is clear that greater the number of molecules capable of absorbing light of a given wavelength, the greater the extent of light absorption. This is the basic principle of UV spectroscopy.


1. Introduction

Refractive indices of biomolecules are fundamental properties that play key roles in a number of optical imaging and microscopy techniques, which include optical coherence tomography, confocal reflectance microscopy, light scattering spectroscopy, and quantitative phase microscopy [1]. The refractive index variation within cells and tissue provides the source of contrast for these different optical imaging modalities, which can be further related to the structural or morphological features of the sample. The refractive index of a material is wavelength dependent, which is known as the dispersion property of the material. The importance of dispersion is widely recognized in multiphoton microscopy and optical coherence tomography because of the large bandwidth of the light source used [2,3]. However, most often dispersion is viewed as a deleterious effect that requires compensation, either by optics or numerical post-processing. Nonetheless, there have been a few interesting studies utilizing the refractive index dispersion of biomolecules to quantify molecular concentration. For example, the dispersion of hemoglobin was used to extract the concentration of hemoglobin in intact red blood cell [4]. In another study, the dispersion of an exogenous dye was used to decouple refractive index measurement from height measurement of cells in digital holographic microscopy [5]. However, most biomolecules do not have significant dispersion in the visible wavelength region due to their inherently low absorption [6]. It would be of great interest to directly measure the dispersion of biomaterials, including cells, to study their biochemical compositions.

The majority components of a eukaryotic cell are proteins, nucleic acids, lipids, and polysaccharides. Both proteins and nucleic acids have strong absorption in the middle UV region. This characteristic has previously been successfully used to map the quantities of proteins and nucleic acids in living cells [7]. However, imaging directly at the absorption peak poses significant challenges because physical and chemical damage of the cell is unavoidable [8], thus long term observation of the cell is extremely difficult. This constraint also places stringent requirements on the UV transmission of the system and the detection sensitivity of the charge coupled device (CCD). Moreover, the scattering contribution of cellular components could interfere with the absorption of biomolecules and lead to erroneous analysis. According to the Kramers-Kronig relationship, the spectrum of refractive index is much broader than that of absorption. Therefore, it is possible to image refractive index dispersion of biological cells in the near UV (NUV, 300-400nm) while minimizing the damage caused by strong protein and nucleic acid absorptions. With that objective in mind, we designed a dual-wavelength quantitative phase microscope to study the refractive index dispersion of live cells.

Previously we have shown that proteins exhibit substantial dispersion near their absorption peak at 280 nm [9]. Here we report the dispersion imaging of living eukaryotic cells, for the first time to our knowledge, in the NUV range using dual wavelength quantitative phase microscopy. The dispersion parameter is typically defined as dn/dλ. However, because we only measure at two wavelengths, for simplicity we used an alternative parameter to characterize dispersion: α2/α1, where α2 and α1 are the refractive index increment of biomolecules (will be discussed in details in the experimental results section) at the two measured wavelengths. This definition will be used throughout the whole manuscript. The dispersion of protein and DNA molecules is also calibrated independently using a total internal reflection (TIR) method [10]. We show that the dispersion of live HeLa cells agrees well with that measured for pure proteins solutions using the TIR method.


Optical microscopy in photosynthesis

Emerging as well as the most frequently used optical microscopy techniques are reviewed and image contrast generation methods in a microscope are presented, focusing on the nonlinear contrasts such as harmonic generation and multiphoton excitation fluorescence. Nonlinear microscopy presents numerous advantages over linear microscopy techniques including improved deep tissue imaging, optical sectioning, and imaging of live unstained samples. Nonetheless, with the exception of multiphoton excitation fluorescence, nonlinear microscopy is in its infancy, lacking protocols, users and applications hence, this review focuses on the potential of nonlinear microscopy for studying photosynthetic organisms. Examples of nonlinear microscopic imaging are presented including isolated light-harvesting antenna complexes from higher plants, starch granules, chloroplasts, unicellular alga Chlamydomonas reinhardtii, and cyanobacteria Leptolyngbya sp. and Anabaena sp. While focusing on nonlinear microscopy techniques, second and third harmonic generation and multiphoton excitation fluorescence microscopy, other emerging nonlinear imaging modalities are described and several linear optical microscopy techniques are reviewed in order to clearly describe their capabilities and to highlight the advantages of nonlinear microscopy.

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Future perspectives

Extensive use of single-molecule fluorescence microscopy techniques have enabled visualization of an enormous range of different biological processes which was previously restricted by traditional population ensemble average methods. Many of the biological processes studied are components of very basic and fundamental systems in the cell. However, they have been essentially invisible until now: long-standing ‘old’ problems that have been simply intractable until the arrival of modern single-molecule fluorescence microscopy methods. The new tools have provided novel insights into the basic mechanisms of live cells as well as the identification of previously unknown functions of molecules which are essential to life as we know it. Despite recent achievements in making the invisible visible, experimental limitations do remain. For example, the signal-to-noise ratio can still be improved, especially when very rapid imaging is required to address biological questions at the submillisecond time scale. There is still a need for novel fluorescent proteins with enhanced brightness and photostability which would increase the possible illumination times and thus enable longer observations of molecules and processes in which they partake. Similarly, fluorescent proteins significantly increase the overall size of the tagged protein construct, since a fluorescent protein is often of comparable molecular weight with the native protein itself, which might affect its natural molecular conformations and thus its physiological behaviour and function. Therefore, the next generation of fluorescent molecules we would hope might become much smaller in size or even disappear completely.

For example, attempts to use digital holography as a super-resolution microscopy technique have already been made [187,188], with label-free imaging rendering, for example promising structural details of the dynamic morphology of filaments which enable single swimming cells to be motile [189]. Another example of a label-free technique is an interferometric scattering microscopy (iSCAT) with a single-molecule precision, applied recently to a range of biological questions by the group of Kukura et al. [190,191]. iSCAT has now been used in studies of motor proteins dynamics [192] which enabled visualization of microtubule disassembly [193], uncovered unknown details of myosin-5 stepping mechanism [194], and provided novel insights into kinesin-1 stepping cycle [195].

At present, there is no unique, single technique which can enable the simultaneous visualization of proteins and their post-translational modifications, for example as occurs during signal transduction. It would, in principle, also be valuable if we were able to obtain data concerning the molecular conformational states of intrinsically disordered regions during protein–protein or protein–nucleic acid interactions. However, attempts to study molecular conformational changes upon mechanical stretching perturbations have already been made by combining single-molecule fluorescence microscopy techniques with non-fluorescence approaches. For example, Fernandez et al. have utilized TIRF and AFM simultaneously to study the dynamics of stretching and unfolding of ubiquitin protein domains [196]. Combinations of AFM and FRET were also applied in studies of HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) conformation [197]. TIRF and AFM-based single-cell force spectroscopy were also used in non-mechanistic studies and revealed protein cluster formation of integrins and their recruitment of adhesome protein [198].

There is no doubt that scientific excellence in the development of novel biophysical tools and techniques will continue to push back the borders of our understanding of life’s complex processes much further than at present. Interdisciplinary science approaches, when appropriately funded, are the best way forward to achieve these new developments.


The LSCM uses a point light source (laser) and a pinhole to reject out of focus light. It enables optical sectioning of fluorescently stained samples to provide a 3-Dimensional view of the structure. For more information on confocal microscopy, please go to resource section.

Applications

  1. To examine fluorescently labeled specimens for single or multiple colors localization of molecules within cell/tissue.
  2. To carry out physiological studies such as ratio imaging, time-lapse recording of live cell/tissue.
  3. Photo manipulation of the fluorescence signal (e.g. FRAP (photo bleaching after fluorescence recovering) FLIP (Fluorescence Loss Imaging after photobleaching), photoactivation/switching, etc.) to study the kinetics of molecules in living cells.

This system is mainly used for detection of fluorescence labeling in fixed samples. However, it is also equipped with necessary accessories (temperature, CO2   controls, O2) for live cell imaging. Additionally, the system is equipped with an FCS module which also allows imaging using the sensitive Avalance Photodiode Detector (APD, Zeiss Confocor 3, see FCS section below).

The instrument is equipped with a spectral detector which uses a PMT (Photon Multiplier Tube) array and optical grating elements to collect spectral information for fluorophores. Spectral information from 405nm to 720nm with step size of 10.7nm can be detected with the setup. Then, using the built-in, non-linear un-mixing tool, signals from different fluorophores can be separated mathematically. The system eliminates the need for emission filter and offers the advantage of being able to separate fluorophores with extensive emission spectra overlap. For example, GFP and YFP can be separated using this setup (which is impossible with conventional filter based imaging system). The system is also particularly useful for imaging highly auto-fluorescence sample with fluorescence imaging as auto-fluorescence has very different spectral signature than fluorophores.

Zeiss LSM 710 Specifications

Zeiss AxioObserver (inverted)

3 fluorescence PMTs
1 transmission PMT
2 APDs

This is a complex system with multiple capabilities:

  1. Super resolution microscope with STED (STimulated Emission depletion) which is capable of obtaining fluorescence images with resolution down to <50nm.
  2. Multiphoton microscope with tunable laser from 680-1064nm.
  3. Fluorescence Lifetime Imaging system based on time domain for FLIM measurements.
  4. Fluorescence correlative Spectroscopy system for detecting molecular associations.
  5. Combination of optics and software module capable of obtaining fluorescence images down to 𞲨nm.

STED uses a donut shaped depletion laser to modify the point spread function of the beam down to sub-diffraction limit level to achieve super resolution microscopy at resolution below 50nm (STED principle). The system is equipped with 594nm, 660nm and 775nm depletion lasers for variety of dyes. For detailed system information, please visit the Leica website

Multi-photon microscope uses an ultra-fast pulsing laser to excite fluorescent molecules. Briefly, 2 (multi)-photon microscopy is based on the principle that a given fluorescent molecules which normally would only be excited by absorbing the energy of a single photon of certain wavelength can also be excited by combination of the energies produced by simultaneous absorption of 2 (or multi-) lower-energy photons of double (multiple) wavelength. The emission of the fluorescence is quadratically dependent on the excitation intensity. This steep dependence of absorption rate on photon concentration gives multi-photon Laser Scanning microscope the intrinsic three-dimensional resolution with the depth of field defined by:

  1. intensity of the excitation light
  2. numerical aperture of the lens used
  3. the wavelengths of the lights.

This z-resolution is comparable to conventional Laser Scanning confocal microscope.

Advantages over confocal microscope

  1. Longer wavelength used for excitation allows imaging deeper into thick specimens due to less scattering of longer wavelength (IR) light.
  2. Photo-bleaching and damaging are confined to the focus points only.
  3. It is possible to image UV dyes with infra-red light. This is particularly useful for live cell imaging where UV light is highly damaging to the cells

Therefore, multi-photon microscopy is highly suitable for imaging of live, thick specimens.
The system is also capable of measuring fluorescence life time with the equipped pulse lasers. The system is equipped with a white laser which is pulsed and could be tuned continuously from 470-690nm in addition to the IR laser with tuning range of 680-1024nm. In addition, the system is able to perform Fluorescence correlative spectroscopy, deconvolution and high speed imaging.

In the below image,  COS cells were stained with an anti-nuclear pore protein conjugated to Star635P dye and imaged with Confocal (top) and STED (bottom) at the same optical plane to demonstrate the improvement in resolution with STED (scale bar 2um).

Leica Falcon SP8 STED system with Spectra-physics femto-second laser Specifications

The PerkinElmer UltraVIEW system (PerkinElmer Life Sciences Inc., MA, USA) is a Yokogawa (Yokogawa Corp. Japan) Nipkow spinning disk confocal system. It uses a spinning disk with multiple pinholes to achieve confocality (e.g. the rejection of out-of-focus lights). Nipkow disk refers to scanning disk with symmetrically placed spirals of pinholes through which illumination light is passed. Such pinholes split illumination lights into multiple 'minibeams'. When the disk spins, the light scans the sample in a raster pattern. Emission lights from the sample are detected through the pinhole to generate a confocal image of the sample that can be detected (with an EMCCD (Electron Multiplification Charge-Coupled Device) camera). Because the pinholes on a Nipkow disk must be placed up to 10 diameters apart in order to avoid cross-talking problem, the light throughput of traditional Nipkow disks is only ӭ% of the light shining onto the disk. The Yokogawa scanhead has overcome this problem by using an innovative, collector disk containing microlenses placed in front of the Nipkow disk. The microlenses ensure that most of the light illuminating the disk is focused onto the pinholes. Transmission efficiency is thus increased from ӭ% to 70% of the light falling on the disks allowing the sample to be illuminated with a sufficient quantity of light.

Advantages of the UltraVIEW system

The system has mainly 2 advantages over a conventional Laser Scanning confocal microscope:

The Laser Scanning Confocal Microscopy (LSCM) is a sequential scanning system where a single point of the specimen is illuminated at a time and LSCM uses a point detector (Photon Multiplier Tube (PMT)). Therefore, for LSCM, an expensive scanner is needed and electronic processing is necessary for image formation. The LSCM system is consequently relatively slow (typically 0.5-10sec/frame, slower scan can take up to a minute/frame). Whereas Nipkow disk system uses multi-point scanning disk and a cooled CCD camera which is a parallel array detector. This enables the Nipkow system to acquire images at higher speed (up to 360frames/sec) than with LSCM (typically 0.5-1 frame/sec). This will allow many rapid cellular processes (e.g. calcium imaging, vesicular trafficking) to be monitored in real time. More importantly, it has been demonstrated that the spinning disk confocal system reduces phototoxicity and photobleaching by as much as 5 folds comparing to a LSCM. It is speculated that the reduction in phototoxicity and photobleaching is probably due to the fact that the system splits the laser light into thousands of minibeams.

While the mechanism of such reduction in phototoxicity and photobleaching is still a subject of studying, spinning disk confocal is becoming increasingly the instrument of choice for live cell imaging. The system is particularly powerful for applications such as real-time (4-D) confocal microscopy, calcium signaling, vesicular trafficking green fluorescence protein studies.

System Description

The system is based on a Zeiss Axiovert 200M inverted microscope with the following laser lines for excitation of fluorophores: 404nm, 440nm, 488, 514nm, 561nm and 633nm. It is equipped with a piezo focusing motor and all necessary accessories (Temperature, CO2) for high speed live cell imaging. The scope is mounted with a high precision motorized stage for monitoring of multiple positions in a single sample holder. This system was upgraded with a FRAP (Fluorescence Recovery After Photobleaching) module in 2009.

Applications

The system is well suited for high-speed, live cell imaging with reduced phototoxicity. The system is particularly useful for 3-D timelapse to monitor fast cellular events because of the high focusing/acquisition speed than other systems in the Facility. With its FRAP module, FLIP, FRAP and photoactivation could be performed on the system as well.

Perkin Elmer Ultraview ERS FRAP Specifications

10x 0.3NA EC Plan-Neofluar
20x 0.8NA Plan Fluar
40x 1.3NA oil Plan-Neofluar
63x 1.2NA Water C-Apochromat
63x 1.4NA Oil DIC Plan-Apochromat
100X 1.4NA, oil DIC plan-Apochromat

Diode: 405nm
Diode: 440nm
Argon: 458, 488, 514nm
Solid state: 561nm
Solid state 633nm

DIMs offer alternative ways of imaging biological samples with advantages of low photo-bleaching, high-photon efficiency and relatively low cost. In combination with deconvolution, high resolution imaging could be performed on these systems.

There are 6 DIM setups in the Facility. Each differs from the others by the software and hardware configuration for its main purposes:

DIM station 1-4   contains Metamorph (Universal Imaging Corp , Molecular Devices), a sensitive, cooled CCD camera (Sensicam from Optikon , Cascade II EMCCD or CoolSnapHQ (Photometrics)) and a Zeiss microscope (AxioImagerZ, Axioplan IIM or Axiovert 200M). All of them are equipped with DIC (differential Interference Contrast) optics and fluorescence optics. The setups are mainly set for low-level fluorescent video microscopy. All these digital microscopes can perform multiple wavelength detection, 3-dimensional image acquisition and 3-D time lapse experiments. One setup is equipment with necessary filter wheels for Ca/pH ratiometric imaging and for FRET analysis with CFP and YFP dye pairs. It is also equipped with a live cell environment control that long term (days) timelapse can be performed on.

DIM station 5   is composed of an Axioscope 2 from Zeiss for routine fluorescent examination and a high resolution digital color camera (Axiocam HR, Zeiss) for color digital photography.

DIM station 6   is composed of a Zeiss Axiovert 100M, cooled CCD camera (Sensicam HE) and Metamorph software. The main difference between this setup and others is that this one is equipped with an Eppendorff microinjection system which allows injecting small amount of molecules in adherent cells. The system is, also available for routine fluorescence imaging.

System Specifications

All of these scopes (except 7) have interchangeable optics and are based on either upright or inverted configurations. Please contact staff for your particular application needs.

This is a PALM CombiSystem mounted on a Zeiss Axiovert 200M microscope. The setup is used primarily for manipulating cells with laser or selectively picking up cells or sub-cellular structures for biochemical analysis (e.g. single cell PCR). The workstation consists of a pulsed nitrogen laser, which allows precise cutting or micro-dissection. It is also equipped with an infrared laser for trapping and positioning cells. More information about the system can be found on the   Zeiss   website.

Applications

Select morphologically identified cells/fragment of cells in pathological sample to study the sample biochemically.

Using the laser tweezers to physically position 2 cells together to study cell-cell interactions.

Selective ablation of cells in living tissue or cell culture.

The Facility is equipped with a 200kv JEOL 2100 Transmission Electron Microscope (TEM). TEM use an electron beam as light source (Lab6 crystal in this case) and the beam goes through (transmission) the specimen and the image is projected to an imaging device (e.g. fluorescence screen, film or CCD camera). The TEM can obtain resolution much higher than a light microscopy could offer (sub nm resolution versus 𞳸nm) due to the much shorter wavelength of the electron beam than visible light.

Fixation of the specimen   which preserve the sample as close to the native status as possible before viewing under the TEM. This are usually achieved through one of the following methods: i) Chemical fixation which typically use cross linker molecules such as glutaraldehyde to fix major cellular components. ii) Cryofixation which involved in freezing the sample so rapidly that the samples are frozen in vitreous state. Some of the fixation reagent also enhance the contrast of the specimen under the TEM (e.g. OsO4).

Contrast enhancing: since most biological material yield low contrast under electron beam, it is necessary to apply some heavy metal reagents to increase the contrast of the sample. Some of the commonly used one are   OsO4   (for lipid staining),   Uranyl acetate   (for nucleus and negative staining)   Lead citrate   for general electron opaque contrast enhancing.

Resin infiltration and plastic embedding: Since typical cellular structure is too thick to observe under TEM, it must be sectioned to thin sections (typically 70nm) prior viewing under TEM. This requires the specimen to be embedded in plastic resin. Typically, the specimen goes through steps like dehydration, resin infiltration and polymerization of resin (either in an oven or under UV light).

Thin sectioning (ultra microtomy). Typical biological TEM has an acceleration voltage of 200kv or below and at this acceleration voltage, electrons can penetrate a specimen of thickness of less than 𞳸nm. A special instrument is used with a diamond knife to cut the specimen down to ㅾ-100nm for TEM observation and the sections are placed on to a specimen grid.

Post staining   if needed. Additional contrast enhancement is possible at this stage.

TEM images are formed by the interactions of electrons and the specimen and the TEM can operate in different modes to extract different information from the sample:

Brightfield   is the most common operation mode where most of the contrasts are formed by absorption of the electrons by the specimen yielding an image of different levels of shade which reflects the degree of electron absorptions of the sample.

Darkfield mode   explores the scattered electrons. A bright spot in the image means the structure is highly scattering (e.g. a gold particle).

Electron Energy Loss Spectroscopy (EELS)  detects the electrons which under inelastic interactions with the specimen (therefore loss some energy) and gates electrons of different energy level to the detector. Using this information, element composition of the specimen can be mapped. This mode is also very effective way to enhance contrast by filtering out the scattered electrons from the final image.

Applications

TEM can be used to obtain details view of a specimen at atomic resolution level. For biological samples, TEM can give unambiguous identification of cellular compartments and organelles. In combination with specific molecular marker (e.g. antibody) and electron dense labels (immunogold particles or Nanoparticles), it is possible to identify association of a particular molecules with a specific organelle or with another type of molecules. With Tomography, 3-dimensional information can be obtained. With EELS, an elementary composition of the specimen can be mapped. For biological samples, for example, phosphorous rich and nitrogen rich domains can be mapped. The TEM is also equipped with cryo sample holder to observe sample under cryo-conditions.

System Specifications

  • Cryo sample holder for investigating sample at liquid nitrogen temperature.
  • Double tilt sample holder for Tomography.
  • Gatan GIF Tridieum filter for EELS for element mapping.
  • High Angle Annular Dark field detector for dark field imaging.
  • Necessary TEM sample preparation for biological samples. This includes:
    • High pressure freezer for cryofixation.
    • Freeze substitution unit for substituting water from biological sample under cryo condition.
    • Ultramicrotome with Cryo attachment for ultramicrotomy either at room temperature of low temperature
    • Immunogold labeler to perform immunogold labeling.
    • Microwave automatic tissue processor for rapid tissue processing for TEM.
    • Carbon coater with glowing discharge and metal shadowing capability.
    • The scope is equipped with Gatan DigitalMicrograph software with Low-dose function for radiation sensitive sample (cryo specimen), Montaging for reconstruction of large field of view. For tomography, it uses   SerialEM.

    Fluorescence is a cyclical process where lifetime of the fluorophore is not only the property of molecule itself but also a function of its environment. In situation such as Fluorescence Resonance Energy Transferring (FRET), the lifetime of donor molecule will be shortened. Therefore, FLIM can be used as a way to measure molecular interactions. Unlike conventional FRET analysis, FLIM measurement is not subjected to fluorescence photobleaching or concentration variations which are difficult to control in live cells.

    The FLIM module is an attachment to the Zeiss NLO 510 system which uses time-correlated single photon counting technique to construct the decay curves of fluorophore in every pixel of the image. The system is equipped with a Hamamatsu RS-39 Multi-channel plate detector, a filter wheel and a SPC730 photon-counting board from   Becker Hickl for photon counting. The system uses a photodiode to obtain synchronization information from the laser pulses to construct the fluorescence decay curve.

    Applications

    The main application for the setup in biology is for FRET analysis where donor life time can be measured both in presence and absence of acceptor molecules. Then the FRET transfer efficiency can be calculated according to the following formula: - Et =1-   t   D,A/   tD

    Where   t   D,A   is the life time of donor molecule in presence of acceptor and   t   D   is the life time of the donor molecules in absence of acceptor.

    The system is integrated part of multi-photon microscope. There is no special need for specimen preparation other than that the specimen must be suitable for confocal observation. As all FRET analysis, all control samples are needed (e.g. donor alone, acceptor alone, donor acceptor combined and specimen without any staining for auto-fluorescence).

    The system does not have an overly user friendly interface, therfore it is only available by assisted use. Please contact staff for more details.

    FCS is a spectroscopic technique for the study of molecular interactions in solution. FCS monitors the random motion of fluorescently labelled molecules inside a  defined volume element irradiated by a focused laser beam. These fluctuations provide information on the rate of diffusion (diffusion time) of a particle and this, in turn, is directly dependent on the particle's mass. As a consequence, any increase in the mass of biomolecules, e.g. as a result of an interaction with a second molecule, is readily detected as an increase in the particle's diffusion time.

    Applications

    Because FCS measurement is made through diffraction limited volume, FCS can be used to study molecule-molecule interactions in living cell. The system can be used to study:

    Transcription factor-DNA interactions

    Lipid-protein interactions, etc.

    The FCS system at the Facility is an integrated part of the Multi-photon and the LSM710/Zeiss LSM NLO systems with all the laser lines for common fluorophores and 2 detectors which enable cross correlation analysis.

    Micro-injection is one of the techniques to introduce minute amount of substance into live cell/tissue. The Facility is equipped with an Eppondorff micro-injection system mounted on a Zeiss Axiovert 100M fluorescent microscope. It is suitable to inject small amount of substance (e.g., antibody, dye, drug, etc.) into adherent cultured cells. The system is also equipped with a cooled CCD camera (Sensicam) and Metamorph for fluorescence imaging.

    The Facility is equipped with various up-to-date computer workstations for image processing. These include several high end workstations with powerful graphics and large amount of RAM and hard drive space dedicated for image processing and analysis. Here is a list of software tools available for the Facility users:

    Deconvolution   software

    More information regarding Deconvolution can be found   here.

    3-D image processing and analysis software

    2-D image processing and analysis and image acquisition software

    Some of the computers are equipped with   Zeiss LSM software (ZEN)   for offline processing of confocal/FCS data.


    Methods

    Experimental set-up

    The asynchronous optical sampling (ASOPS 27 ) pump probe system (see Fig. 2) controls two 150 femtosecond pulsed lasers with repetition rates of

    100 MHz and allows the delay between the lasers to be set and swept electronically without the need for a mechanical delay line 21,22 . In our system, the delay repetition rate between the probe and the pump is 10 kHz which means that a measurement (of the complete 10 ns delay sweep) is taken every 100 μs.

    As seen in Fig. 2, both beams (λprobe = 780 nm, λpump = 390 nm) are combined and focused together through a 50x (NA = 0.55) long working distance objective. Adjustable mirrors allows coaligning of the pump spot to the probe spot. The probe beam is detected after being collected by an objective lens (20x, NA = 0.42) and focused to a photodiode. The sample is scanned by moving electromechanical stages with a minimum step motion of 100 nm. Typically 10000 averages are taken per point which takes

    2 s to acquire limited by data acquisition element. The system uses typical average powers of 1 mW (0.3 mW at cell) in the probe and 0.5 mW (0.05 mW at cell) in the pump corresponding to pulse energies of 10 pJ and 5 pJ and peak powers of

    Optical imaging is performed with two cameras: one CCD is used for brightfield imaging (using the 50x objective lens) and the other (emCCD) for fluorescence (using the 20x objective lens). A spectrally-distinct LED source (530+/−25 nm) provides brightfield illumination of the sample as well as excitation for red-emitting fluorescence dyes. Epifluorescence was detected via a TRITC cube (Ex: 535/15, DCX: 565, Em: 615/35 nm).

    Cell methods

    3T3 fibroblast cells were cultured on the EtOH-sterilised transducers for 24 hrs in standard culture medium. Living cells were kept in Hanks balanced salt solution (HBSS) buffered with 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES, 25 mM) to maintain physiological pH (7.4) under ambient conditions during the experiments. Media was pumped at 0.05 μLs −1 using a syringe pump into a chamber (chamilde CF-T25 produced by Live Cell Instruments, Seoul) comprising a transducer substrate and a closing coverslip. Constant flow of media allowed specimens to remain alive for several hours at room temperature (21 °C).

    A fluorescence assay was used to confirm cell viability (Fig. 6). Propidium iodide (PI, abs: 510–560 nm, em: 600–650 nm) binds to DNA in the nuclei of dead cells, and is non-fluorescent when excluded from entering living cells by the intact cell membrane. PI was added as a 1 mM EtOH stock to a concentration of 1 μM in bathing medium. A fluorescence picture of the targeted region of cells was obtained before starting the ultrasonic imaging and another following the ultrasound imaging experiment (see supplementary Fig. 1). Finally, all cells were deliberately killed using a detergent (Triton X-100 in phosphate buffered saline (PBS) solution, Sigma-Aldrich). Cells which survived the ultrasound imaging experiments continued to exclude PI from their nuclei throughout and following the experiment, confirming that the cells remained viable (see supplementary information).

    Signal processing

    Raw signals are composed of several parts: coincidence peak, thermal response and signals of interest - which were extracted by established signal processing 24,33 . A fast Fourier transform (FFT) is then performed on the resultant trace to measure the Brillouin frequency. Signal to noise ratio (SNR) was evaluated in the frequency domain by measuring the peak amplitude of the acoustic signal with the standard deviation of the noise background in the absence of signal (pump off) and in the same band.

    Because the acoustic waves are propagating axially through the sample, different moments in time represent different locations in space. Axial sectioning information was therefore obtained by resolving the Brillouin frequency in time. This was possible using the short time Fourier transform method (STFT) where a small time window (length: two acoustic cycles or more) is shifted in time. In this way, it is possible to section the optical volume. The resolution of this process was estimated by modelling and experimental measurements of an edge response revealing the axial resolution is approximately half of one measuring window when the window lasts for two cycles or more.


    Introduction

    Why do we care about detecting single molecules in cells?

    Experimental investigations in the life sciences have traditionally been performed on a population ‘ensemble average’ level. An example of this is the use of cell cultures, which contain a population of many thousands of cells. A cell population is, in general, intrinsically heterogeneous, even if cells are genetically identical. In other words, different cells exhibit a range of different physical, chemical and biological properties. Such heterogeneity is potentially valuable at a level of the originator species, in that they allow rapid adaptation in a dynamic, fluctuating environment, and so may impart a biological advantage to the ultimate survival of the species [1–3]. Using a population signature as a metric for the physical or chemical status of different cellular parameters is valuable at one level, since it averages out the observations of potential minor and anomalous cells in that population, in effect smoothing out the ‘noise’. However, the main problem with this approach is that there may be valuable information hidden in this ‘noise’ we run the risk of losing potentially useful data concerning biologically relevant heterogeneity. We potentially limit the extent to which we can investigate ‘subpopulations’ [4,5].

    For example, ensemble average analysis will not pinpoint the drug-resistant bacteria or cancer cells in a general cellular population. When subpopulations are identified, the only way to determine which cells contribute to which group, hence, to separate competing signals, is to analyse the whole population cell-by-cell [6,7]. Population heterogeneity can arise due to environmental alterations affecting the soft matter of biological material [8], as well as through genetic variation that affects gene expression and can invoke fluctuations in various cellular components [9]. Differences in transcriptional regulation affect signal transduction pathways and hence responses to various stress factors, such as pH and oxidative stress. Therefore, an ideal single-cell experiment should be performed under precise environmental control. Moreover, the age of a cell and its phase in the cell cycle may also significantly influence the cell response [4].

    Even an apparently simple unicellular organism represents a heterogeneous system on a molecular level [10]. Analysis of the ensemble average of molecular properties results in loss of information concerning any molecular heterogeneity, and may ultimately lead to misinterpretations of the underlying physiological relevance of subpopulations of molecules [11]. Focusing on molecules as the minimal ‘functional’ units in a biological system, single-molecule biophysics research has an important impact on a range of fields of biological investigation. These include fields where biological complexity is rife, such as medical immunology, synthetic and systems biology, but also several others at a more basic mechanistic level, ultimately through an ability to enhance both the effective spatial and temporal resolution of data [11]. Modern techniques [12] enable, for example the probing of the cellular signal transduction dynamics directly [13], which facilitates a deeper and more precise understanding of important biological processes, e.g. the human immune response, gene expression and cellular differentiation. One of the most important techniques used currently in single-molecule biophysics research is, unquestionably, fluorescence microscopy [14,15].

    Identification and investigation of molecular subpopulations within the cell enables us to study not only cellular responses but also the precise underlying molecular mechanisms. Arguably, the first clear demonstration that single-molecule fluorescence microscopy could yield insight which were genuinely unanticipated from bulk ensemble average measurements was reported in 1998. Here, the researchers used the native photoblinking behaviour of the common metabolite FAD inside a binding site of the enzyme cholersterol oxidase to demonstrate that its activity could be affected by a type of ‘molecular memory’ stored in the molecular confirmation [16]. Single-molecule fluorescence microscopy approaches since then have uncovered many fundamental molecular scale biological processes that were previously not studied primarily due to the limitations imposed by population methods, including studies of the bacterial flagellar motor rotation [17–21], protein folding, translocation and movement [11,22–25], signal transduction [26], biopolymer mechanics [27–32], DNA replication and remodelling [33–37], oxidative phosphorylation [38–41], as well as biomedically relevant areas such as the probing of processes relating to infection and general pathology [42–44], cell division mechanisms [45], mitochondrial protein dynamics [46], viral infection processes [47], endocytocis and exocytosis pathways [48], osmolarity receptor dynamics [49], cell wall synthesis [50], and structural dynamics of DNA [51]. This list above should not be taken as exclusive nor exhaustive, but rather we present it here to exemplify the very wide range of biological processes to which single-molecule fluorescence microscopy tools have been applied.

    One of the primary requirements for all the single-cell/single-molecule approaches is the ability to faithfully detect small signals over sometimes relatively large noise levels [52]. Combining improvements in a range of different approaches, such as minimizing the sample volume, engineering better photostability for newer variants of fluorescent proteins, and improving the sensitivity of camera detectors, have resulted in higher detection levels of photon signals for fluorescence emission, though still there are limitations due to poor signal-to-noise ratios when sampling at very high imaging rates. Various analytical tools have been developed to improve the signal-to-noise ratio, such as automated methods of ‘segmentation’ of cellular images [53,54], robust software algorithms for the tracking of fluorescently labelled molecules [55–57], and stoichiometry analysis of molecular complexes which those tracked molecules form. We steer the reader to recent comprehensive reviews that discuss these different approaches on how to increase the fidelity of signal detection over background noise [52,58].

    Fluorescence and fluorescent proteins

    The physical process of fluorescence occurs when a photon of light is absorbed by a ‘fluorophore’, which may be an atom or a molecule, and consequently re-emitted as a photon with a longer wavelength. The loss of energy occurs due to vibrational processes which result from oscillations between the atomic/molecular orbitals due to the perturbation of a different negative electron charge distribution relative to the positively charged nucleus. Upon standard ‘single photon excitation’, light absorption of a single photon (of light) occurs which results in a ground state electron in the fluorophore undergoing an excitation transition to a higher energy state, in a process characterized by a time scale of ∼10 −15 s. Following this relatively transient state, the excited electron loses energy through vibrational losses over a time scale of 10 −14 –10 −11 s. The electron then undergoes an energy transition back to the ground state, characterized by a time scale of 10 −9 –10 −7 s, accompanied by photon emission, whose wavelength is longer than the incident wavelength (i.e. has a smaller associated energy). Jablonski [59] described the different energy states and transitions between them in a useful pictorial form called Jablonski diagram (Figure 1). Although the physical process of fluorescence was properly formulated by the British scientist Stokes et al. [60], it was more than half a century later that the first operational fluorescence microscope was developed, reported in 1911, which obtained the relatively standard design as we know it today only in 1967 [61].

    Jablonski diagram

    An electron of a fluorophore at the ground state (S0) receives energy from the absorption of a single photon of light which results in an excitation transition to a higher energy state (absorption). When the excited electron relaxes to the ground state, following vibrational losses, energy, lower than the incident photon and thus with a higher wavelength, is emitted as a single photon which causes fluorescence.

    An electron of a fluorophore at the ground state (S0) receives energy from the absorption of a single photon of light which results in an excitation transition to a higher energy state (absorption). When the excited electron relaxes to the ground state, following vibrational losses, energy, lower than the incident photon and thus with a higher wavelength, is emitted as a single photon which causes fluorescence.

    In 2008, the Nobel Prize in Chemistry was awarded jointly to Osamu Shimomura, Martin Chalfie and Roger Y. Tsien for the ‘discovery and development of green fluorescent protein, GFP’ [62]. GFP had been isolated from the jellyfish Aequorea victoria, described in an article in 1962 [63]. A step change came when the GFP gene was sequenced in the early 1990s, accompanied by developments in molecular cloning technologies enabling the integration of its DNA directly into DNA in other organisms. Nowadays, it is an invaluable tool which is widely used as a fluorescent tag and can be relatively easily integrated into the genome. GFP is a β-barrel protein consisting of 11 β-sheets and an α-helix, composed of 238 amino acids residues in total. The wild-type GFP chromophore is encoded by the Ser 65 -Tyr 66 -Gly 67 sequence which forms a heterocyclic photoactive state spontaneously through the processes of intramolecular autocatalytic rearrangement and subsequent oxidation [64]. This final oxidation stage is crucial for the protein to function as an active fluorophore.

    Numerous mutations of wild-type GFP have now been generated, with one of the principle aims of improving its biophysical characteristics. Photostability and fluorescence output increases were achieved by using an S65T mutation [65], while the A206K was developed to prevent self-oligomerization [66], and various colour mutations were added, including, for example blue Y66H, cyan Y66W and yellow T203Y [67] variants. Standard fluorescent proteins will undergo irreversible photobleaching after a characteristic time interval when excited to fluorescence, most likely to be due to the accumulation of free radicals in the surrounding water solvent formed from the lysis of water molecules upon absorption of photons of light, and their subsequent chemical damage to the fluorescent protein structure. Standard fluorescent proteins cannot therefore be tracked longer than their photobleaching point, which thus limits their application in long time scale experiments.

    Certain newly engineered fluorescent proteins, e.g. mEos [68], Dendra [69] and KikGR [70] can be photoactivated and undergo irreversible photoconversion from green to red emitting state upon irradiation with UV light [71,72]. Although such approaches potentially can appear to extend the lifetime of a tracking experiment in which proteins can be photoconverted before they bleach, there is no intrinsic improvement as such to photostability in these proteins. Monomeric forms of these proteins [73,74] as well as different variants of photoconvertible proteins with enhanced features have also been designed. For example, mMaple protein exhibits reversible photoconversion under certain conditions [75], with yellow-to-cyan (EYFP-to-CFP) photoconversion upon green light illumination [76], and cyan-to-green photoswitch of PS-CFP2 [18]. The fluorescent protein mOrange undergoes orange-to-red activation upon illumination with blue light (typically using the common laser line with wavelength 488 nm), which is thus less harmful for live cells compared with UV-convertible proteins in regard to photodamage effects [77]. Photoconversion can be used stroboscopically to divide up the finite photon budget prior to photobleaching (i.e. acquiring fluorescence images over extended time intervals instead of continuously illuminating samples), which has been used to monitor complex live samples such as developing embryos for up to several hours [78]. Another type of fluorescent protein, phytochrome-based near IR fluorescent proteins (iRFP), has been developed recently [79]. Compared with conventional fluorescent proteins, such as GFP, iRFP has a higher effective signal-to-noise ratio and allows imaging deeper into tissues due to smaller elastic scattering effects at higher wavelengths of electromagnetic radiation, relevant for applications in live-animal or excised-tissue models.

    Some fluorescent proteins have a characteristic time over which they change their emission wavelength from blue to red based on the chromophore maturation time. Such proteins can be used, therefore, as fluorescent timers, such as to study protein transport. For example, an mCherry-derived monomeric variant with various timing behaviours has been used for probing the kinetics of protein trafficking [80].

    Fluorescent probes may be added to a protein of interest directly or via linkers, such as SNAP- and HALO-tags. Here, the encoding DNA for a protein probe is first genomically fused next to the protein under investigation, technologically similar to the approach used in developing fluorescent protein fusion constructs. In most applications of HALO/SNAP, this probe consists of a DNA repair protein (for SNAP) or a haloalkane dehalogenase enzyme (for HALO) [81,82]. The cell can then be incubated with a secondary probe which is fluorescently labelled with a bright organic dye fluorophore. The secondary probe is designed to bind to the primary protein probe. The use of these tags avoids ‘direct’ fluorescent protein labelling, which might impair their physiological behaviour due to steric hindrance. This methodology enables a far brighter and more photostable fluorophore to be used compared with conventional fluorescent proteins. Since the localization precision improves with the brightness of the fluorophore used (roughly with a reciprocal dependence on the square root of the brightness) the use of a brigher dye facilitates improvements in localization precision for determining the position of individual fluorophores. This method also implies a potential improvement to temporal resolution in ultimately enabling faster sampling for a given spatial localization precision. That being said, the primary probes for SNAP and HALO are themselves reasonably large whose molecular weight is only ∼40% less than that of fluorescent proteins of ∼28 kDa [5], and so a potential steric hindrance effect is still present. Also, the efficiency of labelling during the secondary probe incubation step is sometimes difficult to achieve as the primary protein probe is often not easily accessible, e.g. the primary probe protein is deep inside a cell and thus there are technical issues in how to deliver the secondary probe to these regions. However, this approach has resulted in significant advances in super-resolution imaging of accessible cell surface structures, such as the cell wall architecture of bacteria [83].


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    Materials and methods

    Sample preparation

    Freshly withdrawn venous blood, anti-coagulated by EDTA (1.8 gL −1 ), was collected from six healthy, non-smoking volunteers (A, B, C, D, E and F) with the vacutainer system from BD (BD, Heidelberg, Germany) and immediately processed. Informed consent was obtained from all donors in written form. The blood samples were withdrawn in accordance with the transfusion law of Germany. The use of donor blood samples for scientific purposes was approved by the ethics committee of the Charité–Universitätsmedizin Berlin (# EA1/137/14). The blood samples were characterised by determining the complete blood counts (CBCs) using a XS 800i hematology analyser (SysmexEurope GmbH), located in the central laboratory. In healthy individuals, free Hb concentrations in blood serum are less than 0.1% 52 and negligible for the analysis of our measurements. A blood gas analyser (ABL 725, Radiometer GmbH, Germany) served to determine the relative metHb and carbomonoxy-Hb (COHb) concentrations, being <1.2% and <2.5%, respectively, for the six samples investigated. Subsequently, for WBC and platelet depletion, 10 mL of whole blood were washed three times (150 g, 5 min) in 50 mL of phosphate buffered saline (PBS sigma, Germany). Washed RBCs were re-suspended in PBS to a final volume of 10 mL. To control the washing cycles the concentrations of RBCs, WBCs and platelets were measured on site before and after each washing step by an ABX Micros 60 analyser (Axon Lab AG, Germany). In this way we ensured that WBC and platelet concentrations are low and extinction spectra of RBCs are not distorted. The sphering reagent is a commercially available substance (CELL-DYN diluents/sheath reagent, Abbott GmbH & Co. KG, Diagnostik, Germany) used for the isovolumetric sphering of RBCs in hematology analysers. For sphering, washed RBCs were diluted 1:100 in the sphering reagent. This pre-diluted suspension was used as stock solution for dilution series.

    Typically, the preparation took 90 minutes. Since during this time the sample was exposed to atmospheric oxygen (i. e., pO2 = 212 hPa = 159 mmHg), saturation is reached and the deoxygenated Hb variant is converted to oxygenated Hb. Time constants for the oxygen uptake amount to about 500 ms for 50% saturation 53 . In Ref. 53 it was also shown the this time reduces with decreasing HCT value, i. e., the reaction is accelerated when RBCs are diluted as in our measurements. Absorption spectra of lysed RBCs were measured with the same experimental setup used for extinction measurements. They were found to agree with literature data for oxyHb 27,29 up to the concentration error from volumetric dilution. Hence we can use the literature values of oxygenated Hb 27 for γ(λ) in our analysis.

    Experimental setup

    The optical setup for spectral transmittance measurements is shown in Fig. 4. A high-power, continuous HPX-2000 Xenon light source is applied to irradiate the sample in the wavelength range between 185 nm to 2000 nm. For spectral analysis between 200 nm and 1100 nm, a Maya2000 Pro spectrometer was used (Ocean Optics, Inc., USA). With the help of 4 mirrors M1–M4 the folded light path features a length of approximately 2.5 m between the light source and the sample cuvette. The lense L1 is used as condenser to obtain an approximately parallel light beam. The apertures A1–A3 serve to reduce the size of the beam to a diameter of about 1 mm corresponding to a divergence of 0.2 mrad or 0.01° (half angle). The samples are filled in a quartz cuvette (Hellma Analytics, Germany) with d = (10 ± 0.01) mm optical path length. Aperture A4 blocks the light scattered in the non-forward direction by the sample to suppress background light. The spectrometer is placed 1.5 m from the sample via mirrors M5–M7 and equipped with an entrance slit of 50 μm width and 1.0 mm height. The slit width results in a spectral resolution of approximately 0.45 nm, the slit height corresponds to an observation angle of 0.3 mrad or 0.02 (half angle). The long distance of 1.5 m between the cuvette and the detector serves to effectively suppress light scattered at small angles into the spectrometer’s aperture. This allows to neglect unwanted contributions to the directed transmittance when analysing the measurements. The experimental setup in Fig. 4 allows to measure the same quantity as the monochromator-based setup previously used by Gienger et al. 42 to validate the method for spectral RI determination of particles. However, the setup in Fig. 4 offers a significant advantage, since due to the parallel detection of the spectrum in contrast to the previously used wavelength scanning, the measurement time is reduced from typically 20 min to about 10 s.

    Optical layout to measure extinction spectra.

    Measurement of transmittance and calculation of extinction cross sections

    For transmission measurements, pre-diluted sphered RBCs were further diluted with the sphering reagent and the spectral intensity (_<< m>,j>(lambda )) was measured for 6 to 8 different dilutions per sample. The number concentrations cj of the cells were selected such that the transmittance (_(lambda )=_<< m>,j>(lambda )/_<0>(lambda )) ranged from roughly 95% down to 30%. I0(λ) is the null measurement where the cuvette filled with the sphering reagent only. The offset due to dark counts and read out procedure of the diode array were subtracted from all spectra. This measurement of concentration series enables us to exclude multiple scattering effects and to compute the extinction cross section (>_<< m>,j>(lambda )) according to

    as this formula implies extinction caused by single scattering. Since the (<ar>_<< m>< m>< m>,j>(lambda )) curves thus computed lie on top of each other inside the measurement accuracy, multiple scattering can be excluded.

    The volumetric dilution by adjustable pipettes contributes to the uncertainty of the concentrations cj of an estimated 2–4%, depending on dilution. Accounting for the accuracy of hematology analysers, the RBC concentrations of the undiluted samples have a relative uncertainty of about 4%. It follows that (<ar>_<< m>< m>< m>,j>(lambda )) is only measured up to a prefactor corresponding to the relative error of the number concentration of cells in the diluted sample, which accumulates to approximately 6%. However, even larger concentration errors are easily accounted for in the data analysis as described in section “Mathematical model” (see Eq. (8)). The concentration series were recorded such that the cuvette was not moved between measurements: Increasing volumes of the RBC suspension were added to the fluid-filled 10 mm cuvette (starting with 2.2 mL of sphering reagent) and mixed by pipetting back and forth and using the magnetic stir bar for homogenisation. Care was taken not to touch the cuvette walls in the process, as not to change the angle relative to the incident beam. This minimises errors from light reflected at the cuvette and avoids artefacts due to displacement of the transmitted light when tilting the cuvette.

    Optical properties of materials

    Using an Abbe refractometer (ORT 1RS, Kern Optics, Germany) the real part of the RI of the sphering reagent was measured at λ = 590 nm and found to be higher than that of pure water by Δn = 0.0020(3). Furthermore, the absorption spectrum was recorded with the setup in Fig. 4. An absorption band was found between 220 nm and 290 nm with a peak in the imaginary part if the RI of 1 × 10 −5 . This limits the lowest wavelength in our analysis to 290 nm since the transmittance in a 10 mm cuvette drops down to about 1.2% compared to water at the absorption peak, which results in a very low signal to noise ratio.

    Mathematical model

    The measured spectral extinction cross sections (>_<< m>>(lambda )) depend on the quantity to be determined, α(λ), in a complicated nonlinear way. Hence, data analysis requires solving an inverse problem: Find those optical properties of RBCs (and their size and concentration distribution) that explain the data. To solve this problem by nonlinear numerical optimisation a forward model is needed to compute (>_<< m>>(lambda )) for a given parameter set.

    Firstly, we define the ensemble average

    where C(λ cHb, R) is the extinction cross section of a single cell of radius R and intracellular Hb concentration cHb. The cell’s refractive index is given by Eq. (1) and the RI of the surrounding medium (sphering reagent) is (_<< m>>(lambda )in >) . The size distribution in the blood sample is given by r(R) and the distribution of the intracellular Hb concentration cHb is given by q(cHb). Measurements on single RBCs suggest that R and cHb are statistically independent 14,41 , thus motivating a separation of q and r in our treatment.

    The Mie solution allows for efficient computation of C(λ cHb, R). The known quantities in Eq. (1) are (<>>_<<< m>>_<< m<2>>>< m>>) and γ for which we use literature values 27,31 . Furthermore we assume (_<< m>>(lambda )=_<<< m>>_<< m<2>>>< m>>(lambda )+0.002) for all λ, as this RI difference was measured for the sphering reagent at 590 nm. As presented in Ref. 42 , we expand the unknown function α, describing the wavelength-dependent increment of the real RI with concentration, into a finite series

    with real coefficients aj, where the gj are orthonormal basis functions. Here, we use a set of orthonormalized third-order cardinal splines with a uniform grid spacing of Δλ = 10 nm. The approximation error when fitting literature data for α 28,38 with this basis is well below the measurement uncertainties.

    The distributions q(cHb) and r(R) are modelled by a normal distribution and log-normal distribution, respectively, each of which has two parameters μ and σ. Hence the parameter vector of the joint probability distribution is

    Note that the parameter (< heta >_<1>=_<_<< m>>>=< m>) is not a free parameter, but fixed to the value obtained from the CBC. This was done because the MCHC and the absolute value of the real RI increment α(λ) have a very similar effect on the model for the spectral extinction measurements leading to ambiguities and inconsistencies of the regression results of the RI increment. Using the MCHC as a free parameter in the least-squares optimisation described below worked well for the majority of datasets. However, for a few of the samples hematological parameters in disagreement with the CBC were found when this approach was applied to analyse measurements. Hence the MCHC was held constant in the analysis of all datasets. This yields consistent regression results for all data sets and made the results also substantially more robust against perturbations in the measurements.

    A secondary model ( < >^<< m>>(<oldsymbol< heta >>)) computes the vector of blood count parameters z = (MCV, RDW) T from θ. Data analysis consists in minimising the cost function

    where yi are the measured extinction cross sections and zj are the CBC measurements. Weights are set to wi = 1/u(yi) 2 and (_^<< m>>=1/u<(_)>^<2>) , where the standard uncertainties of the extinction spectra yi are estimated from repeated measurements. To find an optimal parameter vector ψ that minimises χ 2 we applied the nonlinear least squares optimisation lsqnonlin in Matlab (Matlab R2018a, The MathWorks Inc.) using the trust-region algorithm.

    Because the objective function χ 2 may have several local minima, initial values of the parameter vector were sampled randomly around a given mean and the local optimisation was repeated several times. The coefficient vector a was initialised randomly such that the wide range of literature values reported for the real RI increment α was covered. Several percent of random variation were allowed for parameters of size and concentration distributions. For each dataset 25 to 50 random initial conditions were sampled and optimised. The parameter vector with the lowest χ 2 was used as the result (hat<<oldsymbol>>) .

    More specifically, the coefficient vector a of the real RI increment α(λ) was initialised in a two-step process: (i) α(λ) was set to a constant (< m>< m>< m>< m>< m>in >(0.235,< m>< m>,<< m>>^<-1>,0.04,< m>< m>,<< m>>^<-1>)) and (ii) additional normally distributed independent random numbers were added to the aj, resulting in random dispersion features of 0.004 mLg −1 standard deviation for α(λ). (>(mu ,sigma )) describes normally distributed random numbers of mean μ and standard deviation σ. For the size and concentration distribution, the parameters θ were randomly initialised around those values obtained from the CBC with the MCHC fixed to the value of the CBC. Standard deviations of the Gaussian random numbers were set to 120 nm for mean(R) and 30 nm for std(R). The width of the Hb concentration distribution and the particle concentration error were sampled from (< m>< m>< m>(_<< m>< m>>)in >(7< m< \% >>< m>< m>< m>< m>,10,< m>,<< m>>^<-1>)) and (eta in >(0,3< m< \% >>)) , respectively.

    25 to 50 random initial conditions were sampled and the optimisation was run for 15 iterations. Afterwards the six parameter vectors with the lowest χ 2 were further optimised for up to 150 iterations or until a given tolerance was met. The parameter vector with the lowest χ 2 was used as the result (hat<<oldsymbol>>) . Typically several initial conditions ended up in the same minimum, but other less deep local minima were found as well.

    Uncertainty propagation

    Using the Jacobi matrix J of the extinction cross section with respect to the parameters with entries



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